ELECTROCHEMISTRY - DETAILED NEET/JEE NOTES

1. INTRODUCTION TO ELECTROCHEMISTRY

Definition: Electrochemistry is the study of production of electricity from energy released during spontaneous chemical reactions and the use of electrical energy to bring about non-spontaneous chemical transformations.

Applications:

2. ELECTROCHEMICAL CELLS

Electrochemical Cell: A device that converts chemical energy into electrical energy (Galvanic cell) or electrical energy into chemical energy (Electrolytic cell).

2.1 GALVANIC (VOLTAIC) CELLS

Galvanic Cell: An electrochemical cell that converts the chemical energy of a spontaneous redox reaction into electrical energy.

Example: Daniell Cell

Components: Half-cell reactions:
Anode (oxidation): Zn(s) → Zn²⁺(aq) + 2e⁻
Cathode (reduction): Cu²⁺(aq) + 2e⁻ → Cu(s)
Overall reaction: Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s)
Cell potential: E°(cell) = 1.1 V (when [Zn²⁺] = [Cu²⁺] = 1 M)

Key Concepts:

Cell Representation Convention:

Format: Anode | Anode solution || Cathode solution | Cathode
Example: Zn(s) | Zn²⁺(aq) || Cu²⁺(aq) | Cu(s)
Notation:

2.2 ELECTROLYTIC CELLS

Electrolytic Cell: A device that uses electrical energy to carry out non-spontaneous chemical reactions.

Working Principle:

3. ELECTRODE POTENTIAL

Electrode Potential: The potential difference that develops between the electrode and the electrolyte when an electrode is dipped in an electrolyte solution.

3.1 Standard Hydrogen Electrode (SHE)

Reference Electrode: Assigned zero potential at all temperatures
Conditions: Half reaction: H⁺(aq) + e⁻ → ½H₂(g), E° = 0.00 V

3.2 Standard Electrode Potential (E°)

Standard Electrode Potential: The potential of an electrode when all species are at unit concentration (1 M for solutions, 1 bar for gases) measured against SHE at 298 K.

Measurement:

Cell setup: Pt(s) | H₂(g, 1 bar) | H⁺(aq, 1 M) || M^n⁺(aq, 1 M) | M(s)
E°(cell) = E°(cathode) - E°(anode)
Since E°(SHE) = 0, therefore E°(cell) = E°(cathode) = E°(M^n⁺/M)

Important Points:

3.3 Standard Electrode Potentials (Important Values)

Half Reaction E° (V) Nature
F₂(g) + 2e⁻ → 2F⁻ +2.87 Strongest oxidizing agent
MnO₄⁻ + 8H⁺ + 5e⁻ → Mn²⁺ + 4H₂O +1.51 Strong oxidizing agent
Cl₂(g) + 2e⁻ → 2Cl⁻ +1.36 Strong oxidizing agent
O₂(g) + 4H⁺ + 4e⁻ → 2H₂O +1.23 Oxidizing agent
Br₂ + 2e⁻ → 2Br⁻ +1.09 Oxidizing agent
Ag⁺ + e⁻ → Ag(s) +0.80 Moderate oxidizing agent
Fe³⁺ + e⁻ → Fe²⁺ +0.77 Moderate oxidizing agent
I₂ + 2e⁻ → 2I⁻ +0.54 Weak oxidizing agent
Cu²⁺ + 2e⁻ → Cu(s) +0.34 Weak oxidizing agent
2H⁺ + 2e⁻ → H₂(g) 0.00 Reference
Pb²⁺ + 2e⁻ → Pb(s) -0.13 Weak reducing agent
Ni²⁺ + 2e⁻ → Ni(s) -0.25 Reducing agent
Fe²⁺ + 2e⁻ → Fe(s) -0.44 Reducing agent
Zn²⁺ + 2e⁻ → Zn(s) -0.76 Strong reducing agent
Al³⁺ + 3e⁻ → Al(s) -1.66 Strong reducing agent
Mg²⁺ + 2e⁻ → Mg(s) -2.36 Very strong reducing agent
Na⁺ + e⁻ → Na(s) -2.71 Very strong reducing agent
Li⁺ + e⁻ → Li(s) -3.05 Strongest reducing agent

