Question

A reaction is spontaneous at low temperature but non-spontaneous at high temperature. Which of the following is true for the reaction?

• A. $\Delta$H > 0, $\Delta$S > 0
• B. $\Delta$H < 0, $\Delta$ S > 0
• C. $\Delta$H > 0, $\Delta$ S = 0
• D. $\Delta$H < 0, $\Delta$ S < 0

Answer 1

Answer: (D)

$\Delta$H < 0, $\Delta$ S < 0

Answer 2

The spontaneity of a reaction is determined by the Gibbs free energy change ($\Delta G$), which is related to enthalpy change ($\Delta H$), entropy change ($\Delta S$), and temperature ($T$) by the equation:

$$\Delta G = \Delta H - T\Delta S$$

For a reaction to be spontaneous, $\Delta G < 0$. For a reaction to be non-spontaneous, $\Delta G > 0$.

Given: Spontaneous at low T ($\Delta G < 0$) and non-spontaneous at high T ($\Delta G > 0$).

This behavior occurs when $\Delta H$ is negative (favorable for spontaneity) and $\Delta S$ is negative (unfavorable for spontaneity).

• At low T, the $-T\Delta S$ term (which is positive because $\Delta S < 0$) is small, so the negative $\Delta H$ term dominates, making $\Delta G < 0$.
• At high T, the $-T\Delta S$ term becomes large and positive, overcoming the negative $\Delta H$ term, making $\Delta G > 0$.

Therefore, both $\Delta H$ and $\Delta S$ must be negative.