5.1.1(i) - Rate-determining step

Slow Step Evidence

Many reactions do not happen in one collision. They happen through a sequence of elementary steps, and the slowest step controls the overall rate in the same way that the narrowest point of a route controls the flow through the whole route.

The key OCR idea is evidence-based: a rate equation is found experimentally, then used to test whether a proposed mechanism is consistent with the evidence. You cannot usually predict the rate equation from the balanced overall equation alone.

For a simple elementary slow step, the species taking part in that slow step appear in the rate equation. If one particle of $A$ and one particle of $B$ collide in the slow step, the rate equation is first order with respect to $A$ and first order with respect to $B$:

If two particles of the same species take part in the slow step, that species appears squared:

A reactant that only appears after the slow step does not control the rate in this simple OCR reasoning. It may be in the overall equation, but absent from the rate equation.

Worked reasoning: suppose a proposed mechanism has this slow step:

The slow step involves one $X$ and two $Y$ particles, so the predicted rate equation is:

The rate equation does not include $Z$, because $Z$ is a product of the slow step rather than a reactant in that step.

Predicting Rate Equations

When the slow step is given, work from the reactants in that step, not from the whole equation. The overall equation tells you what changes from start to finish; the slow step tells you which collision or rearrangement limits the rate.

Worked example: nitrogen dioxide and carbon monoxide

The overall reaction is:

A possible two-step mechanism is:

The slow step contains two $\ce{NO2}$ molecules and no $\ce{CO}$ molecule. The predicted rate equation is therefore:

This does not mean $\ce{CO}$ is unreactive. It means $\ce{CO}$ is used in a later fast step, so changing the concentration of $\ce{CO}$ does not affect the rate in this proposed mechanism.

Check that the steps really add to the overall equation:

Cancel $\ce{NO3}$, because it is made in one step and used in another. Cancel one $\ce{NO2}$, because it appears on both sides. The remaining equation is:

That matches the overall equation.

Building Possible Mechanisms

OCR can also ask the reverse question: given the experimental rate equation and the balanced overall equation, suggest possible steps in the mechanism.

Use this route:

1. Start the slow step with the species shown in the rate equation.
2. For a proposed first elementary slow step, use the powers as its reactant particle counts. If a fast step precedes it, check how that earlier step relates the intermediate concentration to measured reactants; do not infer that relation merely from the intermediate's origin.
3. Create an intermediate if the slow step cannot directly make the final products.
4. Add one or more fast steps so that all steps add up to the overall equation.
5. Check atoms, charge and cancellation.