For the reduction of silver ions with copper metal, the standard cell potential was found to be $+0.46…

For the reduction of silver ions with copper metal, the standard cell potential was found to be $+0.46 \mathrm{~V}$ at $25^{\circ} \mathrm{C}$. The value of standard Gibbs energy, $\Delta \mathrm{G}^{\circ}$ will be $\left(\mathrm{F}=96500 \mathrm{C} \mathrm{mol}^{-1}\right)$
  1. $-89.0 \mathrm{~kJ}$
  2. $-89.0 \mathrm{~J}$
  3. $-44.5 \mathrm{~kJ}$
  4. $-98.0 \mathrm{~kJ}$

Solution

We know that, standard Gibbs energy, $\Delta G^{\circ}=-n \mathrm{nF}_{\text {cell }}^{\circ}$ For the cell reaction, $\begin{aligned} 2 \mathrm{Ag}^{+} & +\mathrm{Cu} \longrightarrow \mathrm{Cu}^{2+}+2 \mathrm{Ag} \\ \Delta \mathrm{E}_{\text {cell }}^{\circ} & =+0.46 \mathrm{~V} \\ \Delta \mathrm{G}^{\circ} & =-2 \times 96500 \times 0.46 \\ & =-88780 \mathrm{~J} \\ & =-88.7 \mathrm{~kJ} \approx-89.0 \mathrm{~kJ} \end{aligned}$

Asked in: NEET 2010 (Screening)

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