Cell Potential

Standard cell EMF: $E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode}$

Nernst equation (general form): $E = E^\circ - \frac{RT}{nF}\ln Q$

Nernst equation at 25°C (298 K): $E = E^\circ - \frac{0.0592}{n}\log Q$

Note: $\frac{2.303RT}{F}\bigg|_{298K} = \frac{2.303 \times 8.314 \times 298}{96485} = 0.05916 \approx 0.0592 \text{ V}$

Equilibrium and Thermodynamics

At equilibrium (E = 0, Q = K): $E^\circ = \frac{0.0592}{n}\log K \quad \Leftrightarrow \quad \log K = \frac{nE^\circ}{0.0592}$

Gibbs energy and EMF: $\Delta G^\circ = -nFE^\circ$ $\Delta G = -nFE = \Delta G^\circ + RT\ln Q$

Faraday constant: $F = 96485 \approx 96500 \text{ C mol}^{-1}$

Faraday's Laws

Mass deposited (Faraday's combined law): $w = ZIt = \frac{MIt}{nF}$

Electrochemical equivalent: $Z = \frac{M}{nF} \text{ (g C}^{-1}\text{)}$

Charge = current × time: $Q_{charge} = It \text{ (in Coulombs, t in seconds)}$

Conductance

Specific conductance: $\kappa = \frac{1}{\rho} = G \times \frac{l}{A} \quad [\text{S cm}^{-1}]$

Molar conductivity: $\Lambda_m = \frac{\kappa \times 1000}{M} \quad [\text{S cm}^2 \text{mol}^{-1}]$

where M = molarity in mol/L.

Debye-Hückel-Onsager (strong electrolytes): $\Lambda_m = \Lambda^\circ_m - A\sqrt{C}$

Kohlrausch's law (limiting molar conductivity): $\Lambda^\circ_m = \nu_+\lambda^\circ_+ + \nu_-\lambda^\circ_-$

Degree of dissociation (weak electrolytes): $\alpha = \frac{\Lambda_m}{\Lambda^\circ_m}$

Acid dissociation constant from conductance: $K_a = \frac{C\alpha^2}{1-\alpha} \approx C\alpha^2 \text{ (if } \alpha \ll 1\text{)}$

Key Numerical Values