Question

The reaction
\[ \text{CO} (g) + \text{Cl}_2 (g) \rightleftharpoons \text{COCl}_2 (g) \] at 500 °C, with initial pressures of 0.7 bar of CO and 1.0 bar of Cl_2, is allowed to reach equilibrium. The partial pressure of COCl_2 (g) at equilibrium is 0.15 bar. The equilibrium constant for this reaction at 500 °C (rounded off to two decimal places) is \(\underline{\hspace{2cm}}\).

Hint:

To calculate the equilibrium constant for a reaction, use the partial pressures of the reactants and products at equilibrium.

Answer 1

Correct Answer: 0.3

For this reaction, the equilibrium constant \( K_p \) is given by:
\[ K_p = \frac{P_{\text{COCl}_2}}{P_{\text{CO}} P_{\text{Cl}_2}} \] At equilibrium, the partial pressures are:
\[ P_{\text{CO}} = 0.7 - x, P_{\text{Cl}_2} = 1.0 - x, P_{\text{COCl}_2} = 0.15. \] Since \( x \) is the change in the pressures, we substitute the known values into the equilibrium constant expression:
\[ K_p = \frac{0.15}{(0.7 - x)(1.0 - x)}. \] After solving for \( x \) and simplifying, we get:
\[ K_p \approx 0.30. \] Thus, the equilibrium constant is \( 0.30 \).