Question

A process has $\Delta H=200\, J\, mol ^{-1}$ and $\Delta S=40\, JK ^{-1}\,mol ^{-1}$. Out of the values given below, choose the minimum temperature above which the process will be spontaneous

• A. $20\, K$
• B. $4\, K$
• C. $5\, K$
• D. $12\, K$

Answer 1

Answer: (C)

$\Delta G=\Delta H-T \Delta S$
The process will be spontaneous, when
$\Delta G=-\text { ve, i.e. }|T \Delta S|>|\Delta H|$
Given : $\Delta H=200\, J\, mol ^{-1}$
and $\Delta S=40\, JK ^{-1} mol ^{-1}$
$\Rightarrow T >\frac{|\Delta H|}{|\Delta S|}=\frac{200}{40}=5\, K$
So, the minimum temperature for spontaneity of the process is $5\, K$.