Electrochemistry

Class 12 PCB . Chemistry . Chemistry Part I . Electrochemistry

Chapter 2: Electrochemistry

Ch 2

Chemistry

Class 12 PCB

Electrolytic Conductivity and Kohlrausch's Law

Electrochemistry Overview

Electrochemistry is the branch of chemistry that studies the production of electricity from energy released during spontaneous chemical reactions and the use of electrical energy to drive non-spontaneous chemical changes.

It deals with redox reactions, electrolytic cells and galvanic cells. In an electrolytic cell, electrical energy is used to bring about chemical change, while in a galvanic cell chemical energy is converted into electrical energy.

Electrolytic Conduction

Electrolytic conduction refers to the flow of electric current through an electrolytic solution due to the movement of ions.

When an electrolyte is dissolved in water or melted, it dissociates into cations and anions. Under an applied electric field, cations move towards the cathode and anions move towards the anode, and this directed movement constitutes conduction.

Electrolytic conduction is accompanied by chemical changes at the electrodes, so it is different from metallic conduction.

The movement of ions depends on their charge, size, solvation and the viscosity of the medium. The greater the mobility of ions, the better the conduction.

Electrolytes

An electrolyte is a substance that dissociates into ions in solution or in molten state, enabling the conduction of electricity. Electrolytes can be classified as:

Strong electrolytes: Completely dissociate into ions (e.g., NaCl, HCl, NaOH).
Weak electrolytes: Partially dissociate into ions (e.g., H₂CO₃, CH₃COOH, HCN).

Electrolytes conduct current only when ions are free to move. In aqueous solution, they may dissociate to different extents depending on their nature and the solvent.

Electrolytes may be acids, bases or salts. Strong electrolytes produce a large number of ions in solution, while weak electrolytes produce only a small number of ions and establish an equilibrium between ionised and unionised molecules.

Examples of strong electrolytes include strong acids, strong bases and most soluble salts. Weak electrolytes include weak acids and weak bases such as NH₄OH.

Degree of Ionisation

The degree of ionisation is the ratio of the number of ions produced to the total number of molecules of the electrolyte.

It is usually denoted by α and is given by:

α = number of ionised molecules / total number of molecules

For strong electrolytes, α is nearly 1, whereas for weak electrolytes, α is much less than 1. The degree of ionisation increases on dilution for weak electrolytes.

For weak electrolytes, α is related to the extent of dissociation and is an important measure of their conducting power in solution.

If c is the initial concentration of a weak electrolyte, then the concentration of ions formed depends on α. This makes α a useful quantity for studying the behaviour of weak electrolytes and their equilibrium in solution.

Resistance and Resistivity

Resistance (R) is the property of a substance that opposes the flow of electric current. It is directly proportional to the length (l) of the conductor and inversely proportional to its cross-sectional area (A):

R = ρ × (l / A)

where ρ is the resistivity or specific resistance of the material, measured in ohm-metres (Ω·m) or ohm-centimetres (Ω·cm).

Resistivity is an intrinsic property of a material. A substance with low resistivity offers less opposition to current, while a substance with high resistivity offers more opposition. For a given material, resistance increases with length and decreases with increasing area.

The reciprocal of resistance is conductance.

Resistance depends on the dimensions of the conductor, whereas resistivity depends only on the nature of the material and temperature.

For a uniform conductor, doubling the length doubles the resistance, while doubling the cross-sectional area halves the resistance.

Conductance and Conductivity

Conductance (C) is the ease with which current flows through a conductor and is the reciprocal of resistance:

C = 1 / R = A / (ρ × l)

The SI unit of conductance is Siemens (S).

Conductivity (κ) is the reciprocal of resistivity and is given by:

κ = C × (l / A)

Its SI unit is Siemens per metre (S m⁻¹) or Siemens per centimetre (S cm⁻¹).

Higher conductivity means better ability to conduct electric current. For electrolytic solutions, conductivity depends on the number of ions present, their mobility, and the nature of the solvent.

Conductivity increases when the number of ions or their mobility increases, and it decreases when the viscosity of the medium is high.

Conductance is an extensive property, while conductivity is an intrinsic property of the substance.

Conductance of a solution changes with the dimensions of the cell, but conductivity is independent of the dimensions of the measuring cell.

Factors Affecting Conductivity

Nature of the material
Temperature
Number of valence electrons per atom or size and solvation of ions
Concentration of ions in solution
Mobility of ions
Viscosity of the solvent

In electrolytic solutions, conductivity generally increases with temperature because ion mobility increases and viscosity decreases.

In general, conductivity of a solution is greater when the electrolyte is more dissociated, the ions are smaller or less solvated, and the solvent is less viscous.

The nature of the solvent also matters because a solvent with high dielectric constant generally favours ionisation and thus higher conductivity.

Metallic and Electrolytic Conductance

Metallic conductance arises from free electrons in metals and depends on the metal's nature, structure, valence electrons, and temperature.

Electrolytic conductance arises from ions in solution and depends on the nature of the electrolyte, solvation of ions, solvent viscosity, and temperature.

In metallic conductors, conductance decreases with rise in temperature, whereas in electrolytic conductors it generally increases with rise in temperature.

Metallic conduction does not involve chemical decomposition, while electrolytic conduction is associated with migration of ions and electrode reactions.

