Question

Gibbs-Helmholtz equation relates the free energy change to the enthalpy and entropy changes of the process as $(\Delta G{)}_{PT}=\Delta H-T\Delta S$.

The magnitude of $\Delta H$ does not change much with the change in temperature but the entropy factor $T\Delta S$ changes appreciably. Thus, spontaneity of a process depends very much on temperature.

For the reaction at $298K$, $2A+B⟶C,$ $\Delta H=100Kcal$ and $\Delta S=0.020Kcal{K}^{-1}$. If $\Delta H$ and $\Delta S$ are assumed to be constant over the temperature range, at what temperature will the reaction become spontaneous?

• A. $1000K$
• B. $3500K$
• C. $5000K$
• D. $1500K$

Answer 1

The correct option is C $5000K$

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

For spontaneous process, $\Delta G=-ve<0$

or $\Delta H<T\Delta S$

$\therefore$ $T>\frac{\Delta H}{\Delta S}$ $=\frac{100Kcal}{0.02Kcal{K}^{-1}}$ $=5000K$

Hence, option C is correct.