Please help me solve this

Question

Phosgene, COCl2(g) is an extremely toxic gas. It was used during World War 1. Today it is used to manufacture pesticides, pharmaceuticals, dyes, and polymers. It is prepared by mixing carbon monoxide and chlorine gas.

CO(g) + Cl2 ⇌ COCl2(g)

0.055 mol of CO and 0.072 mol of Cl2 are placed in a 5.0 L container. At 870 K, the equilibrium constant is 0.20. What are the equilibrium concentrations of the mixture at 870K?

Answer 1

[CO] = 0.055 mol / 5.0 L = 0.011 M

[Cl₂] = 0.072 mo / 5.0 L = 0.0144 M

Set up an ICE talbe:

CO(g) + Cl₂(g) ===> COCl₂(g)

0.011........0.0144................0.........Initial

-x............-x......................+x.........Change

0.011-x...0.0144-x..............x..........Equilibrium

K = [COCl₂] / [CO][Cl₂]

0.20 = (x) / (0.011-x)(0.0144-x)

x = 0.2 (0.000158 - 0.0254x + x²)

Solve for x and x = 3.14x10^-5 (be sure to check the math)

[CO] = 0.011 - 0.0000314 = 0.011 M

[Cl₂] = 0.0144 - 0.0000314 = 0.014 M

[COCl₂] = 0.0000314 M