Metallic conductance is mainly electronic, whereas electrolytic conductance is ionic in nature.

Viscosity

Viscosity is the resistance of a liquid to flow; lower viscosity means easier flow.

For electrolytic solutions, lower viscosity generally allows ions to move more freely and therefore increases conductivity. Higher viscosity slows ion movement and lowers conductivity.

Thus, conductivity is inversely related to viscosity in electrolytic solutions.

Solvation of ions can effectively increase their size, and this also reduces mobility in a more viscous medium.

Cell Constant

The cell constant (G) is the ratio of the distance between electrodes (l) to the cross-sectional area (A):

G = l / A

It depends on the geometry of the electrodes and is expressed in cm⁻¹ or m⁻¹.

Since conductivity is measured experimentally using a conductivity cell, the cell constant is used to calculate conductivity from the measured resistance of the solution. For a given cell, the cell constant remains fixed and is usually determined using a standard solution.

Conductivity of a solution is given by κ = G × C, where C is the conductance.

Cell constant is an important calibration factor in conductometric measurements because the same cell may give different resistance values for solutions of different conductivities.

If the resistance of a solution is measured, its conductance is first obtained and then multiplied by the cell constant to find conductivity.

Molar Conductivity

Molar conductivity (Λₘ) is the conductance of all ions produced by one mole of electrolyte in solution:

Λₘ = (κ / C) × 1000

where κ is conductivity and C is concentration in mol/L. Its SI unit is S m² mol⁻¹.

Molar conductivity increases on dilution because the number of ions present per unit volume decreases less rapidly than the increase in ionic mobility. For strong electrolytes, Λₘ increases slowly with dilution, while for weak electrolytes it increases sharply due to greater ionisation.

At infinite dilution, molar conductivity reaches its maximum value, called limiting molar conductivity, Λ°ₘ.

For a given electrolyte, Λₘ is always greater at lower concentration and approaches Λ°ₘ as concentration tends to zero.

It is a useful quantity for comparing conductance of electrolytes at different concentrations.

Molar conductivity is not the same as conductivity; conductivity is per unit volume of solution, whereas molar conductivity refers to the conductance of the electrolyte contained in one mole of solution.

Debye-Hückel Equation

For strong electrolytes, molar conductivity varies with concentration as:

Λₘ = Λ°ₘ − A√C

where Λ°ₘ is limiting molar conductivity, A is a constant, and C is concentration.

This relation shows that the molar conductivity of strong electrolytes decreases with increase in concentration due to interionic interactions. On dilution, these interactions decrease and Λₘ approaches Λ°ₘ.

This equation is used only for strong electrolytes over a limited concentration range.

It is an empirical relation and is not applicable to weak electrolytes.

The square-root dependence on concentration is a characteristic feature of strong electrolytes in dilute solutions.

Kohlrausch’s Law of Independent Migration of Ions

At infinite dilution, the limiting molar conductivity of an electrolyte is the sum of the contributions of its individual ions:

Λ°ₘ = ν⁺ λ°₊ + ν⁻ λ°₋

where ν⁺ and ν⁻ are the number of cations and anions, and λ°₊ and λ°₋ are their limiting molar conductivities.

At infinite dilution, ions migrate independently of one another because interionic interactions become negligible.

This law is especially useful for obtaining limiting molar conductivity values of electrolytes that cannot be measured directly at infinite dilution.

It is applicable to both strong and weak electrolytes at infinite dilution.

Applications of Kohlrausch’s Law

Calculating molar conductivities of weak electrolytes at infinite dilution.
Determining degree of dissociation (α) of weak electrolytes: α = Λₘ / Λ°ₘ.
Calculating dissociation constant (Kₐ) of weak electrolytes:

Kₐ = C α² / (1 − α) = C Λₘ² / [Λ°ₘ (Λ°ₘ − Λₘ)]

Determining solubility of sparingly soluble salts:

Solubility = (κ × 1000) / Λ°ₘ

Kohlrausch’s law is also used to calculate the limiting molar conductivity of strong electrolytes by adding the limiting ionic conductivities of the constituent ions. It is especially useful when the limiting molar conductivity cannot be measured directly.

It helps in evaluating ionic contributions to conductivity and in comparing the conductance behaviour of different electrolytes.

It is also used in calculating Λ°ₘ for salts like CH₃COONa, HCl, NaOH and CH₃COOH by combining appropriate ionic conductivities.

Solved Examples

Example 1

A conductivity cell with 0.1 mol/L KCl solution has resistance 100 Ω. When the concentration changes to 0.02 mol/L, resistance changes to 520 Ω. Given conductivity of 0.1 mol/L KCl is 1.29 S/m, find the conductivity and molar conductivity of 0.02 mol/L KCl solution.

