Question

For a given reaction, $\Delta H=35.5kJ{\text{mol}}^{-1}$ and $\Delta S=83.6kJ{\text{mol}}^{-1}$. The reaction is spontaneous at : (Assume that $\Delta H$ and $\Delta S$) do not vary with temperature)

• A. $T>425K$
• B. all temperatures
• C. $T>298K$
• D. $T<425K$

Answer 1

The correct option is A $T>425K$

$Thereactionis\{\begin{array}{cc}\text{spontaneous}& if\Delta G<0\\ \text{non-spontaneous}& if\Delta G>0\end{array}$

As we know that,
$\Delta G=\Delta H-T\Delta S$
$\because$ The reaction is spontaneous.
$\therefore \Delta G<0$
$\Delta H-T\Delta S<0$
$\Rightarrow T>\frac{\Delta H}{\Delta S}$

Given:-
$\Delta H=35.5KJ/mol=35500J/mol$
$\Delta S=83.6J/mol.K$
$\therefore T>\frac{35500}{83.6}$
$\Rightarrow T>425K$

Hence the reaction will be spontaneous at $T>425K$