Nernst Equation & Electrochemistry | Class 12 Chemistry Notes & Quiz

Nernst Equation

Electrochemistry Class 12 | Theory, Formulas, and Practice

1. Introduction

The Nernst Equation provides a mathematical relationship between the electrode potential ($E$), the standard electrode potential ($E^\circ$), temperature, and the concentration of metal ions. It enables the calculation of cell potential under non-standard conditions.

2. The General Equation

For a general electrode reaction: $M^{n+} (aq) + ne^- \rightarrow M(s)$

$$ E_{(M^{n+}/M)} = E^\circ_{(M^{n+}/M)} - \frac{RT}{nF} \ln \frac{[M(s)]}{[M^{n+}(aq)]} $$

Where:

• $R$ = Gas constant ($8.314 \, J K^{-1} mol^{-1}$)
• $F$ = Faraday constant ($96487 \, C \approx 96500 \, C$)
• $T$ = Temperature in Kelvin
• $[M(s)]$ = Concentration of solid (taken as unity, 1)

3. Equation at 298 K ($25^\circ C$)

Substituting the values of R, T (298K), and F, and converting natural log ($\ln$) to base-10 log ($\log$) by multiplying by 2.303:

$$ E_{cell} = E^\circ_{cell} - \frac{0.0591}{n} \log Q $$

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

$$ Q (\text{Reaction Quotient}) = \frac{[C]^c [D]^d}{[A]^a [B]^b} $$

4. Equilibrium Constant ($K_c$)

At chemical equilibrium, the cell potential becomes zero ($E_{cell} = 0$).

$$ 0 = E^\circ_{cell} - \frac{0.0591}{n} \log K_c $$

$$ E^\circ_{cell} = \frac{2.303 RT}{nF} \log K_c \quad \text{or} \quad \log K_c = \frac{n E^\circ_{cell}}{0.0591} $$

5. Relation with Gibbs Free Energy

The electrical work done by the cell corresponds to the decrease in Gibbs Free Energy.

$$ \Delta G^\circ = -nFE^\circ_{cell} $$ $$ \Delta G^\circ = -2.303 RT \log K_c $$

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