Solution:

Given:

R₁ = 100 Ω, C₁ = 0.1 mol/L
R₂ = 520 Ω, C₂ = 0.02 mol/L
Conductivity at 0.1 mol/L, κ₁ = 1.29 S/m = 1.29 Ω⁻¹ m⁻¹

Calculate cell constant (G):

G = κ₁ × R₁ = 1.29 × 100 = 129 m⁻¹ = 1.29 cm⁻¹

Calculate conductivity at 0.02 mol/L:

κ₂ = G / R₂ = 1.29 / 520 = 0.00248 Ω⁻¹ cm⁻¹ = 2.48 × 10⁻³ Ω⁻¹ cm⁻¹

Convert concentration to mol/cm³:

C₂ = 0.02 mol/L = 2 × 10⁻⁵ mol/cm³

Calculate molar conductivity:

Λₘ = κ₂ / C₂ = (2.48 × 10⁻³) / (2 × 10⁻⁵) = 124 Ω⁻¹ mol⁻¹ cm²

Example 1

Solution:

Given:

R₁ = 100 Ω, C₁ = 0.1 mol/L
R₂ = 520 Ω, C₂ = 0.02 mol/L
Conductivity at 0.1 mol/L, κ₁ = 1.29 S/m = 1.29 Ω⁻¹ m⁻¹

Calculate cell constant (G):

G = κ₁ × R₁ = 1.29 × 100 = 129 m⁻¹ = 1.29 cm⁻¹

Calculate conductivity at 0.02 mol/L:

κ₂ = G / R₂ = 1.29 / 520 = 0.00248 Ω⁻¹ cm⁻¹ = 2.48 × 10⁻³ Ω⁻¹ cm⁻¹

Convert concentration to mol/cm³:

C₂ = 0.02 mol/L = 2 × 10⁻⁵ mol/cm³

Calculate molar conductivity:

Λₘ = κ₂ / C₂ = (2.48 × 10⁻³) / (2 × 10⁻⁵) = 124 Ω⁻¹ mol⁻¹ cm²

Example 1

Solution:

Given:

R₁ = 100 Ω, C₁ = 0.1 mol/L
R₂ = 520 Ω, C₂ = 0.02 mol/L
Conductivity at 0.1 mol/L, κ₁ = 1.29 S/m = 1.29 Ω⁻¹ m⁻¹

Calculate cell constant (G):

G = κ₁ × R₁ = 1.29 × 100 = 129 m⁻¹ = 1.29 cm⁻¹

Calculate conductivity at 0.02 mol/L:

κ₂ = G / R₂ = 1.29 / 520 = 0.00248 Ω⁻¹ cm⁻¹ = 2.48 × 10⁻³ Ω⁻¹ cm⁻¹

Convert concentration to mol/cm³:

C₂ = 0.02 mol/L = 2 × 10⁻⁵ mol/cm³

Calculate molar conductivity:

Λₘ = κ₂ / C₂ = (2.48 × 10⁻³) / (2 × 10⁻⁵) = 124 Ω⁻¹ mol⁻¹ cm²

Example 1

Solution:

Given:

R₁ = 100 Ω, C₁ = 0.1 mol/L
R₂ = 520 Ω, C₂ = 0.02 mol/L
Conductivity at 0.1 mol/L, κ₁ = 1.29 S/m = 1.29 Ω⁻¹ m⁻¹

Calculate cell constant (G):

G = κ₁ × R₁ = 1.29 × 100 = 129 m⁻¹ = 1.29 cm⁻¹

Calculate conductivity at 0.02 mol/L:

κ₂ = G / R₂ = 1.29 / 520 = 0.00248 Ω⁻¹ cm⁻¹ = 2.48 × 10⁻³ Ω⁻¹ cm⁻¹

Convert concentration to mol/cm³:

C₂ = 0.02 mol/L = 2 × 10⁻⁵ mol/cm³

Calculate molar conductivity:

Λₘ = κ₂ / C₂ = (2.48 × 10⁻³) / (2 × 10⁻⁵) = 124 Ω⁻¹ mol⁻¹ cm²

Example 1

Solution:

Given:

R₁ = 100 Ω, C₁ = 0.1 mol/L
R₂ = 520 Ω, C₂ = 0.02 mol/L
Conductivity at 0.1 mol/L, κ₁ = 1.29 S/m = 1.29 Ω⁻¹ m⁻¹

Calculate cell constant (G):

G = κ₁ × R₁ = 1.29 × 100 = 129 m⁻¹ = 1.29 cm⁻¹

Calculate conductivity at 0.02 mol/L:

κ₂ = G / R₂ = 1.29 / 520 = 0.00248 Ω⁻¹ cm⁻¹ = 2.48 × 10⁻³ Ω⁻¹ cm⁻¹

Convert concentration to mol/cm³:

C₂ = 0.02 mol/L = 2 × 10⁻⁵ mol/cm³

Calculate molar conductivity:

Λₘ = κ₂ / C₂ = (2.48 × 10⁻³) / (2 × 10⁻⁵) = 124 Ω⁻¹ mol⁻¹ cm²

Example 1

Solution:

Given:

R₁ = 100 Ω, C₁ = 0.1 mol/L
R₂ = 520 Ω, C₂ = 0.02 mol/L
Conductivity at 0.1 mol/L, κ₁ = 1.29 S/m = 1.29 Ω⁻¹ m⁻¹

Calculate cell constant (G):

G = κ₁ × R₁ = 1.29 × 100 = 129 m⁻¹ = 1.29 cm⁻¹

Calculate conductivity at 0.02 mol/L:

κ₂ = G / R₂ = 1.29 / 520 = 0.00248 Ω⁻¹ cm⁻¹ = 2.48 × 10⁻³ Ω⁻¹ cm⁻¹

Convert concentration to mol/cm³:

