Class 12 Chemistry: Electrochemistry - Quick Revision Notes (MP Board)

1. Introduction & Basic Terms

Electrochemistry: It is the branch of chemistry which deals with the study of production of electricity from energy released in spontaneous chemical reactions and the use of electrical energy to bring about non-spontaneous chemical transformations.
Electrochemical Cell: A device that converts chemical energy into electrical energy (e.g., Daniell Cell).
Electrolytic Cell: A device that uses electrical energy to carry out a non-spontaneous chemical reaction.

2. Daniell Cell & Electrode Potential

Cell Representation: Zn(s) | Zn^2+(aq) || Cu^2+(aq) | Cu(s)
Oxidation Half-Cell (Anode): Zn(s) -> Zn^2+(aq) + 2e^-
Reduction Half-Cell (Cathode): Cu^2+(aq) + 2e^- -> Cu(s)
Overall Cell Reaction: Zn(s) + Cu^2+(aq) -> Zn^2+(aq) + Cu(s)

Standard Electrode Potential (`E^0`)

It is the potential of an electrode measured under standard conditions (1 M concentration of ions, 1 bar pressure, and 298 K temperature).
Standard Cell Potential (E^0_cell): E^0_cell = E^0_cathode - E^0_anode E^0_cell = E^0_right - E^0_left

3. Nernst Equation

The Nernst equation relates the cell potential to the concentration of species and temperature.

For a General Electrochemical Reaction:

aA + bB <=> cC + dD

$$\text{Cell Potential: } E = E^0 - \frac{RT}{nF} \ln \left( \frac{[C]^c [D]^d}{[A]^a [B]^b} \right)$$

At 298 K (25°C), converting natural log ($\ln$) to base 10 ($\log$):

$$E = E^0 - \frac{0.0591}{n} \log \left( \frac{[C]^c [D]^d}{[A]^a [B]^b} \right)$$

E = Cell potential under non-standard conditions
E^0 = Standard cell potential
R = Gas constant ($8.314 \text{ J K}^{-1} \text{ mol}^{-1}$)
T = Temperature in Kelvin
n = Number of electrons exchanged in the balanced equation
F = Faraday constant ($96487 \text{ C mol}^{-1}$ or approx. $96500 \text{ C mol}^{-1}$)

4. Equilibrium Constant from Nernst Equation

At equilibrium, the cell potential E_cell = 0.

$$E^0 = \frac{0.0591}{n} \log K_c \quad (\text{at } 298\text{ K})$$

K_c = Equilibrium constant

5. Electrochemical Cell and Gibbs Energy (`\Delta G`)

Work done = Electrical energy produced \Delta G = -nFE_cell
Standard Gibbs Energy: \Delta G^0 = -nFE^0_cell
Note: For a spontaneous reaction, E^0_cell must be positive and \Delta G^0 must be negative.

6. Conductance in Electrolytic Solutions

Key Definitions & Formulas:

Resistance (R): Measured in ohms ($\Omega$). R = \rho \frac{l}{A}
Resistivity ($\rho$, rho): Resistance of a conductor of unit length and unit cross-sectional area. Unit: $\Omega \text{ m}$ or $\Omega \text{ cm}$.
Conductance (G): Reciprocal of resistance. G = \frac{1}{R} (Unit: $\text{ohm}^{-1}$ or Siemens, $\text{S}$)
Conductivity ($\kappa$, kappa): Reciprocal of resistivity. $$\kappa = \frac{1}{\rho} = \frac{1}{R} \times \frac{l}{A}$$ Unit: $\text{S m}^{-1}$ or $\text{S cm}^{-1}$
Cell Constant (G*): G* = \frac{l}{A} = R \times \kappa Unit: $\text{m}^{-1}$ or $\text{cm}^{-1}$

7. Molar Conductivity ($\Lambda_m$)

It is the conducting power of all the ions produced by dissolving one mole of an electrolyte in solution.

