Final answer:
The equilibrium concentration of N₂ in the nitrogen fixation reaction can be calculated using the given values and the equilibrium expression. The equilibrium concentration of N₂ is approximately 3.2 x 10⁻³ M at 500 degrees C.
Step-by-step explanation:
The equilibrium constant, K, is a measure of the extent of a reaction at equilibrium. It is equal to the ratio of the product concentrations raised to their coefficients divided by the reactant concentrations raised to their coefficients.
In the given nitrogen fixation reaction, 32(g) + N₂(g) ⇌ 2NH₃(g), K = 6.0 x 10⁻² at 500 degrees C.
Given that the equilibrium concentrations of H₂ and NH₃ are 0.250 M and 0.050 M respectively, we can use these values to calculate the equilibrium concentration of N₂.
Using the equilibrium expression, K = [NH₃]²/([N₂][H₂]³), we can substitute the given concentrations to find:
K = (0.050 M)²/((x)(0.250 M)³)
Simplifying the expression and solving for x, we find the equilibrium concentration of N₂ to be approximately 3.2 x 10⁻³ M.