Final answer:
The equilibrium concentration of C is 1.76 x 10⁻⁵ M.
Step-by-step explanation:
Given that the equilibrium constant (Kc) for the reaction is 1.10 x 10⁻⁴, we can use this information to determine the equilibrium concentration of C. The equilibrium constant expression for this reaction is Kc = [C] / ([A]²[B]).
Let's assume that the equilibrium concentration of C is x M. Since the initial concentration of A is 0.200 M and the initial concentration of B is 0.400 M, we can set up the following equation:
1.10 x 10⁻⁴ = x / ((0.200)²(0.400))
Simplifying the equation, we have:
1.10 x 10⁻⁴ = x / (0.1600)
Multiplying both sides by 0.1600, we get:
x = (1.10 x 10⁻⁴)(0.1600)
x = 1.76 x 10⁻⁵ M