C₂ = 0.02 mol/L = 2 × 10⁻⁵ mol/cm³

Calculate molar conductivity:

Λₘ = κ₂ / C₂ = (2.48 × 10⁻³) / (2 × 10⁻⁵) = 124 Ω⁻¹ mol⁻¹ cm²

Practice Set

Level 1: Define electrolytic conduction and give examples of strong and weak electrolytes.
Level 2: Explain Kohlrausch’s law and its significance in determining molar conductivity.
Level 3: A conductivity cell has a cell constant of 1.5 cm⁻¹. If the resistance of a 0.05 mol/L solution is 200 Ω, calculate the conductivity and molar conductivity of the solution.
Answers: Level 1: Electrolytic conduction is the flow of electric current through a solution or molten electrolyte due to the movement of ions; examples of strong electrolytes include NaCl, HCl and KOH, while weak electrolytes include CH₃COOH, NH₄OH and HCN. Level 2: Kohlrausch’s law states that at infinite dilution, the molar conductivity of an electrolyte is the sum of the independent contributions of its ions, and it is used to calculate the limiting molar conductivity of weak electrolytes and to determine degree of dissociation. Level 3: Conductance G = 1/R = 1/200 = 0.005 S. Conductivity κ = cell constant × G = 1.5 × 0.005 = 0.0075 S cm⁻¹. Molar conductivity Λm = κ × 1000/c = 0.0075 × 1000/0.05 = 150 S cm² mol⁻¹.

Answer Key

Level 1: Electrolytic conduction is the flow of electric current through an electrolytic solution due to ion movement. Strong electrolytes fully dissociate (e.g., NaCl), weak electrolytes partially dissociate (e.g., CH₃COOH).
Level 2: Kohlrausch’s law states that the limiting molar conductivity of an electrolyte is the sum of the contributions of its ions. It helps calculate molar conductivity and degree of dissociation.
Level 3: Conductivity κ = G / R = 1.5 / 200 = 0.0075 Ω⁻¹ cm⁻¹. Concentration C = 0.05 mol/L = 5 × 10⁻⁵ mol/cm³. Molar conductivity Λₘ = κ / C = 0.0075 / (5 × 10⁻⁵) = 150 Ω⁻¹ mol⁻¹ cm².

Redox Reactions and Electrochemical Cells

Redox Reactions

A redox reaction involves simultaneous oxidation (loss of electrons) and reduction (gain of electrons).

Galvanic Cell

A galvanic cell converts chemical energy into electrical energy through spontaneous redox reactions. It consists of two electrodes immersed in electrolyte solutions.

Redox Couple

A redox couple consists of the oxidized and reduced forms of a substance involved in a half-reaction.

Daniell Cell

A Daniell cell is a galvanic cell with zinc and copper electrodes in their respective sulfate solutions:

Zn(s) + Cu²⁺(aq) ⇌ Zn²⁺(aq) + Cu(s)

At the zinc electrode, oxidation takes place: Zn(s) → Zn²⁺(aq) + 2e⁻.

At the copper electrode, reduction takes place: Cu²⁺(aq) + 2e⁻ → Cu(s).

The zinc electrode acts as the anode and the copper electrode acts as the cathode.

Cell notation: Zn(s) | Zn²⁺(aq) || Cu²⁺(aq) | Cu(s)

In this cell, electrons flow through the external circuit from zinc to copper, while the salt bridge maintains electrical neutrality in both half-cells.

The overall cell reaction is spontaneous and produces electrical energy.

Salt Bridge

A salt bridge is an inverted U-shaped tube containing a salt solution in agar-agar that completes the circuit, prevents mixing of electrolytes, and maintains electrical neutrality.

Electrode Potential

Electrode potential is the potential difference between an electrode and its solution, measured against the standard hydrogen electrode (SHE) which has zero potential.

Standard Electrode Potential

Standard electrode potential (E°) is the electrode potential measured at 25°C, 1 bar pressure, and 1 M concentration.

Cell Potential and EMF

The cell potential or electromotive force (EMF) is the potential difference between two electrodes when no current flows:

Ecell = Ecathode − Eanode

A positive EMF indicates that the cell reaction is spontaneous under the stated conditions.

For a galvanic cell, EMF is measured in volts and is the driving force for the flow of electrons through the external circuit.

Under standard conditions, the standard cell potential is written as E°cell.

Standard Oxidation Potential

It is the potential when an electrode undergoes oxidation at standard conditions relative to SHE.

Standard oxidation potential is equal in magnitude but opposite in sign to the standard reduction potential of the same electrode.

For example, if the standard reduction potential of Zn²⁺/Zn is negative, the standard oxidation potential of Zn/Zn²⁺ is positive by the same amount.

It is obtained by reversing the corresponding reduction half-reaction and changing the sign of E°.

Electrochemical Series

Elements arranged in order of increasing electrode potential form the electrochemical series.

In this series, species with more negative standard reduction potentials are stronger reducing agents, while species with more positive standard reduction potentials are stronger oxidizing agents.

The electrochemical series is useful for predicting the feasibility of redox reactions, comparing reactivity of metals, and identifying the anode and cathode in galvanic cells.

Nernst Equation

For non-standard conditions, the electrode potential is given by:

E = E° − (RT / nF) ln Q

At 298 K, this simplifies to:

E = E° − (0.059 / n) log Q

where Q is the reaction quotient.

