Chapter 9

Ionic Equilibrium

Equilibrium Involving Ions in Aqueous Solution

Most Important Chapter for JEE Main & NEET (4–6 Questions)

Introduction

In chemical equilibrium we studied reaction involving molecules only but in ionic equilibrium we will study reversible reactions involving formation of ions in water. When solute is polar covalent compound then it reacts with water to form ions.

At moderate concentrations, there exists an equilibrium between the ions and undissociated molecules. This equilibrium state is called ionic equilibrium.

Electrical Conductors & Electrolytes

Substances, which allow electric current to pass through them, are known as conductors or electrical conductors.

Types of Conductors

TypeCharacteristicsExamples
Metallic/Electronic ConductorsConduct electricity without undergoing any chemical changeMetals
Electrolytic ConductorsUndergo decomposition (chemical change) when electric current passedElectrolytes

Types of Electrolytes

TypeDegree of Ionisation (α)Examples
Strongα ≈ 1HCl, H₂SO₄, NaCl, HNO₃, KOH, NaOH, AgNO₃, CuSO₄, all strong acids/bases/salts
Weakα << 1CH₃COOH, NH₄OH, HCN, H₂O, Liq. SO₂, HCOOH, weak acids/bases

Arrhenius Theory of Electrolytic Dissociation

Postulates: (i) In aqueous solution, molecules of electrolyte undergo spontaneous dissociation to form positive and negative ions. (ii) Degree of ionization (α) = Number of dissociated molecules / Total number of molecules before dissociation. (iii) At moderate concentrations, equilibrium exists between ions and undissociated molecules. (iv) Each ion behaves osmotically as a molecule.

Factors Affecting Degree of Ionisation (α)

Nature of Electrolyte

Strong electrolytes: α ≈ 1; Weak electrolytes: α << 1

Solvent

Higher dielectric constant → higher ionising power; Water has highest dielectric constant

Dilution/Concentration

α ∝ 1/Concentration ∝ 1/Weight of solution ∝ Dilution ∝ Amount of solvent

Temperature

Degree of ionisation increases with rise in temperature

Common Ion

Degree of ionisation decreases in presence of strong electrolyte having common ion

Ostwald's Dilution Law

The strength of an acid or base is measured by its dissociation constant. For acetic acid:

CH₃COOH + H₂O ⇌ CH₃COO⁻ + H₃O⁺
Kₐ = [CH₃COO⁻][H₃O⁺] / [CH₃COOH]
For weak electrolytes: Kₐ = Cα²/(1-α) ≈ Cα²
α = √(Kₐ/C) = √(KₐV)

Similarly for weak base NH₄OH: α = √(K_b/C) = √(K_bV)

Ostwald's Dilution Law: For a weak electrolyte, the degree of ionisation is inversely proportional to the square root of molar concentration or directly proportional to the square root of volume containing one mole of the solute.

Dissociation Constants (K_a, K_b)

For Weak Acid HA

HA ⇌ H⁺ + A⁻
Kₐ = [H⁺][A⁻] / [HA]

For Polybasic Acids

Stepwise dissociation with K₁ > K₂ > K₃

H₃PO₄ ⇌ H⁺ + H₂PO₄⁻ (K₁)
H₂PO₄⁻ ⇌ H⁺ + HPO₄²⁻ (K₂)
HPO₄²⁻ ⇌ H⁺ + PO₄³⁻ (K₃)
Overall K = K₁ × K₂ × K₃

For Weak Base BOH

NH₄OH ⇌ NH₄⁺ + OH⁻
K_b = [NH₄⁺][OH⁻] / [NH₄OH]

Common Ion Effect

The degree of dissociation of an electrolyte (weak) is suppressed by the addition of another electrolyte (strong) containing a common ion.

