Ionic Equilibrium


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Ionic Equilibrium Confusion

Ionic Equilibrium is a critical chapter for your CBSE and competitive exams, but it's often the one students find most challenging. Do you face these problems?

  • Complex Theories: Juggling Arrhenius, Brønsted-Lowry, and Lewis acid-base concepts.

  • Tricky Calculations: Getting stuck on pH, solubility product (Ksp), and hydrolysis constant (Kh) problems.

  • Forgetting Formulas: Forgetting key equations like the Henderson-Hasselbalch equation during exams.

  • Lack of Practice: Not having enough solved examples and questions to build confidence.

Your Ultimate Solution for Acing Ionic Equilibrium

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What's Inside?

Our comprehensive notes cover every topic you need to know, logically structured for better understanding.

  • Fundamentals First: Clear explanations of Electrolytes, Degree of Dissociation, and Ostwald's Dilution Law.

  • All Acid-Base Theories: Master the Arrhenius, Brønsted-Lowry, and Lewis concepts with simple examples.

  • pH and Kw Mastery: Deep dive into the pH scale and the Ionic Product of Water (Kw).

  • Buffer Solutions Explained: Understand how acidic and basic buffers work and learn to calculate their pH using the Henderson-Hasselbalch equation.

  • Salt Hydrolysis Demystified: Learn why solutions of salts like CH3COONa are basic or why NH4Cl solutions are acidic.

  • Solubility Product (Ksp): Predict precipitation with the concepts of Ionic Product and Solubility Product.

  • Key Applications: Learn about the Common Ion Effect and its role in qualitative analysis, plus the use of indicators in acid-base titrations.


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Electrolytes

The compound which gives ions and conduct electricity in molten state or in aqueous solution are called electrolytes.

Strong electrolytes

These electrolytes dissociate almost completely in a polar medium. For example, NaOH, HCl, HNO₃.

Weak electrolytes

These electrolytes dissociates only to a small extent. For example, CH₃COOH, HCN, NH₄OH etc.

Degree of dissociation

It is the fraction of total amount of an electrolyte which dissociated into ions.

α = Number of moles dissociated / Number of moles taken

Ostwald's dilution law

It states that the degree of dissociation of weak electrolyte is proportional to the square root of dilution.

α = √(Ka/C) or, α ∝ 1/√C or, α ∝ √V
acid base concepts

where V = volume of solution containing one mole of solute.

Note: The law holds good only for weak electrolytes because ionic equilibrium is set up only in case of weak electrolytes. Degree of dissociation of strong electrolytes is very high and approaches to unity.

ACID-BASE CONCEPTS

Arrhenius concept of acids and bases

An acid is a substance which gives H⁺ ions in aqueous solution whereas a base is a substance which gives OH⁻ ions in aqueous solution. For example, HCl is an acid and NaOH is a base.

Bronsted Lowry concept of acids and bases

An acid is a substance which gives proton and a base is a substance which accepts a proton. For example, in the reaction:

NH₃ + H₂O ⇌ NH₄⁺ + OH⁻

NH₃ is the base as it accepts proton to form NH₄⁺ and H₂O is an acid as it donates proton.

Note: A substance which can act both as an acid as well as base is called amphoteric.

Conjugate acid base pairs

An acid base pair which differ by one proton is called conjugate acid base pair. In the reaction:

CH₃COOH + H₂O ⇌ CH₃COO⁻ + H₃O⁺
acid₁ + base₁ ⇌ base₂ + acid₂

CH₃COO⁻ is conjugate base of CH₃COOH and H₃O⁺ is conjugate acid of H₂O. A strong acid has weak conjugate base and vice versa.

conjugate base

Exercise 1: The correct order of conjugate base strength is
(A) H₃O⁺ > H₂O > OH⁻ > O²⁻
(B) O²⁻ > OH⁻ > H₂O > H₃O⁺
(C) H₂O > H₃O⁺ > O²⁻ > OH⁻
(D) H₃O⁺ > H₂O > O²⁻ > OH⁻

Leveling effect

All acid above H₂O show same acid strength in H₂O. This is called leveling effect. The acid strength of HClO₄, H₂SO₄, HCl, and HNO₃ in water is same but in acetic acid follows the order HClO₄ > H₂SO₄ > HCl > HNO₃.

