In the Habers process, for manufacturing ammonia, the reaction $\mathrm{N}_3 + 3\mathrm{H}_2 \rightleftharpoons 2\mathrm{NH}_3$ is performed at 200 atm. pressure in the presence of a catalyst and at a temperature of $500^{\circ}\mathrm{C}$. This is considered as optimum temperature for the process because

This is an exothermic reaction, so increasing temperature decreases equilibrium yield of ammonia, meaning the yield is not maximum at $500^{\circ}\mathrm{C}$. So $\mathrm{(A)}$ is false. A catalyst does not work only at one temperature; it speeds the reaction over a range of temperatures. So $\mathrm{(B)}$ is false. The reason for choosing $500^{\circ}\mathrm{C}$ is a compromise between rate and yield. At lower temperature, equilibrium yield is better but the reaction is too slow. At higher temperature, the reaction becomes faster but the equilibrium yield falls for an exothermic process. Thus at $500^{\circ}\mathrm{C}$ the catalytic reaction rate is sufficiently fast and the yield remains appreciable. After checking all options, the correct choice is $\mathrm{D}$.