CH₃COOH ⇌ CH₃COO⁻ + H⁺
Add CH₃COONa → CH₃COONa → CH₃COO⁻ + Na⁺
[CH₃COO⁻] increases, equilibrium shifts left

Applications: Qualitative analysis to adjust S²⁻ concentration in second group and OH⁻ concentration in third group.

Isohydric Solutions

Solutions with same common ion concentration show no change in degree of dissociation when mixed.

For isohydric acids HA₁ and HA₂: α₁/V₁ = α₂/V₂

Solubility Product (K_sp)

Product of concentrations of ions raised to a power equal to the number of times the ions occur in the equation representing dissociation of electrolyte at given temperature when solution is saturated.

For AₓB_y ⇌ xAʸ⁺ + yBˣ⁻
K_sp = [Aʸ⁺]ˣ [Bˣ⁻]ʸ

Difference: Ionic Product vs Solubility Product

Ionic ProductSolubility Product
Applicable to all solutions (unsaturated/saturated)Applied only to saturated solutions
Varies with concentrationConstant at given temperature
Broad meaningSpecific to saturated equilibrium

Expressions for Different Salt Types

Salt TypeExampleK_sp ExpressionSolubility (x)
AB (1:1)AgCl, BaSO₄K_sp = x²x = √K_sp
AB₂ (1:2)PbCl₂, CaF₂K_sp = 4x³x = ³√(K_sp/4)
A₂B (2:1)Ag₂CrO₄K_sp = 4x³x = ³√(K_sp/4)
A₂B₃ (2:3)As₂S₃, Sb₂S₃K_sp = 108x⁵x = ⁵√(K_sp/108)
AB₃ (1:3)AlCl₃, Fe(OH)₃K_sp = 27x⁴x = ⁴√(K_sp/27)

Precipitation Criteria

CaseConditionResult
IIP < K_spUnsaturated, no precipitation
IIIP = K_spSaturated, no precipitation
IIIIP > K_spSupersaturated, precipitation occurs

Applications of Solubility Product

Precipitation Prediction

IP > K_sp → precipitation

Solubility Calculation

Knowing K_sp to find solubility

Purification of Common Salt

HCl gas through NaCl solution precipitates pure NaCl

Soap Salting Out

Concentrated NaCl precipitates soap

Qualitative Analysis

Group separation based on K_sp and common ion effect

Remaining Concentration

After precipitation if ion in excess

Simultaneous Solubility

Two electrolytes with common ion in same solution

Acids and Bases

Arrhenius Concept

Acids give H⁺ ions in water; Bases give OH⁻ ions in water.

Limitations: Requires water, doesn't explain non-aqueous behavior, limited neutralization concept, can't explain acidic character of salts like AlCl₃.

Bronsted-Lowry Concept

Acid: Proton donor; Base: Proton acceptor.

HCl + H₂O ⇌ H₃O⁺ + Cl⁻
Acid Base Conjugate Conjugate
acid base

Conjugate pairs: HCl/Cl⁻ and H₃O⁺/H₂O

Utility: Includes ionic species, explains basic character of Na₂CO₃, NH₃, explains non-aqueous reactions.

Limitations: Can't explain reactions in non-protonic solvents, acid-base oxide reactions without proton transfer, behavior of BF₃, AlCl₃ as acids.

Lewis Concept

Acid: Electron pair acceptor; Base: Electron pair donor.

Types of Lewis Acids: Molecules with incomplete octet (BF₃, AlCl₃), all cations, molecules with empty d-orbitals (SiF₄, SnCl₄), molecules with multiple bond between atoms of dissimilar electronegativity (CO₂, SO₂).

Types of Lewis Bases: Neutral species with lone pair (NH₃, R-OH), negatively charged species/anions.

