Explain that reagents and reaction conditions are chosen to optimise the yield and rate for chemical synthesis processes, including the production of ammonia (Haber process) and sulfuric acid (contact process).

In the contact process for sulfuric acid production, sulfur dioxide is oxidised to sulfur trioxide according to the equation: \(2\text{SO}_2(g) + \text{O}_2(g) \rightleftharpoons 2\text{SO}_3(g)\) \(\Delta H = -197 \text{ kJ mol}^{-1}\) Which combination of temperature and catalyst conditions is chosen to optimise both the yield and rate of sulfur trioxide production?

In the Haber process for ammonia production, nitrogen and hydrogen react according to the equation: \( \text{N}_2(g) + 3\text{H}_2(g) \rightleftharpoons 2\text{NH}_3(g) \quad \Delta H = -92 \text{ kJ mol}^{-1} \) Which combination of conditions is used in industrial plants to optimise both the rate and yield of ammonia?

In the contact process for sulfuric acid production, sulfur dioxide is oxidised to sulfur trioxide using a vanadium(V) oxide catalyst at \(450\,^{\circ}\text{C}\). Explain why both the catalyst and the temperature are chosen for this step.