Question

For the following reaction, Kc = 255 at 1000 K.
CO(g)+Cl2(g)⇌COCl2(g)
A reaction mixture initially contains a COconcentration of 0.1470 M and a Cl2concentration of 0.173 M at 1000 K

A)What is the equilibrium concentration of COat 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

Let's prepare the ICE table

[CO] [Cl2] [COCl2]

initial 0.147 0.173 0

change -1x -1x +1x

equilibrium 0.147-1x 0.173-1x +1x

Equilibrium constant expression is

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

255.0 = (1*x)/((0.147-1*x)(0.173-1*x))

255.0 = (1*x)/(0.02543-0.32*x + 1*x^2)

6.4849-81.6*x + 255*x^2 = 1*x

6.4849-82.6*x + 255*x^2 = 0

Let's solve this quadratic equation

Comparing it with general form: (ax^2+bx+c=0)

a = 2.55*10^2

b = -82.6

c = 6.485

solution of quadratic equation is found by below formula

x = {-b + √(b^2-4*a*c)}/2a

x = {-b - √(b^2-4*a*c)}/2a

b^2-4*a*c = 2.082*10^2

putting value of d, solution can be written as:

x = {82.6 + √(2.082*10^2)}/5.1*10^2

x = {82.6 - √(2.082*10^2)}/5.1*10^2

solutions are :

x = 0.1903 and x = 0.1337

x can't be 0.1903 as this will make the concentration negative.so,

x = 0.1337

At equilibrium:

[CO] = 0.147-1x = 0.147-1*0.13367 = 0.01333 M

[Cl2] = 0.173-1x = 0.173-1*0.13367 = 0.03933 M

[COCl2] = +1x = +1*0.13367 = 0.13367 M

A)

[CO] = 0.0133 M

B)

[Cl2] = 0.0393 M

C)

[COCl2] = 0.134 M