Question

For the following reaction, K c = 255 at 1000 K . CO (g) + C l 2 (g) ⇌ COC l 2 (g) A reaction mixture initially contains a CO concentration of 0.1550 M and a C l 2 concentration of 0.170 M at 1000 K

Part A

What is the equilibrium concentration of CO at 1000 K ?

Part B

What is the equilibrium concentration of Cl2 at 1000 K ?

Part C

What is the equilibrium concentration of COCl2 at 1000 K ?

.

Answer 1

[CO] [Cl2] [COCl2]

initial 0.155 0.17 0

change -1x -1x +1x

equilibrium 0.155-1x 0.17-1x +1x

Equilibrium constant expression is

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

255.0 = (1*x)/((0.155-1*x)(0.17-1*x))

255.0 = (1*x)/(0.02635-0.325*x1*x^2)

6.71925-82.875*x255*x^2 = 1*x

6.71925-83.875*x255*x^2 = 0

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

a = 2.55*10^2

b = -83.88

c = 6.719

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 = 1.814*10^2

roots are :

x = 0.1909 and x = 0.1381

x can't be 0.1909 as this will make the concentration negative.so,

x = 0.1381

At equilibrium:

A)

[CO] = 0.155-1x

= 0.155-1*0.13805

= 0.01695 M

Answer: 0.0170 M

B)

[Cl2] = 0.17-1x

= 0.17-1*0.13805

= 0.03195 M

Answer: 0.0320 M

C)

[COCl2] = 0+1x

= 0+1*0.13805

= 0.13805 M

Answer: 0.138 M