The relative strength of acids

The relative strength of acids depends upon their degree of ionization (α).

We know that, α = √(Ka/C) and for equimolar concentration, α ∝ √Ka

Hence, Strength of acid₁/Strength of acid₂ = √(Ka₁/Ka₂)

Similarly, Strength of base₁/Strength of base₂ = √(Kb₁/Kb₂)
Ex.: In which of the following cases the acid strength is highest
(A) Ka = 10⁻⁶
(B) pKa = 5
(C) pKb = 10
(D) Kb = 10⁻¹¹
Solution: (D). Smaller the Kb value lesser is the basicity and more is the acidity.

Types of Solvents

Protophilic solvents

Solvents which have greater tendency to accept protons. For example, water, liquid NH₃, alcohol etc.

Protogenic solvents or protic solvents

Solvent which have tendency to produce protons. For example, water, HCl, glacial acetic acid.

Note: The first, second and third dissociation constants of a polyprotic acid (e.g., H₃PO₄, H₂CO₃ etc) are in the order of Ka₁ > Ka₂ > Ka₃ ...

Amphiprotic solvents

Solvents which act both as protophilic and protogenic, e.g. water, alcohol, NH₃ etc.

Aprotic solvents

Solvents which neither donates nor accepts protons, e.g. benzene, carbon tetrachloride carbon disulphide etc.

Lewis concepts of acid and bases

An acid is a substance which can accepts a pair of electrons and a base is a substance which donates a pair of electrons. For example, BF₃ is a lewis acid and NH₃ is a lewis base.

ACID BASE NEUTRALIZATION–SALTS

Neutralization of a base with acid involves the interaction between OH⁻ and H⁺ ions, e.g.

HCl(aq) + NaOH(aq) → NaCl(aq) + H₂O(l)
or, H⁺(aq) + Cl⁻(aq) + Na⁺(aq) + OH⁻(aq) → Na⁺(aq) + Cl⁻(aq) + H₂O(l)
or H⁺(aq) + OH⁻(aq) → H₂O(l)

Simple salt

Salt formed by neutralization of an acid and a base is called simple salt. These are of following types.

(i) Normal salts

Salts which do not contain any replaceable H⁺ or OH⁻ ions are called normal salts, e.g. NaCl, KNO₃ etc.

(ii) Acidic salts

Salts formed by incomplete neutralization of polybasic acids and containing replaceable H⁺ ions called acidic salt, e.g. KHSO₄, NaH₂PO₄ etc.

(iii) Basic salts

Salts formed by incomplete neutralisation of polyacidic bases and containing replaceable OH⁻ ions are called basic salts, e.g. Zn(OH)Cl, Mg(OH)Cl etc.

(iv) Double salts

The compounds formed by combination of two simple salts are called double salts, e.g. Mohr's salt (FeSO₄.(NH₄)₂SO₄. 6H₂O), potash alum (K₂SO₄. Al₂(SO₄)₃.24H₂O) etc.

Mixed salts

The salt which furnishes more than one cation or anion in solution is called mixed salt, e.g. Ca(OCl)Cl, KNaSO₄ etc.

IONIC PRODUCT OF WATER

It is defined as the product of molar concentrations of H₃O⁺ and OH⁻ ions, i.e. Kw = [H₃O⁺] [OH⁻]. Its value is 10⁻¹⁴ at 25°C and increases with increase of temperature as dissociation of H₂O increases.

