Comparison of True Solution, Colloidal Solution and Suspension

Classification of Colloids

(A) Types of colloids based on physical state of dispersed phase and dispersion medium

Depending on the nature of dispersion medium. the colloids can be named as hydrosols or aquasols (for water), alcohols (for alcohols), benzosols (for benzene) and aerosols (for gases),

(B) Types of colloids based on nature of interaction between dispersed phase and dispersion medium

1. Lyophilic colloids
2. Lyophobic colloids

(C) Types of colloids based on type of particles of the dispersed phase

1. Macromolecular colloids.
2. Multimolecular colloids.
3. Associated colloids

Kraft temperature (T_k) It is the minimum temperature of the colloidal system above which the formation of micelles takes place.

Critical micelle concentration (CMC) The minimum concentration of the surfactant at which the formation of a micelle takes place is called critical micelle concentration, e.g., CMC for soaps is ~ 10^-4 to 10^-3 mol L^-1.

Preparation of Colloids

• Lyophilic sols can be easily prepared by shaking the lyophilic material with the dispersion medium, e.g., preparation of starch sol.
• Lyophobic sols can be prepared by following methods.

Condensation / Aggregation Method

These methods involve the joining of a large number of small particles to form particles of colloidal size. Some methods are

Dispersion/Disintegration Method

In this method, bigger particles are broken down to colloidal size. Some methods are

(i) Mechanical disintegration In this method, suspension is ground well in a colloid mill consisting of two steel discs which rotate in opposite directions at very high speed, to obtain the particles of colloidal size.

(ii) Electrical disintegration/Bredig’s Arc method In this method, electric arc is struck between electrodes of the metal (gold, silver, platinum, etc) immersed in the dispersion medium. The intense heat produced vapourises the metal which then condense to form particles of colloidal size.

(iii) Peptization This method is used to convert fresh precipitate into colloidal state by shaking with dispersion medium in the presence of small amount of electrolyte. The electrolyte used for this purpose is called peptizing agent.

Purification of Colloidal Solutions

The process used for reducing the amount of impurities to a requisite minimum of a colloid, is known as purification of colloidal solutions.

(i) Dialysis It is based upon the principle that impurities of true solutions can pass through the parchment paper or cellophane membrane while colloidal particles cannot.

In this process, dissolved substances are removed from the colloidal solution by means of diffusion through a suitable membrane.

(ii) Electro-dialysis The process of dialysis is quite slow. So,if the dissolved substance in the impure colloidal solution is only the electrolyte then electric field is applied. The colloidal solution is placed in a bag of suitable membrane, while pure water is taken outside.

(iii) Ultrafiltration Ultrafiltration is the process of separation of colloidal particles from the solvent and soluble solutes present in the colloidal solution by specially prepared filters, called ultrafilters.

Properties of Colloidal Solution

General Properties

(i) Colligative property Due to high average molecular masses of colloidal particles, mole fraction of the dispersed phase is very low. So, the values of colligative property are very small.

(ii) Colour The colour of colloidal solution depends on the wavelength of light scattered by the dispersed particles. The wavelength of light further depends on the size and nature of the particles. The colour of colloidal particles also depends on the manner in which the observer receives the light.

(iii) Visibility The particles of colloidal solution are not visible to naked eye or under ordinary microscope.

(iv) Filterability Colloidal particles can pass through ordinary filter papers, but can’t pass through parchment paper or animal membrane.

Optical and Mechanical Properties

(i) Brownian movement Sol particles move in a random zig-zag manner due to the unequal impacts of the particles of dispersion medium on the particles of colloidal sol. It is called Brownian motion. Smaller the size of the particle and lesser the viscosity of the solution, faster is the motion.

(ii) Tyndall effect If a colloidal solution is placed in dark and a beam of light is passed through the sol, the path of light becomes visible with a bluish light. This phenomenon is called Tyndall effect. The scattering of light illuminates the path of beam in the colloidal dispersion.

Tyndall effect is observed only when the following two conditions are satisfied:

(i) The diameter of the dispersed particles is not much smaller than the wavelength of the light used.

(ii) The refractive indices of the dispersed phase and the dispersion medium differ greatly in magnitude.

Tyndall effect is also observed when sunlight enters in a dark room through a slit or when light is thrown from a light projector in a cinema hall. Tale of comets is seen as a Tyndall cone due to scattering of light by the tiny solid particles. left by the comet in its path.

Electrical Properties

• Charge on colloidal particles Colloidal particles always carry an electric charge. The nature of this charge is the same on all the particles in a given colloidal solution and may he either +ve or -ve.

The charge on the particles is due to either the given reasons

1. Due to preferential absorption of either +ve or -ve ion which common and present in excess. e.g., When AgNO₃ and KI solution are mixed. the particles of Agl arc precipitated. These particles can adsorb Ag⁺ or I^– ions. If KI is in excess, I^– ions would be absorbed giving [AgI] I^–negative sol but if AgNO₃ is in excess, a positive sol [AgI] Ag⁺ is obtained. SnO₂ can net as positively charged as well as negatively charged colloid depending upon the nature of medium.
2. Due to electron capture by sol particles during electro dispersion method
3. By frictional electrification.
4. By the dissociation of molecules followed by aggregation of ions. Two layers are developed on the particle. one is fixed layer and the other is diffused layer. Potential difference across this electric double layer is called zeta potential or electrokinetic potential.

Positively charged colloids are metal hydroxides, basic dyes like methylene blue sol. Protein in acidic medium. oxides like TiO₂ sol. Examples of negatively charged colloids are metals (like Cu. Ag, Au. etc.) metal sulphide. acid dyes like eosin and sols of starch, gum. gelatin. clay. charcoal, etc.

• Electrophoresis The phenomenon of movement of colloidal particles towards the oppositely charged electrodes under the influence of applied electric field is called electrophoresis.
• Coagulation / flocculation The process of conversion of sol into a suspension is called flocculation or coagulation or precipitation.

It can be brought about by :

1. addition of suitable electrolyte solution
2. continuous electrophoresis
3. prolonged dialysis
4. mixing two oppositely charged colloidal solution
5. heating or cooling

Coagulating value is the minimum amount of electrolyte (in millimoles/litres) needed to coagulate the colloidal solution. Smaller the coagulating or flocculating value of an electrolyte, greater is its coagulating power.

Coagulating power ∝ 1 / Flocculating value

Hardy-Schulz rule Greater the valency of the oppositely charged ions of the electrolyte, more will be its coagulating power, i.e. coagulating power ∝ charge of ion, e.g., for As₂ O₃ sol the order is

Protective Colloids

In the presence of a lyophilic colloids, lyophobic sol gets protected towards the action of electrolyte This phenomenon is called protection and the lyophilic colloid is termed as protective colloid.

Gold Number

The protective power of protective colloid IS measured in terms of gold number which is defined as the number of mg of the protective colloid which just prevents the coagulation of 10 ml, of standard gold sol when 1 mL of 10 % solution of NaCl is added to it.

[Smaller the gold number of a protective colloid, greater is its protective power.]

Gold number of gelatin is 0.005 – 0.01 and oi starch is 20·25.

Emulsion

It is a colloidal dispersion in which both dispersed phase and dispersion medium are liquid.

Types of Emulsions

• Oil ill water [oil is disperse phase and water is dispersion medium], e.g., milk.
• Water in oil [water is disperse phase and oil is dispersion medium]. e.g., cod liver oil.

Dye test and dilution test must be used to distinguish between the two types of emulsions.

Emulsifiers

Emulsifying agents or emulsifiers are the substances added in small quantity to stabilize the emulsions of fairly high concentration.

Demulsification The separation of an emulsion into its constituent liquids is called demulsification. It can be carried out by freezing boiling. centrifugation, etc

Gels

Gel is a liquid-solid colloidal system in which a liquid is dispersed in a solid.

Gels are of two types: elastic gels e.g. gelatin, agar-agar, starch) and non-elastic gels (e.g., silica. alumina and ferric oxide).

When gels are allowed to stand. they give out small quantity of trapped liquid and the gel shrinks in volume. This phenomenon is called syneresis or weeping of gel.

Applications of Colloids

1. In medicine e.g., argyrol (a silver sol used as eye lotion).
2. In chrome tanning.
3. In sewage disposal.
4. In purification of drinking water.
5. In the preparation of nanomaterials often use as catalyst.
6. In photography.
7. 10 producing artificial rain.
8. Blood clotting by ferric chloride or potash alum.
9. In smoke precipitation (cottrell precipitator)

Types of Redox Reactions

(i) Intermolecular redox reactions In such reactions, oxidation and reduction take place separately in two compounds. e.g.,

(ii) Intramolecular redox reactions In these reactions, oxidation and reduction take place in a single compound. e.g.,

(iii) Disproportionation reactions These reactions involve reduction and oxidation of same element of a compound. e.g.,

This reaction is also known as autoredox reaction.

Classification of Redox Reactions

1. Direct Redox Reactions

Chemical reaction in which oxidation as well as reduction is carried out simultaneously in the same container, is known as direct redox reaction In such reactions, energy is generally liberated in the form of heat energy.

2. Indirect Redox Reactions

A reaction in which oxidation and reduction are carried out separately in two separate half-cells, is known as indirect redox reaction. In such reactions, energy is generally liberated in the form of electrical energy.

oxidation and Reduction

Reductants and Oxidants

Oxidant or oxidising agent is a chemical substance which can accept one or more electrons and causes oxidation of some other species. In other words, the oxidation number of oxidant decreases in a redox reaction.

Important Oxidants

Molecules of most electronegative elements such as O₂, O₃, halogens.

Compounds having element in its highest oxidation state e.g.,

K₂Cr₂O₇, KMnO₄, HCIO₄, H₂SO₄, KCIO₃, Ce(SO₄)₂,

Oxides of metals and non-metals such as MgO, CrO₃, CO₂, etc.

Reductant or reducing agent is a chemical.substance which can give one or more electrons and causes reduction of some other species. In other words, the oxidation number of reductant increases in a redox reaction.

Important Reductants

All metals such as Na, AI, Zn, etc., and some non – metals, e.g., C, S. P, H₂, etc.

Metallic hydrides like NaH, LiH. KH, CaH₂ etc.

Oxidation Number

The oxidation number is defined as the charge in which an atom appears to have when all other atoms are removed from it as ions. It may have + or – sign.

[An element may have different values of oxidation number depending upon the nature of compound in which it is present.]

Oxidation number of an element may be a whole number (positive or negative) or fractional or zero.

Important Points for Determining Oxidation Number

1. The algebraic sum of the oxidation numbers of aU the atoms in an uncharged (neutral) compound is zero. In an ion, the algebraic sum is equal to the charge on the ion.
2.  All elements in the elementary state have oxidation number zero, e.g., He, Cl₂, S₈, P₄ etc.
3.  As fluorine is the most electronegative element, it always has an oxidation number of – 1 in all of its compounds.
4.  In compounds containing oxygen, the oxidation number of oxygen is – 2 except in peroxides (-1) such as Na₂O₂, in OF₂ and in O₂ F₂ (+2 and + 1 respectively).
5. In all compounds. except ionic metallic hydrides, the oxidation number of hydrogen is +1. In metal hydrides like NaH, MgH₂, CaH₂, LiH, etc the oxidation number of hydrogen is -1.
6. Oxidation number for alkali metals is +1 and for alkaline earth metals is + 2.
7.  Oxidation number of metal in amalgams is zero.
8.  In case of coordinate bond, it gives +2 value of oxidation number to less electronegative atom and -2 values to more electronegative atom when coordinate bond is directed formless electronegative atom to more electronegative atom .
9. If coordinate bond is directed from more electronegative to less electronegative atom then its contribution be zero for both the atoms.
10. For p-block elements [Except F and 0], the highest oxidation number is equal to their group number and lowest oxidation number is equal to the group number minus eight.
11. In transition elements the lowest oxidation number is equal to the number of ns electrons and highest oxidation number is equal to number of ‘ns’ and (n – l)d unpaired electrons.

Determination of Oxidation Number of Underlined Element

Oxidation number of Na = + 1

Oxidation number of 0 = – 2

∴ 2 (1) + 4x + 6 x – 2 = 0

a = 5 / 2, this is average oxidation number. because the compound has two types of sulphur atom.

OX of sulphur bonded with coordinate bond = 5

ON of sulphur which have S-S bond = 0

Average oxidation number = 5 + 5 + 0 + 0 / 4 = 5 / 2

(vii) NH₄ NO₃

There are two types of nitrogen atoms. Therefore. evaluation should be made separately as

Oxidation number of N in NH⁺₄

x + 4 (+ 1)= + 1

x = – 3

Oxidation number of N in NO^–₃

y + 3 x (- 2) = – 1

y = 5

Stock Notations

The oxidation states of elements exhibiting variable oxidation states are specified by Roman numerals such as I, II, III, IV, etc., within parenthesis after the symbol or name of the element. This system was introduced for the first time by German chemist, Alfred Stock and is known as Stock notation. This may be illustrated as

Balancing of Redox Chemical Equations

Every chemical equation must be balanced according to law of conservation of mass. In a balanced chemical equation the atoms of various species involved in the reactants and products must be equal in number. Redox reaction can be balanced through (i) Ion electron method (ii) Oxidation number method

Ion Electron Method

This method of balancing was developed by Jette and Lamer in 1927.

For example. balance the equation

Cu + HNO₃ → Cu(NO₃)₂ + NO + H₂O

It involves the following steps.

Step I Write the redox reaction in ionic form

Cu + H⁺ + NO^–₃ → Cu²⁺ + NO + H₂O

Step II Split the redox reaction into its oxidation-half and reduction half-reaction.

Step III Balance atoms of each half-reaction (except H and O) by using simple multiples.

Cu → Cu²⁺ and NO^–₃ → NO

(Except H and O, all atoms are balanced)

Step IV Balance H and O as

(i) For acidic and neutral solutions Add H₂O molecule to the side deficient in oxygen and H+ to the side deficient in hydrogen.

(ii) For alkaline solutions For each excess of oxygen, add one water molecule to the same side and OH^– ion to the other side to balance H.

Step V Add electrons to the side deficient in electrons.

Step VI Equalize the number of electrons in both the reactions by multiplying a suitable number

Step VII Add the two balanced half reactions and cancel common terms of opposite sides

Step VIII Convert the ionic reaction into molecular form by adding spectator ions

(Ions which are present in solution but do not take part in the redox reaction, are omitted while writing the net ionic equation of a reaction and are known as spectator ions.)

Oxidation Number Method

For example, balance the equation

Mg + HNO₃ → Mg(NO₃)₂ + N₂O + H₂O

It involves the following steps.

Step I Write the skeleton equation (if not given)

Step II Assign oxidation number of each atom

Step III Balance atoms other than H and O in two processes.

Step IV Equalize the total increase or decrease in oxidation number

4Mg + 2HNO₃ → 4Mg(NO₃)₂ + NO₂O

Step V Balance H and O

8H⁺ + 4 Mg + 2HNO₃ + 8NO₃^– → 4 Mg (NO₃)₂ + N₂O + 5H₂O

4 Mg + 10 HNO₃ → 4 Mg (NO₃)₂ + N₂O + 5H₂O

Redox Reactions in Daily Life

e.g.,

CH₃ COOH ⇔ CH₃COO^– + H^–

Electrolytes

Chemrcal substances which can ccnduct electricity in their aqueous stare or tn molten state are called electrolytes. The conduction of current through electrolyte is due to the movement of ions.

