The standard electrode potential E^- and its temperature coeffici… - Vidyadip

MCQ

The standard electrode potential $E^-$ and its temperature coefficient $\left( {\frac{{d{E^ - }}}{{dT}}} \right)$ for a cell are $2\,V$ and $-\,5\times10^{-4}\,V\,K^{-1}$ at $300\,K$ respectively. The cell reaction is

$Zn\left( s \right) + C{u^{2 + }}\left( {aq} \right) \rightleftharpoons Z{n^{2 + }}\left( {aq} \right) + Cu\left( s \right)$

Standard reaction enthalpy $\left( {{\Delta _r}{H^ - }} \right)$ ....... $\mathrm{kJ}$

✓
$-412.8$
B
$-384.0$
C
$1920$
D
$206.4$

✓

Answer

Correct option: A.

$-412.8$

a
$\Delta G\, = \, - \,nFE_{cell}\, = \, - \,2$ $ \times \,96500\, \times \,2\,\, = \, - \,386\,\,kJ$

$\Delta S=nF\left( \frac{dE}{dT} \right)=2\times 96500\,\,\times (-5\times {{10}^{-4}}J{{/}^{o}}C)=-96.5\,kJ$

at $298\,K$

$T\Delta S=298\times \,(-96.5\,\,J)\,=\,-\,28.8\,kJ$

at constant $T\,(=\,248\,K)$ and pressure

$\Delta G\, = \,\,\Delta H\, - \,\,T\Delta S{\mkern 1mu} $

$\Delta H\, = \,\,\Delta G\, + \,\,T\Delta S{\mkern 1mu} $

$=-386-28.8=-412.8\,kJ$

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