$$\Lambda_m = \frac{\kappa \times 1000}{M}$$

\kappa = Conductivity ($\text{S cm}^{-1}$)
M = Molarity ($\text{mol L}^{-1}$)
Unit of $\Lambda_m$: $\text{S cm}^2 \text{ mol}^{-1}$ (or $\text{S m}^2 \text{ mol}^{-1}$ when concentration is in $\text{mol m}^{-3}$)

8. Variation of Conductivity and Molar Conductivity with Dilution

Conductivity ($\kappa$): Decreases with dilution because the number of current-carrying ions per unit volume of solution decreases.
Molar Conductivity ($\Lambda_m$): Increases with dilution because the total volume of solution containing 1 mole of electrolyte increases largely, overcoming the decrease in $\kappa$.

9. Kohlrausch’s Law of Independent Migration of Ions

"The limiting molar conductivity of an electrolyte can be represented as the sum of the individual contributions of the anion and cation of the electrolyte."

$$\Lambda^\circ_m (\text{AX}) = \nu_+ \lambda^\circ_+ + \nu_- \lambda^\circ_-$$

\lambda^\circ_+ and \lambda^\circ_- = Limiting molar conductivities of cation and anion respectively.
\nu_+ and \nu_- = Number of cations and anions per formula unit of electrolyte.

Applications:

Calculation of $\Lambda^\circ_m$ for weak electrolytes.
Determination of the degree of dissociation ($\alpha$) of weak electrolytes: $$\alpha = \frac{\Lambda_m}{\Lambda^\circ_m}$$
Calculation of dissociation constant ($K_a$): $$K_a = \frac{c \alpha^2}{1 - \alpha}$$

10. Electrolysis and Faraday’s Laws

Faraday’s First Law of Electrolysis:

The amount of chemical substance deposited or liberated at any electrode is directly proportional to the quantity of electricity (charge) passed through the electrolyte. m \propto Q or m = Z \cdot Q = Z \cdot I \cdot t

m = Mass of substance deposited
Q = Charge in Coulombs (Q = I \times t)
I = Current in Amperes
t = Time in seconds
Z = Electrochemical equivalent

Faraday’s Second Law of Electrolysis:

When the same quantity of electricity is passed through different electrolytes, the masses of different substances deposited at the electrodes are directly proportional to their chemical equivalent weights ($E$). $$\frac{m_1}{m_2} = \frac{E_1}{E_2}$$

11. Batteries and Fuel Cells

Primary Batteries: Cannot be recharged; reaction occurs only once (e.g., Dry Cell, Mercury Cell).
Secondary Batteries: Can be recharged by passing current in the opposite direction (e.g., Lead Storage Battery, Nickel-Cadmium cell).
- Lead Storage Battery Discharge Reactions:
  - Anode: Pb(s) + SO_4^{2-}(aq) -> PbSO_4(s) + 2e^-
  - Cathode: PbO_2(s) + SO_4^{2-}(aq) + 4H^+(aq) + 2e^- -> PbSO_4(s) + 2H_2O(l)
Fuel Cells: Galvanic cells designed to convert the energy of combustion of fuels (like $H_2, CH_4, CO$) directly into electrical energy.
- Example: Hydrogen-Oxygen Fuel Cell.
  - Anode reaction: 2H_2(g) + 4OH^-(aq) -> 4H_2O(l) + 4e^-
  - Cathode reaction: O_2(g) + 2H_2O(l) + 4e^- -> 4OH^-(aq)

12. Corrosion

It is an electrochemical process where metals are slowly eaten away by the action of atmospheric oxygen, moisture, and gases.
Rusting of Iron (Chemical Formula): Fe_2O_3 \cdot xH_2O
At Anode (Oxidation): Fe(s) -> Fe^{2+}(aq) + 2e^-
At Cathode (Reduction): O_2(g) + 4H^+(aq) + 4e^- -> 2H_2O(l)

Electrochemistry

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