Le Chatelier's Principle in Ammonia Synthesis
The Haber process for ammonia synthesis is given by: [ \text{N}_2(g) + 3\text{H}_2(g) \rightleftharpoons 2\text{NH}_3(g) \quad \Delta H = -92.4, \text{kJ/mol} ] A chemical engineer operates the reactor at 450°C and 200 atm with a catalyst. At equilibrium, the mixture contains 12% NH3 by volume. The engineer considers two changes: (1) increasing the pressure to 300 atm while keeping temperature constant, and (2) increasing the temperature to 500°C while keeping pressure constant. The engineer wants to maximize the equilibrium yield of ammonia but is concerned about reaction rate and energy costs.
1. Predict and explain the effect of each change on the equilibrium yield of ammonia. Justify your answer using Le Chatelier's principle.
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Change (1): Increasing pressure shifts the equilibrium to the side with fewer moles of gas. The reaction has 4 moles of gas on the left and 2 moles on the right. An increase in pressure favors the formation of NH3 (right side), so the equilibrium yield of ammonia increases. Change (2): Increasing temperature favors the endothermic direction. Since the forward reaction is exothermic (ΔH = -92.4 kJ/mol), the reverse reaction is endothermic. Therefore, an increase in temperature shifts the equilibrium to the left, decreasing the yield of ammonia. Thus, higher pressure increases yield, while higher temperature decreases yield.
2. The engineer decides to increase the pressure to 300 atm but also considers raising the temperature to 500°C to speed up the reaction. Discuss the trade-off between yield and rate, and suggest which condition (450°C or 500°C) is more suitable for maximizing ammonia production. Consider that the reaction is exothermic and that the catalyst is effective in both cases.
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Increasing temperature increases the reaction rate, so equilibrium is reached faster, but it decreases the equilibrium yield because the reaction is exothermic. At 500°C, the rate is higher but the equilibrium constant is smaller, leading to lower NH3 concentration at equilibrium. At 450°C, the yield is higher but the rate is slower. Since the goal is to maximize ammonia production, one must balance yield and rate. Typically, a moderate temperature like 450°C is chosen because it provides a reasonable rate with a higher equilibrium yield. The catalyst allows the reaction to proceed at a sufficient rate at 450°C. Therefore, 450°C is more suitable for maximizing ammonia production, especially when combined with high pressure.