Explain how temperature, pressure and catalyst conditions in the Haber process are chosen to compromise between reaction rate and equilibrium yield.

What this dot point is asking

You must explain how each condition is chosen by applying Le Chatelier's principle and collision theory together, and recognise that yield and rate pull in opposite directions.

The reaction

It is reversible, exothermic, and goes from $4$ moles of gas to $2$ moles of gas.

What favours high yield

Applying Le Chatelier's principle to maximise $\text{NH}_3$:

• Low temperature shifts the exothermic equilibrium toward products, increasing yield (and increasing $K_c$).
• High pressure shifts equilibrium toward the side with fewer gas moles (the $2$-mole product side), increasing yield.

Why low temperature is a problem

Although low temperature gives the highest yield, it gives a very low rate - the reaction would take impractically long. Collision theory explains this: at low temperature few collisions have the activation energy, so very little ammonia forms per unit time, even if the eventual equilibrium position is favourable.

The compromise

The conditions used industrially are therefore:

• Temperature ~ $400$-$450\ ^\circ\text{C}$: a compromise - high enough for a workable rate, low enough for a reasonable yield.
• Pressure ~ $200\ \text{atm}$ (varies by plant): high pressure boosts both yield and rate, but very high pressures are limited by the cost and safety of building strong reactors.
• Iron catalyst: speeds up attainment of equilibrium so the moderate temperature still gives a fast enough rate. It does not change the position of equilibrium or the yield.

The bigger picture

The Haber process is the textbook example of managing a chemical process: the chosen conditions are not those that maximise yield in isolation, but those that give the best overall economic outcome by balancing yield, rate and cost.