Single Choice

The standard electrode potential $$E^{\ominus}$$ and its temperature coefficient $$\left (\dfrac {dE^{\ominus}}{dT}\right )$$ for a cell are $$2V$$ and $$-5 \times 10^{-4} VK^{-1}$$ at $$300\ K$$ respectively. The cell reaction is $$Zn(s) + Cu^{2+}(aq) \rightarrow Zn^{2+}(aq + Cu(s)$$ The standard reaction enthalpy $$(\triangle_{r}H^{\ominus})$$ at $$300\ K$$ in $$kJ\ mol^{-1}$$ is: $$[Use\ R = 8jK^{-1} mol^{-1}$$ and $$F = 96,000\ Cmol^{-1}]$$

A$$-412.8$$
Correct Answer
B$$-384.0$$
C$$206.4$$
D$$192.0$$

Solution

We have,
$$\Delta G=\Delta H-\Delta S$$ ---------(1)
Also,
$$\Delta G=-nFE_{cell}=-2\times 96500\times 2=-4\times 96500$$
Now, $$\Delta S=nF\dfrac{dE}{dT}=2\times 96500 \times (-5\times 10^{-4})=96.5 J$$
Now from equation (1)
$$\Delta H=\Delta G+T\Delta S=-4\times 96500+298\times (-96.5)\approx -412.8$$

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