Final answer:
The shelf life of diphenhydramine is the time until only 90% remains active, and it decomposes via first-order kinetics with a rate constant of 6.0 x 10^-4 day^-1 at 25 °C. Half-life is related to the rate constant, important for shelf life calculation.
Step-by-step explanation:
The shelf life of a drug like diphenhydramine, used in allergy medications, is determined by the time during which 90% of it remains active. Diphenhydramine decomposes by first-order kinetics, which means the rate at which it becomes inactive is proportional to its current amount. The rate constant (k) for diphenhydramine has been given as 6.0 x 10^-4 day^-1 at 25 °C.
The relationship between the half-life of a drug and its rate constant in first-order kinetics is represented by the formula: t1/2 = 0.693 / k. Since half-life is required to calculate the shelf life, we can use this formula to determine how long it takes for the concentration of diphenhydramine to decrease to half of its original amount.
However, to calculate the shelf life, one would need to apply the integrated first-order rate law and solve for time when only 90% of the drug remains. While the half-life remains constant regardless of the concentration for first-order reactions, different calculations are needed for determining the exact shelf life based on the given rate constant and percentage of activity remaining.