Which expression correctly represents the instantaneous rate law for a first-order reaction in terms of concentration?

• A. rate = k
• B. rate = k[A]^2
• C. -d[A]/dt = k[A]
• D. rate = [A]/t

Answer: (C)

First-order reactions have a rate that depends linearly on the concentration, and the instantaneous rate is the negative time derivative of the concentration of A. So the rate law is expressed as the rate of disappearance of A: -d[A]/dt = k[A]. This form makes clear that as [A] decreases, the rate decreases proportionally. It also connects to the integrated form ln[A] = -kt + ln[A]0. The constant k has units of s^-1 for a first-order process. The other expressions don’t describe first-order behavior: a constant rate (rate = k) would be zero order, a rate proportional to [A]^2 would be second order, and rate = [A]/t isn’t a standard rate law and has mismatched dimensions.