Question

At 250 degree Celsius, 0.188 M PCl5 is added to an empty flask. If Kc=1.80, what is the equilibrium concentration of PCl5? (Requires the quadratic formula).

PCl5(g)->-<-PCl3)g) + Cl2(g)

Please explain in steps.

Answer 1

ICE Table:

Equilibrium constant expression is

Kc = [PCl3]*[Cl2]/[PCl5]

1.8 = (1*x)(1*x)/((0.188-1*x))

1.8 = (1*x^2)/(0.188-1*x)

0.3384-1.8*x = 1*x^2

0.3384-1.8*x-1*x^2 = 0

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

a = -1

b = -1.8

c = 0.3384

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 = 4.594

roots are :

x = -1.972 and x = 0.1716

since x can't be negative, the possible value of x is

x = 0.1716

At equilibrium:

[PCl5] = 0.188-1x = 0.188-1* 0.1716 = 0.0164 M

Answer: 0.0164 M