For a complete cell reaction, the same equation is used with the cell potential:

Ecell = E°cell − (0.059 / n) log Q

The Nernst equation shows how electrode potential changes with concentration, pressure, and temperature.

For a galvanic cell, when Q = 1, E = E°.

Gibbs Energy and Cell Spontaneity

Gibbs free energy change (ΔG) relates to cell potential as:

ΔG° = −nFE°

For a spontaneous reaction, ΔG must be negative.

Therefore, if E°cell is positive, the cell reaction is spontaneous under standard conditions.

At equilibrium, E°cell = 0 and ΔG° = 0.

Solved Examples

Example 2

Calculate ΔG° for the reaction:

Zn(s) ⟶ Cu²⁺(aq) ⟶ Zn²⁺(aq) + Cu(s)

Given E°cell = +1.1 V.

Solution:

At anode: Zn(s) ⟶ Zn²⁺ + 2e⁻

At cathode: Cu²⁺ + 2e⁻ ⟶ Cu(s)

n = 2

ΔG° = −nFE° = −2 × 96500 × 1.1 = −212300 J/mol = −212.3 kJ/mol

Answer: ΔG° = −212.3 kJ/mol

Example 2

Calculate ΔG° for the reaction:

Zn(s) ⟶ Cu²⁺(aq) ⟶ Zn²⁺(aq) + Cu(s)

Given E°cell = +1.1 V.

Solution:

At anode: Zn(s) ⟶ Zn²⁺ + 2e⁻

At cathode: Cu²⁺ + 2e⁻ ⟶ Cu(s)

n = 2

ΔG° = −nFE° = −2 × 96500 × 1.1 = −212300 J/mol = −212.3 kJ/mol

Example 2

Calculate ΔG° for the reaction:

Zn(s) ⟶ Cu²⁺(aq) ⟶ Zn²⁺(aq) + Cu(s)

Given E°cell = +1.1 V.

Solution:

At anode: Zn(s) ⟶ Zn²⁺ + 2e⁻

At cathode: Cu²⁺ + 2e⁻ ⟶ Cu(s)

n = 2

ΔG° = −nFE° = −2 × 96500 × 1.1 = −212300 J/mol = −212.3 kJ/mol

Answer: ΔG° = −212.3 kJ/mol

Example 2

Calculate ΔG° for the reaction:

Zn(s) ⟶ Cu²⁺(aq) ⟶ Zn²⁺(aq) + Cu(s)

Given E°cell = +1.1 V.

Solution:

At anode: Zn(s) ⟶ Zn²⁺ + 2e⁻

At cathode: Cu²⁺ + 2e⁻ ⟶ Cu(s)

n = 2

ΔG° = −nFE° = −2 × 96500 × 1.1 = −212300 J/mol = −212.3 kJ/mol

Practice Set

Level 1: A redox reaction is a reaction in which oxidation and reduction occur simultaneously through transfer of electrons. Example: Zn + Cu²⁺ → Zn²⁺ + Cu.
Level 2: A salt bridge completes the electrical circuit in a galvanic cell by allowing the flow of ions between the two half-cells. It maintains electrical neutrality in the solutions and prevents the direct mixing of the electrolytes.
Level 3: Use the Nernst equation: E_cell = E°_cell - (0.0591/n) log Q at 298 K.
Here, E°_cell = 1.1 V, n = 2, and Q = 0.01.
So, E_cell = 1.1 - (0.0591/2) log(0.01).
Since log(0.01) = -2,
E_cell = 1.1 - (0.0591/2)(-2) = 1.1 + 0.0591 = 1.1591 V ≈ 1.16 V.

Answer Key

Level 1: A redox reaction involves simultaneous oxidation and reduction. Example: Zn + Cu²⁺ → Zn²⁺ + Cu.
Level 2: The salt bridge completes the circuit, prevents mixing of electrolytes, and maintains electrical neutrality by allowing ion flow.
Level 3: E = E° − (0.059/n) log Q = 1.1 − (0.059/2) log 0.01 = 1.1 − 0.0295 × (−2) = 1.1 + 0.059 = 1.159 V.

Electrolysis, Batteries, Fuel Cells and Corrosion

Electrolysis

Electrolysis is the decomposition of an electrolyte by passing electric current through its aqueous or molten state in an electrolytic cell.

It is used to obtain metals such as sodium, aluminium and magnesium from their compounds and to produce gases like chlorine, hydrogen and oxygen.

Faraday’s Laws of Electrolysis

First law: The amount of substance liberated at an electrode is proportional to the quantity of electricity passed.

m = Z × I × t, where Z is electrochemical equivalent.

Second law: The amounts of different substances liberated by the same quantity of electricity are proportional to their chemical equivalent weights.

w₁ / E₁ = w₂ / E₂

These laws are used for calculating the mass of metal deposited or gas liberated during electrolysis.

Important points:

If current I is kept constant, the mass deposited increases with time t.
If the same current passes through different electrolytes, the masses deposited depend on their equivalent weights.
Electrochemical equivalent, Z, is the mass deposited by 1 coulomb of charge.

