Question

A reaction has a enthalpy $\left(\Delta H\right)=-40\text{kcal}$ at $400K$. Above $400K$, the reaction is spontaneous and below this temperature, it is non spontaneous. The values of Gibbs free energy ($\Delta G$) and entropy ($\Delta S$) at $400K$ are respectively:

• A. $0,-10{\text{cal K}}^{-1}$
• B. $0,100{\text{cal K}}^{-1}$
• C. $-10\text{kcal},-100{\text{cal K}}^{-1}$
• D. $0,-100{\text{cal K}}^{-1}$

Answer 1

The correct option is D $0,-100{\text{cal K}}^{-1}$

We know that,
$\Delta G=\Delta H-T\Delta S$
Given: $\Delta H=-40\text{K cal}=-40000\text{cal}$
Since, the reaction is not spontaneous below $400K$ and spontaneous above $400K$.
So, the reaction is in equilibrium at $400K$, at equilibrium $\Delta G=0$.
$0=\Delta H-T\Delta S$
$\Delta S=\frac{\Delta H}{T}=\frac{-40000}{400}=-100\text{cal/K}$