Question

For the following reaction, KcKc = 255 at 1000 KK.
CO (g) + Cl2 (g) ⇌ COCl2 (g)CO (g) + Cl2 (g) ⇌ COCl2 (g)
A reaction mixture initially contains a COCO concentration of 0.1550 MM and a Cl2Cl2 concentration of 0.173 MM at 1000 KK.

a) What is the equilibrium concentration of COCO at 1000 KK?

b) What is the equilibrium concentration of Cl2Cl2 at 1000 KK?

c) What is the equilibrium concentration of COCl2COCl2 at 1000 KK?

please show work!

Answer 1

ICE Table:

                    [CO]                [Cl2]               [COCl2]           

initial             0.155               0.173               0                 

change              -1x                 -1x                 +1x               

equilibrium         0.155-1x            0.173-1x            +1x               

Equilibrium constant expression is
Kc = [COCl2]/[CO]*[Cl2]
255.0 = (1*x)/((0.155-1*x)(0.173-1*x))
255.0 = (1*x)/(2.681*10^-2-0.328*x + 1*x^2)
6.838-83.64*x + 2.55*10^2*x^2 = 1*x
6.838-84.64*x + 2.55*10^2*x^2 = 0
This is quadratic equation (ax^2+bx+c=0)
a = 2.55*10^2
b = -84.64
c = 6.838

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 = 1.893*10^2

roots are :
x = 0.1929 and x = 0.13898

x can't be 0.1929 as this will make the concentration negative.so,
x = 0.13898

At equilibrium:
[CO] = 0.155-1x = 0.155-1*0.13898 = 0.01602 M
[Cl2] = 0.173-1x = 0.173-1*0.13898 = 0.03402 M
[COCl2] = +1x = +1*0.13898 = 0.13898 M

Answer:
[CO] = 0.0160 M
[Cl2] = 0.0340 M
[COCl2] = 0.139 M