Topic 5.8 Reaction Mechanism and Rate Law: identify the rate-determining (slow) step of a mechanism and use it to write the rate law, and check a proposed mechanism against the experimental rate law.

What this topic is asking

The College Board (Topic 5.8) wants you to identify the rate-determining (slow) step of a mechanism and use it to write the rate law, then check whether a proposed mechanism is consistent with the experimental rate law. This is where mechanism and rate law meet: the slow step is the bottleneck that controls how fast the whole reaction goes.

The rate-determining step

Think of a multi-step process as a chain of tasks: the slowest task limits the throughput of the whole chain. Speeding up a fast step does nothing; only the slow step matters for the rate. This is why the overall rate law often involves only some of the reactants.

Writing the rate law from the slow step

The simplest and most common AP case is a slow first step: the rate law is just $k$ times the concentrations of the slow step's reactants, each raised to its coefficient. A species that reacts only later, in a fast step, is consumed after the bottleneck and so has no effect on the overall rate.

When the slow step is not first

If the slow step comes after a fast initial equilibrium, its rate law may contain an intermediate, which cannot appear in the final rate law because intermediates are not measurable starting materials. You handle this by using the fast equilibrium before the slow step: set the forward and reverse rates equal and solve for the intermediate concentration in terms of reactant concentrations, then substitute. This can produce a rate law with unusual orders, which is exactly why such orders signal a multi-step mechanism.

Checking a mechanism against data

A proposed mechanism must pass two tests: the steps must sum to the overall equation (Topic 5.7), and the rate law predicted by the slow step must match the experimental rate law. A mechanism that fails either test is rejected. Passing both does not prove the mechanism is correct, but it makes it a viable proposal, which is all chemistry can claim.

Try this

Q1. A mechanism has a slow first step $\text{A} + \text{B} \rightarrow \text{C}$ (elementary). Write the overall rate law. [2 points]

• Cue. $\text{rate} = k[\text{A}][\text{B}]$, straight from the slow elementary step.

Q2. Explain why a reactant that appears only in a fast step after the slow step does not appear in the rate law. [2 points]

• Cue. The rate-determining step sets the rate; species consumed after it have already passed the bottleneck and cannot speed the reaction, so they do not enter the rate law.