1. Strong Electrolytes

Electrolytes which dissociate almost completely into constituent ions in aqueous solution are known as strong electrolytes. e.g.. all salts (except HgCl₂, CdBr₂)’ mineral acids like HCl, H₂)SO₄, HNO₃ etc.. and bases like NaOH. KOH. etc.

2. Weak Electrolytes

Electrolytes which dissociate to a lesser extent in aqueous solution are called weak electrolyte. All organic acids (except sulphonic acids), and bases like NH₃. NH₄OH, amines etc.

Degree of Ionisation or Degree of Dissociation (α)

It is the fraction of the total number of molecules which ionise (dissociate)into constituent ions.

α = (number of molecules ionised or dissociated/total number of molecules taken)

For strong electrolytes,

α = 1

For weak electrolytes

α < 1

Values of the degree of dissociation (ex)depends upon the following factors

1. nature of solute
2. nature of solvent
3. concentration
4. temperature

Ostwald’s Dilution Law

According to Ostwald. the degree of dissociation (ex)of weak electrolyte is inversely proportional to the square root of the molar concentration of the solution.

Hore K is dissociation constant and C is molar concentration of the solution.

Acids and Bases

Earlier Definitions of Acids and Bases

Earlier definitions of acids and bases was given by Robert Boyle, who classified them on the basis of their properties. According to him, acids are the substance which have sour taste. turns blue litmus red. liberate hydrogen with metals, conduct electricity in aqueous solution and neutralise bases.

Bases are the substance which have bitter taste, turns red litmus blue, soapy to touch, conduct electricity in aqueous solution and neutralise acids.

Arrhenius Concept of Acids and Bases

• Acid is a chemical substance which dissociates in aqueous solution to give hydrogen ions (H⁺) or hydronium ions (H₃O⁺).
• Base is a chemical substance which dissociates in aqueous solution to give hydroxyl ions (OH^–).
• Arrhenius theory fails to explain the acidic and basic behaviour in non-aqueous solutions. It cannot explain the acidic character of A1Cla. BFa and basic character of NH₃, PH₃, etc.

Bronsted Concept of Acids and Bases

Acid is a chemical substance that can donate a proton (H⁺) to some other substance and a base is a chemical substance that can accept a proton from other substance. Thus, an acid is a proton donor (protongenic) and a base is proton acceptor (protopbilic).

Strong acid has weak conjugate base and weak acid has strong conjugate basco Strong base has weak conjugate acid and weak base has strong conjugate acid.

HClO₄ is the strongest while HCN is the weakest hydracid known.

CsOH is the strongest base known.

Amphoteric or arnphiprotic substance or ampholytes are the substance which act as an acid as well as a base, e.g.• water acts as an acid with NH₃ and a base with acetic acid.

The order of acidic strength of some acids is

HClO₄ > HBr> H₂SO₄ > HC1> HNO₃

Greater the K_a value of an acid (or lesser the pK_a), stronger is the acid. Similarly. greater the K_b(or lesser the pK_b) of a base. stronger is the base.

Levling Effect

The adds like HClO₄ H₂SO₄, HNO₃ etc. react with water almost completely to form H₃O⁺ions.Therefore,all the strong acids in aqueous solutionsappear equally strong and their relative strengths in aqueous solution cannot be compared. Since H₃O⁺ is the strongest acid in water. the strength of above acids come down to the level of H₃O⁺ strength in water. Similarly.strong bases like NaOH. KOH. Ba(OH)₂ come down to the strength of OH^– ion in water.

This is called levling effect.

Lewis Concept of Acids and Bases

Lewis acid is a chemical substance which can accept a pair of electrons,

e.g.,

1. Molecules with incomplete octet of central atom like AlCl₃ ,BeCl₂, MgCl₂, etc.
2.  Simple cations like Ag⁺, Na⁺, etc.
3. Molecules in which the central atom has vacant d-orbital, e.g.,SF₄, SnC1₄ PF₃ etc.

Lewis base is a chemical substance which can donate a pair of electrons. e.g.,

1. Neutral molecules containing lone pairs like NH₃, RNH₂, ROH etc.
2. Negatively charged species like CN, Cl. OH, etc.
3. In coordination complexes, the ligands act as Lewis base.

Limitations of Lewis Concept

1. It does not explain the behaviour of protonic acids such as HCl, H₄SO₄, HNO₃ etc.
2. It does not predict the magnitude of relative strength of acids and bases.

All Bronsted-Lowry’s acids are Lewis acids while acids need not be Bronsted-Lowry’s acids.

The Ionization Constant of Water Ionic product is the product of the concentration of hydronium ions and hydroxyl ion in pure water, which remains constant at a particular temperature. It is symbolized by K_w. At 298 K, ionic product of water (K_W) is given as K_W: = [H₃O⁺] [OH^–] = 1 x 10^-14mol²L^–.

The value of K_w increases with increase in temperature.

The pH Scale

pH is defined as the negative logarithm of hydrogen ion concentration.

pH = – log [H⁺] and [H⁺J = lO^-pH

Total [H⁺] or [OH^–] in a mixture of two strong acids or bases = (ΣNV/ΣV)

Similarly, negative logarithm of hydroxyl ion concentration is pOH.

pH value of an acid having H+ concentration less than 10^-7, is always in between 6 and 7. For 10^-8N HCl solution. it is 6.958.Similarly for 10^-8 NaOH solution, the pH is 7.04 (because basic solutions always have pH 77.)

pH of solution is accurately measured by pH meter or emf method or roughly by pH paper or indicator paper.

(PH can be zero in 1 N Hel solution or it can be negative for more. concentrated solution like 2N, 3N, lON, etc,

pH range for some important substances are :

Gastric juice = 1 – 3
Vinegar = 2.4 – 3.4
Tears – 7.4
Human urine – 4.8 – 8.4
Blood plasma – 7.3 – 7.4
Boil water – 6.5625

Dissociation Constant of Weak
Acid and Weak Base

Let us consider the dissociation of weak acid (HA) as

Dissociation constant for polyprotic acids and bases. For a tribasic acid,

The overall dissociation constant (K) is given as

K = K₁ x K₂ x K₃

where, K₁ x K₂ x K₃

Similarly, for a dibasic acid like H₂CO₃

pH = pk_a1 + pk_a2/2)

Buffer Solution

Solution which resists the change in its pH value by addition of a small amount of acid or a base, is called buffer solution.

• Acidic buffer They have pH value < 7, e.g., CH₃COOH/CH₃COONa, bone acid/borax.
• Basic buffer They have pH value> 7 e.g., NH₄OH/NH₃₄Cl

Buffer system present in blood is H₂CO₃ + NaHCO₃.

Henderson-Hesselbalch Equation

Equation used to calculate the pH of a buffer solution.

(i) For acidic buffer,

pH = pK_a + log[salt/acid]

(i) pOH = pK_b + log[salt/acid]

and pH = 14 – pOH

Here, pK_a = -log K_a, pK_b = -log K_b and K_a and K_b are dissociation constants of acid and base.

[salt), [acid] and [base) represent molar concentrations of salt, acid and base respectively.

If addition of a strong acid or base changes the pH of a buffer by/unit, the buffer solution is assumed to destroyed, i.e.,

New pH = pKo ± 1

This means the ratio.

[salt]/[acid) or [salt]/[base] = 10 or (1/10)

Buffer Capacity

It is defined as the number of moles of acid or base added in 1 L of solution Lochange the pH by unity.

Buffer capacity (φ)

= (no. of moles of acids or base added to 1 L of buffer/change in pH)

Salts

These are the product of reaction between an acid and a base.
This reaction is called neutralisation reaction.

Types of Salts

(a) Normal salts These are obtained by complete neutralisation of an acid with a base, e.g., NaCI, K₂SO₄, etc.

(b) Acidic salts These are formed by incomplete neutralisation of polybasic acids. e.g., NaHCO₃, Na₂SO₄ etc.

(c) Basic salts These are formed by incomplete neutralization of polyacidic base, e.g., Mg(OH)Cl, Bi(OH)₂Cl, etc.

(d) Double salts These are formed by the combination of two simple salts and exist only in solid state, e.g., Mohr salt or ferrous ammonium sulphate (FeSO₄.(NH₄)₂SO₄.6H₂O], alum, etc.

(e) Complex salts These are formed by the combination of simple salts or molecular compounds. These are stable in solid state well as in solutions.

The properties of their solutions are different from the properties of substances from which they have been constituted.

(f) Mixed salts These salts furnish more than one cation or more than one anion when dissolved in water, e.g., Ca(OCl)Cl, NaKSO₄, etc.

Salt Hydrolysis

Salts are strong electrolytes and on dissolution in water split up into ions which react with H⁺ or OH^– ions furnished by water yielding acidic or basic solution. The process is known as salt hydrolysis.

Aqueous solution of salt of strong acid and strong base is neutral Aqueous solution of salt of a weak acid and a strong base is alkaline due to anionic hydrolysis, and aqueous solution of salt of strong acid and a weak base is acidic due to cationic hydrolysis with dilution degree of hydrolysis increases.

Hydrolysis is a reverse process of neutralisation.

Common Ion Effect

It is.defined as the suppression of the dissociation of a weak electrolyte by the addition of a strong electrolyte having some common ion, e.g., degree of dissociation of ammonium hydroxide decreases in the presence of ammonium chloride.

According to Le-Chatelier principle, because of the presence of common ion. degree of dissociation of NH₄OH decreases.

Colnmon ion effect is used in

1. Purification of common salt
2. Salting out of soap
3. Qualitative analysis, II group radicals are precipitated out in the presence of HCI which suppress the S^2- ion concentration, which is just sufficient to precipitate only II group radicals.

Similarly in group III, NH₄OH is added in presence ofNH₄Cl to avoid the precipitation of V group radicals.

Isohydric Solutions

If the concentration of the common ions in the solution of two alectrolytes, e.g., OH- ion concentration in Ca(OH)₂ and Ba(OH)₂ solutions, is same then on mixing them there is no change in degree of dissociation of either of the electrolytes. Such solution are called isohydric solutions.

Solubility Product

It is defined as the product of the concentrations of the ions of the salt in its saturated solution at a given temperature raised to the power of the ions produced by the dissociation of one mole of the salt. It is denoted by K_sp.

Consider the dissociation of an electrolyte A_xB_y

Application of Solubility

1. The concept Product of K_sp helps in predicting the formation of precipitate. In general if

1. Ionic product < K_sp,no ppt. is formed.
2. Ionic product > K_sp, ppt. is formed.

2. In predicting the solubility of a sparingly soluble salt

knowing the values of K_sp, x and y, the solubility of the salt can be Computed.

K_sp of AgI is lower than t.hat of Agel. So the former gets precipitated in preference to later.

Distinction Between Solubility Product and Ionic Product

Acid-Base Indicator

An acid-base indicator is a substance which possesses one colour in acid solution and altogether different colour in alkaline medium or the substance which shows colour change with change in pH. The point where the indicator shows a sudden change in colour during the titration is called end point. End point is the point at which the reaction is observed to be complete.

Theory of indicators

(i) Ostwald theory
(ii) Quinonoid theory

Titration Curves and Indicator Used

(a) Titration curve for the neurralisation of strong acid vs strong base pH curve of strong acid (say HCl) and strong base

(say NaOH) is vertical over almost the pH range 4-10. So. the indicators phenolphthalein (pH range 8.3 to 10.5). methyl red (pH range 4.4-6.5 and methyl orange (pH range 3.2-4.5) are suitable for such a titration.

b) Titration curve for the neutralisation of strong acid vs weak base pH curve of strong acid (say HCl or H₂SO₄” or HNO₃) with a weak base (say NH₄OH) is vertical over the pH range of 4 to 7. So the indicators methyl red and methyl orange are suitable for such a titration.

(c) Titration curve for the neutralisation of weak acid vs strong base pH curve of weak acid (say CH₃COOH or oxalic acid) and strong base (say NaOH) is vertical over the approximate pH range 7 to 11. So phenolphthalein is the suitable indicator for such a titration.

d) Titration curve for the neutralisation of weak acid vs weak base pH curve of weak acid and weak base indicates that there is no vertical part and hence, no suitable indicator can be used for such a titration.

Physical processes involve such changes, which only affects the physical properties of the substance undergoing changes but have no effect on the chemical composition and properties.

Chemical processes involve changes in chemical composition and properties. Whenever a chemical change occurs, we can say that a chemical reaction has taken place.

Types of Chemical Reactions

1. Combination Reactions

In such reactions two or more substances combine to form a single compound.

e.g.,

2Mg + O₂ → 2MgO

2. Decomposition Reactions

In these reactions. a compound decomposes to produce two or more different substances.

e.g., PCI₅ ⇔ PCI₃ + CI₂

Digestion of food is also a decomposition reaction.

[Decomposition by heat IS called thermal decomposition and decomposition by sunlight is called photo decomposition.]

3. Displacement Reactions

These reactions involve displacement of one element or group by another. These are infact, redox reactions, e.g.,

Zn(s) + H₂SO₄

4. Double Displacement or Metathesis Reactions

In these. reactions two compounds react to form two new compounds and no change in oxidation state take place, e.g., precipitation reactions, neutralisation, reactions.

AgNO₃(aq) + NaCI(aq) → → AgCl(s) + NaNO₃(aq)

Equilibrium State

Under given set of conditions if a reversible process or chemical reaction is carried out in a closed container, a constancy in some observable properties like colour intensity, pressure, density, is observed. Such a state is referred to as an equilibrium state.

Equilibrium may be classified as :

Physical Equilibrium

Equilibrium set up in physical processes like evaporation of water, melting of solids, dissolution of solutes, etc., is called physical equilibrium, e.g., Ice ⇔ Water

At equilibrium,

Rate of melting of ice = Rate of freezing of water

Chemical Equilibrium

If a reversible reaction is carried out in a closed vessel, a stage is attained where the speed of the forward reaction equals the speed of the backward reaction. It corresponds to chemical equilibrium. At equilibrium,

Rate of forward reaction = Rate of backward reaction

Characteristics of Chemical Equilibrium

1. Equilibrium can be attained from either side.

2. Equilibrium is dynamic in nature, i.e., at equilibrium reaction does not stop.

3. At equilibrium, there is no change in the concentration of various species.

4. The equilibrium state remains unaffected by the presence of catalyst. Catalyst helps to attain the equilibrium state rapidly.

6. The observable physical properties of the process become constant.

Law of Mass Action

Guldberg and Waage states that the rate of a chemical reaction is directly proportional to the product of the active masses of the reacting substances. For a general reaction,

where, k_f and k_b are rate constants.

In heterogeneous equilibrium, the active mass of pure solids and liquids are taken as

At equilibrium,

Rate of forward reaction = Rate of backward reaction

K_c is called the equilibrium constant.

Use of Partial Pressures Instead of Concentration

For gaseous reactions, partial pressures are conveniently used since at any fixed temperature partial pressure is directly proportional to concentration. For a general gaseous reaction,

Relation between K_c and K_c

where, Δn_g = moles of products – moles of reactants (gaseous only)

Relation between K_c and K_p for different types of reactions

(i) When Δn_g = 0, K_p = K_c

(ii) When Δn_g = +ve, K_p > K_c

(iii) When Δn_g = -ve, K_p < K_c

Units of K_p and K_c

(i) Unit of K_p = (atm)^Δn_g

(ii) Unit of K_c = (mol L^-1)^Δn_g

Characteristics of Equilibrium Constant K_p or K_c

1. It has definite value for every chemical reaction at a particular temperature.

2. The more is the value of K_c or K_p, the more is the extent of completion of reaction, i.e., K_c < 1 indicates lesser concentration of products than reactants.