Ex.: The pH of a saturated solution of Ca(OH)₂ in water at 25°C is 12.67. What is the concentration of OH⁻ in the saturated solution, in moles of OH⁻ per litre?
(A) 10⁻¹⁴/12.67
(B) 10⁻¹⁴ ×10⁻¹²·⁶⁷
(C) 10⁻¹⁴/10⁻¹²·⁶⁷
(D) 10⁻¹⁴/10⁻¹²·⁶⁷

Solution: (D). pH = -log[H⁺] = -log([10⁻¹⁴]/[OH⁻])

pH SCALE

It was introduced by Sorensen to express the acidic or basic strength of a solution. pH scale is from 0–14 as shown below.

ph scale

pH = –log [H⁺] = –log [H₃O⁺]
Also pOH = –log [OH⁻]
Nature of solutions [H⁺] [OH⁻] pH pOH
Acidic solution > 10⁻⁷ < 10⁻⁷ < 7 > 7
Neutral solution = 10⁻⁷ = 10⁻⁷ = 7 = 7
Basic solution < 10⁻⁷ > 10⁻⁷ > 7 < 7
pKa = –log Ka
where, Ka is the ionisation constant of the weak acid.
pKb = –log Kb
where, Kb it the ionisation constant of the weak base
pKw = –log Kw also pH + pOH = pKw
where, Kw is ionic product of water and pKw = 14 at 25°C
Note: The dissociation constant of weak acid and weak base are related as pKa + pKb = pKw.
Ex.: Among the following statements which is true?
(A) Kw is independent of temperature
(B) At 65°C pH of water is not equal to 7
(C) pKw increases with temperature
(D) pH + pOH = 14, at all temperatures
Solution: (B). pH of water=7 at 25°C. With increase in temperature Kw value increases (i.e. pKw decreases) and pH of water becomes lesser than 7.
Ex.: Which of the following solution(s) have pH between 6 and 7?
1. 2×10⁻⁶ M NaOH
2. 2×10⁻⁶ M HCl
3. 10⁻⁸ M HCl
4. 10⁻¹³ M NaOH
(A) 1, 2
(B) 2, 3
(C) 3, 4
(D) 2, 3, 4

ACID BASE TITRATIONS USING INDICATORS

Acid–Base indicators are complex–organic molecules which are either weak acids or weak base [Phenolphthalein is a weak acid (HPh) and methyl orange is a weak base (MeOH)] and they change their colour on ionisation, e.g.

HPh ⇌ H⁺ + Ph⁻
(Colourless) (Pink)

As the medium change from acidic to basic and vice–versa, the equilibrium shifts and the colour changes.

Selection of suitable indicators

The indicator used should be such that it shows colour change in the same pH range as required around the equivalence point.

Indicators used in different titrations

Type of titration Indicator used
Strong acid vs strong base Phenolphthalein, methyl orange, methyl red
Weak acid vs strong base Phenolphthalein
Strong acid vs weak base Methyl orange and methyl red

pH–range of some indicators

Indicator pH Acidic colour Basic colour
Methyl orange 3.1 – 4.5 Red Yellow
Methyl red 4.2 – 6.2 Pink Yellow
Bromo cresol green 3.8 – 4.6 Yellow Blue
Bromothymol blue 6.0 – 7.5 Orange Blue
Phenolphthalein 8.3 – 10.0 Colourless Pink
Thymol pH 9.3 – 10.5 Colourless Blue

Universal indicator

It is a mixture of number of indicators which shows colour change over different pH ranges. At the equivalence point pK(indicator) = pH. However, as indicator has a useful colour change over pH range of 2 units. We have, at the equivalence point pH = pK(indicator) ± 1

Note: At half neutralization of acid, pH = pKa, and Similarly for base, pH = pKb

COMMON ION EFFECT

The degree of dissociation of a weak electrolyte is suppressed by the addition of another electrolyte containing a common ion. This is termed as common ion effect. For example, addition of CH₃COONa in the solution of CH₃COOH suppress the dissociation of CH₃COOH.

Note: In qualitative analysis, precipitation of cations is based on the principle of common ion effect.

SOLUBILITY PRODUCT

For a sparingly soluble salt solubility product is the product of molar concentration of its ions in a saturated solution, e.g.

AxBy ⇌ xA⁺ + yB⁻

Initially 1 0 0
At equilibrium 1-s xs ys

Ksp = [A⁺]ˣ [B⁻]ʸ = [xs]ˣ[ys]ʸ = xˣ.yʸ.sˣ⁺ʸ

where, s is the solubility of AxBy in moles/litre.

