Explain the need for a temperature compromise in the Haber Process: N2(g) + 3 H2(g) ⇌2 NH3(g) (ΔH = -92 kJ mol-1)

The Haber process is used to produce ammonia (NH3), so we want the equilibrium position to be as far over to the right hand side of the equation as possible to maximise the yield of NH3. As the enthalpy for the forward reaction is negative, the reaction is exothermic: it gives out energy. According to Le Chatelier's principle, a dynamic equilibrium will shift to oppose a change in its surroundings. This means that lowering the energy of the surroundings will cause the equilibrium to shift to give out more energy and heat them back up. In this case, the exothermic reaction that accomplishes this is the forward reaction: the one we want! As a result, a lower temperature should produce a higher yield of ammonia from the equilibrium reaction.
However lower temperatures lead to slower reaction rates. The particles have less energy, so move more slowly, and don't collide as much, or with as much energy. Low temperatures make our reaction very slow, so even with a high yield, we won't get much ammonia unless we wait a very long time. Therefore we need a compromise between a low temperature (for our equilibrium position) and a high temperature (for a high rate of reaction.) The temperature often used in industry is ~400 - 450 °C.