K ≥ 10³ shows completion of reaction and K ≤ 10^-3 shows that the reaction does not proceed at all.

3. When the reaction can be expressed as sum of two other reactions, the K_c of overall reaction is equal to the product of equilibrium constants of individual reactions.

4. The equilibrium constant is independent of initial concentrations of reactants.

5. Equilibrium constant is independent of presence of catalyst.

6. K_c for backward reaction is inverse of K_c for forward reaction.

7. If an equation is multiplied by n, the K becomes Kⁿ, and if it is divided by m, the k becomes ^m√k.

8. In equilibrium constant expression if activities are used in places of molar concentration, h becomes dimensionless.

Types of Equilibrium

Homogeneous Equilibrium

In homogeneous equilibrium, the reactants and products arc present in the same phase or physical suite (gaseous or liquid).

2SO₂(g) + O₂(g) ⇔ 2SO₃(g)

Heterogeneous Equilibrium

In heterogeneous equilibrium the reactants and products are present in two or more physical states or phases.

3Fe(s) + 4H₂O(g) ⇔ Fe₃O₄(s) + 4H₂(g)

Reaction Quotient

For any reversible reaction at any stage other than equilibrium, the ratio of the molar concentrations of the products to that of the reactants. where each concentration term is raised to the power equal to the stoichiometric coefficient to the substance concerned, is called the reaction quotient, Q_c.

For a general reaction

aA + bB ⇔ cC + dD

which is not at equilibrium,

Q_c = [C]^c + [D]^d / [A]^a [B]^b

If

(i) Q_c > K_c, the value of Q_c will tend to decrease to reach the value of K_c (towards equilibrium) and the reaction will proceed in the reverse direction.

(ii) Q_c < K_c it will lend to increase and the reaction will proceed in the forward direction.

(ii) Q_c = K_c, the reaction is at equilibrium.

Le – Chatelier’s Principle

There are three main factors which affect the state of equilibrium.

They are

1. concentration
2. temperature
3. pressure.

Le – Chatelier’s principle states that if a system at equilibrium is subjected to a change in concentration. pressure or temperature. the equilibrium equilibrium change.

Effect of Change of Concentration

If at equilibrium the concentration of one of the reactants is increased. the equilibrium will shift in the forward direction and vice-versa.

Effect of Change in Pressure

No effect of pressure on equilibria having same moles of reactants and products. e.g., N₂ + O₂ ⇔ 2NO.

When there is change in the number of moles, the equilibrium will shift in the direction having smaller number of moles when the pressure is increased and vice-versa, e.g.,

N₂ + 3H₂ ⇔ 2NH₃ [High p. high yield of NH₃]

Effect of Temperature

When process is exothermic, low temperature favours the forward reaction. When process is endothermic. high temperature favours the formation of products.

Effect of Addition of Inert Gas

(i) Addition of inert gas at constant pressure At constant pressure. if an inert gas is added. it will increase the volume of the system. Therefore. the equilibrium will shift in a direction in which there is an increase in the number of moles of gases.

(ii) Addition of inert gas at constant volume If keeping volume of the system constant, an inert gas is added. the relative molar concentration of the substance will not change. Hence. the equilibrium position of the reaction remains unaffected.

Effect of Catalyst

The presence of catalyst does not change the position of equilibrium. It simply fastens the attainment of equilibrium.

Le-Chatelier’s Principle Applicable to Physical Equilibrium

(i) Effect of pressure on solubility The increased pressure, will increase the solubility of gas and vice-versa.

(ii) Effect of temperature on solubility Some substances dissolve with the absorption of heat. Solubility of such substances will increase with increase of temperature and vice-versa, e.g., dissolution of NH₄CI, KCI, KNO₃, etc. The dissolution of calcium acetate and calcium hydroxide is exothermic, so their solubility is lowered at higher temperature.

(iii) Effect of pressure on the melting point of ice

Ice ⇔ liquid water

The ice occupy the more volume than liquid water, so increased pressure will result in melting of ice according to Le-Chatelier principle.

Favourable conditions for some chemical equilibria to get higher yield of product.

Calculation of the Degree of Dissociation (α) from Density Measurement

α = D – d / d

where, D = theoretical vapour density

d = observed vapour density

Now, molecular mass = 2 * VD

∴ α = M_c – M_o / M_o

where, M_c = calculated molecular weight

M_o = observed molecular weight

Some Important Terms Related to Thermodynamics

(i) System It refers to the part of universe in which observations are carried out.

(ii) Surroundings The part of universe other than the system is known as surroundings.

(ill) Boundary The wall that separates the system from the surroundings is called boundary.

(iv) Thermodynamic equilibrium A system in which the macroscopic properties do not undergo any change with time is called thermodynamic equilibrium.

(v) Thermal equilibrium If there is no flow of heat from one portion of the system to another, the system is said to be in thermal equilibrium.

(vi) Mechanical equilibrium If no mechanical work is done by one part of the system on another part of the system. it is said to be in mechanical equilibrium. Such a condition exists when pressure remains constant.

Types of Systems

(i) Open system The system in which energy and matter both can be exchanged with the surroundings.

(ii) Closed system The system in which only energy can be exchanged with the surroundings.

(iii) Isolated system The system in which neither energy nor matter can be exchanged with the surroundings.

Thermodynamics Properties

1. Intensive Properties

Properties of the system which depend only on the nature of matter but not on the quantity of matter are called Intensive properties, e.g., pressure, temperature, specific heat, etc

2. Extensive Properties

Properties of the system which are dependent on the quantity of matter are called extensive properties, e.g., internal energy, volume, enthalpy, etc.

State of System

When microscopic properties have definite value, the conditions of existence of the system is known as state of system.

State functions When values of a system is independent of path followed and depend only on initial and final state, it is known as state function,e.g., Δ U, Δ H, Δ G etc.

Path functions These depend upon the path followed, e.g., work, heat, etc.

Thermodynamic Process

It is the operation which brings change in the state of the system.

Thermodynamic processes are

(i) Isothermal process In which temperature remains constant, i.e., (dT = 0, Δ U = 0).

(ii) Isochoric process In which volume remains constant, i.e., (Δ V = 0).

(iii) Isobaric process In which pressure remains constant, i.e., (Δp = 0).

(iv) Adiabatic process In which heat is not exchanged by system with the surroundings, i.e., (Δq = 0).

(v) Cyclic process It is a process in which system returns to its original state after undergoing a series of change, i.e., Δ U _cyclic = 0; Δ H _cyclic = 0

(vi) Reversible process A process that follows the reversible path, i.e., the process which occurs in infinite number of steps in this Way that the equilibrium conditions are maintained at each step, and the process can be reversed by infinitesimal change in the state of functions.

(vii) Irreversible process The process which cannot be reversed and amount of energy increases. All natural processes are Irreversible.

Internal Energy (E or U)

It is the total energy within the substance. It is the sum of many types of energies like vibrational energy, translational energy. etc. It is a extensive property and state function.

Its absolute value cannot be determined but experimentally change in internal energy (Δ) can be determined by

ΔU = U₂ – U₁ or ΣU_p – ΣU_R

For exothermic process, ΔU = -ve, whereas for endothermic process ΔU = +ve

U depends on temperature, pressure, volume and quantity of matter.

Zeroth Law of Thermodynamics or Law of Thermal Equilibrium

The law states that if the two systems are in thermal equilibrium with a third system then they are also in thermal equilibrium with each other. Temperature is used here to know, the system is in thermal equilibrium or not.

First Law of Thermodynamics

Energy can neither be created nor destroyed although it can be converted from one form to the other.

Mathematically, ΔU = q + W

where, ΔU = internal energy change

q = heat added to system

W = work added to system

Sign convention

(i) q is + ve = heat is supplied to the system

(ii) q is – ve = heat is lost by the system

(iii) Wis + ve = work done on the system

(iv) Wis – ve =work done by the system

Modes of Transference of Energy

Heat (q)

It occurs when there is a difference of temperature between system and surroundings. It is a random form of energy and path dependent. Its units are joule or calorie.

Work (W)

If the system involves gaseous substances and there is a difference of pressure between system and surroundings. work is referred as pressure – volume work (W_pV).

Expression for Pressure – Volume Work

(i) Work of Irreversible expansion against constant pressure B under isothermal conditions

W_pV = – p_ext ΔV

(ii) Work of reversible expansion under isothermal conditions

(iii) Work of reversible expansion under adiabatic conditions

(iv) Work of irreversible expansion under adiabatic conditions

(v) When an ideal gas expands in vacuum then

p_ext = 0

Work done is maximum in reversible conditions

Units CGS system – erg

SI system – joule

Work and heat both appear only at the boundary of the system during a change in state.]

Heat Capacity of a System

Heat Capacity (c) of a system is defined as the amount of heat required to raise the temperature of a system by 1° C.

1. Molar Heat Capacity

It is the heat capacity 1 mole of substance of the system.

2. Specific Heat Capacity

It is the heat capacity of 1 g of substance of the system

q = mc Δ T.

where, m = mass of substance

c = specific heat or heat capacity

Molar heat capacity, at constant pressure,

C_p = C_p * M

Molar heat capacity. at constant volume

C_V = C_V * M

(c_p and C_V are specific heats at constant pressure and constant volume respectively and M is molecular weight of gas)

c_p – C_V = R (R = Molar gas constant)

C_p – C_V = R / M

The molar heat capacity at constant volume,

C_V = (3 / 2) R

The molar heat capacity at constant pressure,

C_p = (3 / 2) R + R = (5 / 2)R

Poisson’s ratio, γ = C_p / C_V = (5 / 3) = 1.66

γ = 1.66 for monoatomic gas

γ = 1.40 for diatomic gas

γ = 1.33 for triatomic gas

Enthalpy (H)

It is the sum of internal energy and pV-energy of the system. It is a state function and extensive property. Mathematically,

H = U + pV

Like U. absolute value of H also cannot be known, ΔH is determined experimentally.

ΔH = H₂ – H₁

or ΣH_p = ΣH_R

For exothermic reaction (the reaction in which heat is evolved), ΔH = -ve whereas for endothermic reaction (the reaction in which heat is absorbed), ΔH = +ve.

Relationship between ΔH and ΔU

ΔH = ΔU + Δp Δ V

or ΔH = ΔU + Δn_(g) RT

Here, Δn_(g) = change in the number of gas moles.

Enthalpy or Heat of Reaction (ΔrH)

It is the change in enthalpy that accompanies a chemical reaction represented by a balanced chemical equation.

ΔrH = ΣH_(p) – ΣH_(R)

Enthalpy of reaction expressed at the standard state conditions is called standard enthalpy of reaction (ΔH).

Factors affecting enthalpy of reaction

(i) Physical state of reactants and products.

(ii) Allotropic forms of elements involved.

(iii) Chemical composition of reactants and products.

(iv) Amount of reactants.

(v) Temperature.

Various Forms of Enthalpy of Reaction

1. Enthalpy of Formation (ΔH_f)

It is heat change when one mole of compound is obtained from Its constituent elements.

Enthalpy of formation at standard state is known as standard enthalpy of formation Δ_fH° and is taken as zero by convention. It also gives the idea of stability.

2. Enthalpy of Combustion

It is the Enthalpy change taking place when one mole of a compound undergoes complete combustion In the presence of oxygen (ΔH_c.)

ΔH_c because process of combustion is exothermic.

3. Enthalpy of Solution

It is the Enthalpy change when one mole of a substance is dissolved in large excess of solvent, so that on further dilution no appreciable heat change occur.

4. Enthalpy of Hydration

It is the enthalpy change when one mole of anhydrous substances undergoes complete combustion. It is an exothermic process.

5. Enthalpy of Fusion

It is the enthalpy change that accompanies melting of one mole of solid substance.

6. Enthalpy of Vaporisation

It is the enthalpy change that accompanies conversion of one mole of liquid substance completely into vapours.

7. Enthalpy of Neutralisation

It is the enthalpy change that takes place when 1 g-equivalent of an acid (or base) is neutralised by 1 g-equivalent of a base (or acid) in dilute solution.

Enthalpy of neutralisation of strong acid and strong base is always constant, i.e., 57.1 kJ.

[Enthalpy of neutralisation of strong acid and weak base or weak acid and strong base is not constant and numerically less than 57.1 kJ due to the fact that here the heat is used up in ionisation of weak acid or weak base. This is known as enthalpy of ionisation of weak acid / or base.]

8. Enthalpy of Transition

It is the enthalpy change when one mole of the substance undergoes transition from one allotropic form to another.

9. Enthalpy of Atomisation

It is the enthalpy change occurring when one mole of the molecule breaks into its atoms.

10. Enthalpy of Dilution

It is the enthalpy change, when one mole of a substance is diluted from one concentration to another.

11. Enthalpy of Sublimation

It is the enthalpy change, when one mole of a solid substance sublines.

12. Lattice Enthalpy

It is the enthalpy change, when one mole of an ionic compound dissociates into its ions in gaseous state.

Laws of Thermochemistry

1. Lavoisier Laplace Law

Th enthalpy change during a reaction is equal in magnitude to the enthalpy change in the reverse process but it is opposite in sign.

2. Hess’s Law of Constant Heat Summation

The standard enthalpy of a reaction. which takes place in several steps, is the sum of the standard enthalpIes of the intermediate reactions into which the overall reactions may be divided at the same temperature.

According to Hess’s law

ΔH = ΔH₁ + ΔH₂ + ΔH₃

Applications of Hess’s law are

(a) In determination of beat of formation.

(b) In determination of heat of transition.

(c) In determination of heat of hydration.

(d) To calculate bond energies.

3. Trouton’s Rule

According to this law, “The ratio of enthalpy of vaporization and normal boiling point of a liquid IS approximately equal to 88 J per mol per kelvin. i.e.,

ΔH_vap / T = 88 J / mol / K

4. Dulong and Petit Law

This law states “The product of specific heat and molar mass of any metallic element is equal to 6.4 cal/ mol/ °C. i.e.,

5. kirchhoff’s Equation

ΔC_p = ΔH₂ – ΔH₁ / T₂ – T₁

and ΔC_v = ΔE₂ – ΔE₁ / T₂ – T₁

6. Clausius – Clapeyron Equation

– 2.303 log p₂ / p₁ = ΔH_v / R (T₂ – T₁ / T₁ T₂)

where, ΔH_v = molar heat of vaporisation.

Bond Enthalpy

It is the average amount of energy required to break one mole of bonds in gaseous molecules.

Bond Dissociation Enthalpy

The energy required to break the particular bond in a gaseous molecule is called bond dissociation enthalpy. It is definite in quantity and expressed in kJ mol^-1.

In diatomic molecule, bond dissociation enthalpy = Bond enthalpy

In polyatomic molecule, bond dissociation enthalpy ≠ Bond Enthalpy

ΔH = [sum of bond enthalpies of reactants] – [sum of bond enthalpies of products]

Factors affecting bond enthalpy

(i) Size of atoms

(ii) Electronegativity

(iii) Bond length

(iv) Number of bonding electrons

Entropy (S)

It is the measurement of randomness or disorder of the molecules. It is a state function and extensive property.

