Question

Equilibrium constant $\mathrm{(K_c)}$ is related to $\mathrm{E^\circ_{cell}}$, but not to $\mathrm{E_{cell}}$. Why ?

Hint:

ΔG° = −nFE° = −RT ln K_c (constant); E_cell changes with concentration.

Answer 1

Concept: The equilibrium constant $\mathrm{K_c}$ is a single fixed number for a reaction at a given temperature. So it can only match up with another quantity that is also fixed.

Step 1: Why it links to $\mathrm{E^\circ_{cell}}$
There is a fixed relation $\mathrm{\Delta G^\circ = -nFE^\circ_{cell} = -RT\ln K_c}$. Here $\mathrm{E^\circ_{cell}}$ is the standard cell potential, measured when all concentrations are 1 M, so it is a constant for the reaction. A constant matched with a constant works fine, so $\mathrm{K_c}$ ties neatly to $\mathrm{E^\circ_{cell}}$.

Step 2: Why it cannot link to $\mathrm{E_{cell}}$
$\mathrm{E_{cell}}$ is the potential under the actual working conditions. By the Nernst equation it depends on the real ion concentrations, and these keep changing as the cell runs and discharges. So $\mathrm{E_{cell}}$ is not a fixed number. A value that keeps changing cannot be tied to the fixed $\mathrm{K_c}$.

Answer: $\mathrm{E^\circ_{cell}}$ is a constant (linked to $\mathrm{K_c}$ through $\mathrm{-nFE^\circ = -RT\ln K_c}$), while $\mathrm{E_{cell}}$ varies with concentration, so only $\mathrm{E^\circ_{cell}}$ is related to the fixed $\mathrm{K_c}$.