3.4 Cell EMF Calculation

EMF of Cell:
E°(cell) = E°(cathode) - E°(anode)
E°(cell) = E°(right) - E°(left)
E°(cell) = E°(reduction) - E°(oxidation)
Example: Calculate E°(cell) for the reaction:
Cu(s) + 2Ag⁺(aq) → Cu²⁺(aq) + 2Ag(s)

Solution:
Cathode (reduction): 2Ag⁺ + 2e⁻ → 2Ag, E° = +0.80 V
Anode (oxidation): Cu → Cu²⁺ + 2e⁻, E° = +0.34 V
E°(cell) = 0.80 - 0.34 = 0.46 V
Cell representation: Cu(s) | Cu²⁺(aq) || Ag⁺(aq) | Ag(s)

4. NERNST EQUATION

Nernst Equation: Relates electrode potential at any concentration to standard electrode potential.

4.1 For Electrode (Single Half-Cell)

For the reaction: M^n⁺(aq) + ne⁻ → M(s)

General form:
E(M^n⁺/M) = E°(M^n⁺/M) - (RT/nF) ln(1/[M^n⁺])

At 298 K (using log₁₀):
E(M^n⁺/M) = E°(M^n⁺/M) - (0.0591/n) log(1/[M^n⁺])

Or:
E(M^n⁺/M) = E°(M^n⁺/M) + (0.0591/n) log[M^n⁺]

Constants:

4.2 For Complete Cell

For general reaction: aA + bB → cC + dD

Nernst Equation:
E(cell) = E°(cell) - (RT/nF) ln Q

At 298 K:
E(cell) = E°(cell) - (0.0591/n) log Q

Where Q = [C]^c[D]^d / [A]^a[B]^b (Reaction quotient)

For Daniell Cell:
Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s)
E(cell) = E°(cell) - (0.0591/2) log([Zn²⁺]/[Cu²⁺])
Example: Calculate E(cell) for Daniell cell when [Zn²⁺] = 0.1 M and [Cu²⁺] = 0.01 M
Given: E°(cell) = 1.1 V

Solution:
E(cell) = 1.1 - (0.0591/2) log(0.1/0.01)
E(cell) = 1.1 - 0.02955 × log(10)
E(cell) = 1.1 - 0.02955 × 1
E(cell) = 1.1 - 0.03 = 1.07 V

4.3 Applications of Nernst Equation

A. Equilibrium Constant Calculation

At equilibrium: E(cell) = 0 and Q = K(equilibrium constant)

Therefore:
0 = E°(cell) - (0.0591/n) log K
E°(cell) = (0.0591/n) log K
Or:
log K = (n × E°(cell))/0.0591
K = 10^(n × E°(cell)/0.0591)
Example: Calculate K for: Cu(s) + 2Ag⁺(aq) → Cu²⁺(aq) + 2Ag(s)
Given: E°(cell) = 0.46 V

Solution:
log K = (2 × 0.46)/0.0591 = 15.6
K = 10^15.6 = 3.92 × 10¹⁵

B. Gibbs Energy Relationship

Fundamental Equations:
ΔᵣG = -nFE(cell)
ΔᵣG° = -nFE°(cell)

Also:
ΔᵣG° = -RT ln K = -2.303RT log K

Combining:
-nFE°(cell) = -2.303RT log K
E°(cell) = (2.303RT/nF) log K
E°(cell) = (0.0591/n) log K (at 298 K)
Spontaneity Criteria:
Example: Calculate ΔᵣG° for Daniell cell
Given: E°(cell) = 1.1 V, n = 2

Solution:
ΔᵣG° = -nFE°(cell)
ΔᵣG° = -2 × 96487 × 1.1
ΔᵣG° = -212271 J mol⁻¹
ΔᵣG° = -212.27 kJ mol⁻¹

5. CONDUCTANCE IN ELECTROLYTIC SOLUTIONS

5.1 Basic Definitions and Formulas

A. Resistance (R)

R = ρ(l/A)

Where:
ρ = Resistivity (specific resistance)
l = Length of conductor
A = Area of cross-section

Unit: Ohm (Ω) or kg m²/(s³ A²)

