Question

For the cell reaction, $C u^{2+}\left(C_{1}, a q\right)+Z n(s) \rightleftharpoons Z n^{2+}\left(C_{2}, a q\right)+C u(s)$ of an electrochemical cell, the change in free energy $(\Delta G)$ at a given temperature is a function of

• A. $In(C_1) $
• B. $In(C_2/C_1 ) $
• C. $In(C_2) $
• D. $In(C_1+C_2) $

Answer 1

Answer: (B)

$\Delta ; G=-n F E^{0}$
For concentration cell,
From Nernst equation,
$E=E_{c e l l}^{0}-\frac{R T}{n F} \text{In} \frac{C_{1}}{C_{2}}$
$E_{\text {cell }}^{0}=0.00 V$
$E=\frac{-R T}{n F} \text{In} \frac{C_{2}}{C_{1}}$
$E=\frac{R T}{n F} \text{In} \frac{C_{2}}{C_{1}}$
$C_{2}>C_{1}$
$E=\frac{R T}{n F} \text{In} \frac{C_{2}}{C_{1}}$
( $R, T, n$ and $F$ are constant)
therefore, $E^{0}$ is based upon $\ln \frac{C_{2}}{C_{1}}$
$\Delta ; G=-n F E^{0} $
$=-n F \times \frac{R T}{n F} \text{In} \frac{C_{2}}{C_{1}}$
$=-R T \text{In} \frac{C_{2}}{C_{1}}$
Hence, at constant temperature Gibbs free energy $\Delta ; G$ depends upon $\ln \frac{C_{2}}{C_{1}}$.