Question

For the reaction $CO\left(g\right)+\frac{1}{2}{O}_2\left(g\right)\to C{O}_2\left(g\right),\Delta H$ and $\Delta S$ are $-283\text{kJ}$ and $-87{\text{J K}}^{-1}{\text{mol}}^{-1}$ respectively. It was intended to carry out this reaction at $1000,1500,3000$ and $3500\text{K}$. At which of these temperatures would this reaction be thermodynamically spontaneous?

• A. $1500and3500\text{K}$
• B. $3000and3500\text{K}$
• C. $1000,1500and3000\text{K}$
• D. $1500,3000and3500\text{K}$

Answer 1

The correct option is C $1000,1500and3000\text{K}$

By using the equation,
$\Delta G=\Delta H-T\Delta S\text{At}1000\text{K},\Delta G=-283-(-1000\times 0.087)=-196\text{kJ}\left(\text{spontaneous}\right)\text{At}1500\text{K},\Delta G=-283-(-1500\times 0.087)=-152.5\text{kJ}\left(\text{spontaneous}\right)\text{At}3000\text{K},\Delta G=-283-(-3000\times 0.0987)=-22\text{kJ}\left(\text{spontaneous}\right)\text{At}3500\text{K},\Delta G=-283-(-3500\times 0.087)=+21.5\text{kJ}\left(\text{Non-spontaneous}\right)$