Chemca Formula Sheet - Electrochemistry

CHEMCA

EXAM MASTER FORMULA SHEET

Electrochemistry

High-Yield Revision for JEE Main, Advanced & NEET

1. Electrolytic Conduction & Kohlrausch's Law

Conductivity / Specific Conductance ($\kappa$)

\[ R = \rho \frac{l}{A} \implies G = \frac{1}{R} \implies \kappa = G \times \left(\frac{l}{A}\right) \]

$G$ = Conductance ($\Omega^{-1}$ or $S$), $l/A = G^*$ (Cell Constant in $\text{cm}^{-1}$).

$\kappa$ DECREASES with dilution!

Molar ($\Lambda_m$) & Equivalent ($\Lambda_{eq}$) Conductivity

\[ \Lambda_m = \frac{\kappa \times 1000}{M} \quad | \quad \Lambda_{eq} = \frac{\kappa \times 1000}{N} \]

Unit: $S \cdot \text{cm}^2 \cdot \text{mol}^{-1}$ or $S \cdot \text{cm}^2 \cdot \text{eq}^{-1}$

$\Lambda_m$ and $\Lambda_{eq}$ INCREASE with dilution!

Kohlrausch's Law (Independent Migration of Ions):

Limiting molar conductivity ($\Lambda_m^\circ$) of an electrolyte is the sum of limiting ionic conductivities.

\[ \Lambda_m^\circ (A_xB_y) = x \lambda_m^\circ (A^{y+}) + y \lambda_m^\circ (B^{x-}) \]

Debye-Hückel-Onsager Eq:

\[ \Lambda_m = \Lambda_m^\circ - A\sqrt{C} \]

(For Strong Electrolytes only)

Weak Electrolytes ($\alpha$ & $K_a$):

\[ \alpha = \frac{\Lambda_m}{\Lambda_m^\circ} \quad \text{and} \quad K_a = \frac{C \alpha^2}{1-\alpha} \]

2. Electrolysis & Faraday's Laws

Faraday's First Law

\[ w = Z \cdot Q = Z \cdot I \cdot t = \frac{E \cdot I \cdot t}{96500} \]

Mass deposited ($w$) is proportional to charge ($Q$).
1 Faraday ($F$) = $96500 \text{ C/mol of } e^-$

Faraday's Second Law

\[ \frac{w_1}{w_2} = \frac{E_1}{E_2} \implies \frac{w}{E} = \text{No. of Equivalents} \]

When same charge is passed, equivalents deposited are equal.
$E$ = Equivalent Weight = $\frac{\text{Molar Mass}}{\text{n-factor}}$

Preferential Discharge Theory (Aqueous Electrolysis)

In aqueous solutions, water competes with ions at the electrodes.

At Cathode (Reduction):

Species with Higher SRP (Standard Reduction Potential) reduces first.

$\ce{Ag+ > Cu^2+ > H+ > Pb^2+ > Fe^2+ > Zn^2+ > \text{Water} > Al^3+ > Mg^2+ > Na+}$

*Alkali/Alkaline earth metals are NEVER reduced from aqueous solutions (Water reduces to $H_2$ gas instead).*

At Anode (Oxidation):

Species with Lower SRP (Higher SOP) oxidizes first.

$\ce{I- > Br- > Cl- > OH- (\text{Water}) > NO3- > SO4^2- > F-}$

*Polyatomic anions ($\ce{SO4^2-, NO3-}$) and Fluoride are NEVER oxidized from aq. solutions (Water oxidizes to $O_2$ gas instead).*

3. Galvanic Cells & Nernst Equation

Standard Cell Potential ($E^\circ$)

\[ E_{cell}^\circ = E_{cathode}^\circ - E_{anode}^\circ \]

Note: Both values must be Standard Reduction Potentials (SRP).

Concentration Cell

Same electrodes, different concentrations. $E_{cell}^\circ = 0$.

\[ E_{cell} = -\frac{0.0591}{n} \log \frac{[C_{anode}]}{[C_{cathode}]} \]

The Nernst Equation

\[ E_{cell} = E_{cell}^\circ - \frac{2.303 RT}{nF} \log Q \]

At Standard Temp (298 K):

\[ E_{cell} = E_{cell}^\circ - \frac{0.0591}{n} \log \frac{[\text{Products}]^x}{[\text{Reactants}]^y} \]

At Equilibrium ($E_{cell} = 0, Q = K_{eq}$):

\[ E_{cell}^\circ = \frac{0.0591}{n} \log K_{eq} \]

4. Cell Thermodynamics

Thermodynamic Quantity	Equation	Significance
Gibbs Free Energy ($\Delta G$)	$\Delta G = -n F E_{cell}$ $\Delta G^\circ = -n F E_{cell}^\circ$	Maximum useful electrical work obtained from a galvanic cell. $\Delta G < 0$ (Spontaneous) requires $E_{cell} > 0$.
Entropy Change ($\Delta S$)	$\Delta S = nF \left( \frac{\partial E}{\partial T} \right)_P$	$\left( \frac{\partial E}{\partial T} \right)_P$ is the Temperature Coefficient of the cell.
Enthalpy Change ($\Delta H$)	$\Delta H = -nFE + nFT \left( \frac{\partial E}{\partial T} \right)_P$	Derived from $\Delta G = \Delta H - T\Delta S$.

5. Commercial Cells, Batteries & Corrosion

Lead Storage Battery (Secondary)

Electrolyte: 38% $\ce{H2SO4}$ solution.

Discharging Reactions (Galvanic):
Anode: $\ce{Pb + SO4^2- -> PbSO4 + 2e-}$
Cathode: $\ce{PbO2 + 4H+ + SO4^2- + 2e- -> PbSO4 + 2H2O}$

During charging (Electrolytic cell), the reactions are reversed and $\ce{H2SO4}$ is regenerated.

$\ce{H2 - O2}$ Fuel Cell

Converts combustion energy of fuels directly into electrical energy. Efficiency ~70%.

Anode: $\ce{2H2(g) + 4OH-(aq) -> 4H2O(l) + 4e-}$ Cathode: $\ce{O2(g) + 2H2O(l) + 4e- -> 4OH-(aq)}$

Net: $\ce{2H2(g) + O2(g) -> 2H2O(l)}$

Corrosion (Rusting of Iron)

Electrochemical phenomenon where metal is oxidized by oxygen in presence of moisture.

Anodic Spot:

$\ce{2Fe(s) -> 2Fe^2+ + 4e-}$

Cathodic Spot:

$\ce{O2(g) + 4H+(aq) + 4e- -> 2H2O(l)}$

The $\ce{Fe^2+}$ ions are further oxidized to $\ce{Fe^3+}$ to form Rust: $\ce{Fe2O3 \cdot xH2O}$

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