Question

Phosgene (COCl2) is a toxic substance that forms readily from carbon monoxide and chlorine at elevated temperatures: CO (g)+ Cl2 (g) ⇋ COCl2 (g). If 0.55 mol of each reactant is placed in a 0.500 L flask at 600 K, what are the concentrations of all three substances at equilibrium (Kc = 4.95 at this temperature)?

Answer 1

we know that

concentration = moles / volume (L)

so

initially

[CO] = 0.55 / 0.5 = 1.1

[Cl2] = 0.55 / 0.5 = 1.1

now

CO + Cl2 ---> C0Cl2

at equilibrium

[CO]eq = 1.1 - x

[Cl2]eq = 1.1 - x

[COCl2]eq = x

now

Kc = [COCl2] / [CO] [Cl2]

4.95 = [x] / [1.1-x][1.1-x]

4.95 [1.1-x]^2 = x

4.95 [ 1.21 - 2.2x + x2] = x

5.9895 - 10.89x + 4.95x2 = x

4.95x2 - 11.89x + 5.9895 = 0

x= 0.7189

so

at equilibrium

[COCl2] = x = 0.7189 M

[CO] = [Cl2] = 1.1 - x = 1.1 - 0.7189 = 0.3811 M