Two different redox reactions, A and B

CHEMISTRY · Multi-part · A Level · Chemistry · Thermodynamics · Thermodynamics

Problem

Two different redox reactions, A and B, are being considered as potential cathode processes for a new molten-salt battery. At

1\,\text{bar}

, each reaction exhibits a linear dependence of

\Delta G

on temperature over the range

300\,\text{K}

–

1200\,\text{K}

. A research summary states: • Reaction A: the

\Delta G

–

T

line intersects the

\Delta G

axis at

-60\,\text{kJ mol}^{-1}

and has a slope of

+0.050\,\text{kJ mol}^{-1}\,\text{K}^{-1}

. • Reaction B: the

\Delta G

–

T

line intersects the

\Delta G

axis at

+40\,\text{kJ mol}^{-1}

and has a slope of

-0.030\,\text{kJ mol}^{-1}\,\text{K}^{-1}

. Assume both lines remain linear across the stated temperature range. (a) For each reaction, derive an explicit expression for

\Delta G

as a function of

T

(in

\text{K}

). (b) Determine the temperature at which each reaction becomes nonspontaneous. Show all algebraic steps. (c) Identify the temperature interval, if any, over which both reactions are simultaneously spontaneous. Explain how you arrived at that interval. (d) The battery is expected to operate between

650\,\text{K}

and

900\,\text{K}

. Recommend which reaction should be chosen as the cathode process and defend your recommendation with quantitative evidence.

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