Phosgene decomposes into carbon monoxide and elemental chlorine. If the initial concentration of COCl2 (g) is 0.50 M, what is the equilibrium concentration of CO (g)? Ke = 6.6 x 10^-8

• A. 6.6 x 10^-8 M
• B. 9.1 x 10^-5 M
• C. 1.7 x 10^-8 M
• D. 1.8 x 10^-4 M

Answer: (D)

This problem tests how to apply the equilibrium constant to a decomposition reaction and how a very small K value indicates little product formation.

For COCl2 ⇌ CO + Cl2, the equilibrium expression is Ke = [CO][Cl2]/[COCl2]. Start with 0.50 M COCl2 and no CO or Cl2. Let x be the amount that decomposes, so at equilibrium [CO] = x, [Cl2] = x, and [COCl2] = 0.50 − x. Plugging in gives x^2/(0.50 − x) = 6.6 × 10^-8. Since Ke is tiny, x ≪ 0.50, so 0.50 − x ≈ 0.50. Then x^2 ≈ (6.6 × 10^-8)(0.50) = 3.3 × 10^-8, so x ≈ √(3.3 × 10^-8) ≈ 1.8 × 10^-4 M.

Thus the equilibrium concentration of CO is about 1.8 × 10^-4 M. The small value reflects that the reaction lies far to the left due to the small equilibrium constant.