Question

determine the equilibrium constant for a reaction at 200 k if \\( \delta g^{\circ}=27.7 \mathrm{~kj} / \mathrm{mol} \\). \\( r=8.314 \mathrm{~j} \cdot \mathrm{mol}^{-1} \mathrm{~k}^{-1} \\).

Explanation:

Step1: Convert the unit of $\Delta G^{\circ}$

$$\Delta G^{\circ}=27.7\ \text{kJ/mol}=27700\ \text{J/mol}$$

Step2: Use the formula $\Delta G^{\circ}=-RT\ln K$

Rearrange the formula to solve for $K$: $\ln K =-\frac{\Delta G^{\circ}}{RT}$
Substitute the values: $R = 8.314\ \text{J}\cdot\text{mol}^{-1}\text{K}^{-1}$, $T = 200\ \text{K}$, $\Delta G^{\circ}=27700\ \text{J/mol}$
$$\ln K=-\frac{27700}{8.314\times200}$$
$$\ln K =-\frac{27700}{1662.8}\approx - 16.66$$

Step3: Calculate $K$

Since $\ln K=-16.66$, then $K = e^{-16.66}$
$$K\approx1.8\times10^{-7}$$

Answer:

$1.8\times 10^{-7}$