Pasteurized milk kept at 4 °C (277 K) typically remains unspoiled for about 7 days, whereas the same milk left on a countertop at 25 °C (298 K) can sour in roughly 10 h. Assume that spoilage is governed by a single elementary biochemical reaction whose activation energy remains constant over this temperature range.
(a) Express the average time required for spoilage at each temperature in hours, then calculate the factor by which the rate of spoilage increases when the milk warms from 4 °C to 25 °C.
(b) Using the concepts of activation energy and molecular energy distributions, provide a detailed explanation for how a temperature increase of only 21 °C can produce the dramatic change in rate calculated in part (a).
(c) Sketch qualitative Maxwell–Boltzmann curves for 277 K and 298 K on the same set of axes. Indicate the position of the activation energy barrier and shade the regions corresponding to effective collisions at each temperature.
(d) Other than refrigeration, propose one practical method that could slow the spoilage process. Explain how your suggestion relates to the reaction energy profile you have discussed.