At the equilibrium constant for the reaction has the value . Are the following mixtures

Chapter 20, Problem 15.45

(choose chapter or problem)

At \(100^{\circ} \mathrm{C}\) the equilibrium constant for the reaction \(\mathrm{COCl}_2(\mathrm{~g}) \rightleftharpoons \mathrm{CO}(\mathrm{g})+\mathrm{Cl}_2(\mathrm{~g})\) has the value \(K_c=\) \(2.19 \times 10^{-10}\). Are the following mixtures of \(\mathrm{COCl}_2\), CO, and \(\mathrm{Cl}_2\) at \(100^{\circ} \mathrm{C}\) at equilibrium? If not, indicate the direction that the reaction must proceed to achieve equilibrium.

(a) \(\left[\mathrm{COCl}_2\right]=2.00 \times 10^{-3} \mathrm{M}, \quad[\mathrm{CO}]=3.3 \times 10^{-6} \mathrm{M}\), \(\left[\mathrm{Cl}_2\right]=6.62 \times 10^{-6} \mathrm{M}\);

(b) \(\left[\mathrm{COCl}_2\right]=4.50 \times 10^{-2} \mathrm{M}\), \([\mathrm{CO}]=1.1 \times 10^{-7} \mathrm{M},\left[\mathrm{Cl}_2\right]=2.25 \times 10^{-6} \mathrm{M}\);

(c) \(\left[\mathrm{COCl}_2\right]=\) \(0.0100 \mathrm{M},[\mathrm{CO}]=\left[\mathrm{Cl}_2\right]=1.48 \times 10^{-6} \mathrm{M}\)