Question

If the enthalpy and entropy change for a reaction at 298 K are -145 kJ mol$^{-1}$ and -650 J K$^{-1}$ mol$^{-1}$ respectively, which one of the following statements is correct?

• A. $\Delta G = -50$ kJ mol$^{-1}$, the reaction is spontaneous
• B. $\Delta G = -48.7$ kJ mol$^{-1}$, the reaction is non-spontaneous
• C. $\Delta G = +50$ kJ mol$^{-1}$, the reaction is spontaneous
• D. $\Delta G = 48.7$ kJ mol$^{-1}$, the reaction is non-spontaneous

Hint:

Use $\Delta G = \Delta H - T \Delta S$ to determine spontaneity: If $\Delta G<0$, the reaction is spontaneous; if $\Delta G>0$, it is non-spontaneous.

Answer 1

The Correct Option is D

We use the formula: \[ \Delta G = \Delta H - T\Delta S = -145\ \text{kJ mol}^{-1} - 298\ \text{K} \times (-0.650\ \text{kJ K}^{-1}\text{mol}^{-1}) = -145 + 193.7 = +48.7\ \text{kJ mol}^{-1} \] Since $\Delta G>0$, the reaction is non-spontaneous.