Units : jK^-1 mol^-1

The change in entropy during a process is mathematically given as

Δ_rS° = Σ S° (products) – Σ S° (reactants) = q_rev / T = ΔH / T

Where, q_rev heat absorbed by the system in reversible manner

T = temperature

Δ S > 0, Increase in randomness, heat is absorbed

Δ S < 0, Decrease in randomness, heat is evolved.

Entropy of even elementary substances are not zero.

Entropy change of an ideal gas is given by

Δ S = _nC_V In (T₂ / T₁) + nR In (V₂ / V₁)

Entropy Change During Phase Transition

The change of matter from one state to another state is called phase transition.

The entropy changes at the time of phase transition:

Spontaneous Process

The physical or chemical process which proceeds by its own in a particular direction under given set of conditions without outside heir is called spontaneous process. It cannot be reversed.

All natural processes are spontaneous process.

Spontaneous process where no initiation is needed

(i) Sugar dissolves in water.

(ii) Evaporation of water.

(iii) Nitric oxide (NO) reacts with oxygen.

Spontaneous process where some initiation is required

(i) Coal keeps on burning once initiated.

(ii) Heating of CaCO₃ to give calcium oxide and CO₂ is initiated by heat.

Enthalpy Criterion of Spontaneous Process

All the processes which are accompanied by decrease of energy (exothermic reactions, having negative value of ΔH) occur spontaneously.

It fails when some endothermic reactions occur spontaneously.

Entropy Criterion of Spontaneous Process

A process is a spontaneous if and only if the entropy of the universe increases.

For a process to be Spontaneous

(ΔS_universe > 0 or ΔS_syst + ΔS_surr > 0)

At equilibrium state, ΔS = 0,

Limitations of ΔS criterion and need for another term We cannot find entropy change of surroundings during chemical changes. So we need another parameter for spontaneity viz Gibbs’ energy of system (G).

Second Law of Thermodynamics

The entropy of the universe is always Increasing in the course of every spontaneous or natural change.

Or

All spontaneous processes or natural change are thermodynamically irreversible without the help of an extemal work. i.e., heat cannot flow itself from a colder to hotter body.

Joule-Thomson Effect

The phenomenon of cooling of a gas when it is made to expand adiabatically from a region of high pressure to a region of extremely. low pressure is known as Joule-Thomson effect. This effect is zero when an ideal gas expands in vacuum.

[When an ideal gas undergoes expansion under adiabatic condition in vacuum, no change takes place in its internal energy, i.e., (∂E / ∂V)_T = 0 where, (∂E / ∂V)_T is called the Internal pressure.]

Joule-Thomson Coefficient

The number of degrees of temperature change produced per atmospheric drop in pressure at constant enthalpy when a gas is allowed to expand through a porous plug is called Joule-Thomson coefficient. It is given as

μ = dT / dp

where, μ = Joule-Thomson coefficient

dT = change in temperature

dp = change in pressure.

Inversion Temperature

The temperature below which a gas becomes cooler on expansion is known as the inversion temperature. It is given as

T_i = 2a / Rb

where, a and b = van der Waals’ constant

At inversion temperature T_i, the the Joule Thomson coefficient μ = 0, i.e., the gas neither heated nor cooled.

Carnot Cycle

It is an imaginary cycle which demonstrates the maximum conversion of heat into work. It involves four processes

(i) isothermal reversible expansion;

(ii) adiabatic reversible expansion;

(ii) adiabatic reversible expansion;

(iv) adiabatic reversible compression.

The efficiency of a heat engine in a Carnot cycle,

η = T₂ – T₁ / T₂

= q₂ – q₁ / q₂ = w / q₂

Gibbs Energy or Gibbs Free Energy

It is the energy available for a system at some conditions and by which useful work can be done. It is a state function and extensive property.

Mathematically,

G = H – TS

Change in Gibbs energy during the process 1S given by Gibbs Helmholtz equation.

(ΔG = G₂ – G₁ = ΔH – TΔS)

where, ΔG = Gibbs free energy

H = enthalpy of system

TS = random energy

ΔG_system = – TΔS_total

The Gibbs energy criterion of spontaneity

ΔG > 0, process is non-spontaneous

ΔG < 0, 0, process is spontaneous

ΔG = 0, process is in equilibrium state

Effect of Temperature on Spontaneity

Now an exothermic reaction which is non-spontaneous at high temperature may become spontaneous at low temperature. Similarly, endothermic reactions which are non-spontaneous at low temperature may become spontaneous at high temperature.

Standard Free Energy Change (Δ G)

It is the change in free energy which takes places when the reactants are converted into products at the standard states, i.e., (1 atm and 298 K)

where, ΔG°_f = standard energy of formation

Standard energy of formation of all free elements is zero.

Gibbs Energy Change and Equilibrium

Criterion for equilibrium,

⇒ We also know that

Relation between ΔG° and EMF of the Cell

Third Law of Thermodynamics

This law was formulated by Nernst in 1906. According to this law, “The entropy of a perfectly crystalline substance at zero K or absolute zero is taken to be zero”. We can find absolute entropies of pure substances at different temperature.

where, C_p = heat capacities

T = temperature between 0 K and T K

This law is on1y applicable for perfectly crystalline substances. If there is imperfection at 0 K, the entropy will be larger than zero.

It is defined as the attractive forces which hold the various chemical constituents (atoms, ions, etc.) together in different chemical species.

Bond forms to get the stability. with a release of energy.

Kossel-Lewis Approach to Chemical Bonding

According to this theory. atoms take part in the bond formation to complete their octet or to acquire the electronic configuration of the nearest inert gas atoms (Octet rule). This can be achieved by gaining, losing or sharing the electrons.

Lewis Symbols

Valence electrons are reported by dots around the chemical symbol of element, e.g.,

Ionic Bond

A chemical bond formed by complete transference of electrons from one atom (metal) to another (non-metal) and hence, each atom acquire the stable nearest noble gas configuration, is called ionic bond or electrovalent bond, e.g., formation of sodium chloride

Favourable factors for the formation of ionic bonds

(i) Metal should have lowest ionisation enthalpy.

(ii) Non-metal must have highest electron gain enthalpy.

(iii) The energy released during the formation of 1 mole of crystal lattice, i.e., lattice enthalpy must be high.

[Some elements exhibit variable electrovalency. The reason for this iS unstable configuration of penultimate orbit and inert pair effect].

Ions

Species carrying either positive or negative charge are termed as ions. Species carrying positive charge are called cations and that carrying negative charge are called anions. Metals usually form cation while non-metals (except H) usually form anions.

General Characteristics of Ionic Compounds

1. Ionic compounds are usually solids in nature.

2. Ionic compounds have high melting and boiling points.

3. Ionic compounds are soluble in polar solvents like water but insoluble in non-polar solvents like benzene, C014 etc.

4. Ionic compounds are good conductor in molten state and in aqueous solution.

5. Ionic compounds has crystal structure.

Born Haber Cycle

This cycle is based upon the fact that the formation of an ionic compound may occur either by direct combination of the elements or by an alternate process in which :

1. The reactants (metal) are vaporised to convert into gaseous state.

2. The gaseous atoms are converted into ion.

3. The gaseous ions are combined to form ionic lattice of molecule. e.g., formation of NaCI can be shown as

where, S = enthalpy of sublimation

I = ionisation energy

D = dissociation energy

E = electron affinity

U = lattice energy

Q = total enthalpy change

Method of Writing Formula of Ionic Compound

1. Write the symbol of cation at the left and anion at the right.

2. Write their electrovalencies in figures on the top of each symbol as AXBY.

3. Divide their valencies by HCF.

4. Now apply criss-cross rule asi.e., formula is A_yB_x.

e.g., formula of aluminum sulphateis Al₂(So₄)₃.

Covalent Bond

A chemical bond formed between two atoms by mutual sharing of electrons between them so as to complete their octets or duplets, is known as covalent bond and the number of electrons contributed by each atom is known as covalency. e.g., formation of CI₂/

In covalent bonding, the shared pairs of electrons present between the atoms are called bond pairs while unshared pairs or non-bonding electron pairs are known as lone pairs.

Polar Covalent Bond

If a covalent bond is formed between the different ~toms, the shared pair is displaced towards the more electronegative atom causing greater concentration of electron density around the more electronegative atom. Such a covalent bond develops some ionic character and is called polar covalent bond (e.g., H-CI).

Properties of Covalent Compounds

1. In general, covalent compounds exist in the liquid or gaseous state at room temperature due to magnitude of intermolecular forces.

2. Covalent compounds have low melting and boiling points.

3. Covalent compounds are generally poor conductors of electricity because they do not contain free electrons or ions to conduct electricity.

4. They are soluble in non-polar solvents like benzene but usually insoluble in water.

Octet Rule

According to Octet rule during the formation of a covalent bond, the atom attain an inert gas electronic configuration (valence shell contains 8e^– or shell is completely filled). An atom may attain this configuration by gaining, losing or sharing electrons with other atoms

Exceptions of the Octet Rule

(i) Incomplete octet of the central atom, e.g., LiCl, BeH₂ and BCl₃

(ii) Odd electron molecules

(iii) Expanded octet of central atoms

Formal Charge on an Atom in a Molecule/Ion

Formal charge (F.C) on an atom in a Lewis structure

= [total number of valence electrons in the free atom]

– [total number of Don-bonding (lone pair) electrons]

– 1 / 2 [total number of bonding (shared) electrons].

F.C. on O₁ = 6 – 2 – 1 / 2 (6) = + 1

Hence, O₃ along with the formal charges can be represented as follows

Bond Characteristics

Bond Length

In a covalently bonded molecule. distance between the nuclei of the two atoms is known as bond length. Bond length increases with increases is the size of bonded atoms and decreases with an increase in the number of bonds between bonded atoms.

Bond length is determined by X·ray diffraction or electron differences method.

Bond Angle

In a covalently bonded molecule having more than two atoms, the bonds form an angle with each other, which is known as bond angle. In general an increase in the size of central atom decreases the bond angle. Factors affecting bond angle (i) Lone pair repulsion (ii) hybridisation of central room.

It is determined by X-rays diffraction method.

Bond Order

It is defined as the number of covalent bonds present in a molecule.

Bond order = 1 / 2 [Number of electrons in bonding orbitals – Number of electrons in anti-bonding orbitals]

Bond order ∝ 1 / bond length

If bond order comes out to be zero, the molecule does not exist.

Bond Enthalpy

It is the amount of energy released when one mole of covalent bonds is formed while the bond dissociation enthalpy is the amount of energy required to break the one mole of bonds of the same kind so as to separate the bonded atoms in the gaseous state.

The bond enthalpy and bond dissociation enthalpy are equal in magnitude and opposite in sign.

[Bond dissociation enthalpy is determined by thermal or spectroscopic methods.]

As the bond order increases, bond enthalpy also increases and bond length decreases.

Factors affecting bond enthalpy

(i) atomic size

(ii) electronegativity

(iii) extent of overlapping

(iv) bond order

Dipole Moment (μ)

It is defined as the product of the magnitude of the charge and the distance between the centres of positive and negative charge.

μ = charge (Q) x distance of separation (r)

Dipole Moment is expressed in Debye. (D).

1 D = 1 * 10^-18 esu-cm = 3.33564 * 10^-30 C-m

where, c is coulomb and m is meter.

(The shift in electron density is symbolised by broken arrow)

NH₃ has higher dipole moment than NF₃.

Resultant dipole moment.

μ = √μ²₁ + μ²₂ + 2μ₁μ₂ cos θ

Applications of Dipole Moment

1. Dipole moment is helpful in predicting the geometry of the molecule.

2. Dipole moment helps in determining the polarity

Hannay-Smith equation

Percent ionic character = 16 [X_A – X_B] + 3.5 [X_A – X_B]²

where, X_A and X_B are the electronegativities of atoms.

Percent ionic character can also be calculated by dipole moment as

Percent ionic character = observed dipole moment / calculated dipole moment * 100

3. Non-polar molecule has zero dipole moment like Bf₃, CCI₄, etc.

4. cis and trans isomers can be distinguished by dipole moments usually cis isomer have higher dipole moment and hence, higher polarity.

5. Dipole moment is greatest for ortho isomer, zero for para isomer and less than that of ortho for meta isomer.

Fajan’s Rule

The partial covalent character of ionic bonds was discussed by Fajan’s in terms of following rules :

The smaller the size of calion and the larger the size of the anion, the greater the covalent character of an ionic bond,

The greater the charge on the cation or anion, the greater the covalent character of the ionic bond.

Resonance

According to the concept of resonance, a single Lewis structure cannot explain all the properties of the molecules. The molecule is then exposed to have many structures, each of which can explain most of the properties. The actual structure lies in between of all these contributing structures and is called resonance hybrid and the different individual structures are called resonating structures or canonical structures. This phenomenon is known as resonance.

Resonance stabilises the molecule as the energy of the resonance hybrid is less than the energy of any single canonical structure.

Resonance averages the bond characteristics as a whole.

The difference in the energy of the resonance hybrid and the most stable contributing structure (having least energy) is called resonance energy. Greater the resonance energy, greater is the stability of the molecule.

[Calculation of bond order for molecules showing resonance Bond order

= total number of bonds between two atoms in all the structures / total number of resonating structures]

The Valence Shell Electron Pair Repulsion (VSEPR) Theory

According to this theory,

1. The geometry of a molecule or ion depends on the number of electron pairs in the valence shell of its central atom.

2. To attain minimum repulsive state electron pairs try to stay as far away as possible.

3. If the central atom is surrounded by only bonded electron pairs of similar atoms, the repulsive interactions are similar and the moleCular geometry is regular.

4. If the central atom is surrounded by only bonded electron pairs of dissimilar atoms, the repulsive interactions are not equivalent and hence. the geometry of molecule will not be regular.

5. If the central atom is surrounded by both bonded pairs (bp) as well as lone pairs (lp) of electrons. repulsive interactions are not equivalent and hence, geometry of the molecule will be irregular.

The repulsive interactions decrease in the order

lp – lp > lp – bp > bp – bp

Shapes (Geometry) of Molecules Containing Bond Pairs Only or Bond Pairs and Lone Pairs

Valence Bond Theory of Covalent Bond

According to this theory, a covalent bond is formed by the overlapping of two half-filled atomic orbitals having electrons with opposite spins. It is based on wave nature of electron.

1. Sigma Bond (σ bond)

The following result in the formation of σ bond.

(i) s-s overlapping

(ii) Sop overlapping

(iii) Pop head to head overlapping (axial)

The strength of 0 bond depends upon the extent of overlapping between atomic orbitals. The greater the extent of overlapping, the stronger is the σ bond.

2. Pi Bond (π bond)

It is formed by the sidewise or lateral overlapping between p- atomic orbitals [pop side by side or lateral overlapping]

π bond is a weaker bond than σ bond.

Comparison of Sigma and Pi Bonds

Limitations of VBT

1. The magnetic properties. of some molecules. It fails to explain.

2. Bonding in electron deficient compounds.

Hybridisation

It is defIned as the mixing of the atomic orbitals belonging to the same atom but having slightly different energies so that a redistribution of energy takes place between them resulting in the formation of new orbital of equal energies and identical shapes. The new orbitals thus formed are known as hybrid orbitals and are more stable,

Method for Finding the Hybridisation

Apply tho following formula to find the hybridisation of central atom.

