Which differential equation correctly describes the rate of change of B in a consecutive A → B → C mechanism?

Which differential equation correctly describes the rate of change of B in a consecutive A → B → C mechanism?

• A. d[A]/dt = -k1 [A]
• B. d[C]/dt = k2 [B]
• C. d[B]/dt = k1 [A] - k2 [B]
• D. d[A]/dt = k2 [B]

Answer: (C)

In a consecutive A → B → C mechanism, the intermediate B is formed from A and is consumed to become C. So the rate of change of B is the formation rate minus the consumption rate. Formation occurs as A converts to B at a rate k1[A], and consumption occurs as B converts to C at a rate k2[B]. Net: d[B]/dt = k1[A] − k2[B]. This aligns with the idea that A is depleted as it forms B (d[A]/dt = −k1[A]) and C is formed from B (d[C]/dt = k2[B]). An expression implying A changes as k2[B] would be inconsistent with the mechanism, since A does not get regenerated from B.

In a consecutive A → B → C mechanism, the intermediate B is formed from A and is consumed to become C. So the rate of change of B is the formation rate minus the consumption rate. Formation occurs as A converts to B at a rate k1[A], and consumption occurs as B converts to C at a rate k2[B]. Net: d[B]/dt = k1[A] − k2[B].

This aligns with the idea that A is depleted as it forms B (d[A]/dt = −k1[A]) and C is formed from B (d[C]/dt = k2[B]). An expression implying A changes as k2[B] would be inconsistent with the mechanism, since A does not get regenerated from B.