Hard and Soft Acids and Bases (HSAB)

TypeCharacteristicsExamples
Hard AcidsSmall size, high positive charge, not easily polarizedLi⁺, Na⁺, Be²⁺, Mg²⁺, Al³⁺, BF₃, SO₃
Soft AcidsLarge size, low positive charge, easily polarizedPb²⁺, Cd²⁺, Pt²⁺, Hg²⁺, I₂
Hard BasesHold electrons stronglyOH⁻, F⁻, H₂O, NH₃, CH₃OCH₃
Soft BasesElectrons easily polarized/removedI⁻, CO, CH₃S⁻, (CH₃)₃P

Principle: Hard acids prefer hard bases (ionic bonding); Soft acids prefer soft bases (covalent bonding).

Relative Strength of Acids and Bases

Relative Strength Formulas

For weak acids HA₁ and HA₂: Strength ratio = √(Kₐ₁/Kₐ₂)
For weak bases BOH₁ and BOH₂: Strength ratio = √(K_b₁/K_b₂)

Inorganic Acids

TypeOrderBasis
HydridesHF > H₂O > NH₃ > CH₄
HCl > H₂S > PH₃ > SiH₄
Electronegativity
HydridesHF < HCl < HBr < HI
H₂O < H₂S < H₂Se < H₂Te
Atomic size
OxyacidsHOI < HOBr < HOCl
HIO₄ < HBrO₄ < HClO₄
Electronegativity
Oxyacids (same element)HOCl < HClO₂ < HClO₃ < HClO₄
H₂SO₃ < H₂SO₄
HNO₂ < HNO₃
Oxidation number
Oxyacids (across period)H₄SiO₄ < H₃PO₄ < H₂SO₄ < HClO₄Left to right
Oxyacids (same oxidation state)HNO₃ > HPO₃; H₃PO₄ > H₃AsO₄; HClO₄ > HBrO₄ > HIO₄Size of central atom

Organic Acids

Compound acidic if conjugate base stabilized through resonance. Phenol acidic (C₆H₅O⁻ stabilized), ethanol neutral (C₂H₅O⁻ not stabilized).

Acidity: HC≡CH > CH₂=CH₂ > CH₃-CH₃
(sp > sp² > sp³ hybridization)

Inorganic Bases

FactorEffectExample
ElectronegativityBasicity decreases with increaseNH₃ > H₂O > HF
Atomic sizeLarger size → lesser availabilityF⁻ > Cl⁻ > Br⁻ > I⁻; O²⁻ > S²⁻
ChargeNegative charge increases basicity; Positive decreasesOH⁻ > H₂O > H₃O⁺
Alkali hydroxidesIncreases down groupLiOH < NaOH < KOH < RbOH < CsOH
Alkaline earth hydroxidesIncreases down groupBe(OH)₂ < Mg(OH)₂ < Ca(OH)₂ < Sr(OH)₂ < Ba(OH)₂
Group 15 hydridesDecreases down groupNH₃ > PH₃ > AsH₃ > SbH₃ > BiH₃

Organic Bases

Higher electron density on nitrogen → more basic. Guanidine strong base due to resonance-stabilized conjugate acid.

Acid-Base Neutralisation & Salts

Acid + Base → Salt + Water. Nature of resulting solution depends on particular acid and base.

Classification of Salts

TypeCharacteristicsExamples
Simple SaltsFormed by acid-base interaction-
Normal SaltsNo replaceable H or OHNaCl, NaNO₃, K₂SO₄, Ca₃(PO₄)₂
Acidic SaltsIncomplete neutralization of polybasic acidsNaHCO₃, NaHSO₄, NaH₂PO₄
Basic SaltsIncomplete neutralization of polyacidic basesZn(OH)Cl, Mg(OH)Cl, Fe(OH)₂Cl
Double SaltsCombination of two simple saltsFerrous ammonium sulphate, Potash alum
Complex SaltsCombination of simple salts/molecular compoundsK₄[Fe(CN)₆]
Mixed SaltsFurnishes more than one cation/anionCa(OCl)Cl, NaNH₄HPO₄

Salt Hydrolysis

Reaction of cation or anion or both ions of salt with water to produce acidic or basic solution. Reverse of neutralization.