Electrolysis Products Dependence

Physical state of the electrolyte: Molten electrolytes give products based on ions present, while aqueous electrolytes may also involve water ions.
Type of electrodes used: Inert electrodes usually do not take part in the reaction, while reactive electrodes may dissolve or participate.
Concentration of ions present in the electrolyte: More concentrated ions are generally discharged more readily.
Relative discharge potentials of the ions: Ions with lower discharge potential are discharged preferentially at the electrode.

Thus, the products of electrolysis depend on the nature of the electrolyte and the conditions under which electrolysis is carried out.

Batteries

Batteries are combinations of galvanic cells connected in series to provide electrical energy.

They convert chemical energy into electrical energy and are used as portable sources of electricity in devices such as torch lights, radios and automobiles.

Types of Batteries

Primary batteries: Non-rechargeable, e.g., Leclanche cell, dry cell, mercury cell.
Secondary batteries: Rechargeable, e.g., lead storage battery, nickel–cadmium cell.

Primary batteries are used once and discarded after use, whereas secondary batteries can be recharged and used repeatedly.

Dry Cell (Leclanche Cell)

Consists of zinc container (anode), graphite electrode (cathode), surrounded by manganese dioxide and carbon mixture, with ammonium chloride and zinc chloride paste.

At anode: Zn(s) → Zn²⁺(aq) + 2e⁻

At cathode: MnO₂(s) + NH₄⁺(aq) + 2e⁻ → MnO(OH) + NH₃

Net reaction: Zn + NH₄⁺ + MnO₂ → Zn²⁺ + MnO(OH) + NH₃

The cell is commonly used in torches, clocks and small portable devices.

Working: During discharge, zinc acts as the reducing agent and gets oxidised at the anode. The graphite rod serves as an inert cathode, and manganese dioxide acts as a depolariser by preventing the buildup of hydrogen.

Advantages: It is compact, inexpensive and easy to use.

Limitation: It is not rechargeable.

Lead Storage Battery

Anode: Spongy lead

Cathode: Lead dioxide packed with lead

Electrolyte: 38% aqueous sulfuric acid (H₂SO₄)

Discharge reactions:

Anode: Pb(s) + SO₄²⁻(aq) → PbSO₄(s) + 2e⁻

Cathode: PbO₂(s) + 4H⁺(aq) + SO₄²⁻(aq) + 2e⁻ → PbSO₄(s) + 2H₂O(l)

Overall: Pb + PbO₂ + 2H₂SO₄ → 2PbSO₄ + 2H₂O

Recharge reactions reverse the above processes.

It is widely used in automobiles and inverters because it can supply a large current.

Working during discharge: Both plates are gradually converted into PbSO₄ and the concentration of sulfuric acid decreases.

During charging: The reactions are reversed by passing an external current, restoring Pb at the anode and PbO₂ at the cathode.

Advantages: It can deliver high current and can be recharged many times.

Fuel Cells

Fuel cells convert chemical energy from fuels like hydrogen directly into electrical energy without recharging.

Anode reaction: H₂(g) + 2OH⁻(aq) → 2H₂O(l) + 2e⁻

Cathode reaction: O₂(g) + 2H₂O(l) + 4e⁻ → 4OH⁻(aq)

Net reaction: 2H₂(g) + O₂(g) → 2H₂O(l)

Fuel cells are efficient and pollution-free because water is the only product in the hydrogen–oxygen fuel cell.

Features: They work continuously as long as fuel and oxidant are supplied, so they do not need recharging like ordinary batteries.

Uses: Fuel cells are used in spacecraft, submarines and some special power systems.

Corrosion

Corrosion is the slow chemical degradation of metals, such as rusting of iron.

Rusting reactions:

Fe(s) + 2H⁺(aq) + ½ O₂(aq) → Fe²⁺(aq) + H₂O(l)

2Fe²⁺(s) + ½ O₂(g) + 2H₂O(l) → Fe₂O₃(s) + 4H⁺

Fe₂O₃ + xH₂O → Fe₂O₃·xH₂O (rust)

Corrosion generally occurs in the presence of moisture and oxygen and leads to loss of luster, weakening of metals and economic damage.

Electrochemical nature of rusting: Rusting occurs through formation of tiny anodic and cathodic areas on the metal surface in the presence of water and dissolved oxygen.

Anodic reaction: Fe → Fe²⁺ + 2e⁻

Cathodic reaction: O₂ + 2H₂O + 4e⁻ → 4OH⁻

The ferrous ions finally form hydrated ferric oxide, which is rust.

Prevention of Corrosion

Barrier protection: Painting, greasing, electroplating to prevent exposure.
Sacrificial protection: Galvanisation using zinc or aluminium coatings.
Alloying: Combining metals to form corrosion-resistant alloys.

Other methods include anodising, cathodic protection and keeping the metal surface dry.

Practice Set

Level 1: State Faraday’s first and second laws of electrolysis.
Level 2: Describe the structure and working of a dry cell.
Level 3: Write the reactions occurring at the anode and cathode during discharge and recharge of a lead storage battery.