Examples

Hybridisation of NH₃ = 1 / 2[5 + 3 + 0 – 0] = 4 ⇒sp³

Hybridisation of^2-₄ = 1 / 2[6 + 0 + 2 – 0] = 4 ⇒sp³

Some Common Types of Hybridisation with Shapes and Examples

Coordinate or Dative Bond

It is a type of covalent bond in which the electron pair (lone pair) is donated by one atom but shared by both the atoms so as to complete their octets. e.g.,

Molecular Orbital Theory

According to this theory, the atomic orbitals combine to form the molecular orbitals. The number of molecular orbitals formed is equal is the number of atomic orbitals involved. According to this theory.

1. The molecular orbitals are formed by LCAO (Linear combination of atomic orbitals) method, i.e., by addition or subtraction of wave functions of individual atoms, thus

Ψ_MO = Ψ_A ± Ψ_B

Ψ_b = Ψ_A + Ψ_B

Ψ_a = Ψ_A – Ψ_B

2. Molecular orbital of lower energy is known as bonding molecular orbital and that of higher energy is known as anti-bonding molecular orbital.

3. Aufbau rule, Pauli’s exclusion principle and Hund’s rule are all applicable for molecular orbitals.

4. The shape is governed by the shape of atomic orbitals, e.g., s-s and p-p overlapping.

(i) Combination between s-atomic orbitals

(ii) Combination between 2s and 2s orbitals gives σ2s and σ 2s orbitals.

(iii) Combination between p-atomic orbitals

(iv) Combination between 2 p_x and 2 p_y atomic orbitals

2 p_y atomic orbitals will also overlap in the same way and thus, resulting molecular orbitals are π 2 p_y and π 2 p_y.

If molecular orbital has symmetry with respect to centre, it is called gerade (g) otherwise ungerade (u). All σ bonding and π anti-bonding MO are g while all π bonding and σ anti-bonding MO are u.

Electronic Configuration and Bond Order (BO) Of Molecular

The order of energy of molecular orbitals has been determined experimentally by spectroscopy for the elements of the second period. The increasing order of energies of the molecular orbitals in homonuclear diatomic molecules is

[Molecular species having unpaired electrons are paramagnetic, while if all the electrons in the orbitals are paired then the molecule is diamagnetic.]

Hydrogen Bond

It is defined as the force of attraction existing between hydrogen atom covalently bonded to highly electronegative atom (N, O or F) and the electronegative atom belonging to another molecule of the same or different substance. It is represented by dotted lines. The chains possess a zig – zag structure.

(Hydrogen bond is purely electrostatic and a weak bond. The strength of the strongest hydrogen bond is about 5-10 kcal per mol. The more the electronegativity of atom involved in H-bonding, the more is the bond strength, e.g.,

Types of hydrogen bonds are

(i) Intermolecular H-bonding : H-bonding involving two or more molecules.

(ii) Intramolecular H-bonding : H-bonding within a molecule.

Applications of Intermolecular H-bonding

(i) Melting point and boiling point of water Water has the lowest molecular weight among the hydrides of group 16 elements yet it has the highest melting and boiling points. It is due to intermolecular H-bonding in H₂ O.

(ii) Ice has less density than water In crystal structure of ice every water molecule is associated with four other water molecules by H-bonding in a cage like tetrahedral structure. On melting, the ice H-bonds are broken and space between water molecules decreases and density of water increases up to 4^o C Above 4°C. more H-bonds are broken. the water molecules get apart from each other and the density again decreases. Thus, water has maximum density at 4°C.

(iii) Melting point and boiling point of alcohols The marked difference between the melting and boiling points of alcohols is also due to H-bonding.

Applications of Intramolecular H-bonding

Volatile character of nitrophenols o-nitrophenol is more volatile (b.p. 214°C) as compared to meta (b.p. 290°C) and para (b.p. 279°C). It is due to chelation.

In meta and para isomer chelation is not possible due to the formation of desired size of ring.

Metallic Bond

Metallic bond is the force of attraction between a metal ion to a number of electrons within its sphere of influence. Electron-sea theory of metallic
bond explains number of the properties of the metal

Strength of bonds

Ionic bond > covalent bond > metallic bond > H-bond

Interconversion of States of Matter

These stateS are interconvertible.

(i) Melting point This is the temperature at which a matter converts from its solid state to liquid state. It decreases in the presence of impurity.

(ii) Boiling point This is the temperature at which the vapour” pressure of a liquid becomes equal to the atmospheric pressure. It increases in the presence of impurity and with rise in pressure. Boiling point of water is 100°C.

(iii) Freezing point At this temperature, a matter converts from its fluid state into solid state.

Freezing point of water is 0°C.

(iv) Evaporation It is the process of conversion of a liquid into vapours at any temperature.

Due to evaporation,

(a) water droplets appear on the outer surface of a glass containing ice-cold water.

(b) water kept in earthen pot becomes cool during summer.

(c) desert cooler cool better on a hot dry day.

In short,

The temperature and pressure at which all the three states of a substance can exist together in equilibrium is called triple point, e.g.,
ice, liquid water and water vapours can coexist

(i. e., ice ⇔ water ⇔ vapour) at 0.0098°C and 4.58 mm.

Plasma

It is a state of matter similar to gas in which a certain portion of the gaseous particles are ionised. Because of the average strength of the electrical forces, the plasma is neutral. It is commonly found in the universe.

On earth, plasma is naturally occurring in flames, lightnings and the auroras.

Bose-Einstein Condensate

A Bose-Einstein condensate is a gaseous superfluid phase formed by atoms cooled to temperature very near to absolute zero.

This state was first predicted by Satyendra Nath Bose and Albert Einstein in 1924-25. Such first condensate was produced by Eric Cornell and Carl Wieman in 1995. It can be thought of as the opposite of a plasma.

Factors Deciding Physical State of a Substance

For gaseous state,

Forces of attraction << thermal energy For liquid state, Forces of attraction > Thermal energy

For solid state,

Forces of attraction >> Thermal energy

Intermolecular Forces

The forces of attraction existing among the molecules of a substance (gaseous, liquid or solid) are called intermolecular forces

[Greater the intermolecular forces, higher is the melting and boiling point.

Attractive intermolecular forces are known as van der Waals’ forces.]

The different types of intermolecular forces are briefly explained below

(i) Dipole-dipole interactions Dipole-dipole forces act between the molecules possessing permanent dipoles.

The interaction is stronger than London forces and weaker than ion-ion interaction.

(ii) Dipole-induced dipole forces Dipole-induced dipole forces act between the polar molecules having permanent dipole and the molecules lacking permanent dipole

(iii) Dispersion forces or London forces Dispersion forces or London forces are present among non-polar atoms and molecules, e.g., among the atoms or chlorine molecules. These are the weakest intermolecular forces. These forces increases with

(i) increase in number of electrons in molecules,

(ii) increase in molecular size

The Gaseous State

This is the simplest state of matter. Characteristics of this ‘state of matter are

1. In gases, the intermolecular forces are weakest.
2. Gases are highly compressible.
3. Gases exert pressure equally in all directions.
4. Gases have much lower density than the solids and liquids.
5. The volume and the shape of gases are not fixed.
6. Gases mix evenly and completely in all proportions without any mechanical aid.

Measurable Properties of Gases

(i) Mass It is expressed in gram or kg.

(ii) Volume It is equal to the volume of the container and is expressed in terms of litre (L), millilitre (mL), cubic centimetre (cm³), cubic metre (m³) or cubic decimetre (dm³).

1 L = 1000 mL = 1000 cm³ = 1 dm³

1 m³ = 10³ dm³ = 10⁶ cm³ = 10⁶ mL = 10³L

(iii) Pressure Gas pressure is measured with manometer and atmospheric pressure is measured by barometer.

1 atm = 76 em of Hg = 760 mm of Hg = 760 torr

1 atm = 101.325 kPa = 101325 Pa = 101.325 Nm^-2 = 1.01325 bar

1 bar = 10⁵ Pa.

Measurement of pressure of gas

(i) Open end manometer, p_gas = p_atom – h

(ii) Closed end manometer, p_gas = h

where h is difference in the mercury levels in the two columns of density (d) (of a gas).

(iv) Temperature It is measured in celsius scale (OC) or in Kelvin scale (K). SI unit of temperature is kelvin (K), T (K) = t°C+ 273

Standard temperature and pressure (STP or NTP) means 273.15 K (O°C) temperature and 1 bar (i.e., exactly 10⁵ pascal) pressure. At STP, molar volume of an ideal gas is 22.71098 L mol^-1

Boyle’s Law

The volume of a given mass of a gas is inversely proportional to its pressure at constant temperature.

V ∝ 1 / p or Vp = K

K is a constant and its value depends on mass, temperature and nature of gas.

∴ p₁V₁ = p₂V₂

Isotherms Graphs of V vs p or pV vs p at constant temperature known as Isotherms .

IAirisdense at the sea level because it is compressed by the mass of above it.

Charles’ Law

The volume of the given mass of a gas increases or decrease by 1 / 273 of its volume for each degree rise or fall of temperature respectively at constant pressure.

V_t = V_o (1 + t / 273) t constant p

or

The volume of a given mass of a gas is directly proportional to the absolute temperature at constant pressure.

V ∝ T (at constant p), V / T = constant or V₁ / T₁ = V₂ / T₂

Absolute zero is the theoretically possible temperature at which the volume of the gas becomes zero. It is equal to O°C or 273.15K.

Isobars A graph of V vs T at constant pressure is known as isobar

Charles’law explains that gases expand on heating, so hot air is less dense than cold air.

Gay Lussac’s Law

The pressure of a given mass of gas increases or decreases by 1 /273 of its pressure for each degree rise or fall of temperature respectively at constant volume.

p_t = p_o (1 + t / 273) at constant V and n

or

The pressure of a given mass of a gas at constant volume is directly proportional to absolute temperature.

p ∝ T or p = KT or p / T = K at constant V and n or P₁ / T₁ = P₂ / T₂

Isochores A graph of p vs T at constant volume is known as isochore

Avogadro’s Law

It states that equal volumes of all gases under the same conditions of temperature and pressure contain equal number of molecules.

Mathematically

V infi; n (at constant T and p)

or V / n = K

Molar gas volume The volume of one mole of a gas, i.e., 224 Lat STP(0°C, 1 atm) i_!S known as molar gas volume

Ideal Gas Equation

• V ∝1 / p, T and n constant (Boyle’s law)
• V ∝ T, p and n constant (Charles’ law)
• V ∝ n, p and T constant (Avogadro’s law)

⇒ V ∝ nT / p

or pV ∝ nT

or pV = nRT.

This is known as ideal gas equation. R is known as universal gas constant.

From the ideal gas equation, density.

d = pM / RT (where, M = molecular mass)

• ideal gas The gas which obeys the equation pV = nRT at every temperature and pressure range strictly Is known as Ideal gas.
• Real gases Since none of the gases present in universe strictly obey the equation pV =nRT. hence they are known as real or non-ideal gases. Real gases behave, ideally at low p and high T.

Graham’s Law of Diffusion

Under Similar conditions of temperature and pressure, the rates of diffusion of gases are inversely proportional to the square root of their densities.

Mathematically, r₁ / r₂ = √d₂ / √d₁ = √M₂ / √M₁

[Diffusion is the tendency of gases to distribute itself uniformly throughout the available space while effusion is the movement of gas through a small hole when it is subjected to pressure].

Dalton’s Law of Partial Pressure

At constant temperature. the total pressure. exerted by a mixture of non-reacting gases. is the sum of partial pressures of different gases present in the mixture.

p = p₁ + p₂ + p₃ + ….

partial pressure of a gas = mole fraction of the gas * total pressure.

If n₁, n₂ and n₃ are moles of non-reacting gases filled in a vessel of volume V at temperature T, the total pressure, p is given by

pV = (n₁ + n₂ + n₃)RT

This is the equation of state of a gaseous mixture,

[Aqueous tension It is the pressure exerted by water vapours at a particular temperature. It depends upon temperature.]

Pressure of a dry gas can be determined by Dalton’s law. When a gas is collected over water, its observed pressure is equal to the sum of the pressure of dry gas and the pressure of water vapour (aqueous tension) then

Pressure of dry gas = pressure of moist gas – aqueous tension.

Kinetic Theory of Gases

Main assumptions of this theory are:

1. A gas consists of large number of small particles, called molecules.

2. Volume occupied by gas molecules, is negligible as compared to the total volume of the gas.

3. There is continuous rapid random motion of gas molecules. The molecules collide with each other and with the walls of container.

4. The molecules are perfect elastic bodies and there is no loss of kinetic energy during collisions.

5. There are no attractive forces between the gaseous molecules.

6. The pressure exerted by a gas is due to the bombardment of gas molecules against the walls of the container.

7. The different molecules possess different velocities and hence, different energies. The average KE is directly proportional to absolute temperature.

KE = 3 / 2 RT

∴ Average kinetic energy per molecule = 3 / 2 kT

Here k is Boltzmann constant, it is gas constant per molecule.

k = R / N_A = 1.38 * 10^-23 JK^-1 mol^-1

From the above postulates, the kinetic gas equation derived is

pV = 1 / 3 mn U²

where, U = root mean square velocity = √3RT / M

Velocities of Gas Molecules

The different velocities possessed by gas molecules are :

(i) Most probable velocity (α) It is the velocity possessed by maximum fraction of gas molecules at a particular temperature.

α = √2RT / M

(ii) Average velocity (v) This is the average of the different velocities of all the molecules.

v = √8RT / πM

(iii) Root mean square velocity (U_rms) It is the square root of the mean of the square of the different velocities of the molecules.

Deviation from Ideal Behaviour

At high pressure and low temperature, the gases deviate considerably from the ideal behaviour, Deviation can be expressed in terms of compressibility factor (Z), expressed as

Z = pV / nRT

In case of ideal gas, pV = nRT, Z = 1

In case of real gas, pV ≠ nRT, Z ≠ 1

Negative deviation In such case. Z < 1, gas is more compressible.

Positive deviation In such case. Z > 1 gas is less compressible.

The factors affecting the deviation are

(i) Nature of the gas In general. the most easily liquefiable and highly soluble gases show larger deviation.

(ii) Pressure The deviation is more at high pressure. CO₂ and N₂ show negative deviation at low pressure and positive derivation at high pressure.

(iii) Temperature The deviation is more at low temperature and H₂ and He always show positive deviations at O°C.

Cause of deviation from the ideal behaviour It is due to two faulty assumptions of kinetic theory of gases. particularly not valid at high pressure and low temperature

1. Volume occupied by the gas molecules is negligible as compared to the total volume of the gas.

2. There are no attractive forces between the gas molecules

van der Waals’ Equation

After volume and pressure correction, van der Waals’ obtained the following equation for n. moles of a gas.

where,

b = excluded volume or co-volume = 4 * actual volume of gas molecules

a = magnitude of attractive forces between gas molecules.

The greater the value of ‘a’, the greater the strength of van der Waals’ forces and greater is the ease with which a gas can be liquefied.

Units for van der Waals’ constant

Pressure correction

Limitation of van der Waals’ equation

There is specific range of temperature and pressure, to apply the equation. It deviates at very high pressure and very low temperature.

Liquefaction of Gases and Critical Points

The phenomenon of conversion of a gas into liquid is known as liquefaction. The liquefaction of a gas takes place when the intermolecular forces of attraction becomes so high that exist in the liquid. A gas can be liquefied by

(i) increasing pressure

(ii) decreaSing temperature

(i) Critical temperature (T_C) It may be defined as the temperature above which no gas can be liquefied. Critical temperature of CO₂ is 31.1° C.

