Calculate K for Rearranged equations

Question

The equilibrium constant, K_c, for the following reaction is 11.5 at 345 K.

2CH₂Cl₂(g) CH₄(g) + CCl₄(g)

Calculate K_c at this temperature for the following reaction:

1/2CH₄(g) + 1/2CCl₄(g) CH₂Cl₂(g)

K_c = 

Answer 1

When you reverse a reaction, you change the sign of K

When you multiply a reaction by a constant, you raise the value of K to that constant.

2CH₂Cl₂(g) <==> CH₄(g) + CCl₄(g) ... K = 11.5

1/2 CH₄(g) + 1/2 CCl₄(g) <==> CH₂Cl₂(g) ... K = ?

Since the reaction is the reverse of the previous one, and also 1/2 of the original, we would need to change the sign of the original K, and also raise it to the 1/2 power (take the square root).

K = -√11.5 = -3.39