Question

For the following reaction, Kc = 255 at 1000 K.
CO (g) + Cl2 (g) ⇌ COCl2 (g)

If a reaction mixture initially contains a CO concentration of 0.1530 and a Cl2 concentration of 0.174 at 1000K. 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

ICE Table:

                    [CO]                [Cl2]               [COCl2]           

initial             0.153               0.174               0                 

change              -1x                 -1x                 +1x               

equilibrium         0.153-1x            0.174-1x            +1x               

Equilibrium constant expression is
Kc = [COCl2]/[CO]*[Cl2]
255.0 = (1*x)/((0.153-1*x)(0.174-1*x))
255.0 = (1*x)/(0.02662-0.327*x + 1*x^2)
6.78861-83.385*x + 255*x^2 = 1*x
6.78861-84.385*x + 255*x^2 = 0
This is quadratic equation (ax^2+bx+c=0)
a = 2.55*10^2
b = -84.38
c = 6.789

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 = 1.964*10^2

roots are :
x = 0.1929 and x = 0.138

x can't be 0.1929 as this will make the concentration negative.so,
x = 0.138

At equilibrium:
1)
[CO] = 0.153-1x = 0.153-1*0.13798 = 0.01502 M
Answer: 0.0150 M

2)
[Cl2] = 0.174-1x = 0.174-1*0.13798 = 0.03602 M
Answer: 0.0360 M

3)
[COCl2] = +1x = +1*0.13798 = 0.13798 M
Answer: 0.138 M