For a chemical reaction \(\mathrm{A + B \rightleftharpoons C + D}\)
(\(\Delta_r H^\Theta = 80\ \mathrm{kJ\ mol^{-1}}\)) the entropy change \(\Delta_r S^\Theta\) depends on the temperature T (in K) as \(\Delta_r S^\Theta = 2T\ (\mathrm{J\ K^{-1}\ mol^{-1}})\).
Minimum temperature at which it will become spontaneous is ___________ K. (Integer)
(\(\Delta_r H^\Theta = 80\ \mathrm{kJ\ mol^{-1}}\)) the entropy change \(\Delta_r S^\Theta\) depends on the temperature T (in K) as \(\Delta_r S^\Theta = 2T\ (\mathrm{J\ K^{-1}\ mol^{-1}})\).
Minimum temperature at which it will become spontaneous is ___________ K. (Integer)
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Correct Answer: 200
Solution and Explanation
\(\Delta_r G = 80000 - T(2T) = 80000 - 2T^2\).
The reaction is spontaneous when \(\Delta_r G \lt 0\): \(2T^2 \gt 80000\), so \(T^2 \gt 40000\) and \(T \gt 200\ \mathrm{K}\).
The minimum temperature (at which \(\Delta G = 0\)) is 200 K.
Answer: 200
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