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 0.450 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

Kc = [COCL2]/[CO][Cl2]

Kc = 4.95

initially

[CO] = 0.45/0.5 = 0.9

[Cl2] = 0.45/0.5 = 0.9

[COCl2] = 0

in equilibrium

[CO] = 0.9 - x

[Cl2] = 0.9 - x

[COCl2] = 0 + x

therefore

substitute in K

Kc = [COCL2]/[CO][Cl2]

4.95= (0+x)/( 0.9 - x)( 0.9 - x)

(0.9 - x)^2= 1/4.95*x

0.9^2 -2*0.9x + x^2 =  1/4.95*x

x^2 + (-2*0.9 -1/4.95)x + 0.9^2 = 0

x = 0.5516

[CO] = 0.9 - x = 0.9 - 0.5516 = 0.3484

[Cl2] = 0.9 - x  = 0.9 - 0.5516 = 0.3484

[COCl2] = 0 + x = 0.5516