In a competing pathway scenario where A can form P via k1 and Q via k2, what is the observed rate of disappearance of A?

In a competing pathway scenario where A can form P via k1 and Q via k2, what is the observed rate of disappearance of A?

• A. -(d[A]/dt) = k1 [A], with kobs = k1
• B. -(d[A]/dt) = k2 [A], with kobs = k2
• C. -(d[A]/dt) = (k1 + k2) [A], with kobs = max(k1, k2)
• D. -(d[A]/dt) = (k1 + k2) [A], with kobs = k1 + k2

Answer: (D)

When a species A is removed by two parallel first-order routes, the overall disappearance rate is the sum of both routes. The rate of loss through the first path is k1[A] and through the second is k2[A]. Since these occur simultaneously, the total rate of disappearance is k1[A] + k2[A] = (k1 + k2)[A]. This means the observed first-order rate constant is kobs = k1 + k2, and the rate law is -(d[A]/dt) = (k1 + k2)[A]. The idea is that both pathways contribute to consume A, so you add the two rates rather than taking just one.

When a species A is removed by two parallel first-order routes, the overall disappearance rate is the sum of both routes. The rate of loss through the first path is k1[A] and through the second is k2[A]. Since these occur simultaneously, the total rate of disappearance is k1[A] + k2[A] = (k1 + k2)[A]. This means the observed first-order rate constant is kobs = k1 + k2, and the rate law is -(d[A]/dt) = (k1 + k2)[A]. The idea is that both pathways contribute to consume A, so you add the two rates rather than taking just one.