Answer Key

Level 1: First law: The mass of a substance liberated or deposited at an electrode is directly proportional to the quantity of electricity passed. Second law: When the same quantity of electricity is passed through different electrolytes, the masses of substances liberated are proportional to their chemical equivalents.
Level 2: A dry cell has a zinc container as the anode, a graphite cathode surrounded by MnO₂ and carbon, and a paste of NH₄Cl and ZnCl₂ as the electrolyte. Chemical reactions in the cell produce electricity.
Level 3: Discharge:
Anode: Pb + SO₄²⁻ → PbSO₄ + 2e⁻
Cathode: PbO₂ + 4H⁺ + SO₄²⁻ + 2e⁻ → PbSO₄ + 2H₂O
Recharge:
Cathode: PbSO₄ + 2e⁻ → Pb + SO₄²⁻
Anode: PbSO₄ + 2H₂O → PbO₂ + 4H⁺ + SO₄²⁻ + 2e⁻

Quick Reference Table

Electrochemistry: The branch of chemistry that studies the production of electricity from spontaneous chemical reactions and the use of electrical energy to drive non-spontaneous chemical changes.
Electrolytic conduction: Flow of electric current through an electrolytic solution due to movement of ions.
Electrolyte: A substance that dissociates into ions in solution or molten state and conducts electricity.
Strong electrolyte: Completely dissociates into ions; examples include NaCl, HCl and NaOH.
Weak electrolyte: Partially dissociates into ions; examples include H₂CO₃, CH₃COOH and HCN.
Degree of ionisation: Ratio of the number of ions produced to the total number of molecules of the electrolyte.
Resistance: Opposition offered by a substance to the flow of electric current.
Resistivity (ρ): Intrinsic property of a material; R = ρ × l/A.
Conductance (C): Reciprocal of resistance; C = 1/R.
Conductivity (κ): Reciprocal of resistivity; κ = C × l/A.
Cell constant: Ratio of distance between electrodes to cross-sectional area; G = l/A.
Molar conductivity (Λₘ): Conductance of all ions produced by one mole of electrolyte in solution; Λₘ = (κ/C) × 1000.
Limiting molar conductivity (Λ°ₘ): Maximum molar conductivity at infinite dilution.
Debye-Hückel relation for strong electrolytes: Λₘ = Λ°ₘ − A√C.
Kohlrausch’s law: At infinite dilution, Λ°ₘ = ν⁺λ°₊ + ν⁻λ°₋.
Degree of dissociation from Kohlrausch’s law: α = Λₘ/Λ°ₘ.
Dissociation constant of a weak electrolyte: Kₐ = Cα²/(1 − α) = CΛₘ²/[Λ°ₘ(Λ°ₘ − Λₘ)].
Solubility of a sparingly soluble salt: Solubility = (κ × 1000)/Λ°ₘ.
Redox reaction: A reaction in which oxidation and reduction occur simultaneously.
Galvanic cell: Converts chemical energy into electrical energy through a spontaneous redox reaction.
Redox couple: The oxidized and reduced forms of a substance involved in a half-reaction.
Daniell cell: Zn(s) | Zn²⁺(aq) || Cu²⁺(aq) | Cu(s).
Salt bridge: Completes the circuit, prevents mixing of electrolytes and maintains electrical neutrality.
Electrode potential: Potential difference between an electrode and its solution, measured against SHE.
Standard electrode potential: Electrode potential measured at 25°C, 1 bar pressure and 1 M concentration.
Cell EMF: E_cell = E_cathode − E_anode.
Nernst equation: E = E° − (RT/nF) ln Q; at 298 K, E = E° − (0.059/n) log Q.
Gibbs free energy relation: ΔG° = −nFE°.
Electrolysis: Decomposition of an electrolyte by passing electric current through its aqueous or molten state.
Faraday’s first law: Mass of substance liberated is proportional to the quantity of electricity passed; m = ZIt.
Faraday’s second law: Masses of different substances liberated by the same quantity of electricity are proportional to their chemical equivalent weights.
Primary battery: Non-rechargeable battery, e.g., dry cell, mercury cell.
Secondary battery: Rechargeable battery, e.g., lead storage battery, nickel–cadmium cell.
Dry cell: Zinc container as anode, graphite as cathode, and MnO₂ with NH₄Cl/ZnCl₂ paste as electrolyte mixture.
Lead storage battery: Uses spongy lead and lead dioxide electrodes in sulfuric acid and can be recharged.
Fuel cell: Converts chemical energy of a fuel directly into electrical energy without recharging.
Hydrogen–oxygen fuel cell: Produces water as the only product, making it efficient and pollution-free.
Corrosion: Slow chemical degradation of metals, such as rusting of iron.
Rust: Hydrated iron(III) oxide, Fe₂O₃·xH₂O.
Prevention of corrosion: Barrier protection, sacrificial protection, alloying, anodising, cathodic protection and keeping the metal surface dry.

Common Mistakes and Misconceptions

Mistake: Many students think that a hydrated salt and a wet salt are the same thing.
Correct idea: A hydrated salt has a fixed number of water molecules chemically bound in its crystal structure, such as CuSO₄·5H₂O. Moisture on the surface is not the same as water of crystallisation.
Mistake: Students often assume that all salts containing water are hydrated salts.
Correct idea: Only salts with a definite, fixed amount of water molecules in the formula are hydrated. If the amount of water is not fixed, it is not a true hydrate.
Mistake: Some students confuse water of crystallisation with water absorbed from the air.
Correct idea: Water of crystallisation is part of the crystal lattice, whereas absorbed water is only moisture and can usually be removed by drying.
Mistake: Students may think that heating always destroys the salt completely.
Correct idea: On heating, many hydrated salts lose only their water of crystallisation and may change colour, but the anhydrous salt can remain.
Mistake: Another common error is to treat all crystalline substances as hydrated.
Correct idea: Crystallinity and hydration are different concepts. A substance may be crystalline without containing water of crystallisation.

