Question

What will be $\Delta H$ (in cal) for the reaction $Ag ( s )+\frac{1}{2} Hg _{2} Cl _{2}( s ) \longrightarrow AgCl ( s )+ Hg ( l )$ at $25^{\circ} C$, if this reaction can be conducted in a cell for which the emf $=0.0455$ volt at this temperature with temperature coefficient $3.389 \times 10^{-4}$ volt deg $^{-1}$.

Answer 1

$\Delta S ^{\circ}=-\left[\frac{\partial\left(\Delta G^{\circ}\right)}{\partial T}\right]$
$=+ nF \frac{\partial}{\partial T}\left( E ^{\circ}\right)$
$\frac{\partial E^{\circ}}{\partial T}=+\frac{\Delta S^{\circ}}{n F}$
$\Rightarrow 3.389 \times 10^{-4}=+\frac{\Delta S^{\circ}}{96500}$
$\Delta S ^{\circ}=+3.389 \times 10^{-4} \times 96500$
$=327038.5 \times 10^{-4} J / K$
$=32.70385\, J / K$
$\Delta G ^{\circ}=- nFE ^{\circ}{ }_{\text {cell }}=-96500 \times 0.0455\, J / mol$
$=-4390.75\, J / mol$
$\Delta H ^{\circ}=\Delta G ^{\circ}+ T \Delta S ^{\circ}$
$=-4390.75+298 \times 32.70385$
$=1280\, cal$