Question

Which of the following must be spontaneous at all temperatures?

• A. $\Delta H_{sys}=-ve;\Delta S_{sys}=-ve$
• B. $\Delta H_{sys}=-ve;\Delta S_{sys}=+ve$
• C. $\Delta H_{sys}=+ve;\Delta S_{sys}=+ve$
• D. $\Delta H_{sys}=+ve:;\Delta S_{sys}=-ve$

Answer 1

The correct option is A $\Delta H_{sys}=-ve;\Delta S_{sys}=-ve$

A reaction is spontaneous when the Gibbs free energy change ($\Delta G<0$)

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

where $\Delta H$ is the change in enthalpy and $\Delta s$ is the change in entropy.

A. $\Delta H=-Ve$ $\Delta S$ = $-ve$ at low temperatures reaction is spontaneous.

B. $\Delta H=-Ve$ $\Delta S$ = $+ve$ at all temperatures reaction is spontaneous.

C. $\Delta H=+Ve$ $\Delta S$ = $+ve$ at high temperatures reaction is spontaneous.

D. $\Delta H=+Ve$ $\Delta S$ = $-ve$ at all temperatures reaction is non-spontaneous.

Note: Low $T$ and high $T$ is relative to the entropy. Here, low $T$ means the $T-factor$ can not dominate $\Delta S-factor$. However, high $T$ means that the $T-factor$ will dominate $\Delta S-factor$.

Hence, the correct option is B.