By Brooke Yool
Updated Aug 30, 2022

Chemical kinetics, the study of reaction rates, relies on understanding how reactant concentrations influence the speed of a reaction. A rate law mathematically links these concentrations to the reaction rate and is essential for predicting and controlling chemical processes.

A typical rate law takes the form:

rate = k [A]^m [B]^n

Here, k is the rate constant unique to the reaction, and the exponents m and n (often 1 or 2) reflect the reaction’s order with respect to each reactant. The constants and orders are derived from experimental data and provide a quantitative description of the reaction’s kinetics.

Writing a Rate Law

Although many reactions are represented as single steps, they often consist of multiple elementary steps. The overall reaction rate is governed by the slowest of these, known as the rate‑determining step. The steps below outline how to translate this step into a rate law.

Step 1: Identify the Rate‑Determining Step

Examine kinetic data or a proposed mechanism to pinpoint the slowest elementary reaction. This step is crucial because it controls the overall rate.

Step 2: Translate Reactants into the Law

List the reactants involved in the rate‑determining step. For instance, if the slow step involves the collision of two O₂ molecules, the preliminary rate law becomes:

rate = k [O₂][O₂]

Note that this can be simplified to rate = k[O₂]² once exponents are determined.

Step 3: Determine Reaction Orders from Experimental Data

Conduct experiments varying one reactant concentration at a time while keeping others constant. Analyze how the rate changes:

• If doubling the concentration of a reactant doubles the rate, the reaction is first order in that reactant (exponent = 1).
• If doubling the concentration quadruples the rate, the reaction is second order in that reactant (exponent = 2).

Apply this analysis to each reactant in the rate‑determining step to assign accurate exponents.

TL;DR

Because the rate‑determining step may differ from the overall reaction, your final rate law can differ from the initial reaction equation. Use experimental data to refine exponents and ensure the law accurately reflects the kinetic behavior.