Question

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

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

Answer 1

The correct option is A T > 425 K

Solution:- (A) $T>425K$

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

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 $T>425K$.