Question

${\text{Zn|Zn}}^{2+}\left(C_1\right)||{\text{Zn}}^{2+}\left(C_2\right)|\text{Zn}.$ For this cell, Gibb's free energy change, $\Delta G$ is negative if:

• A. $C_1=C_2$
• B. $C_1>C_2$
• C. $C_1<C_2$
• D. $\text{None of these}$

Answer 1

The correct option is C $C_1<C_2$

For a concentration cell according to Nernst equation, we have
$E=E^{\circ }-\frac{0.0591}{\text{n}}log\frac{C_1}{C_2}$
Here $E^{\circ }=0$ because we have same electrode (at different concentrations) as anode and cathode.
$\text{n}=2$, because it is the number of electrons involved in the oxidation or reduction.
Substituting the values we get
$\text{E}=\frac{0.0591}{2}\log \frac{C_2}{C_1}$
We have studied another equation
$\Delta G=-nFE$
to make $\Delta G=\text{negative}$ the value of $E$ will have to be positive.
Hence $C_2>C_1$