Question

For the following reaction, Kc = 255 at 1000 K.
CO (g) + Cl2 (g) ⇌ COCl2 (g)
A reaction mixture initially contains a COconcentration of 0.1510 M and a Cl2concentration of 0.179 M at 1000 K.

What is the equilibrium concentration of CO at 1000 K?

What is the equilibrium concentration of Cl2 at 1000 K?

What is the equilibrium concentration of COCl2 at 1000 K?

Answer 1

CO (g)   +   Cl2 (g) <--------> COCl2 (g)
0.1510         0.179                           0           (initial)
0.1510-x     0.179-x                        x      (at equilibrium)

Kc = [COCl2]/[CO][Cl2]
255 = x / {(0.1510-x)(0.179-x)}
255 = x / (0.02703 + x^2 - 0.33*x)
6.893 + 255*x^2 - 84.15*x = x
255*x^2 - 85.15*x + 6.893 = 0

This is quadratic equation (ax^2+bx+c=0)
a = 255.000
b = -85.150
c = 6.893

Roots can be found by
x = {-b + sqrt(b^2-4*a*c)}/2a
x = {-b - sqrt(b^2-4*a*c)}/2a

b^2-4*a*c = 219.663

roots are :
x = 0.196 and x = 0.138

x can't be more than 0.1510

so, x = 0.138 M

[CO ] = 0.1510 - x = 0.1510 - 0.138 = 0.013 M
[Cl2] = 0.179 - x = 0.179 - 0.138 = 0.041 M
[COCl2] = x = 0.138 M