B. Resistivity (ρ)

Resistivity: Resistance of a material of length 1 m and cross-sectional area 1 m²
Unit: Ω m or Ω cm
Conversion: 1 Ω m = 100 Ω cm

C. Conductance (G)

G = 1/R = κ(A/l)

Unit: Siemens (S) or mho (Ω⁻¹)
1 S = 1 Ω⁻¹ = 1 A V⁻¹

D. Conductivity (κ)

κ = 1/ρ = l/(RA) = G × (l/A)

Unit: S m⁻¹ or S cm⁻¹
Conversion: 1 S cm⁻¹ = 100 S m⁻¹

Definition: Conductance of a material of length 1 m and cross-sectional area 1 m²

E. Cell Constant (G*)

G* = l/A = R × κ

Unit: m⁻¹ or cm⁻¹

Determination: Using standard KCl solutions of known conductivity
Measurement of Conductivity:
  1. Determine cell constant using standard KCl solution
  2. Measure resistance (R) of unknown solution
  3. Calculate: κ = G*/R

5.2 Molar Conductivity (Λₘ)

Molar Conductivity: The conductance of volume of solution containing 1 mole of electrolyte kept between two electrodes at unit distance apart.
Λₘ = κ/c

Where:
κ = Conductivity (S m⁻¹ or S cm⁻¹)
c = Concentration (mol m⁻³ or mol L⁻¹)

Units:
If κ in S m⁻¹ and c in mol m⁻³: Λₘ in S m² mol⁻¹
If κ in S cm⁻¹ and c in mol L⁻¹: Λₘ in S cm² mol⁻¹

Conversion:
1 S m² mol⁻¹ = 10⁴ S cm² mol⁻¹

Alternative formulas:
Λₘ (S cm² mol⁻¹) = [κ (S cm⁻¹) × 1000 (cm³ L⁻¹)] / Molarity (mol L⁻¹)
Λₘ = κV (where V is volume in cm³ containing 1 mole)
Example: Calculate Λₘ for 0.02 M KCl solution
Given: κ = 0.248 × 10⁻² S cm⁻¹

Solution:
Λₘ = (κ × 1000)/Molarity
Λₘ = (0.248 × 10⁻² × 1000)/0.02
Λₘ = 124 S cm² mol⁻¹

5.3 Variation of Conductivity and Molar Conductivity with Concentration

A. Conductivity (κ)

Effect of Dilution:

B. Molar Conductivity (Λₘ)

Effect of Dilution:

C. For Strong Electrolytes

Kohlrausch Equation:
Λₘ = Λ°ₘ - A√c

Where:
Λ°ₘ = Limiting molar conductivity (at infinite dilution)
A = Constant (depends on type of electrolyte)
c = Concentration

Behavior:

D. For Weak Electrolytes

Behavior:

5.4 Limiting Molar Conductivity (Λ°ₘ)

Limiting Molar Conductivity: The molar conductivity at infinite dilution (c → 0), when electrolyte is completely dissociated and interionic interactions are negligible.

5.5 Kohlrausch Law of Independent Migration of Ions

Kohlrausch Law: At infinite dilution, each ion migrates independently and contributes to total molar conductivity regardless of the nature of other ions present.
Mathematical Form:
Λ°ₘ = n₊λ°₊ + n₋λ°₋

Where:
n₊, n₋ = Number of cations and anions per formula unit
λ°₊, λ°₋ = Limiting molar conductivities of individual ions

Examples:
Λ°ₘ(NaCl) = λ°(Na⁺) + λ°(Cl⁻)
Λ°ₘ(CaCl₂) = λ°(Ca²⁺) + 2λ°(Cl⁻)
Λ°ₘ(Al₂(SO₄)₃) = 2λ°(Al³⁺) + 3λ°(SO₄²⁻)

Limiting Molar Conductivities of Some Ions at 298 K

Cation λ° (S cm² mol⁻¹) Anion λ° (S cm² mol⁻¹)
H⁺ 349.6 OH⁻ 199.1
Na⁺ 50.1 Cl⁻ 76.3
K⁺ 73.5 Br⁻ 78.1
Ca²⁺ 119.0 CH₃COO⁻ 40.9
Mg²⁺ 106.0 SO₄²⁻ 160.0
Note: H⁺ and OH⁻ have exceptionally high conductivities due to proton jump mechanism (Grotthuss mechanism).

