Le Chatelier Reasoning in an Industrial Equilibrium
A simplified model of an exothermic equilibrium is studied in a closed vessel: A(g) + B(g) ⇌ C(g), ΔH = −92 kJ/mol. At 400 °C and 200 atm the equilibrium mixture contains 60% C by volume. A student predicts that raising the temperature will increase the yield of C because 'more energy makes the reaction go faster and produce more product'. She also predicts that adding a catalyst will shift the equilibrium to the right and increase the yield. The plant manager wants to know which changes genuinely raise the equilibrium yield of C and which only affect the rate.
1. Evaluate the student's two predictions using Le Chatelier's principle and the distinction between rate and equilibrium position.
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Temperature prediction is wrong. The forward reaction is exothermic (ΔH = −92 kJ/mol). Raising temperature favours the endothermic direction, i.e. the reverse reaction, absorbing heat. So the equilibrium shifts left, decreasing the yield of C. The student has confused 'faster' with 'more product'. Higher temperature does increase the rate of both directions, but it shifts the position toward reactants. Yield of C falls.
Catalyst prediction is wrong. A catalyst lowers the activation energy and speeds up the approach to equilibrium equally in both directions. It does not change the equilibrium position or the equilibrium yield; it only reduces the time to reach equilibrium. So the catalyst will not increase the percentage of C.
Both predictions confuse kinetics with thermodynamics. The student needs to separate 'how fast equilibrium is reached' from 'where equilibrium lies'.
2. Using the equation A(g) + B(g) ⇌ C(g), predict the effect of increasing pressure and of removing some C, and explain which change the plant should prioritise for yield.
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Pressure: Count gas moles. Left side: 1 + 1 = 2 mol gas. Right side: 1 mol gas. Increasing pressure favours the side with fewer gas moles, i.e. the right. So raising pressure increases the yield of C. This is a genuine equilibrium shift, favourable for the plant.
Removing C: Lowering the concentration of product shifts the equilibrium to the right (Le Chatelier), producing more C to replace what was removed. This also genuinely increases conversion of A and B, though it removes product continuously.
Priority for yield: The plant should use high pressure and continuous removal of C, while keeping temperature moderate (not too high, since high temperature lowers yield despite speeding the reaction). A catalyst is still valuable - not for yield, but to reach equilibrium faster at the moderate temperature. So the manager's genuine yield levers are pressure and product removal; temperature must be balanced against rate, and the catalyst is purely a rate tool.