Question

Phosphorus pentachloride decomposes to phosphorus trichloride at high temperatures according to the equation:  

PCl₅(g) ⇌ PCl₃(g) + Cl₂(g)

At 250° 0.250 M PCl ₅ is added to the flask. If  K _c = 1.80, what are the equilibrium concentrations of each gas?

		[PCl5] = 2.27 M, [PCl3] = 2.02 M, and [Cl2] = 2.02 M
		[PCl5] = 1.80 M, [PCl3] = 1.80 M, and [Cl2] = 1.80 M
		[PCl5] = 0.0280 M, [PCl3] = 0.222 M, and [Cl2] = 0.222 M
		[PCl5] = 0.125 M, [PCl3] = 0.474 M, and [Cl2] = 0.474 M

Answer 1

ICE Table:

Equilibrium constant expression is

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

1.8 = (1*x)(1*x)/((0.25-1*x))

1.8 = (1*x^2)/(0.25-1*x)

0.45-1.8*x = 1*x^2

0.45-1.8*x-1*x^2 = 0

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

a = -1

b = -1.8

c = 0.45

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 = 5.04

roots are :

x = -2.022 and x = 0.2225

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

x = 0.222

At equilibrium:

[PCl5] = 0.25-1x = 0.25-1*0.222 = 0.0280 M

[PCl3] = +1x = +1*0.222 = 0.222 M

[Cl2] = +1x = +1*0.222 = 0.222 M

Answer: option 3