Chemca Formula Sheet - Electrochemistry

CHEMCA

EXAM MASTER FORMULA SHEET

Electrochemistry

High-Yield Revision for JEE Main, Advanced & NEET

1. Electrolytic Conduction

Resistance & Conductance:

\[ R = \rho \frac{l}{A} \quad | \quad G = \frac{1}{R} = \kappa \frac{A}{l} \]

Cell Constant (\(G^*\)) = \(l/A\)

Molar Conductivity (\(\Lambda_m\)):

\[ \Lambda_m = \frac{\kappa \times 1000}{M} \]

Unit: \(S \cdot cm^2 \cdot mol^{-1}\)

Kohlrausch's Law (Independent Migration):

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

Degree of Dissoc. (\(\alpha\)): \[ \alpha = \frac{\Lambda_m}{\Lambda_m^\circ} \]

Dissoc. Constant (\(K_a\)): \[ K_a = \frac{C \alpha^2}{1-\alpha} \]

2. Laws of Electrolysis

1st Law:

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

\(Z\) = Electrochemical Equivalent

2nd Law:

\[ \frac{w_1}{w_2} = \frac{E_1}{E_2} \]

\(E\) = Equivalent Weight

1 Faraday (F): Charge of 1 mole of electrons \(\approx 96500 \text{ C}\)

3. Electrochemical Cells

Cell Potential (\(E_{cell}\)): \[ E_{cell}^\circ = E_{cathode}^\circ - E_{anode}^\circ \quad \text{(Both as SRP)} \]

Nernst Equation:

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

At 298 K:

\[ E_{cell} = E_{cell}^\circ - \frac{0.0591}{n} \log Q \]

4. Cell Thermodynamics

Gibbs Free Energy:

\[ \Delta G = -n F E_{cell} \] \[ \Delta G^\circ = -n F E_{cell}^\circ \]

Equilibrium Constant (\(K_{eq}\)):

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

Temp. Coefficient: \[ \Delta S = nF \left( \frac{dE}{dT} \right)_P \quad | \quad \Delta H = -nFE + nFT \left( \frac{dE}{dT} \right)_P \]

5. Concentration Cells & Misc

Concentration Cell:

Same electrodes, different concentrations (\(E_{cell}^\circ = 0\))

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

Corrosion (Rusting)

Anode: \(Fe \to Fe^{2+} + 2e^-\)

Cathode: \(O_2 + 4H^+ + 4e^- \to 2H_2O\)

Reference Electrode

SHE (\(E^\circ = 0.00 \text{ V}\))