5.6 Applications of Kohlrausch Law

A. Calculation of Λ°ₘ for Weak Electrolytes

Example: Calculate Λ°ₘ for CH₃COOH (acetic acid)

Method:
Λ°ₘ(CH₃COOH) = λ°(H⁺) + λ°(CH₃COO⁻)
= λ°(H⁺) + λ°(Cl⁻) + λ°(CH₃COO⁻) + λ°(Na⁺) - λ°(Cl⁻) - λ°(Na⁺)
= Λ°ₘ(HCl) + Λ°ₘ(CH₃COONa) - Λ°ₘ(NaCl)

Using values:
= 426.16 + 91.0 - 126.45
= 390.71 S cm² mol⁻¹

B. Calculation of Degree of Dissociation (α)

For Weak Electrolytes:
α = Λₘ/Λ°ₘ

Where:
α = Degree of dissociation
Λₘ = Molar conductivity at concentration c
Λ°ₘ = Limiting molar conductivity

C. Calculation of Dissociation Constant (Ka)

For Weak Acid/Base:
Ka = (cα²)/(1-α)

Since α = Λₘ/Λ°ₘ

Ka = [c(Λₘ)²] / [Λ°ₘ(Λ°ₘ - Λₘ)]
Example: Calculate Ka for 0.001 M CH₃COOH
Given: κ = 4.95 × 10⁻⁵ S cm⁻¹, Λ°ₘ = 390.5 S cm² mol⁻¹

Solution:
Λₘ = (κ × 1000)/c = (4.95 × 10⁻⁵ × 1000)/0.001 = 49.5 S cm² mol⁻¹
α = Λₘ/Λ°ₘ = 49.5/390.5 = 0.127
Ka = (cα²)/(1-α) = (0.001 × 0.127²)/(1-0.127)
Ka = 1.85 × 10⁻⁵ mol L⁻¹

6. ELECTROLYTIC CELLS AND ELECTROLYSIS

6.1 Electrolysis

Electrolysis: The process of using electrical energy to bring about a non-spontaneous chemical reaction.

Example: Electrolysis of Aqueous CuSO₄

With Copper Electrodes:
Cathode (reduction): Cu²⁺(aq) + 2e⁻ → Cu(s)
Anode (oxidation): Cu(s) → Cu²⁺(aq) + 2e⁻

Result: Copper dissolves at anode and deposits at cathode (basis for purification)

Example: Electrolysis of Aqueous NaCl

At Cathode (possible reactions):
Na⁺(aq) + e⁻ → Na(s), E° = -2.71 V
H⁺(aq) + e⁻ → ½H₂(g), E° = 0.00 V
Preferred: H₂O(l) + e⁻ → ½H₂(g) + OH⁻(aq) (higher E°)

At Anode (possible reactions):
Cl⁻(aq) → ½Cl₂(g) + e⁻, E° = 1.36 V
2H₂O(l) → O₂(g) + 4H⁺(aq) + 4e⁻, E° = 1.23 V
Preferred: Cl⁻ oxidation (due to overpotential of O₂)

Products: H₂ at cathode, Cl₂ at anode, NaOH in solution

6.2 Faraday's Laws of Electrolysis

First Law

The amount of chemical reaction (mass deposited/liberated) at any electrode during electrolysis is directly proportional to the quantity of electricity passed through the electrolyte.

Mathematically: m ∝ Q or m ∝ It

Second Law

When the same quantity of electricity is passed through different electrolytes, the masses of substances deposited/liberated at the electrodes are proportional to their chemical equivalent weights.

Mathematically: m₁/m₂ = E₁/E₂
Where E = Equivalent weight = (Atomic mass)/(Number of electrons)

6.3 Quantitative Aspects

Faraday Constant (F):
F = Charge on 1 mole of electrons
F = NA × e = 6.022 × 10²³ × 1.602 × 10⁻¹⁹
F = 96487 C mol⁻¹ ≈ 96500 C mol⁻¹

Charge passed:
Q = I × t
Where: I = Current (A), t = Time (s)

Mass deposited:
m = (Q × M)/(n × F) = (I × t × M)/(n × F)
Where: M = Molar mass, n = Number of electrons
Example: Calculate mass of Cu deposited when 1.5 A current passes through CuSO₄ solution for 10 minutes.

