To solve this problem, we need to use the concept of equilibrium constant (K). The equilibrium constant is a measure of the extent to which a reaction proceeds to form products at a given temperature.
In the given equation:
2HBr <==> H2 + Br2
The equilibrium constant expression (Kc) is given by:
Kc = [H2][Br2] / [HBr]^2
Given that the equilibrium concentration of Br2 ([Br2]) is 0.0855 mol/L, we need to find the equilibrium concentration of HBr ([HBr]).
From your provided work, it seems you did the initial and change calculations correctly, but made mistakes when calculating the equilibrium concentrations.
To correct your work, let's re-evaluate the equilibrium concentrations:
Initial concentration of HBr: 0.500 mol/L
Change in concentration of HBr: -0.171 mol/L (from the balanced equation)
Equilibrium concentration of HBr: 0.500 - 0.171 = 0.329 mol/L
Now, we can substitute the equilibrium concentrations into the equilibrium constant expression:
Kc = [H2][Br2] / [HBr]^2
= (0.0855 mol/L) / (0.329 mol/L)^2
Calculating this expression, we get:
Kc ≈ 0.725
Thus, the value of the equilibrium constant (Kc) is approximately 0.725.