Critical temperature (T_c) of some gases, He (5.4), H₂(33.2), N₂(126.0), CO(134.4), O₂ (154.3), CO₂(3041), NH₄(405.5).

T_C = 8a / 27Rb

(ii) Critical pressure (P_c) At critical temperature, the pressure needed to liquefy a gas is known as critical pressure.

P_c = a / 27 b²

(iii) Critical volume (V_c) The volume occupied by one mole of a gas at critical temperature and critical pressure is known as critical volume.

V_c = 3b

(iv) Boyle’s temperature (T_b) Temperature at which a real gas exhibits ideal behaviour for considerable range of pressure is called Boyle’s temperature.

T_b = a / bR

Liquid State

If a substance is having melting point below room temperature and boiling point above room temperature. the substance is known as liquid. In liquid state, matter has definite. shape and molecular motion is in between solids and gases.

Properties of Liquids

(i) Vapour pressure The pressure exerted by the vapours above the liquid surface when these are in equilibrium with the liquid at a given temperature is known as vapour pressure of liquid.

The vapour pressure of a liquid depends on :

(i) Nature of liquid

(ii) Temperature: Vapour pressure increases with increasing temperature.

(ii) Boiling point The temperature at which vapour pressure of liquids becomes equal to the atmospheric pressure, is called boiling point.

At 1 atm pressure, boiling point is known as normal boiling point.

At 1 bar pressure, boiling point is known as standard boiling point. Boiling point varies linearly with external pressure.

(iii) Surface tension It is the force acting per unit length perpendicular to the imaginary line drawn on the surface of liquid. It is denoted γ (gamma);

SI unit : Nm^-1

Dimensions: kgs^-2

The magnitude of surface tension of a liquid depends on the attractive forces between the molecules. It is measured with the help of an apparatus, called stalagmometer.

Surface tension decreases as the temperature increases.

Rise or fall of liquid in a capillary tube is due to surface tension.

(iv) Viscosity Viscosity is a measure of resistance to flow which arises due to friction between layers of fluid.

When there is a regular gradation of velocity, in passing from one layer to the next, it is called laminar flow.

F = η Adv / dz

where, F = forces required to maintain the flow of layers.

A = area of contact

dv/ dz = velocity gradient; (the change in velocity with distance.)

‘η’ is proportionality constant and is called coefficient of viscosity. Viscosity coefficient is the force when velocity gradient is unity and the area of contact is unit area. CGS unit of coefficient of viscosity is poise S.I. unit of coefficient of viscosity is Nsm^-2.

With the discovery of a large number of elements, it became difficult to study the elements individually, so classification of elements was done to make the study easier.

Earlier Attempts to Classify Elements

Many attempts were made to classify the known elements from time to time. The earlier attempts are as follows:

Prout’s Hypothesis (1815)

According to this theory, hydrogen atom was considered as the fundamental unit from which all other atoms were made. It is also known as unitary theory.

Dobereiner’s Triads (1829)

Dobereiner classified the elements into groups of three elements with similar properties in such a manner so that the atomic weight of the middle element was the arithmetic mean of the other two, e.g.,

Mean of atomic masses = (7 + 39) / 2 = 23

Similarly CI, Br, I; Ca, Sr, Ba are two more examples of such triads.

Limitations Dobereiner could not arrange all the elements known at that time into triads. He could identify only three such triads that have been mentioned.

Newland’s Octaves (1864) (Law of Octaves

Newland states that when elements are arranged in order of increasing atomic masses, every eighth element has properties similar to the first just like in the musical note [Every eighth musical note 1S the same as the first mentioned note]. This can be illustrated as given below

Limitations

1. This classification was successful up to the element calcium.

2. When noble gas elements were discovered at a later stage, their inclusion in these octaves disturbed the entire arrangement.

Lother Meyer’s Atomic Volume Curve (1869)

Meyer presented the classification of elements in the form of a curve between atomic volume and atomic masses and state that the properties of the elements are the periodic functions of their atomic volumes.

[Here, atomic volume = molecular mass / density

He concluded that the elements with similar properties occupy similar position in the curve.

Mendeleef’s Periodic Table

Mendeleefs Periodic Table is based upon Mendeleefs periodic law which states ‘The physical and chemical properties of the elements are a periodic function of their atomic masses.”

At the time of Mendeleef, only 63 elements were known.

This Periodic Table is divided into seven horizontal rows (periods) and eight vertical columns (groups). Zero group was added later on in the modified Mendeleefs Periodic Table.

Importance of Mendeleers Periodic Table

Few important achievements of Periodic Table are

1 Systematic study of the elements.

2. Prediction of new elements and their properties. he left space for the elements yet to be discovered. e.g., he left spaces for Ga and Ge and named these elements as ERa-aluminium (Ga) and EKa-silicon (Ge) respectively

3. Atomic mass correction of doubtful elements on the basis of their expected positions and properties.

Modified Form of Mendeleef’s Periodic Table

Defects in the Mendeleef’s Periodic Table

(i) Position of hydrogen Hydrogen has been placed in group IA (alkali metals). but it also resembles with halogens of group VIlA. Thus. its position in the Mendeleef’s Periodic Table is controversial.

(ii) Position of isotopes As Mendeleef’s classification is based on atomic weight, Isotopes would have to be placed in different positions due to therr different atomic weights, e.g., ¹H1 ²H1 ³H1 would occupy different positions.

(iii) Anomalous positions of some elements Without any proper justification. in some cases the element with higher atomic mass precedes the element with lower atomic mass. For example, AI (atomic weight = 39.9) precedes K (atomic weight = 39.1) and similarly Co (atomic weight. = 58.9) has been placed ahead of Ni (atomic weight = 58.7).

(iv) Position of Lanthanoids and actinoids Lanthanoids and actinoids were not placed in the main Periodic Table.

Modern Periodic Table (1913)

Moseley modified Mendeleefs periodic law. He stated "Physical and chemical properties of elements are the periodic function of their atomic numbers.” It is known as modern periodic law and considered as the basis of Modern Periodic Table.

When the elements were arranged in increasing order of atomic numbers, it was observed that the properties of elements were repeated after certain regular intervals 01 2, 8, 8, 18, 18 and 32. These numbers are called magic numbers and cause of periodicity in properties due to repetition of similar electronic configuration.

Structural Features of Long Form of Periodic Table

1. Long form of Periodic Table is called Bohr’s Periodic Table. There arc 18 groups and seven periods in this Periodic Table

2. The horizontal rows are called periods.

• First period (₁H – ₂He) contains 2 elements. It is the shortest period
• Second period (₃Li – ₁₀Ne) and third period (₁₁ Na – ₁₈Ar) contain is elements each. These are short periods.
• Fourth period (₁₉K – ₃₆Kr) and fifth period (₃₇Rb – ₅₄Xe) contain 18 elements each. These are long periods.
• Sixth period (₅₅Cs – ₈₆ Rn) consists of 32 elements and is the longest period.
• Seventh period starting with ₈₇Fr is incomplete and consists of 19 elements.

3. The 18 vertical columns are known as groups.

• Elements ot group 1arc called alkali metals.
• Elements of group 2 are called alkaline earth metals.
• Elements of group 16 are called chalcogens [ore forming elements].
• Elements of group 17 are called halogens. [s[s[sea salt forming]>
• Elements of group 18 are called noble gases.

Anomalous behaviour of the first element of a group. The first element of a group differs considerably from its congeners (i.e., the rest of the elements of its group).

This is due to (i) small size (ii) high electronegativity and (iii) non availability of d·orbitals for bonding. Anomalous behaviour is observed among the second row elements (i.e., Li to F).

4. The Periodic Table is divided into foul’ main blocks (s, p, d and n depending upon the subshell to which the valence electron enters into.

(a) s-block elements Ist and IInd group elements belong to this block and the last electron enters in s-subshell.

General electronic configuration is ns^{1 – 2}

(b) p-block elements Group 13th to 18th belong to this block in which last electron enters in p-orbital.

General electronic configuration is ns² np^{1 – 6}

This is the only block which contains metal, non-metal and metalloids. Examples of metalloids are B, SI Ge, As, Sb, Te and At.

The elements of s-and p-block elements are collectively called representative elements.

(c) d-block elements Group 3rd to 12th belong to this block, in which last electron enters in d-orbit.

They have inner incomplete shell. so known as transition elements.

General electronic configuration is ns^{1 – 2} (n – 1)d^{1 – 10}

d-block elements are generally coloured, paramagnetic and exhibit variable valency.

(d) f-block elements They constitute two series 4f (lanthanoids) and 5f (actinides) in which last electron is in 4f and 5f subshell respectively.

General electronic configuration

(n – 2) f^{1 – 14(n – 1) d0 – 1 ns}2

The f-block elements are also called as inner-transition elements.

(Elements with atomic number greater than 92 (U⁹²) are called the transuranium elements. All these elements are man-made through artificial nuclear reactions.

Very recently. on August 16, 2003, IUPAC approved the name for the element of atomic number 110, as Darmstadtium, with symbol Ds].

Limitations of Long Form of Periodic Table

In the long form of the Periodic Table :

1. The position of hydrogen still remains uncertain.

2. The inner-transition elements do not find a place in the main body of the table. They are placed separately.

Predicting the Position of an Element in the Periodic Table

First of all write the complete electronic configuration. The principle quantum number of the valence shell represents the period of the element.

The subshell in which the last electron is filled corresponds to the block of the element.

Group of the element is predicted from the electrons present in the outermost (n) or penultimate (n -1) shell as follows:

For s-block elements;

group number = number of ns-electrons

For p-block elements;

group number = 10 + number of ns and np electrons

For d-block elements;

group number = the sum of the number of (n -1) d

and ns electrons.

For f-block elements; group number is 3.

IUPAC Nomenclature of Elements With Z > 100

The names are derived directly from the atomic numbers using numerical roots for 0 and numbers from 1-9 and adding the suffix ium.

The IUPAC names and symbols of elements with Z > 100 are

Periodic Properties

The properties which are directly or indirectly related to their electronic configuration and show gradual change when we move from left to right in a period or from top to bottom in a group are called periodic properties.

Atomic Radius

It is the distance from the centre of the nucleus to the outermost shell of electrons. Covalent radius for an atom A in a molecule A₂

r_A = r_A + r_A / 2 = d_{A – A} / 2

For heteroatomic molecule AB,

d_{A – B} = r_A + r_B + 0.009 (X_A – X_B)

where, X_A and X_B are electronegativities of A and B.

In general, the atomic size decreases on moving from left to right in a period due to increase in effective nuclear charge and increases on moving from top to bottom in a group due to addition of new shells.

van der Waals’ Radius

It is defined as one-half of the distance between the nuclei of two non – bonded isolated atoms or two adjacent atoms belonging to two neighbOuring molecules of an element in the solid state.

Metallic Radius

It is define as one-half of the distance between the centres of nuclei of the two adjacent atoms in the metallic crystal.

Ionic Radius

An atom can be changed to a cation by 10RS of electrons and to an anion by gain of electrons. A cation is always smaller than the parent atom because during its formation effective nuclear charge increases and sometimes a shell may also decrease. On the other hand, the size of an anton is always larger than the parent atom because during its formation effective nuclear charge decreases.

In case of isoelectronic ions, r he higher the nuclear charge. smaller is the size. e.g., AI³ < Mg²⁺ < Na⁺ < f^– < O^2- < N^3-

The order of radii is

covalent radius < metallic radius < van der Waals’ radius

Ionisation Enthalpy (IE)

It is the amount of energy required to remove the loosely bound electron from the isol~ted gaseous atom.

A(g) + IE → A⁺ (g) + e^–

VarIOUS factors with which IE vanes are :

(i) Atomic size. varies inversely

(ii) Screening effect: varies inversely

(iii) Nuclear charge: varies directly

Generally left to right in periods ionisation enthalpy increases; down the group, it decreases.

IE values of inert gases are exceptionally higher due to stable configuration.

Successive ionisation enthalpies

IE₃ > IE₂ > IE₁

IE₁ of N is greater than that of oxygen due to stable half – filled 2p-orbitals.

Among transition elements of 3d-series, ₂₄Cr and ₂₉Cu have higher IE₂ due to half-filled and fully-filled stable d-orbitals

Electron Gain Enthalpy (EGE or ΔHe _g)

It is the amount of energy released when an electron is added in an isolated gaseous atom. First electron gain enthalpy is negative while the other successive electron gain enthalpy will be positive due to repulsion between the electrons already present in the anion and the electron being added.

Various factors with which electron gain enthalpy varies are :

(i) Atomic size: varies directly

(ii) Nuclear charge: varies directly

Along a period, electron gain enthalpy becomes more and more negative while on moving down the group, it becomes less negative.

Noble gases have positive electron gain enthalpies.

Halogen have maximum value of ΔHe _g with in a period due to smallest atomic size.

F and O atom have small size and high charge density, therefore have lower electron gain enthalpy, than Cl and S respectively

Cl > F; S > O

Elements having half-filled and fully-filled orbitals exhibit more stability. therefore, electron gain enthalpy will be low for such elements.

Electron gain enthalpy can be measured by Born-Haber cycle and elements with high ΔHe _g are good oxidising agent.

Electronegativity (EN)

It is defined as the tendency of an atom to attract the shared electron pair towards itself in a covalent bond. Various factors with which electronegativity varies are :

(i) Atomic size: varies inversely

(ii) Charge on the ion: varies directly, e.g., Li < Li⁺, Fe²⁺ < Fe³⁺

(iii) Hybridisation : (Electronegativity &infi; s-character in the hybrid orbital)

Electronegativity of carbon atom = C₂H₆ < C₂H₄ < C₂H₂

In periods as we move from left to right electronegativity increases, while in the groups electronegativity decreases down the group.

For noble gases, its value is taken as zero.

Electronegativity helps to predict the polarity of bonds and dipole moment of molecules.

Electronegativity order of some elements (on Pauling scale) is

(i) Mulliken scale

Electronegativity (x) = IE + ΔHe _g / 2

(ii) Pauling scale The difference in electronegativity of two atoms A and Bis given by the relationship

x_B – x_A = 0.18 √Δ

where, Δ = E_{A – B} – √E_{A – A} * E_{B – B}

(Δ is known as resonance energy.)

E_{A – B}, E_{A – A} and E_{B – B} represent bond dissociation energies of the bonds A – B, A – A and B – B respectively.

(iii) Allred and Rochow method

Electronegativity = 0.744 + 0.359 Z_eff / r²

where, Z_eff is the effective nuclear charge = Z – σ

where, σ is screening constant. It’s value can be determined by Slater’s rule.

Valency

• It is defined as the combining capacity of the element. The valency of an element is related to the electronic configuration of its atom and usually determined by electrons present in the valence shell,
• On moving along a period from left to right, valency increases from 1 to 4 and then decreases to zero (for noble gases) while on moving down a group the valency remains the same.
• Transition metals exhibit variable valency because they can use electron (rom outer as well as penultimate shell.

Chemical Reactivity

• Reactivity of metal increases with decrease in IE, electronegativity and increase in atomic size as well as electropositive character.
• Reactivity of non-metals increases with increase in electronegativity as well as electron gain enthalpy and decrease in atomic radii.

Melting and Boiling Points

• On moving down the group, the melting point and boiling point for metallic elements go on decreasing due to the decreasing forces of attraction. However, for non-metals, melting point and boiling point generally increase down the group.