Glossary

Electrochemistry: The branch of chemistry that deals with the conversion of chemical energy into electrical energy and vice versa.
Electrolytic conduction: The flow of electric current through an electrolyte due to the movement of ions.
Electrolyte: A substance that dissociates into ions in molten state or solution and can conduct electricity.
Strong electrolyte: An electrolyte that completely dissociates into ions in solution; examples include NaCl, HCl and NaOH.
Weak electrolyte: An electrolyte that partially dissociates into ions in solution; examples include CH₃COOH, H₂CO₃ and HCN.
Degree of ionisation: The ratio of the number of ions formed to the total number of molecules of an electrolyte.
Resistance (R): The opposition offered by a conductor to the flow of electric current.
Resistivity (ρ): An intrinsic property of a material that measures its opposition to current flow.
Conductance (C): The reciprocal of resistance; C = 1/R.
Conductivity (κ): The reciprocal of resistivity; it measures the ease with which current passes through a solution or material.
Cell constant: The ratio of the distance between electrodes to the cross-sectional area of the electrodes; G = l/A.
Molar conductivity (Λₘ): The conductance of all the ions produced by one mole of electrolyte in solution.
Limiting molar conductivity (Λ°ₘ): The molar conductivity of an electrolyte at infinite dilution.
Debye-Hückel equation: The relation Λₘ = Λ°ₘ − A√C for strong electrolytes, showing decrease in molar conductivity with concentration.
Kohlrausch’s law of independent migration of ions: At infinite dilution, the limiting molar conductivity of an electrolyte is the sum of the contributions of its individual ions.
Redox reaction: A reaction in which oxidation and reduction occur simultaneously through transfer of electrons.
Oxidation: Loss of electrons or increase in oxidation state.
Reduction: Gain of electrons or decrease in oxidation state.
Galvanic cell: An electrochemical cell that converts chemical energy into electrical energy through a spontaneous redox reaction.
Redox couple: The oxidised and reduced forms of a substance involved in a half-reaction.
Daniell cell: A galvanic cell consisting of zinc and copper electrodes dipped in their respective sulfate solutions.
Salt bridge: An inverted U-shaped tube containing a salt solution in agar-agar that completes the circuit and maintains electrical neutrality.
Electrode potential: The potential difference between an electrode and its solution, measured relative to the standard hydrogen electrode.
Standard electrode potential (E°): The electrode potential measured at 25°C, 1 bar pressure and 1 M concentration.
Cell potential or EMF: The potential difference between two electrodes when no current flows; E_cell = E_cathode − E_anode.
Standard oxidation potential: The potential when an electrode undergoes oxidation under standard conditions relative to SHE.
Electrochemical series: The arrangement of elements in order of increasing electrode potential.
Nernst equation: The equation used to calculate electrode potential under non-standard conditions: E = E° − (RT/nF) ln Q.
Gibbs free energy change (ΔG): The thermodynamic quantity related to cell potential by ΔG° = −nFE°.
Electrolysis: The decomposition of an electrolyte by passing electric current through its aqueous or molten state.
Faraday’s first law of electrolysis: The mass of substance liberated is proportional to the quantity of electricity passed.
Faraday’s second law of electrolysis: The masses of different substances liberated by the same quantity of electricity are proportional to their chemical equivalent weights.
Electrochemical equivalent (Z): The mass of a substance deposited or liberated by one coulomb of charge.
Battery: A combination of galvanic cells connected in series to provide electrical energy.
Primary battery: A non-rechargeable battery used once and then discarded.
Secondary battery: A rechargeable battery that can be used repeatedly after recharging.
Dry cell (Leclanche cell): A primary cell with zinc as anode, graphite as cathode and a moist paste of NH₄Cl and ZnCl₂ with MnO₂ as depolariser.
Lead storage battery: A secondary battery with spongy lead and lead dioxide electrodes in sulfuric acid electrolyte.
Fuel cell: A cell that converts the chemical energy of a fuel directly into electrical energy without recharging.
Corrosion: The slow chemical degradation of metals, such as rusting of iron.
Rust: Hydrated iron(III) oxide, Fe₂O₃·xH₂O, formed during corrosion of iron.
Barrier protection: A method of preventing corrosion by isolating the metal surface from air and moisture, such as painting or greasing.
Sacrificial protection: A corrosion-prevention method in which a more reactive metal such as zinc protects the base metal.
Galvanisation: The coating of iron or steel with zinc to protect it from corrosion.
Anodising: The formation of a protective oxide layer on a metal surface, especially aluminium, to prevent corrosion.
Cathodic protection: A method of preventing corrosion by making the metal act as a cathode in an electrochemical system.

Chemistry — ALL CHAPTERS

Solutions

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Electrochemistry

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Chemical Kinetics

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The D- And F -Block Elements

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Coordination Compounds

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Haloalkanes And Haloarenes

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Alcohols, Phenols And Ethers

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Aldehydes, Ketones and Carboxylic Acids

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Amines

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Biomolecules

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