Question

Suppose you are studying the decomposition of PCl5 to form PCl3 and Cl2. You know that Kc = 1.20 at a given temperature. PCl5 (g) ⇌ PCl3 (g) + Cl2(g) If the initial concentration of PCl5 is 0.0920 M what will the concentrations of reactant and products be when the system reaches equilibrium?

Answer 1

ICE Table:

                    [PCl5]              [PCl3]              [Cl2]             

initial             0.092               0                   0                 

change              -1x                 +1x                 +1x               

equilibrium         0.092-1x            +1x                 +1x               

Equilibrium constant expression is
Kc = [PCl3]*[Cl2]/[PCl5]
1.2 = (1*x)(1*x)/((0.092-1*x))
1.2 = (1*x^2)/(0.092-1*x)
0.1104-1.2*x = 1*x^2
0.1104-1.2*x-1*x^2 = 0
This is quadratic equation (ax^2+bx+c=0)
a = -1
b = -1.2
c = 0.1104

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 = 1.882

roots are :
x = -1.286 and x = 8.586*10^-2

since x can't be negative, the possible value of x is
x = 8.586*10^-2

At equilibrium:
[PCl5] = 0.092-1x = 0.092-1*0.08586 = 0.00614 M
[PCl3] = +1x = +1*0.08586 = 0.08586 M
[Cl2] = +1x = +1*0.08586 = 0.08586 M

Answer:
[PCl5] = 0.00614 M
[PCl3] = 0.08586 M
[Cl2] = 0.08586 M