At equilibrium a mixture of n2, h2, nh3 gas at 500◦c is determined to consist of 0.551 mol/l of n2, 0.400 mol/l of h2, and 0.184 mol/l of nh3. what is the equilibrium constant for the reaction

The balanced equation for the reaction is
N₂(g) + 3H₂(g) ⇄ 2NH₃(g)

The equilibrium constant, k for the reaction can be written as
k = [NH₃(g)]² / [N₂(g)][H₂(g)]³

The given concentration are at equilibrium state. Hence, we can use those directly for the calculation.

[NH₃(g)] = 0.184 mol/L
[N₂(g)] = 0.551 mol/L
[H₂(g)] = 0.400 mol/L

By applying the formula,
k = (0.184 mol/L)² / ((0.551 mol/L) x (0.400 mol/L)³)
k = 0.960 mol⁻² L²

Hence, the equilibrium constant for the reaction at 500 °C is 0.960 mol⁻² L²

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