⚡ Electrochemistry & Nernst Equation

Electrochemistry investigates the interconversion between chemical Gibbs free energy and electrical potential work. Core examination focuses include non-standard Nernst potentials, concentration cell EMF, solubility product calculation via cell EMF, and Kohlrausch electrolytic conductance limits.

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1. 🔋 Galvanic Cells & Standard Reduction Potentials

$$\mathrm{\Delta }{G}^{\circ }=-nF{E}_{\text{cell}}^{\circ }$$$$E_{\text{cell}}^{\circ }=E_{\text{cathode (reduction)}}^{\circ }-E_{\text{anode (reduction)}}^{\circ }$$

• $n$: Number of moles of electrons transferred in the balanced cell reaction.
• $F$: Faraday constant ($96485\text{ C/mol}\approx 96500\text{ C/mol}$).
• Spontaneity Criterion: $\mathrm{\Delta }G<0⟺E_{\text{cell}}>0$.

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2. 🧮 The Nernst Equation

For a general cell reaction $aA+bB\to cC+dD$:

$$E_{\text{cell}}=E_{\text{cell}}^{\circ }-\frac{RT}{nF}\ln Q=E_{\text{cell}}^{\circ }-\frac{2.303RT}{nF}{\log }_{10}Q$$

At standard temperature $T=298.15\text{ K}$ (${25}^{\circ }\text{C}$):

$${\mathbf{E}}_{\text{cell}}\mathbf{=}{\mathbf{E}}_{\text{cell}}^{\circ }\mathbf{-}\frac{\mathbf{0.05916}}{\mathbf{n}}{\log }_{\mathbf{10}}\left(\frac{\mathbf{[}\mathbf{C}{\mathbf{]}}^{\mathbf{c}}\mathbf{[}\mathbf{D}{\mathbf{]}}^{\mathbf{d}}}{\mathbf{[}\mathbf{A}{\mathbf{]}}^{\mathbf{a}}\mathbf{[}\mathbf{B}{\mathbf{]}}^{\mathbf{b}}}\right)$$

2.1 Equilibrium Constant & $K_{sp}$ from Cell EMF

At equilibrium, the cell is completely discharged: $E_{\text{cell}}=0$ and $Q=K_{\text{eq}}$:

$$E_{\text{cell}}^{\circ }=\frac{0.0591}{n}{\log }_{10}{K}_{\text{eq}}⟹{\log }_{10}{K}_{\text{eq}}=\frac{n{E}_{\text{cell}}^{\circ }}{0.0591}$$

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3. ⚖️ Concentration Cells

Concentration cells generate EMF purely from differences in electrolyte concentration or gas partial pressure ($E_{\text{cell}}^{\circ }=0$):

1. Electrode Concentration Cell (Hydrogen Gas Electrodes):

   $$Pt,H_2(P_1)\mid H^{+}(C)\mid H_2(P_2),Pt$$$$E_{\text{cell}}=\frac{0.0591}{2}\log \left(\frac{P_1}{P_2}\right)(\text{spontaneous if }{P}_1>P_2)$$

2. Electrolyte Concentration Cell:

   $$Zn\mid Z{n}^{2+}(C_1)\parallel Z{n}^{2+}(C_2)\mid Zn$$$$E_{\text{cell}}=\frac{0.0591}{2}\log \left(\frac{C_2}{C_1}\right)(\text{spontaneous if }{C}_2>C_1)$$

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4. 🌊 Electrolytic Conductance & Kohlrausch's Law

4.1 Conductance Metrics

Metric	Symbol & Formula	SI Units	Behavior on Dilution
Conductance	$G=\frac{1}{R}$	$\text{S}={\mathrm{\Omega }}^{-1}=\text{mho}$	Increases (higher ion mobility)
Specific Conductivity	$\kappa =G\times \left(\frac{l}{A}\right)=\frac{G^{\ast }}{R}$	$\text{S}\cdot {\text{cm}}^{-1}={\mathrm{\Omega }}^{-1}{\text{cm}}^{-1}$	Decreases (fewer ions per unit volume)
Molar Conductivity	${\mathrm{\Lambda }}_m=\frac{1000\kappa }{M}$	$\text{S}\cdot {\text{cm}}^2\cdot {\text{mol}}^{-1}$	Increases (for both strong and weak electrolytes)
Equivalent Conductivity	${\mathrm{\Lambda }}_{\text{eq}}=\frac{1000\kappa }{N}=\frac{{\mathrm{\Lambda }}_m}{n\text{-factor}}$	$\text{S}\cdot {\text{cm}}^2\cdot {\text{eq}}^{-1}$	Increases

4.2 Strong vs. Weak Electrolytes & Kohlrausch Law

1. Debye-Hückel-Onsager Equation (Strong Electrolytes):$${\mathrm{\Lambda }}_m={\mathrm{\Lambda }}_m^{\circ }-A\sqrt{C}$$
   • Limiting molar conductivity ${\mathrm{\Lambda }}_m^{\circ }$ can be obtained by linear extrapolation ($C\to 0$).
2. Kohlrausch's Law of Independent Migration of Ions:$${\mathrm{\Lambda }}_m^{\circ }(A_x{B}_y)=x{\lambda }_m^{\circ }(A^{y+})+y{\lambda }_m^{\circ }(B^{x-})$$
3. Degree of Dissociation ($\alpha$) of Weak Electrolyte:$$\alpha =\frac{{\mathrm{\Lambda }}_m}{{\mathrm{\Lambda }}_m^{\circ }}⟹K_a=\frac{C{\alpha }^2}{1-\alpha }=\frac{C({\mathrm{\Lambda }}_m/{\mathrm{\Lambda }}_m^{\circ }{)}^2}{1-{\mathrm{\Lambda }}_m/{\mathrm{\Lambda }}_m^{\circ }}$$