Le Chatelier in a Closed Reaction Vessel
A sealed 2.0 L steel vessel at 700 K contains an equilibrium mixture of nitrogen, hydrogen, and ammonia: N2(g) + 3H2(g) ⇌ 2NH3(g), with ΔH = −92 kJ per mole of N2 reacted. At equilibrium the vessel holds 0.40 mol N2, 0.60 mol H2, and 0.80 mol NH3. A technician proposes three changes: (A) compress the mixture to 1.0 L at constant temperature; (B) raise the temperature to 800 K; (C) inject 0.20 mol of argon inert gas while keeping volume constant. The plant manager wants to know which change increases the ammonia yield and which merely shifts the equilibrium without improving the total amount of ammonia produced.
1. Calculate the equilibrium constant Kc at 700 K and predict the direction of shift for change (A).
Read the worked answer
Kc calculation:
Concentrations: [N2] = 0.40/2.0 = 0.20 M; [H2] = 0.60/2.0 = 0.30 M; [NH3] = 0.80/2.0 = 0.40 M.
Kc = [NH3]^2 / ([N2][H2]^3) = (0.40)^2 / (0.20 × 0.30^3) = 0.16 / (0.20 × 0.027) = 0.16 / 0.0054 ≈ 29.6.
Change (A): compression to 1.0 L doubles all concentrations. The reaction quotient becomes Q = (0.80)^2 / (0.40 × 0.60^3) = 0.64 / (0.40 × 0.216) = 0.64 / 0.0864 ≈ 7.4, which is less than Kc (29.6). Since Q < Kc, the reaction shifts toward products, increasing ammonia. This matches Le Chatelier: fewer gas moles on the product side, so higher pressure favors NH3.
Conclusion: Kc ≈ 30; compression shifts the equilibrium to the right.
2. Evaluate changes (B) and (C): do they increase the amount of ammonia, and why?
Read the worked answer
Change (B), raising temperature to 800 K: the forward reaction is exothermic (ΔH = −92 kJ). Increasing temperature shifts the equilibrium toward the endothermic direction, i.e., toward reactants. So ammonia decreases; the rate increases but the equilibrium yield falls. This is the classic trade-off in the Haber process.
Change (C), adding argon at constant volume: adding an inert gas at constant volume does not change the partial pressures or concentrations of the reacting gases, so the equilibrium position is unchanged. (If volume were allowed to increase to keep total pressure constant, the partial pressures of reactants would fall and the equilibrium would shift toward the side with more gas moles, i.e., reactants.)
Conclusion: neither (B) nor (C) increases ammonia; only compression (A) does.