Ionic product of electrolyte AxBy is also equal to [A⁺]ˣ[B⁻]ʸ but it is applicable to all concentration, may be saturated or unsaturated.

PbCl₂ ⇌ Pb²⁺ + 2Cl⁻

Initially 1 0 0
At equilibrium 1-s s 2s

Ksp = [Pb²⁺][Cl⁻]² = s (2s)² = 4s³

Criteria for precipitation of an electrolyte

  • (i) Ionic product > Ksp; Precipitation takes place (super saturated solution)
  • (ii) Ionic product = Ksp; The reaction is at equilibrium (saturated solution)
  • (iii) Ionic product < Ksp; Number precipitation takes place (Unsaturated solution)

In group II of qualitative analysis H₂S is passed in the acidic solution. Due to common ion effect it decreases the concentration of S²⁻ ion, hence only group II radical (having lower solubility product) are precipitated. In group IV analysis, H₂S is passed in alkaline medium (in NH₄OH) to increase the concentration of S²⁻ so that precipitation of group IV radicals takes place which have higher solubility product.

Ex.: The solubility products of MA, MB, MC and MD are 1.8×10⁻¹⁰, 4×10⁻⁸, 4×10⁻⁸ and 6×10⁻⁵ respectively. If a 0.01 M solution of MX is added drop wise to a mixture containing A⁻, B⁻, C⁻ and D⁻ ions, then the one to be precipitated first will be
(A) MA
(B) MB
(C) MC
(D) MD
Solution: (A). Compound having lowest solubility product is precipitated first.
Ex.: The M(OH)₄ has Ksp 4 × 10⁻⁴² and x then solubility is
(A) 1
(B) 2
(C) 3
(D) None of these
Solution: (D). Ksp = s × (4s)⁴ = 256s⁵
 

BUFFER SOLUTION

A solution whose pH does not change by addition of a small amount of acid or base is called buffer solution. Buffer may be of following types

(i) Acidic buffer

It is the mixture of a weak acid and its salt with strong base, e.g. CH₃COONa + CH₃COOH

(ii) Basic buffer

It is the mixture of a weak base and its salt with strong acid, e.g. NH₄OH + NH₄Cl

(iii) Self buffer or single buffer

It is the salt of weak acid and weak base, e.g. CH₃COONH₄

Note: Blood is a buffer having pH of about 7.4 pH of a buffer.

pH of a buffer

(i) Acidic buffer, pH = pKa + log[salt]/[acid]

or pH = pKa + log[Conjugate base]/[acid]

(ii) Basic buffer, pH = pKb + log[salt]/[base]

or, pH = pKa + log[conjugate acid]/[salt] where, Ka is the ionisation constant of its conjugate acid.
Ex.: The pH of an acidic buffer mixture is
(A) > 7
(B) < 7
(C) = 7
(D) depends on Ka of the acid
Solution: (D). pH = pKa + log[salt]/[acid]
Ex.: 50 mL of a weak acid, HA required 30 mL, 0.2 M NaOH for the end point. During titration, the pH of acid solution is found to be 5.8 upon addition of 20 mL of the above alkali. The pKa of the weak acid is
(A) 6.3
(B) 5.5
(C) 6.1
(D) None of these
Solution: (B). pH = pKa + log[salt]/[acid]
5.8 = pKa + log(20/10)
∴ pKa = 5.5

Buffer capacity

It is defined as the number of moles of an acid or base required to be added to one litre of the buffer solution so as to change its pH by one unit.

Thus, Buffer capacity = Number of moles of acid or base added to one litre of the buffer / Change in pH
Note: The buffer capacity is maximum when the no. of moles of salt = no. of moles of acid or base Hence, pH = pKs or, pH = pKb
Ex.: The pH of a buffer is 4.325. When 0.01 mole of NaOH is added to 1 litre of it, the pH changes to 4.625. It buffer capacity is
(A) 30
(B) 0.0307
(C) 2.3
(D) 1

Solution: (B). Buffer capacity = Number of moles of acid or base added in one litre / Change in pH

SALT HYDROLYSIS

It is the process in which a salt reacts with water to give back the acid and base.

