Question

Nitrosyl chloride decompeses to nitrogen monoxide and chlorine gas
2NOCL (g) <--> 2NO (g) + Cl₂(g) K= 1.6 x10-4
0.0435M nitrosyl chloride is allowed to come to equilibrium.

Find the equilibrium concentrations of all three species: [NOCl], [NO], [Cl₂]

Answer 1

K = NO^2*Cl2/(NOCl^2)

initially

NOCl = 0.0435

NO = 0

Cl2 = 0

in equilibrium

NOCl = 0.0435 - 2x

NO = 0 + 2x

Cl2 = 0 + x

then

K = NO^2*Cl2/(NOCl^2)

1.6*10^-4 = (2x)^2*x/(0.0435 - 2x)^2

(0.0435 - 2x)^2 = (4/(1.6*10^-4))*x^3

(0.0435 - 2x)^2 = 25000x^3

0.0435 ^2 + -2*0.0435 x + 4x^2 =  25000x^3

25000x^3 - 4x^2 +0.087x - 0.00189225 = 0

x = 0.004

then

NOCl = 0.0435 - 2*0.004 = 0.0355

NO = 0 + 2*0.004 = 0.008

Cl2 = 0 + 0.004 = 0.004

proof

K = NO^2*Cl2/(NOCl^2) = (0.008^2)(0.004)/(0.0355^2) = 2.0313429*10^-4 which is pretyt near to K