Question

# 13. Consider the following equilibrium reaction: SO2Cl2 (g) ⇌ Cl2 (g) + SO2 (g) Kc =...

13. Consider the following equilibrium reaction:

SO2Cl2 (g) ⇌ Cl2 (g) + SO2 (g) Kc = 2.99 x 10-7 @227o C

If the initial concentration of SO2Cl2 is 0.1680 M, determine the equilibrium concentrations of SO2Cl2, Cl2, and SO2.

I know that this type of problem requires an ICE chart but im not too sure how to solve it.

First, express Kc:

Kc = [Cl2][SO2] /[SO2Cl2]

and we know that initially:

[SO2CL2] = 0.168

[Cl2] = 0

[SO2] = 0

in equilibrium:

[SO2CL2] = 0.168 - x

[Cl2] = 0 + x

[SO2] = 0 + x

substitute in Kc

Kc = [Cl2][SO2] /[SO2Cl2]

2.99*10^-7 = x*x/(0.168-x)

solve for x

(2.99*10^-7)(0.168) - (2.99*10^-7)x = x^2

x^2 + (2.99*10^-7)x - 5.023*10^-8 = 0

x = 2.23*10^-4

so

[SO2CL2] = 0.168 - x = 0.168-2.23*10^-4 = 0.167777

[Cl2] = 0 + x = 2.23*10^-4

[SO2] = 0 + x = 2.23*10^-4

Proof:

Kc = (2.23*10^-4)(2.23*10^-4) /(0.167777) = 2.97*10^-7 which is pretty near to 2.99*10^-7 so this is correct

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