[A[A[Along a period from left to right, melting point and boiling point increases and reaches a maximum value in the middle of the period and then start decreasing]>

• Tungsten (W) has highest m.p. (3683K) among metals, carbon (diamond) has the highest m..p, (4000 K) among non-metals.
• Li metal has minimum density while iridium (Ir) metal has maximum density.

Electropositivity or Metallic Character

• The tendency of an atom of the element to lose valence electrons and form positive ion is called electropositivity.
• Greater the electropositive character, greater is the metallic character.
• Electropositive character decreases on moving across the period and increases on moving down the group.
• Alkali metals are the most electropositive and halogens are the least electropositive element in their respective period.
• Basic nature of oxides of metallic character, i.e., it also decreases along a period and increases down the group.

Diagonal Relationship

Certain elements of 2nd period show similarity in properties with their diagonal elements in the 3rd period as shown below :

Thus, Li resembles Mg, Be resembles Al and B resembles Si. This is called diagonal relationship and is due to the reason that these pairs of elements have almost identical ionic radii and polarizing power (i.e., charge/size ratio). Elements of third period, i.e., Mg, Al and Si are known as bridge elements.

John Dalton proposed (in 1808) that atom is the smallest indivisible particle of matter. Atomic radii are of the order of 10^-8cm. It contain three subatomic particles namely electrons, protons and neutrons,

Electron

Electron was discovered as a result of study of cathode rays by JJ Thomson. It was named by Stony

It carries a unit negative charge (-1.6 * 10^-19 C).

Mass of electron is 9.11 * 10^-31 kg and mass of one mole of electron is 0.55 mg.

Some of the characteristics of cathode rays are:

1. These travel in straight line away from cathode and produce fluorescence when strike the glass wall of discharge tube.
2. These cause mechanical motion in a small pin wheel placed – their path.
3. These produce X-rays when strike with metal and are deflected by electric and magnetic field

Proton

Rutherford discovered proton on the basis of anode ray experiment.

It carries a unit positive charge (+1.6 * 10^-19) C).

The mass of proton is 1.007276 U.

The e / m ratio of proton is 9.58 * 10^-4 C / g. (e / m ratio is maximum for hydrogen gas.)

Some of the characteristics of anode rays are :

1. These travel in straight line and posses mass many times the mass of an electron.
2. These are not originated from anode.
3. These also cause mechanical motion and are deflected by electric and magnetic field.
4. Specific charge (e / m) for these rays depends upon the nature of the gas taken and is maximum for H₂

Neutron

Neutrons are neutral particles. It was discovered by Chadwick (1932). The mass of neutron is 1.675x 10^-24 g or 1.008665 amu or u.

⁹₄Be + ⁴₂He → ¹²₆C + ¹₀n

Some Uncommon Subatomic Particles

(a) Positron Positive electron (⁰₊₁e), discovered by Dirac (1930) and Anderson (1932).

(b) Neutrino and antineutrino Particles of small mass and no charge as stated by Fermi (1934).

(c) Meson Discovered by Yukawa (1935) and Kemmer. They are unstable particles and include pi ions [pi;⁺, pi;^– or pi;⁰].

(d) Anti-proton It is negative proton produced by Segre and Weigand (1955).

Thomson’s Atomic Model

Atom is a positive sphere with a number of electrons distributed within the sphere. It is also known as plum pudding model. It explains the neutrality of an atom. This model could not explain the results of Rutherford scattering experiment.

Rutherford’s Nuclear Model of Atom

It is based upon a-particle scattering experiment. Rutherford presented that

1. Most part of the atom is empty.
2. Atom possesses a highly dense, positively charged centre, called nucleus of the order 10^-13cm.
3. Entire mass of the atom is concentrated inside the nucleus.
4. Electrons revolve around the nucleus in circular orbits.
5. Electrons and the nucleus are held together by electrostatic forces of attraction.

Drawbacks of Rutherford’s Model

1. According to electromagnetic theory, when charged particles accelerated, they emit electromagnetic radiations, which CODIlE by electronic motion and thus orbit continue to shrink, so atom unstable. It doesn’t explain the stability of atom.

2. It doesn’t say anything about the electronic distribution electrons around nucleus.

Atomic Number

Atomic number of an element corresponds to the total number protons present in the nucleus or total number of electrons present the neutral atom

Mass Number

Mass number of an element

= number of protons + number of neutrons

Electromagnetic Wave Theory (Maxwell)

The energy is emitted from source continuously in the form of radiations and magnetic fields. All electromagnetic waves travel with the velocity of light (3 * 10⁸ m / s) and do not require any medium for their propagation.

An electromagnetic wave has the following characteristics:

(i) Wavelength It is the distance between two successive crests or troughs of a wave. It is denoted by the Greek letter λ (lambda).

(ii) Frequency It represents the number of waves which pass through a given point in one second. It is denoted by v (nu).

(iii) Velocity (v) It is defined as the distance covered in one second by the waves. Velocity of light is 3 * 10¹⁰ cms^-1

(iv) Wave number It is the reciprocal of wavelength and has units cm^-1 It is denoted by v (nu bar).

(v) Amplitude (a) It is the height of the crest or depth of the trough of a wave.

Wavelength (λ), frequency (v) and velocity (c) of any electromagnetic radiations are related to each other as c = vλ

Electromagnetic Spectrum

The different types of electromagnetic radiations differ only in their wavelengths and hence. frequencies. When these electromagnetic radiations are arranged in order to their increasing wavelengths or decreasing frequencies, the complete spectrum obtained is called electromagnetic spectrum.

Different Types of Radiations and Their Sources

Electromagnetic spectra may be emission or absorption spectrum on the basis of energy absorbed or emitted. An emission spectrum is obtained when a substance emits radiation after absorbing energy. An absorption spectra is obtained when a substance absorbs certain wavelengths and leave dark spaces in bright continuous spectrum.

Electromagnetic wave theory was successful in explaining the properties of light such as interference. diffraction etc., but it could not explain the following

1. Black body radiation

2. Photoelectric effect

These phenomena could be explained only if electromagnetic waves are supposed to have particle nature.

1. Black Body Radiation

If the substance being heated is a black body. the radiation emitted is called black body radiation.

2. Photoelectric Effect

It is the phenomenon in which beam of light of certain frequency falls on the surface of metal and electrons are ejected from it.

This phenomenon is known as photoelectric effect. It was first observed by Hertz.

W_o< = hv_o

W_o< = hc / λ_max

Threshold frequency (v_o) = minimum frequency of the radiation

Work function (W_o) = required minimum energy of the radiation

E = KE + W_o

∴ 1 / 2 mv² = h(v – v_o)

[Kinetic energy of ejected electron = h(v – v_o)

where; v = frequency of incident radiation

v_o = threshold frequency

Particle Nature of Electromagnetic Radiation :

Planck’s Quantum Theory

Planck explain the distribution of intensity of the radiation from black body as a function of frequency or wavelength at different temperatures.

E = hv = hc / λ

where, h = Planck’s constant = 6.63 x 10^-34 j-s

E = energy of photon or quantum

v = frequency of emitted radiation

If n is the number of quanta of a particular frequency and E_T be total energy then E_t = nhv

Bohr’s Model

Neils Bohr proposed his model in 1931. Bohr’s model is applicable only for one electron system like H, He⁺, Li²⁺ etc.

Assumptions of Bohr’s model are

1. Electrons keep revolving around the nucleus in certain fixed permissible orbits where it doesn’t gain or lose energy. These orbits are known as stationary orbits.

Number of waves in an orbit = circumstances of orbit / wavelength

2. The electrons can move only in those orbits for which the angular momentum is an integral multiple of h / 2π, i.e.,

mvr = nh / 2π

where, m = mass of electron: v = velocity of electron;

r = radius of orbit

n = number of orbit in which electrons are present

3. Energy is emitted or absorbed only when an electron Jumps from higher energy level to lower energy level and vice-versa.

ΔE = E₂ – E₁ = hv = hc / λ

4. The most stable state of an atom is its ground state or normal state,

From Bohr’s model, energy, velocity and radius of an electron in nth Bohr orbit are

(i) Velocity of an electron in nth Bohr orbit

(v_n) = 2.165 * 10⁶ Z / n m / s

(ii) Radius of nth Bohr orbit

(r_n) = 0.53 * 10^-10 n² / Z m = 0.53 n² / Z A

where, 11 = number of shell; Z = atomic number

As we go away from the nucleus, the energy levels come closer, i.e., with the increase in the value of n, the difference of energy between successive orbits decreases.

Thus. E₂ – E₁ > E₃ – E₂ > E₄ – E₃ > E₅ – E₄etc.

Sommerfeld Extension to Bohr’s Model

According to this theory. the angular momentum of revolving electron in all elliptical orbit is an integral multiple of h / 2π, i.e.,

mur = kh / 2π

From Bohr model, mur = nh / 2π

For K shell. n = 1,k = 1 Circular shape

L shell. n ; 2. k = 1. 2 Circular

M shell, n = 3. k = 1.2.3 Elliptical

N shell. n = 4, k =1 . 2, 3. 4 Elliptical

Emission Spectrum of Hydrogen

According to Bohr’s theory. when an electron jumps from ground states to excited state. it emits a radiation of definite frequency (or wavelength). Corresponding to the wavelength of each photon of light emitted, a bright line appears in the spectrum.

The number of spectral lines in the spectrum when the electron comes from nth level to the ground level = n(n – 1) / 2

Hydrogen spectrum consist of line spectrum.

Wave number v is defined as reciprocal of the wavelength.

v = 1 / λ

v = RZ² (1 / n²₁ – n²₂)

Here, λ = wavelength

R = Rydberg constant = 109677.8 cm^-1

First line of a series is called line of longest wavelength (shortest energy) and last line of a series is the line of shortest wavelength highest energy, n₂ = φ).

Limitations of Bohr’s Theory

1. It is unable to explain the spectrum of atom other than hydrogen like doublets or multielectron atoms.

2. It could not explain the ability of atom to form molecules by chemical bonds. Hence. it could not predict the shape of molecules.

3. It is not in accordance with the Heisenberg uncertainty principle and could not explain the concept of dual character of matter.

4. It is unable to explain the splitting of spectral lines in the presence of magnetic field (Zeeman effect) and electric field (Stark effect)

de-Broglie Principle

de-Broglie explains the dual nature of electron i.e.. both particle as well as wave nature.

λ = h / mv

where, λ = wavelength: v = velocity of particle; m = mass of particle

λ = h / √2m * K E

where, KE = kinetic energy.

Heisenberg’s Uncertainty Principle

According this principle, “it is impossible to specify at any give instant both the momentum and the position of subatomic particles like electron.”

Δx . ΔP ≥ h / 4π

where, Δx = uncertainty in position; Δp = uncertainty in momentum

Quantum Mechanical Model of Atom

It is the branch of chemistry which deals with dual behaviour of matter. It IS given by Werner Heisenberg and Erwin Schrodinger

Schrodinger wave equation is

where. x, y, z = cartesian coordinates

m = mass of electron, E = total energy of electron

U =potential energy of electron, h =Planck’s constant

Ψ (Psi) = wave function which gives the amplitude of wave

Ψ² = probability function

For H-atom. the equation is solved as

HΨ = EΨ

where, H is the total energy operator, called Hamiltonian. If the sum of kinetic energy operator (T) and potential energy operator (U) is the total energy. E of the system,

H = T + U

(T + U)Ψ = EΨ

[The atomic orbitals can be represented by the product of two wave functions (i) radial wave function (ii) angular wave function.

The orbital wave function, Ψ has no significance, but Ψ² has significance, it measures the electron probability density at a point In an atom. Ψ can he positive or negative but ‘I’:? is always positive.

Probability Diagrams

The graph plotted between Ψ² and distance from nucleus is called probability diagrams.

Node

A region or space, where probability of finding an electron is maximum is called a peak, while zero probability space is called node. Nodes are of two types:

(a) Radial nodes

(b) Angular nodes

(i) (n – I – 1) = radial node

(ii) (l) = angular node

(iii) (n – 1) = total + node

Number of Peaks and Nodes for Various Orbitals

Quantum Numbers

Each electron in an atom is identified in terms of four quantum numbers.

Principal Quantum Number (Niels Bohr)

It is denoted by 11. It tells us about the main shell in which electron resides. It also gives an idea about the energy of shell and average distance of the electron from the nucleus. Value of n = any integer.

Azimuthal Quantum Number (Sommerfeld)

It is denoted by I. It tells about the number of subshells (s. p, d, f) in any main shell. It also represent the angular momentum of an electron and shapes of subshells. The orbital angular momentum of an

electron = √l (l + 1) h / 2π

Value of l = 0 to n – 1.
I = 0 for s, I = 2 for d
I = 1 for P. / = 3 for f

Number of subshells in main energy level = n.

Magnetic Quantum Number (Lande)

is denoted by m. It tells about the number of orbitals and orientation of each subshell. Value of m = – l to + 1 including zero.

Number of orbitals in each subshell = ( 2l + 1)

Number of orbitals in main energy level = n²

Spin Quantum Number (Uhlenbeck and Goldsmith)

“It is denoted by m, or s. It indicates the direction of spinning of electron, i.e., clockwise or anti- clockwise.

Maximum number of electrons in main energy level = 2n²

Difference between Orbit and Orbital

Electronic Configuration

Arrangement of electrons in the space around nucleus in an atom known as electronic configuration

Pauli Exclusion Principle

It states, no two electrons in an atom can have identical set of four quantum numbers.

The maximum number of electrons in s subshell is 2, p subshell is 6 d subshell is 10 and f subshell is 14.

Aufbau Principle

According to this principle, in the ground state of an atom, the electrons occupy the lowest energy orbitals available to them, i.e., the orbitals are filled in order of increasing value of n + l. For the orbitals having the same value of n + 1, the orbital having lower value of n is filled up first.

The general order of increasing energies of the orbital is

The energy of atomic orbitals for H-atom varies as

Is < 2s = 2P < 3s 3p = 3d < 4s = 4P = 4d = 4f

Half-filled and completely filled electronic configurations are more stable Hence. outer configuration of Cr is 3d⁵ 4s¹ and Cu is 3d¹⁰ 4s¹.

Hund’s Rule of Maximum Multiplicity

It states.

(i) In an atom no electron pairing takes place in the p, d or ( orbital. until each orbital of the given subshell contains one electron.

(ii) The unpaired electrons present in the various orbitals of the same subshell should have parallel spins.

Methods of Writing Electronic Configuration

(i) Orbital method In this, the electrons present in respective orbitals are denoted. e.g CI(17) = 1s², 2s², 2 p⁶, 3 ², 3 p⁵.

(ii) Shell method In this, the number of electrons in each shell is continuously written. e.g., Cl (17) =

(iii) Box.method In this method, each orbital is denoted by a box and electrons are represented by half-headed (↑) or full-headed (↑) arrows. An orbital can occupy a maximum of two electrons.

e.g.,

Electronic Configuration of Ions

To write the electronic configuration of ions. first write the electronic configuration of neutral atom and then add (for negative charge) or remove (for positive charge) electrons in outer shell according to the nature and magnitude of charge present on the ion. e.g:

O(8) = 1s², 2s² 2 p⁴

O^2- (10) = 1s², 2s² 2 p⁶

Effective Nuclear Charge (Slater’s rule)

In a multielectron atom. the electron of the inner-shell decrease the force of attraction exerted by the nucleus on the valence electrons. This is called shielding effect. Due to this, the nuclear charge (Z) actually present on the nucleus, reduces and is called effective nuclear charge (Z_eff). It is calculated by using the formula

Z_eff = Z – σ

where σ = screening constant

The magnitude of σ is determined by Slater’s rules.

