The equilibrium constant, K_p, has a value of 6.5 × 10^-4 at 308 K for the reaction of nitrogen monoxide with chlorine. 2NO(g) + Cl₂(g) 2NOCl(g)
What is the value of K_c?

Question

The equilibrium constant, K_p, has a value of 6.5 × 10^-4 at 308 K for the reaction of nitrogen monoxide with chlorine. 2NO(g) + Cl₂(g) 2NOCl(g) What is the value of K_c?

Quizplus · Accepted Answer

The equilibrium constant expression for the reverse reaction is:

2NOCl(g) ⇌ 2NO(g) + Cl2(g)

The equilibrium constant for this reaction is the inverse of the given equilibrium constant:

Kc = 1/K = 1/6.5 × 10^-4 = 1.54 × 10^3

The equilibrium constant expression for the forward reaction (as given in the problem) is:

2NO(g) + Cl2(g) ⇌ 2NOCl(g)

And the equilibrium constant is:

Kc = [NOCl]^2/([NO]^2[Cl2])

Since the reaction is at equilibrium, we can use the equilibrium concentrations to calculate Kc:

Kc = (2x)^2/[(1-x)^2(1-x)] = 4x^2/(1-2x+x^2)

where x is the equilibrium concentration of NOCl (in mol/L).

Substituting the equilibrium constant and solving for x:

1.54 × 10^3 = 4x^2/(1-2x+x^2)

x = 0.063 M

Substituting this value of x back into the equilibrium constant expression:

Kc = 4(0.063)^2/(1-2(0.063)+(0.063)^2) = 1.6 × 10^-12

Therefore, the answer is choice C.

The Equilibrium Constant, Kp, Has a Value of 6

The Equilibrium Constant, K_p, Has a Value of 6