What is the unit of the rate constant k for a second-order reaction?

What is the unit of the rate constant k for a second-order reaction?

Step 1: Understand that a second-order reaction has a rate law of the form Rate = k[A]^2, where [A] is the concentration of the reactant.
Step 2: Identify the units of the rate. The rate of a reaction is typically measured in molarity per second (M/s).
Step 3: Recognize that [A] (the concentration) is measured in molarity (M). Since the reaction is second-order, we have [A]^2, which has units of M^2.
Step 4: Substitute the units into the rate law: Rate = k[A]^2 becomes (M/s) = k(M^2).
Step 5: Rearrange the equation to solve for the units of k: k = (M/s) / (M^2).
Step 6: Simplify the units: k = 1/(M·s).

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