Voltage and Equilibrium

Rucete ✏ Chemistry In a Nutshell

1. Nernst Equation

The Nernst Equation is used to calculate the actual cell voltage (E) under non-standard conditions.

$$E=E^{\circ }-\frac{0.0591}{n}\log Q$$

Where:

• E° = standard cell potential
• E = cell potential at non-standard conditions
• n = number of electrons transferred
• Q = reaction quotient (as Q increases, E decreases, approaching 0 at equilibrium)

2. Sample Problem

Q: A zinc electrode is immersed in 2 M Zn²⁺ solution and a silver electrode in 2 M Ag⁺ solution. A salt bridge connects the beakers.

• Anode (oxidation): Zn(s) → Zn²⁺(aq) + 2e⁻
• Cathode (reduction): Ag⁺(aq) + e⁻ → Ag(s)
• Overall Reaction: Zn(s) + 2Ag⁺(aq) → Zn²⁺(aq) + 2Ag(s)
• Standard Cell Potential: E° = 0.80 V − (−0.76 V) = 1.56 V

3. Equilibrium Constant and Cell Voltage

To calculate the equilibrium constant (K) from standard cell potential:

$$E^{\circ }=\frac{0.0591}{n}\log K$$

Rearranged:

$$\log K=\frac{n{E}^{\circ }}{0.0591}$$

Using the example:

$$\log K=\frac{(2)(1.56)}{0.0591}\approx 52.8\Rightarrow K\approx 6\times {10}^{52}$$