Question #44049

Consider a galvanic cell operating at $300\text{ K}$ with the following balanced cell reaction:

$\ce{M(s) + X^{2+}(aq) <=> M^{2+}(aq) + X(s)}$

The standard cell potential at $300\text{ K}$ is $E^{\circ} = 0.10\text{ V}$. The temperature coefficient of the standard cell potential at constant pressure is $\left(\frac{\partial E^{\circ}}{\partial T}\right)_P = -5.0 \times 10^{-4}\text{ V K}^{-1}$.

Assuming that the standard enthalpy ($\Delta H^{\circ}$) and standard entropy ($\Delta S^{\circ}$) of the reaction are independent of temperature, determine the standard enthalpy of the reaction at $300\text{ K}$ and the temperature ($T_{eq}$) at which the cell reaction reverses its direction of spontaneity under standard conditions.

(Given: Faraday's constant $F = 96500\text{ C mol}^{-1}$)