Salt TypeHydrolysisSolutionK_h Expressionh ExpressionpH Expression
Weak acid + Strong baseAnionicBasicK_h = K_w/K_ah = √(K_h/C)pH = 7 + ½pK_a + ½logC
Strong acid + Weak baseCationicAcidicK_h = K_w/K_bh = √(K_h/C)pH = 7 - ½pK_b - ½logC
Weak acid + Weak baseBothDepends on K_a, K_bK_h = K_w/(K_aK_b)h = √(K_h)pH = 7 + ½pK_a - ½pK_b
Strong acid + Strong baseNoneNeutral--7
Hydrolysis constant: K_h = [HA][BOH] / [BA] = K_w / (K_a or K_b)
Degree of hydrolysis: h = (moles hydrolysed) / (total moles taken)

Ionic Product of Water

H₂O ⇌ H⁺ + OH⁻
K_w = [H⁺][OH⁻] = 10⁻¹⁴ at 25°C
[H⁺] = [OH⁻] = 10⁻⁷ M in pure water
ΔH = +57.3 kJ mol⁻¹ (endothermic)

K_w increases with temperature. At 25°C: Neutral [H⁺] = [OH⁻] = 10⁻⁷; Acidic [H⁺] > [OH⁻]; Basic [H⁺] < [OH⁻].

pH Scale

pH = -log[H⁺] = log(1/[H⁺])
pOH = -log[OH⁻]
pH + pOH = pK_w = 14
Solution[H⁺][OH⁻]pHpOH
Acidic>10⁻⁷<10⁻⁷<7>7
Neutral10⁻⁷10⁻⁷77
Basic<10⁻⁷>10⁻⁷>7<7

pH of Common Materials

MaterialpHMaterialpH
Gastric juice1.4Rain water6.5
Lemon juice2.1Pure water7.0
Vinegar2.9Human saliva7.0
Soft drinks3.0Blood plasma7.4
Beer4.5Tears7.4
Black coffee5.0Egg7.8
Cow's milk6.5Household ammonia11.9

Limitations of pH Scale

  • Doesn't give immediate idea of relative strengths
  • pH can be zero or negative for concentrated solutions
  • Very dilute acid (10⁻⁸ M) cannot have pH > 7

pK Value

pKₐ = -log Kₐ; pK_b = -log K_b
For conjugate pair: Kₐ × K_b = K_w; pKₐ + pK_b = pK_w = 14

Weak acids have higher pKₐ; Weak bases have higher pK_b.

pH of Very Dilute Solutions

For 10⁻⁸ M HCl: [H⁺] = 10⁻⁸ + 10⁻⁷ = 1.1×10⁻⁷; pH = 6.96
For 10⁻⁸ M NaOH: [OH⁻] = 10⁻⁸ + 10⁻⁷ = 1.1×10⁻⁷; pOH = 6.96; pH = 7.04

Buffer Solutions

Solution whose pH is not altered greatly by addition of small quantities of strong acid or base. Solution of reserve acidity or alkalinity that resists pH change.

Types of Buffer Solutions

TypeCompositionExamples
Single SubstanceSalt of weak acid and weak baseCH₃COONH₄, NH₄CN
Acidic BufferWeak acid + Salt with strong baseCH₃COOH + CH₃COONa
Basic BufferWeak base + Salt with strong acidNH₄OH + NH₄Cl

Buffer Action

Reserved base neutralizes added H⁺ ions; Reserved acid neutralizes added OH⁻ ions.