Salt + Water ——→ Acid + Base
or, BA + H₂O ——→ HA + BOH

All salts are strong electrolytes and dissociate completely in aqueous solution.

Degree of hydrolysis

It is defined as the fraction of a total salt which is hydrolyzed.

h = No.of moles of salt hydrolysed / Total no.of moles of salt taken

Hydrolysis constant

K = [HA][BOH] / [BA][H₂O]

or, K[H₂O] = Kh = [HA][BOH] / [BA]

The salts are divided into four categories

(i) Salt of strong acid and strong base

NaCl + H₂O ——→ NaOH + HCl
Na⁺ + Cl⁻ + H₂O ——→ Na⁺ + OH⁻ + H⁺ + Cl⁻
or H₂O ——→ H⁺ + OH⁻

Thus, it involves only ionization and no hydrolysis. Thus, in the resulting solution [H⁺]=[OH⁻] and the solution is neutral.

Hence salts of strong acid and strong base do not undergo hydrolysis, e.g. NaCl, NaNO₃, Na₂SO₄, KCl etc.

(ii) Salts of weak acid and strong base

BA + H₂O ——→ HA + BOH
CH₃COONa + H₂O ⇌ CH₃COOH + NaOH
CH₃COO⁻ + H₂O ⇌ CH₃COOH + OH⁻

As it produces OH⁻, the solution is alkaline in nature. Since the anion is undergoing hydrolysis, it is called anionic hydrolysis.

(a) Hydrolysis constant, Kh = Kw/Ka
(b) Degree of hydrolysis, h = √(Kh/C) = √(Kw/Ka·C)
(c) pH = -log[H⁺]
pH = ½[log Kw + log Ka + log C]

Examples are, KCN, Na₂CO₃, Na₃PO₄ etc.

Ex.: The pH of aqueous solution of sodium acetate is
(A) 7
(B) < 7
(C) > 7
(D) None of these
Solution: (C). CH₃COONa + H₂O ——→ CH₃COOH + NaOH
The solution will be basic due to presence of strong base.

(iii) Salt of strong acid and weak base

BA + H₂O ⇌ HA + BOH
NH₄Cl + H₂O ⇌ NH₄OH + HCl
NH₄⁺ + H₂O ⇌ NH₄OH + H⁺

As it produces H⁺ ions hence, the solution is acidic in nature. Since the cation is hydrolysed it is called cationic hydrolysis.

Hydrolysis constant, Kh = Kw/Kb
Degree of hydrolysis, h = √(Kh/C) = √(Kw/Kb·C)
pH = ½[log Kw - log Kb - log C]
Ex.: If 0.1 mol of a salt is added to 1.0 L of water, which of these salts is expected to produce the most acidic solution?
(A) NaC₂H₃O₂
(B) NH₄NO₃
(C) CuSO₄
(D) AlCl₃

Solution: (D). AlCl₃ + H₂O ——→ 3HCl + Al(OH)₃
Since more acid is produced hence, more acidic solution is obtained.

(iv) Salt of weak acid and weak base

BA + H₂O ⇌ HA + BOH
CH₃COONH₄ + H₂O ⇌ CH₃COOH + NH₄OH
or, CH₃COO⁻ + NH₄⁺ + H₂O ⇌ CH₃COOH + NH₄OH

It involves both cationic and anionic hydrolysis.

The final solution may be neutral, slightly acid or basic depending upon the degrees of ionization of weak acid and weak base produced. In the present case the solution is neutral as the CH₃COOH and NH₄OH are almost equally weak.

