Discussion Forum

The electrochemical cell shown below is a concentration cell $M|M^{2+}$ (saturated solution of a sparingly  soluble salt, $MX_{2})$|| $M^{2+}$ (0.001 mol dm^-3)|M. The emf of the cell depends on the difference in concentration of $M^{2+}$ ions at the two electrodes. The emf of  the cell at 298 is 0.059 V. The value of $\triangle G$ (kJ mol^-1) for the given cell is (take 1F=96500C mol^-1)

Answer:

Explanation:

For the given concentration of the cell, the cell reactions are $M \rightarrow M^{2+}$ at left hand electrode

$M^{2+} \rightarrow M$ at right hand electrode

$\Rightarrow$ $M^{2+}$(RHS electrode)$

$\rightarrow M^{2+}$ (LHS elelctrode)

$E^{0}=0$

Applying Nernst equation

$E_{cell}=0.059=0-\frac{0.059}{2}$

$\log\frac{[M^{2+}]at LHS electrode}{0.001}$
$\Rightarrow$ $\log\frac{[M^{2+}]at LHS electrode}{0.001}=-2$
$\Rightarrow$ $[M^{2+}]$ at LHS electrode

=$10^{-2} \times 0.001=10^{-5} M$

$\triangle G=-nEF=-\frac{2 \times 0.059 \times 96500}{1000} kJ$

 =$-11.4 KJ$