Question

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

Explanation:

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

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

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 $K = e^{-16.66}$
Using a calculator, $K\approx1.7\times10^{-7}$

Answer:

$1.7\times 10^{-7}$