Slater Rules

1. Write the electronic configuration in the following order and groups.
(ls) (2s, 2p) (3s, 3p) (3d), (4.9.4p) (4d) (4f) (5s, 5p) etc

2. Electrons of (/1 + 1) shell (shell higher than considering electrons) do not contribute in shielding i.e., σ = 0

3. All other electrons in (ns, np) group contribute σ = 0.35 each

4. All electrons of (n -1) sand p shell contribute σ = 0.85 each

5 All electrons of (n – 2) sand p shell or lower shell contribute σ = 1.00 each

6. All electrons of nd and nf orbital contribute σ = 0.35 and those of (n – 1)and f or lower orbital contribute σ = 1.00 each

e.g.. Be (4) = 1s², 2s²

Different Types of Atomic Species

(a) Isotopes Species with same atomic number but different mass number are called isotopes, e.g. , ₁H¹, ₁H².

(b) Isobars Species with same mass number but different atomic number are called isobars. e.g., ₁₈Ar⁴⁰, ₁₉K⁴⁰.

(c) Isotones Species having same number of neutrons are called isotopes, e.g., ₁H³ and ₂He⁴ are isotones.

(d) Isodiaphers Species with same isotopic number are called Isodiaphers, e.g., ₁₉K³⁹, ₉F¹⁹

Isotopic number = mass number – 2 * atomic number .

(e) Isoelectronic Species with same number of electrons are called isoelectronic species, e.g., Na⁺, Mg²⁺.

(f) Isostere Species having same number of atoms and same number of electrons, are called isostere, e.g., N₂ and CO.

It is the branch of science which deals with the composition, structure and properties of matter.

Antoine Laurent Lavoisier is called the father of chemistry.

Branches of Chemistry

In addition to these biochemistry, war chemistry, nuclear chemistry forensic chemistry, earth chemistry etc., are other branches of chemistry.

Matter

Anything which occupies some space and have some mass is called matter. It 15 made up of small particles which have space between them. The matter particles attract each other and are in a state of continuous monon.

Elements

It is the simplest form of pure substance, which can neither be decomposed into nor built from simpler substances by ordinary physical and chemical methods. It contains only one kind of atoms. The number of elements known till date is 118.

[Hydrogen IS the most abundant element in the universe.

OXYgen (46.6%), a non-metal, is the most abundant element in the earth crust.

AI is the most abundant metal in the earth crust.

An element can be a metal, a non-metal or a metalloid.]

Symbols

A symbol is an abbreviation or shortened form for the full name of an element. The present system of symbols was introduced by Berzelius.

Symbol and Latin Names for Some Elements

Compounds

It is also the form of matter which can be formed by combining two or more elements in a definite ratio by mass. It can be decomposed into its constituent elements by suitable chemical methods, e.g., water (H₂O) is made of hydrogen and oxygen in the ratio 1 : 8 by mass.

Compounds can be of two types :

(i) Inorganic compounds Previously, it was believed that these compounds are derived from non-living sources, like rocks and minerals. But these are infact the compounds of all the elements except hydrides of carbon (hydrocarbons) and their derivatives.

(ii) Organic compounds According to earlier scientists, these compounds are derived from living sources like plants and animals, or these remain buried under the earth (e.g., petroleum). According to modern concept, these are the hydrides of carbon and their derivatives.

Mixtures

These are made up of two or more pure substances. They can possess variable composition and can be separated into their components by some physical methods.

Mixtures may be homogeneous (when composition is uniform throughout) or heterogeneous (when composition is not uniform throughout).

Common methods for the separation of mixtures are

(a) Filtration Filtration is the process of separating solids that are suspended in liquids by pouring the mixture into a filter funnel. As the liquid passes through the filter, the solid particles are held on the filter.

(b) Distillation Distillation is the process of heating a liquid to form vapours and then cooling the vapours to get back the liquid. This is a method by which a mixture containing volatile substances can be separated into Its components.

(c) Sublimation This is the process of conversion of a solid directly into vapours on heating. Substances showing this property are called sublimate, e.g., iodine, naphthalene, camphor. This method is used to separate a sublimate from non-sublimate substances.

(d) Crystallisation It is a process of separating solids having different solubilities in a particular solvent.

(e) Magnetic separation Tills process is based upon tbe fact that a magnet attracts magnetic components of a mixture of magnetic and non-magnetic substances. The non-magnetic substance remains unaffected. Thus. it can be used to separate magnetic components from non-magnetic components.

(f) Atmolysis Tills method is based upon rates of diffusion of gases and used for their separation from a gaseous mixture.

Atoms and Molecules

Atom is the smallest particle of an element which can take part in a chemical reaction. It mayor may not be capable of independent existence.

Molecule is the simplest particle of matter that has independent existence. It may be homoatomic e.g., H₂, CI₂, N₂ (diatomic), O₃ (triatomic) or heteroatomic, e.g., HCI, NH₃, CH₃ etc.

Physical Quantities and Their Measurements

Units

To express the measurement of any physical quantity two things are considered:

(i) Its unit,

(ii) The numerical value.

Magnitude of a physical quantity = numerical value * unit

Units are of two types:

(i) Basic units

(ii) Derived units

(i) The basic or fundamental units are those of length (m), ass (kg), time (s), electric current (A), thermodynamic temperature (K), amount of substance (mol) and luminous intensity (cd).

(ii) Derived units are basically derived from the fundamental units, e.g., unit of density is derived from units of mass and volume.

The systems used for describing measurements of various physical quantities are

(a) CGS system It is based on centimetre, gram and second as the units of length, mass and time respectively.

(b) FPS system A British system which used foot(ft). pound (lb) and second (s) as the fundamental units of length, mass and time.

(c) MRS system Uses metre (m), kilogram (kg) and second (s) respectively for length, mass and time; ampere (A) was added later on for electric current.

(d) SI system (1960)International system of units and contains following seven basic and two supplementary units:

Base Physical Quantities and their Corresponding Basic Units

SUpplementary units It includes plane angle in radian and solid angle in steradian.

Prefixes

The SI units of some physical quantities are either too small or too large. To change the order of magnitude. these are expressed by using prefixes before the name of base units. The various prefixes are listed as

Dimensional Analysis

Often while calculating, there is a need to convert units from one system to other. The method used to accomplish this is called factor label method or unit factor method or dimensional analysis.

In this,

Information sought = Information given * Conversion Factor

Important Conversion Factor

Scientific Notation

In such notation, all measurements (however large or small) are expressed as a number between 1.000 and 9.999 multiplied or divided by 10. In general as

N * 10

Here, N is called digit term (1.000-9.999) and n is known as exponent. e.g., 138.42 cm can be written as 1.3842 * 10² and 0.0002 can be written as 2.0 * 10^-4.

precision and Accuracy

Precision refers the closeness of the set of values obtained from identical measurements of a quantity. Precision is simply a measure of
reproducibility of an experiment.

Precision = individual value – arithmetic mean value

Accuracy is a measure of the difference between the experimental value or the mean value of a set of measurements and the true value.

Accuracy = mean value – true value

In physical measurements, accurate results are generally precise but precise results need not be accurate. In other words good precision does not assure good accuracy.

Significant Figures

Significant figures are the meaningful digits in a measured or calculated quantity. It includes all those digits that are known with certainty plus one more which is uncertain or estimated.

Greater the number of significant figures in a measurement, smaller the uncertainty.

Rules for determining the number of significant figures are:

1. An digits are significant except zeros in the beginning of a number.

2. Zeros to the right of the decimal point are significant. e.g., 0.132, 0.0132 and 15.0, all have three significant figures.

3. Exact numbers have infinite significant figures.

Calculations Involving Significant Figures

1. In addition or subtraction, the final result should be reported to the same number of decimal places as that of the term with the least number of decimal places, e.g.,

(Reported sum should have only one decimal point.)

2. In multiplication and division, the result is reported to the same number of significant figures as least precise term or the term
with least number of significant figures, e.g.,

Rounding Off the Numerical Results

When a number is rounded off, the number of significant figures is reduced. the last digit retained is increased by 1 only if the following digit is ≥ 5 and is left as such if the following digit is ≤ 4, e.g.,

12.696 can be written as 12.7

18.35 can be written as 18.4

13.93 can be written as 13.9

Laws of Chemical Combinations

The combination of elements to form compounds is governed by the following six basic laws:

1. Law of conservation of mass (Lavoisier, 1774)

This law states that during any physical or chemical change, the total mass of the products is equal to the total mass of reactants. It does not hold good for nuclear reactions.

2. Law of definite proportions (Proust, 1799)

According to this law, a chemical compound obtained by different sources always contains same percentage of each constituent element.

3. Law of multiple proportions (Dalton, 1803)

According to this law. if two elements can combine to form more than one compound. the masses of one element that combine with a fixed mass of the other element, are in the ratio of small whole numbers, e.g., in NH₃ and N₂H₄, fixed mass of nitrogen requires hydrogen in the ratio 3 : 2.

4. Law of reciprocal proportions (Richter, 1792)

According to this law, when two elements (say A and 13) combine separately with the same weight of a third element (say C), the ratio in which they do so is the same or simple multiple of the ratio in which they (A and H) combine with each other.

Law of definite proportions, law of multiple proportions and law of reciprocal proportions do not hold good when same compound is obtained by using different isotopes of the same element. e.g H₂O and D₂O

5. Gay Lussac’s law of gaseous volumes

It states that under similar conditions of temperature and pressure. whenever gases react together. the volumes of the reacting gases as well as products (if gases) bear a simple whole number ratio.

6. Avogadro’s hypothesis

It states that equal volumes of all gases under the same conditions of temperature and pressure contain the same number of molecules.

Dalton’s Atomic Theory (1803)

This theory was based on laws of chemical combinations. It’s basic postulates are

1. All substances are made up of tiny. indivisible particles, called atoms.

2. In each element, the atoms are all alike and have the same mass. The atoms of different elements differ in mass.

3. Atoms can neither be created nor destroyed during any physical or chemical change.

4. Compounds or molecules result from combination of atoms in some simple numerical ratio.

Mole Concept

Term mole was suggested by Ostwald (Latin word mole = heap)

A mole is defined as the amount of substance which contains same number of elementary particles (atoms, molecules or ions) as the number of atoms present in 12 g of carbon (C-12).

1 mol = 6.023 * 10²³ atoms = one gram-atom = gram atomic mass

1 mol = 6.023 * 10²³ molecules = gram molecular mass

In gaseous state at STP (T = 273 K, p = 1 atm)

Gram molecular mass = 1 mol

= 22.4 L = 6.022 * 10²³ molecules

Standard number 6.023x 10²³ is called Avogadro number in honour of Avogadro (he did not give this number) and is denoted by N_A.

The volume occupied by one mole molecules of a gaseous substance is called molar volume or gram molecular volume.

Number of moles = amount of substance (in gram) / molar mass

Number of molecule = number of moles * N_A

Number of molecules in Ig compound = N_A / g-molar mass

Number of molecules in 1 cm³ (1 mL) of an ideal gas at STP is called Loschmidt number (2.69x 10¹⁹).

[One amu or u (unified mass) is equal to exactly the 1 / 12th of the mass of ¹²C atom, i.e., 1 amu or u = 1 / 12 * mass of one carbon (C¹²) atom

1 amu = 1 / N_A

= 1 Dalton = 1.66x 10^-24 g

One mole of electrons weighs 0.55 mg (5.5x 10^-4 g).

Atomic Mass

It is the average relative atomic mass of an atom. It indicates that how many times an atom of that element is heavier as compared with 1 / 12 of the mass of an atom of carbon-12.

Average atomic mass = average mass of an atom / 1 / 12 * mass of an atom of C¹²

The word average has been used in the above definition and is very significant because elements occur in nature as mixture of several isotopes. So. atomic mass can be computed as

Average atomic mass

= RA(1) * at. mass(1) + RA(2) * at. mass (2) / RA(l) + RA(2)

Here, RA is relative abundance of different isotopes.

In case of volatile chlorides. the atomic weight is calculated as

At. wt. = Eq. wt. x valency

and valency = 2 * vapour density of chloride / eq. wt. of metal + 35.5

According to Dulong and Petit’s rule,

Atomic weight * specific heat = 6.4

Gram Atomic Mass (GAM)

Atomic mass of an element expressed in gram is called its gram atomic mass or gram-atom or mole-atom.

Molecular Mass

It is the mass of a molecule, i.e., number of times a molecule is heavier than 1 / 12 th mass of C-12 atom. Molecular mass of a substance is an additive property and can be calculated by taking algebraic sum of atomic masses of all the atoms of different elements present in one molecule.

Molecular Mass = average relative mass of one molecule / 1 / 12 th * mass of C-12 atom

[Gram molecular mass or molar mass is molecular mass of a substance expressed in gram.

Molecular mass = 2 * V D ]

Equivalent Mass

It is the mass of an element or a compound which would combine with or displace (by weight) 1 part of hydrogen or 8 parts of oxygen or 35.5 parts of chlorine

Eq. wt. of metal = wt. of metal / wt. of H₂ displaced * 1.008

= wt. of metal / volume of H₂ (in mL) displaced at STP * 11200

Eq. wt. of metal = wt. of metal / wt. of oxygen combined * 8

= wt. of metal / wt. of chlorine combined * 35.5

In general,

Wt. of substance A / Wt. of substance B = Eq. wt. of A / Eq. wt. of B

or for a compound (I) being converted into another compound (II) of same metal

Wt. of compound I / Wt. of compound II

= eq. wt. of metal + eq. wt. of anion of compound I / eq. wt. of metal + eq. wt. of anion of compound II

Eq. mass 0f a salt = formula mass / total positive or negative charge

Equivalent mass = atomic mass or Molecular mass / n factor

n factor for various compounds can be obtained as

(i) n factor for acids i.e., basicity

(Number of ionisable H⁺ per molecule is the basicity of acid.)

(ii) n factor for bases, i.e., acidity.

(Number of ionisable OH^– per molecule is the acidity of a base.)

(iii) In case of ions, 11 factor is equal to charge of that ion.

(iv) In redox titrations, 11 factor is equal to change in oxidation number.

Equivalent mass of organic acid (RCOOH) is calculated by the following formula

Eq. wt. of silver salt of acid (RCOOAg) / Eq. wt. of Ag(or 108) = Vt. of silver salt / Wt. of silver

Stoichiometry

The relative proportions in which the reactants react and the products are formed, is called stoichiometry (from the Greek word meaning ‘to measure an element’.)

Limiting reagent It is the reactant which is completely consumed during the reaction.

Excess reagent It is the reactant which is not completely consumed and remains unreacted during the reaction.

[In a irreversible chemical reaction, the extent of product can be computed on the basis of limiting reagent in the chemical reaction]

Percent Yield

The actual yield of a product in any reaction is usually less than the theoretical yield because of the occurrence of certain side reactions.

Percent yield = actual yield / theoretical yield * 100

Empirical and Molecular Formulae

Empirical formula is the simplest formula of a compound giving simplest whole number ratio of atoms present in one molecule, e.g., CH is empirical formula of benzene (C₆H₆).

Molecular formula is the actual formula of a compound showing the total number of atoms of constituent elements, e.g., C₆H₆ is molecular formula of benzene.

Molecular formula = (Empirical formula)_n

where, n is simple whole number having values 1, 2, 3, … , etc., and can be calculated as

n = molecular formula mass / empirical formula mass