Question

Which of the following conditions are not suitable for a spontaneous reaction?

• A. \(\Delta H\lt 0\) and \(\Delta S\gt 0\) at low temperature
• B. \(\Delta H\lt 0\) and \(\Delta S\lt 0\) at high temperature
• C. \(\Delta H\lt 0\) and \(\Delta S\lt 0\) at low temperature
• D. \(\Delta H\gt 0\) and \(\Delta S\gt 0\) at high temperature

Hint:

Remember the spontaneity criterion: \[ \Delta G=\Delta H-T\Delta S. \] \[ \Delta H\lt 0,\ \Delta S\gt 0 \] is spontaneous at all temperatures. \[ \Delta H\gt 0,\ \Delta S\lt 0 \] is never spontaneous. \[ \Delta H\lt 0,\ \Delta S\lt 0 \] is spontaneous only at low temperature. \[ \Delta H\gt 0,\ \Delta S\gt 0 \] is spontaneous only at high temperature.

Answer 1

The Correct Option is B

Step 1: Use \(\Delta G = \Delta H - T\Delta S\) to screen each option.
Spontaneous requires \(\Delta G < 0\).

Step 2: Check option 2.
\(\Delta H < 0\), \(\Delta S < 0\): \(\Delta G = \Delta H - T\Delta S\). At high temperature, \(-T\Delta S\) becomes a large positive value. This can make \(\Delta G > 0\), so the reaction is non-spontaneous at high temperature. All other options yield \(\Delta G < 0\). \[ oxed{\Delta H \lt 0,\ \Delta S \lt 0 ext{ at high temperature}} \]