Question

$2A+B\to C$
For the above reaction at $298\text{K}$, $\Delta H=400{\text{kJ mol}}^{-1}$ and $\Delta S=0.2{\text{kJ K}}^{-1}{\text{mol}}^{-1}$. At what temperature, will the reaction become spontaneous considering the $\Delta H$ and $\Delta S$ to be constant over the temperature range?

• A. $T>1200\text{K}$
• B. $T<2000\text{K}$
• C. $T<1200\text{K}$
• D. $T>2000\text{K}$

Answer 1

The correct option is D $T>2000\text{K}$

$2A+B\to C$
Here $\Delta H=400{\text{kJ mol}}^{-1}$ and $\Delta S=0.2{\text{kJ K}}^{-1}{\text{mol}}^{-1}$
For a spontaneous reaction, $\Delta G$ has to be negative.
We know that $\Delta G=\Delta H-T\Delta S$
As $\Delta H$ is positive, then
$T\Delta S>\Delta H\Rightarrow T>\frac{\Delta H}{\Delta S}\Rightarrow T>\frac{400}{0.2}\Rightarrow T>2000\text{K}$