Solution:
Q = I × t = 1.5 × 600 = 900 C
For Cu²⁺ + 2e⁻ → Cu: n = 2, M = 63.5 g/mol
m = (900 × 63.5)/(2 × 96500) = 0.296 g

6.4 Products of Electrolysis

Factors Determining Products:
  1. Nature of electrode (inert vs reactive)
  2. Standard electrode potentials of species present
  3. Overpotential requirements
  4. Concentration of ions in solution

Preferential Discharge Theory

7. BATTERIES

Battery: A galvanic cell or series of galvanic cells that converts chemical energy into electrical energy.

7.1 Primary Batteries (Non-rechargeable)

A. Dry Cell (Leclanche Cell)

Components: Reactions:
Anode: Zn(s) → Zn²⁺ + 2e⁻
Cathode: MnO₂ + NH₄⁺ + e⁻ → MnO(OH) + NH₃
Complex formation: Zn²⁺ + 4NH₃ → [Zn(NH₃)₄]²⁺
EMF: ~1.5 V
Uses: Torches, transistors, clocks

B. Mercury Cell

Components: Reactions:
Anode: Zn(Hg) + 2OH⁻ → ZnO(s) + H₂O + 2e⁻
Cathode: HgO + H₂O + 2e⁻ → Hg(l) + 2OH⁻
Overall: Zn(Hg) + HgO(s) → ZnO(s) + Hg(l)
EMF: ~1.35 V (constant throughout life)
Uses: Hearing aids, watches, calculators
Advantage: Constant voltage (no ions in solution)

7.2 Secondary Batteries (Rechargeable)

A. Lead Storage Battery

Components: Discharge Reactions:
Anode: Pb(s) + SO₄²⁻(aq) → PbSO₄(s) + 2e⁻
Cathode: PbO₂(s) + SO₄²⁻(aq) + 4H⁺(aq) + 2e⁻ → PbSO₄(s) + 2H₂O(l)
Overall: Pb(s) + PbO₂(s) + 2H₂SO₄(aq) → 2PbSO₄(s) + 2H₂O(l)

Charging Reactions: (Reverse of above)
2PbSO₄(s) + 2H₂O(l) → Pb(s) + PbO₂(s) + 2H₂SO₄(aq)

EMF: ~2 V per cell (6 cells = 12 V battery)
Uses: Automobiles, inverters

B. Nickel-Cadmium (Ni-Cd) Cell

Components: Discharge Reaction:
Cd(s) + 2Ni(OH)₃(s) → CdO(s) + 2Ni(OH)₂(s) + H₂O(l)

Advantages: Longer life than lead storage
Disadvantages: More expensive
Uses: Emergency lighting, portable devices

8. FUEL CELLS

Fuel Cell: A galvanic cell that converts chemical energy of combustion of fuels directly into electrical energy with high efficiency.

8.1 Hydrogen-Oxygen Fuel Cell

Components: Reactions:
Anode: 2H₂(g) + 4OH⁻(aq) → 4H₂O(l) + 4e⁻
Cathode: O₂(g) + 2H₂O(l) + 4e⁻ → 4OH⁻(aq)
Overall: 2H₂(g) + O₂(g) → 2H₂O(l)

Efficiency: ~70% (vs ~40% for thermal plants)
Advantages: Uses: Apollo space program, experimental vehicles

8.2 Other Fuel Cells

9. CORROSION

Corrosion: The deterioration of metals by electrochemical oxidation in the presence of air and moisture.

