For a specific hypothetical reaction, the standard parameters are given as $\Delta H = 40.0 ext{ k

Question

For a specific hypothetical reaction, the standard parameters are given as $\Delta H = 40.0 	ext{ kJ mol}^{-1}$ and $\Delta S = 100.0 	ext{ J K}^{-1} 	ext{ mol}^{-1}$. Assuming these intrinsic values remain constant, the reaction is guaranteed to be completely spontaneous under which temperature condition?

Professor PC Thomas Classes · Answer

(c) : The rigorous thermodynamic condition for any process to be spontaneous is that its Gibbs free energy change must be negative: $\Delta G = \Delta H - T\Delta S < 0$. This inequality mathematically requires that the temperature $T$ must exceed the ratio $\Delta H / \Delta S$. Resolving the inequality with unit matching: $T > \frac{40000 	ext{ J mol}^{-1}}{100.0 	ext{ J K}^{-1} 	ext{ mol}^{-1}} \implies T > 400 	ext{ K}$. Hence, spontaneity is only achieved when the absolute temperature is strictly greater than 400 K.