Examples of Buffer Systems

  • Phthalic acid + Potassium hydrogen phthalate
  • Citric acid + Sodium citrate
  • Boric acid + Borax
  • Carbonic acid + Sodium hydrogen carbonate (blood, pH 7.4)
  • NaH₂PO₄ + Na₃PO₄ or Na₂HPO₄
  • Glycerine + HCl
  • Gastric juice (pH 1.6-1.7)

Henderson-Hasselbalch Equation

Acidic buffers: pH = pKₐ + log([salt]/[acid])
Basic buffers: pOH = pK_b + log([salt]/[base])

When [salt]/[acid] = 10: pH = pKₐ + 1; When [salt]/[acid] = 1/10: pH = pKₐ - 1

Weak acid can prepare buffers with pH range pKₐ ± 1.

pH doesn't change with dilution but varies with temperature due to K_w change.

Buffer Capacity

φ = (moles acid/base added to 1L) / (change in pH)

Maximum when [salt] = [acid] or pH = pKₐ or pOH = pK_b.

Significance of Buffer Solutions

  • Colorimetric comparison of [H⁺]
  • Removal of phosphate radical in qualitative analysis
  • Precipitation of hydroxides in third group analysis
  • Industrial applications: fermentation (pH 5-6.5), tanning, electroplating, sugar/paper manufacturing
  • Bacteriological research
  • Biological systems (blood pH 7.4)

Indicators

Substances used to determine end point in titration. Weak acids/bases that change color in certain pH range.

IndicatorpH RangeAcid ColorBase Color
Cresol red1.2-1.8RedYellow
Thymol blue1.2-2.8RedYellow
Methyl yellow2.9-4.0RedYellow
Methyl orange3.1-4.4PinkYellow
Methyl red4.2-6.3RedYellow
Litmus5.0-8.0RedBlue
Bromothymol blue6.0-7.6YellowBlue
Phenol red6.4-8.2YellowRed
Thymol blue8.1-9.6YellowBlue
Phenolphthalein8.3-10.0ColorlessPink
Thymolphthalein8.3-10.5ColorlessBlue
Alizarin yellow R10.1-12.0BlueYellow
Nitramine10.8-13.0ColorlessOrange/Brown

Theories of Indicators

Ostwald's Theory and Quinonoid Theory

Selection of Suitable Indicator

Titration TypeSuitable Indicators
Strong acid vs Strong basePhenolphthalein, Methyl red, Methyl orange
Weak acid vs Strong basePhenolphthalein
Strong acid vs Weak baseMethyl red, Methyl orange
Weak acid vs Weak baseNo suitable indicator

Color Change Mechanism

HIn ⇌ H⁺ + In⁻
K_in = [H⁺][In⁻] / [HIn]
[HIn]/[In⁻] = [H⁺]/K_in

Color visible when ratio [HIn]/[In⁻]:

  • = 10: Acid color (pH = pK_in - 1)
  • = 1: Intermediate (pH = pK_in)
  • = 0.1: Base color (pH = pK_in + 1)

Effective pH range: pK_in ± 1

Important Points for JEE Main / NEET

Key Points

  • Strong electrolytes: α≈1; Weak: α<<1; All salts are strong electrolytes
  • Ostwald's Law: α = √(Kₐ/C) for weak acids
  • Common ion effect suppresses dissociation of weak electrolytes
  • Solubility Product: IP > K_sp → precipitation occurs
  • Acid strength increases with oxidation number and electronegativity; decreases down group
  • Hydrolysis: Weak acid + Strong base → basic solution; Strong acid + Weak base → acidic solution
  • K_w = 10⁻¹⁴ at 25°C; pH + pOH = 14
  • Buffers resist pH change; effective range pH = pKₐ ± 1
  • Indicators change color at pH = pK_in ± 1
  • pH of boiling water = 6.5625 (still neutral)
  • At 37°C, pH of neutral solution = 6.8
  • Buffer capacity maximum when [salt] = [acid]
  • Buffers cannot withstand large amounts of acid/base (~0.1 mol/L maximum)

JEE Main & NEET Weightage

High weightage: Ionic equilibrium + acids/bases + buffers + hydrolysis + K_sp → 4-6 questions.

Weightage Very High (4-6 questions)