Hydrolysis constant Kh = Kw/(Ka × Kb)
Degree of hydrolysis h = √(Kw/(Ka × Kb))
pH = ½[log Kw + log Ka - log Kb]
Ex.: Percentage hydrolysis of 0.1 M CH₃COONH₄ when Ka = Kb = 1.8×10⁻⁵ is
(A) 0.55×10⁻²
(B) 0.55
(C) 7.63
(D) 1.8×10⁻²

Solution: (B). h = √(Kw/(Ka × Kb)) = √(10⁻¹⁴/(1.8 × 10⁻⁵)²)
Hydrolysis = h × 100 = 0.55%
 

Solved Examples

1. The pKa of HCN is 9.30. The pH of a solution prepared by mixing 2.5 mole of KCN & 2.5 mole HCN in water and making the total volume 500 ml is
(A) 9.30
(B) 7.30
(C) 10.30
(D) 8.30

Sol. (A). pH = pKa + log[KCN]/[HCN] = 9.30
2. The degree of hydrolysis of which of the following salts is independent of the concentration of the salt solution?
(A) CH₃COONa
(B) NH₄Cl
(C) CH₃COONH₄
(D) NaCl

Sol. (C). It is the salt of weak acid and weak base, hence its degree of hydrolysis will be independent of concentration. h = √(Kw/(Ka × Kb))
3. At 25°C the pH of 10⁻³M NaOH is 11. Now let 10⁻³M solution of NaOH is warmed to 45°C without changing the volume of solution and hence molarity of solution. Choose the correct statement regarding pH and pOH of the solution after heating.
(A) pH will decrease while pOH will remain constant
(B) pH will increase while pOH will remain constant
(C) pH will increase while pOH will decrease
(D) Both pH and pOH will decrease

Sol. (A). Kw will increase and hence, pH + pOH will decrease. Molarity of NaOH solution remaining constant, pOH will remain constant but pH will decrease.
4. A buffer solution can be prepared from a mixture of
(1) Sodium acetate and acetic acid in water
(2) Sodium acetate and hydrochloric acid in water
(3) Ammonia and ammonium chloride in water
(4) Ammonia and sodium hydroxide in water
(A) 1, 3, 4
(B) 1, 3
(C) 1, 2, 4
(D) 2, 4

Sol. (B). Buffer is a solution of a weak acid or base and its salt with strong base or strong acid respectively.
5. The pKa of acetylsalicylic acid (aspirin) is 3.5. The pH of gastric juice in human stomach is about 2–3 and the pH in the small intestine is about 8. Aspirin will be
(A) Unionised in the small intestine and in the stomach
(B) Completely ionized in the small intestine and in the stomach.
(C) Ionised in the stomach and almost unionized in the small intestine
(D) Ionised in the small intestine and almost unionsied in the stomach

Sol. (D). Since pH in small intestine is more, the conditions are basic and aspirin will dissociate.

ASSIGNMENT PROBLEMS

1. Which can act as a buffer?
(A) NH₄Cl + NH₄OH
(B) CH₃COOH+CH₃COONa
(C) 40 ml of 0.1 M NaCN + 20 ml of 0.1M HCl
(D) All of these
2. The degree of dissociation of water was found to be 1.8×10⁻⁹. Then Kw (ionic product of water) is
(A) 1.8×10⁻⁹
(B) 1.8×10⁻¹⁶
(C) 1.0×10⁻¹⁴
(D) Can not be calculated
3. A monoprotic acid in 0.1 M solution ionizes to 0.001%. Its ionization constant is
(A) 1 × 10⁻³
(B) 1 × 10⁻⁶
(C) 1 × 10⁻⁸
(D) 1 × 10⁻¹¹
4. Autoprotolysis constant of NH₃ is
(A) [NH₄⁺][NH₂⁻]
(B) [NH₂⁻][NH₃]
(C) [NH₄⁺][NH₂⁻]
(D) [NH₄⁺]/[NH₂⁻]
5. Which of the following solutions will have pH close to 1.0?
(A) 100 ml of M/10 HCl + 100 ml of M/10 NaOH
(B) 55 ml of M/10 HCl + 45 ml of M/10 NaOH
(C) 10 ml of M/10 HCl + 90 ml of M/10 NaOH
(D) 75 ml of M/5 HCl + 25 ml of M/5 NaOH

ANSWERS TO ASSIGNMENT PROBLEMS

1. D
2. C
3. D
4. C
5. D
6. C
7. C
8. D
9. A
10. C
11. D
12. B
13. B
14. D
15. C