Chemistry
Chemistry
Problem
The gas-phase oxidation of sulfur dioxide by oxygen to form sulfur trioxide is an elementary step in the industrial production of sulfuric acid. The uncatalyzed reaction has an activation energy of 250 kJ mol⁻¹. A chemical plant explores two independent process modifications. • Raising the operating temperature from 600 K to 650 K. • Introducing a vanadium-based catalyst that lowers the activation energy to 180 kJ mol⁻¹. The frequency factor and the orientation requirements are assumed to be unchanged by either modification. (a) Calculate the factor by which the rate constant is expected to change when only the temperature is increased from 600 K to 650 K. (b) Calculate the factor by which the rate constant is expected to change when only the catalyst is added at 600 K. (c) Assuming that the two modifications are implemented simultaneously and that their effects are independent, determine the overall factor increase in the rate constant compared with the original uncatalyzed reaction at 600 K. (d) Evaluate which modification—temperature increase or catalysis—offers the greater improvement per unit cost if raising the temperature by 50 K costs twice as much energy per mole of product as installing and operating the catalyst. Justify your answer with quantitative reasoning. a. Part (a) b. Part (b) c. Part (c) d. Part (d)Intuitive explanation
This problem tests your understanding of how activation energy and temperature control reaction rates through the Arrhenius equation. The key insight is that the rate constant depends exponentially on the ratio , so even modest changes in temperature or activation energy can produce dramatic rate increases—but they work very differently. Temperature affects all molecular collisions uniformly, while a catalyst creates an alternative pathway with lower energy barriers. By comparing the two effects quantitatively, you'll see why industry often prefers catalysis: it's a more efficient lever for speeding up reactions.
Intuitive explanation
This problem tests your understanding of how activation energy and temperature control reaction rates through the Arrhenius equation. The key insight is that the rate constant depends exponentially on the ratio , so even modest changes in temperature or activation energy can produce dramatic rate increases—but they work very differently. Temperature affects all molecular collisions uniformly, while a catalyst creates an alternative pathway with lower energy barriers. By comparing the two effects quantitatively, you'll see why industry often prefers catalysis: it's a more efficient lever for speeding up reactions.