Question

For the following reaction, Kc = 255 at 1000 K. CO (g) + Cl2 (g) ⇌ COCl2 (g) A reaction mixture initially contains a CO concentration of 0.1450 M and a Cl2 concentration of 0.171 M at 1000 K.

A. What is the equilibrium concentration of CO at 1000 K?

B. What is the equilibrium concentration of Cl2 at 1000 K?

C. What is the equilibrium concentration of COCl2 at 1000 K?

Answer 1

ICE Table:

[CO] [Cl2] [COCl2]

initial 0.145 0.171 0

change -1x -1x +1x

equilibrium 0.145-1x 0.171-1x +1x

Equilibrium constant expression is

Kc = [COCl2]/[CO]*[Cl2]

255.0 = (1*x)/((0.145-1*x)(0.171-1*x))

255.0 = (1*x)/(2.48*10^-2-0.316*x + 1*x^2)

6.323-80.58*x + 2.55*10^2*x^2 = 1*x

6.323-81.58*x + 2.55*10^2*x^2 = 0

This is quadratic equation (ax^2+bx+c=0)

a = 2.55*10^2

b = -81.58

c = 6.323

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 = 2.061*10^2

roots are :

x = 0.1881 and x = 0.1318

x can't be 0.1881 as this will make the concentration negative.so,

x = 0.1318

At equilibrium:

[CO] = 0.145-1x = 0.145-1*0.13181 = 0.01319 M

[Cl2] = 0.171-1x = 0.171-1*0.13181 = 0.03919 M

[COCl2] = +1x = +1*0.13181 = 0.13181 M

A) 0.0132 M

B) 0.0392 M

C) 0.132 M