Final answer:
The value of K for the reaction 3X + 6Y ⇌ 3 Z + 3 W is 1.32 x 10^-2 M.
Step-by-step explanation:
In order to calculate the value of K for the reaction 3X + 6Y ⇌ 3 Z + 3 W, we can use the equation:
K = ([Z]^3[W]^3)/([X]^3[Y]^6)
Since the reaction is in equilibrium, we can use the concentrations at equilibrium to calculate the value of K. Plugging in the given values for [X], [Y], [Z], and [W], we get:
K = (3[Z]^3[3W]^3)/([3X]^3[6Y]^6)
K = ([Z]^3[W]^3)/([X]^3[Y]^6) x (3^3)/(3^9 x 6^6)
Substituting the given value of K = 4.2 x 10^-2, we can solve for [Z] and [W]:
K = ([Z]^3[W]^3)/([X]^3[Y]^6)
4.2 x 10^-2 = ([Z]^3[W]^3)/(2.5^3 x 500^6)
[Z]^3[W]^3 = (4.2 x 10^-2)(2.5^3)(500^6)
[Z][W] = (4.2 x 10^-2)^(1/3)(2.5/500)^(1/3)
[Z][W] = 1.32 x 10^-2 M