Question

Find the change in standard gibb's free energy $\left(\Delta G^{\circ }\right)$ for the following reaction.
$2C{u}^{+}\to Cu+C{u}^{2+}$
(Given : $E_{C{u}^{+}/Cu}^{\circ }=0.52\text{V},E_{C{u}^{2+}/C{u}^{+}}^{\circ }=0.16\text{V}$)

• A. $-3.474\text{kJ}$
• B. $-34.74\text{kJ}$
• C. $34.74\text{kJ}$
• D. $3.474\text{kJ}$

Answer 1

The correct option is B $-34.74\text{kJ}$

$C{u}^{+}\to Cu(E_{C{u}^{+}/Cu}^{\circ }=0.52\text{V}).....\left(1\right)C{u}^{2+}\to C{u}^{+}(E_{C{u}^{2+}/C{u}^{+}}^{\circ }=0.16\text{V}).....\left(2\right)$

reversing equation $\left(2\right)$ and adding with equation $\left(1\right)$, we get $2C{u}^{+}\to Cu+C{u}^{2+}$
The standard emf of the reaction is given by
$\therefore E^{\circ }=0.52-0.16=0.36\text{V}$
So, the change in standard gibb's free energy is
$\Delta G^{\circ }=-nF{E}^{\circ }=-1\times 96500\times 0.36=-34740\text{J}=-34.74\text{kJ}$