Question

For the following reaction, Kc = 255 at 1000 K. CO (g) + Cl2 (g) ⇌ COCl2 (g) You may want to reference (Pages 693 - 702)Section 15.8 while completing this problem.

Part A If a reaction mixture initially contains a CO concentration of 0.1550 and a Cl2 concentration of 0.175 at 1000K. What is the equilibrium concentration of CO at 1000 K? Express your answer in molarity to three significant figures. [CO]= nothing M SubmitRequest Answer Part B What is the equilibrium concentration of Cl2 at 1000 K? Express your answer in molarity to three significant figures. [Cl2]= nothing M SubmitRequest Answer Part C What is the equilibrium concentration of COCl2 at 1000 K? Express your answer in molarity to three significant figures. [COCl2]= nothing M SubmitRequest Answer

Answer 1

ICE Table:

[CO] [Cl2] [COCl2]

initial 0.155 0.175 0

change -1x -1x +1x

equilibrium 0.155-1x 0.175-1x +1x

Equilibrium constant expression is

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

255.0 = (1*x)/((0.155-1*x)(0.175-1*x))

255.0 = (1*x)/(2.712*10^-2-0.33*x + 1*x^2)

6.917-84.15*x + 2.55*10^2*x^2 = 1*x

6.917-85.15*x + 2.55*10^2*x^2 = 0

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

a = 2.55*10^2

b = -85.15

c = 6.917

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 = 1.953*10^2

roots are :

x = 0.1944 and x = 0.1396

x can't be 0.1944 as this will make the concentration negative.so,

x = 0.1396

At equilibrium:

[CO] = 0.155-1x = 0.155-1*0.13956 = 0.01544 M

[Cl2] = 0.175-1x = 0.175-1*0.13956 = 0.03544 M

[COCl2] = +1x = +1*0.13956 = 0.13956 M

A) 0.0154 M

B) 0.0354 M

C) 0.140 M