Question

Phosphorus pentachloride decomposes according to the chemical equation

PCl5(g) <------> PCl3(g) + Cl2(g) Kc=1.80 at 250(degrees celcius)

A 0.254 mol sample of PCl5(g) is injected into an empty 3.60 L reaction vessel held at 250 °C. Calculate the concentrations of PCl5(g) and PCl3(g) at equilibrium.

Answer 1

We know that

molarity.. moles / L
Kc = [PCl3]¹ x [Cl2]¹ / [PCl5]¹

Also from the given data
[PCl5] initial = 0.283mol / 3.90L = 0.0726M

Let us assume that X mols / L of PCl5 were consumed to reach equilibrium

As per the chemical reaction we know that.

PCl5(g) <------> PCl3(g) + Cl2(g)   

at t = 0   0.0726M 0 0

at t=equilibrium 0.0726M - X X X

Kc = [PCl3]¹ x [Cl2]¹ / [PCl5]¹ = X x X / (0.0726M - X)

Kc = X² / (0.0726M - X)

putting the value of Kc we get the quadractic equation

X² + 1.80X - 0.1307 = 0

on solving we get X = 0.0699M

[PCl5] = 0.0726M - X

=0.0726M - 0.0699M = 2.7 X 10^(-3) M

[PCl3] = 0.0699M