9.1 Rusting of Iron

Mechanism (Electrochemical Process):

At Anode (oxidation):
2Fe(s) → 2Fe²⁺(aq) + 4e⁻, E° = -0.44 V

At Cathode (reduction):
O₂(g) + 4H⁺(aq) + 4e⁻ → 2H₂O(l), E° = +1.23 V
(H⁺ from H₂CO₃ formed by dissolving CO₂ in water)

Overall Cell Reaction:
2Fe(s) + O₂(g) + 4H⁺(aq) → 2Fe²⁺(aq) + 2H₂O(l)
E°(cell) = 1.67 V

Atmospheric Oxidation:
2Fe²⁺(aq) + 2H₂O(l) + ½O₂(g) → Fe₂O₃(s) + 4H⁺(aq)
(Rust: Fe₂O₃·xH₂O)

Conditions Favoring Corrosion

9.2 Prevention of Corrosion

A. Barrier Protection

B. Metallic Coating

C. Cathodic Protection

Sacrificial Anode Method:

D. Alloying

10. IMPORTANT FORMULAS - QUICK REFERENCE

1. Cell EMF:
E°(cell) = E°(cathode) - E°(anode)

2. Nernst Equation (298 K):
E(cell) = E°(cell) - (0.0591/n) log Q

3. Gibbs Energy:
ΔᵣG° = -nFE°(cell)
ΔᵣG° = -RT ln K

4. Equilibrium Constant:
log K = (n × E°(cell))/0.0591

5. Conductivity:
κ = G*/R = l/(RA)

6. Molar Conductivity:
Λₘ = κ/c = (κ × 1000)/M (if κ in S cm⁻¹, c in mol L⁻¹)

7. Kohlrausch Law:
Λ°ₘ = n₊λ°₊ + n₋λ°₋
For strong electrolytes: Λₘ = Λ°ₘ - A√c

8. Degree of Dissociation:
α = Λₘ/Λ°ₘ

9. Dissociation Constant:
Ka = (cα²)/(1-α) = [c(Λₘ)²]/[Λ°ₘ(Λ°ₘ - Λₘ)]

10. Faraday's Law:
m = (I × t × M)/(n × F)
Q = I × t
F = 96500 C mol⁻¹

11. IMPORTANT POINTS FOR NEET/JEE

A. Galvanic vs Electrolytic Cells
Property Galvanic Cell Electrolytic Cell
Energy conversion Chemical → Electrical Electrical → Chemical
Reaction type Spontaneous (ΔG < 0) Non-spontaneous (ΔG > 0)
E(cell) Positive Negative
Anode charge Negative (-) Positive (+)
Cathode charge Positive (+) Negative (-)
Electron flow Anode → Cathode Cathode → Anode
Salt bridge Required Not required
B. Memory Tips
C. Common Mistakes to Avoid

12. SAMPLE PROBLEMS FOR PRACTICE

Problem 1: Calculate E(cell) for Daniell cell when [Zn²⁺] = 0.01 M, [Cu²⁺] = 0.1 M at 298 K. Given: E°(cell) = 1.1 V

Solution:
E(cell) = E°(cell) - (0.0591/n) log([Zn²⁺]/[Cu²⁺])
E(cell) = 1.1 - (0.0591/2) log(0.01/0.1)
E(cell) = 1.1 - 0.02955 × log(0.1)
E(cell) = 1.1 - 0.02955 × (-1)
E(cell) = 1.1 + 0.03 = 1.13 V
Problem 2: Resistance of 0.01 M KCl solution is 200 Ω. If cell constant is 1.0 cm⁻¹, calculate κ and Λₘ.

Solution:
κ = G*/R = 1.0/200 = 0.005 S cm⁻¹
Λₘ = (κ × 1000)/M = (0.005 × 1000)/0.01 = 500 S cm² mol⁻¹
Problem 3: How much charge is required to deposit 1 mole of Al from Al³⁺ solution?

Solution:
Al³⁺ + 3e⁻ → Al
For 1 mole Al: 3 moles of electrons required
Q = 3F = 3 × 96500 = 289500 C
Problem 4: Calculate equilibrium constant for: Zn + Cu²⁺ → Zn²⁺ + Cu
Given: E°(cell) = 1.1 V

Solution:
log K = (n × E°(cell))/0.0591
log K = (2 × 1.1)/0.0591 = 37.23
K = 10³⁷·²³ ≈ 1.7 × 10³⁷

CONCLUSION

Electrochemistry is a fundamental topic combining thermodynamics, kinetics, and chemical reactions. Master the concepts of electrode potentials, Nernst equation, conductance, and Faraday's laws for NEET/JEE success.

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