Rate vs equilibrium trade-off

Two different measures of success

A factory needs to make a useful quantity of product quickly, not merely obtain a reaction mixture containing a high proportion of it. The reaction rate tells us how fast product forms. The equilibrium position tells us the relative amounts of products and reactants that would be present at equilibrium. For a reversible reaction, conditions that favour the desired product at equilibrium may make the reaction too slow to produce much of it each day.

Equilibrium is a useful guide to choosing conditions, but a continuously operated industrial reactor need not reach equilibrium. Engineers also have to consider how long reactants spend in the reactor, how product is separated and whether unused reactants can be recycled.

Why temperature creates a trade-off

In the Haber process, nitrogen and hydrogen react reversibly to make ammonia:

$\mathrm{N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)}$

The forward reaction releases heat. Lowering the temperature favours ammonia at equilibrium, but it also slows the reaction: fewer successful collisions occur each second. Raising the temperature speeds up ammonia formation, yet favours the reverse reaction at equilibrium, leaving a smaller proportion of ammonia in the equilibrium mixture. A compromise temperature gives a useful rate while retaining a worthwhile equilibrium yield. Ammonia can then be separated and unreacted nitrogen and hydrogen recycled.

The same temperature trade-off applies to the exothermic stage of the Contact process, which makes sulfur trioxide for sulfuric acid:

$\mathrm{2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g)}$

A lower temperature would favour sulfur trioxide at equilibrium but make production too slow. A temperature of about $400$–$450\,^{\circ}\mathrm{C}$ is used as a compromise between a high proportion of sulfur trioxide and a fast enough reaction during the gases’ short time in the reactor.

Rate and yield are not the only costs

Increasing pressure can make gas reactions faster. In both equations above, it also favours the product side because that side has fewer gas molecules. Nevertheless, very high pressures require energy and stronger, more expensive equipment, and increase the consequences of equipment failure. In the Contact process, conversion is already very high near atmospheric pressure, so the small extra gain from much higher pressure is not worth the cost.

A catalyst offers a different advantage: it increases the rates of both forward and reverse reactions without changing the equilibrium position. Engineers therefore choose conditions by weighing up product made per unit time, the attainable yield, energy use, equipment costs and safety—not by maximising just one factor.

Rate versus equilibrium

Rate means how quickly product forms; equilibrium position means the relative amounts of products and reactants at equilibrium. The highest equilibrium yield may be too slow to be commercially useful.

Industrial compromise

For the exothermic formation of ammonia or sulfur trioxide, lower temperature favours product at equilibrium but slows production. Higher temperature speeds reaction but favours reactants at equilibrium. A compromise temperature balances these effects.

Higher pressure favours the side with fewer gas molecules and can increase gas-reaction rates, but costs more and raises safety concerns. A catalyst increases rate without shifting equilibrium. Industrial reactors do not necessarily reach equilibrium; separating product and recycling reactants can increase overall output.