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Electrochemistry

Class 12 • Chapter 2
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Electrochemical Cells

Galvanic (Voltaic) Cell

Converts chemical energy of a spontaneous redox reaction ($\Delta G < 0$) into electrical energy. (e.g. Daniell Cell).

$$\text{Zn}(s) + \text{Cu}^{2+}(aq) \longrightarrow \text{Zn}^{2+}(aq) + \text{Cu}(s)$$

The "LOAN" Trick

  • Left side
  • Oxidation occurs (Loss of $e^-$)
  • Anode
  • Negative terminal
Daniell cell

Salt Bridge & SHE

Salt Bridge Functions

  • Completes the inner electrical circuit.
  • Maintains electrical neutrality in both half-cells.

Standard Hydrogen Electrode (SHE)

Used as primary reference electrode. Assigned potential is exactly $0.00\text{ V}$ at all temperatures.

Reaction: $\text{H}^+(aq) + e^- \rightleftharpoons \frac{1}{2} \text{H}_2(g)$

Standard Hydrogen Electrode

Cell Potential & Series

Standard Cell Potential

The EMF of a cell under standard conditions.

$$E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode}$$ $$E^\circ_{cell} = E^\circ_{Right} - E^\circ_{Left}$$

Electrochemical Series

  • Higher +ve $E^\circ$: Strong tendency to get reduced (Powerful oxidizing agents like $F_2$).
  • Lower -ve $E^\circ$: Strong tendency to get oxidized (Powerful reducing agents like $Li$).
  • Spontaneity: Reaction is feasible if $E^\circ_{cell} > 0$.

Nernst Equation

Calculates cell potential at any concentration/temp.

For a Complete Cell (at 298 K)

$$E_{cell} = E^\circ_{cell} - \frac{0.0591}{n} \log \frac{[\text{Products}]}{[\text{Reactants}]}$$

$n$ = number of electrons transferred.

Hydrogen Electrode & pH

$$E_{\text{H}^+/\text{H}_2} = -0.0591 \times \text{pH}$$

Concentration Cells

Same electrodes, different concentrations. $E^\circ_{cell} = 0$.

$$E_{cell} = - \frac{0.0591}{n} \log \left(\frac{C_1}{C_2}\right)$$

Gibbs & Eq. Constant

Gibbs Free Energy ($\Delta G$)

Represents max useful (non-expansion) work.

$$\Delta_r G = -nFE_{cell}$$ $$\Delta_r G^\circ = -nFE^\circ_{cell}$$

$1\text{ F} = 96487\text{ C mol}^{-1}$

Equilibrium Constant ($K_c$)

At equilibrium, $E_{cell} = 0$.

$$\log K_c = \frac{n \times E^\circ_{cell}}{0.0591}$$
$$\Delta_r G^\circ = -2.303 RT \log K_c$$

Conductance Terms

  • Resistance ($R$): Obstruction to current. $R = \rho \frac{l}{A}$.
  • Conductance ($G$): Ease of flow. $G = \frac{1}{R}$. Unit: $S$.
  • Conductivity ($\kappa$): Conductance of $1\text{ cm}^3$ solution. $\kappa = \frac{1}{\rho}$.

Cell Constant ($G^*$)

$$G^* = \frac{l}{A} \quad \implies \quad \kappa = G \times G^*$$

Molar Conductivity ($\Lambda_m$)

Conducting power of all ions from 1 mole of electrolyte.

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

Unit: $\text{S cm}^2 \text{ mol}^{-1}$. $M$ is Molarity.

Dilution Effects

Conductivity ($\kappa$): Always decreases with dilution (fewer ions per unit volume).

Molar Conductivity ($\Lambda_m$): Always increases with dilution.

Strong vs Weak Electrolytes

  • Strong: Modest increase. Debye-Hückel-Onsager equation: $\Lambda_m = \Lambda_m^\circ - A \sqrt{c}$
  • Weak: Steep increase. Degree of dissociation ($\alpha$) shoots up on dilution. Cannot find $\Lambda_m^\circ$ graphically.
Molar conductivity vs concentration

Kohlrausch's Law

Limiting molar conductivity is the sum of individual ionic contributions at infinite dilution.

$$\Lambda_m^\circ = \nu_+ \lambda_+^\circ + \nu_- \lambda_-^\circ$$

Applications

1. Finding $\Lambda_m^\circ$ for Weak Electrolytes:
$\Lambda_m^\circ(\text{CH}_3\text{COOH}) = \Lambda_m^\circ(\text{CH}_3\text{COONa}) + \Lambda_m^\circ(\text{HCl}) - \Lambda_m^\circ(\text{NaCl})$

2. Degree of Dissociation ($\alpha$): $\alpha = \frac{\Lambda_m^c}{\Lambda_m^\circ}$

3. Dissociation Constant ($K_a$): $K_a = \frac{c \alpha^2}{1 - \alpha}$

Electrolysis & Faraday

Preferential Discharge

  • Cathode: Ion with higher $E^\circ_{red}$ discharges first (e.g., $H^+$ over $Na^+$ in aq. $NaCl$).
  • Anode: Ion with lower $E^\circ_{red}$ discharges first (Exception: Overpotential of $O_2$ makes $Cl^-$ oxidize instead of $H_2O$).

Faraday's Laws

First Law: Mass deposited is proportional to charge $Q$.

$$w = Z \cdot I \cdot t$$

Second Law: When same charge passes through different electrolytes in series, masses are proportional to Equivalent Weights.

$$\frac{w_1}{w_2} = \frac{E_1}{E_2}$$

Batteries & Fuel Cells

Primary Cells (Non-rechargeable)

  • Dry Cell: Voltage drops over time. Complex $[\text{Zn}(\text{NH}_3)_4]^{2+}$ forms.
  • Mercury Cell: Constant potential ($1.35\text{ V}$) because overall reaction has no ions in solution.

Secondary Cells (Rechargeable)

  • Lead Storage: $\text{Pb}$ anode, $\text{PbO}_2$ cathode, $38\%$ $\text{H}_2\text{SO}_4$. Both form $\text{PbSO}_4$ on discharge.
  • Ni-Cd Cell: Longer life, expensive.

Fuel Cells ($H_2-O_2$)

Highly efficient ($\sim 70\%$), zero pollution (produces pure water). Used in Apollo program.

Corrosion

Electrochemical degradation of metals.

Mechanism of Rusting

Anode: $2\text{Fe} \rightarrow 2\text{Fe}^{2+} + 4e^-$
Cathode: $\text{O}_2 + 4\text{H}^+ + 4e^- \rightarrow 2\text{H}_2\text{O}$
Rust: $\text{Fe}_2\text{O}_3 \cdot x\text{H}_2\text{O}$

Prevention Methods

  • Barrier: Paint, oil, grease.
  • Galvanization: Coating iron with Zinc (more active, sacrifices itself).
  • Cathodic Protection: Connecting underground pipes to Mg blocks.
Corrosion of iron