# Relating Reaction Mechanisms to Rate Laws

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OpenStax Chemistry 2e

It’s often the case that one step in a multistep reaction mechanism is significantly slower than the others. Because a reaction cannot proceed faster than its slowest step, this step will limit the rate at which the overall reaction occurs. The slowest step is therefore called the (or rate-determining step) of the reaction.

Rate laws may be derived directly from the chemical equations for elementary reactions. This is not the case, however, for ordinary chemical reactions. The balanced equations most often encountered represent the overall change for some chemical system, and very often this is the result of some multistep reaction mechanisms. In every case, the rate law must be determined from experimental data and the reaction mechanism subsequently deduced from the rate law (and sometimes from other data). The reaction of NO2 and CO provides an illustrative example:

NO2(g) + CO(g) ⟶ CO2(g) + NO(g)

For temperatures above 225 °C, the rate law has been found to be:

rate = k[NO2][CO]

The reaction is first order with respect to NO2 and first-order with respect to CO. This is consistent with a single-step bimolecular mechanism and it is possible that this is the mechanism for this reaction at high temperatures.

At temperatures below 225 °C, the reaction is described by a rate law that is second order with respect to NO2:

rate = k[NO2]2

This rate law is not consistent with the single-step mechanism, but is consistent with the following two-step mechanism:

The rate-determining (slower) step gives a rate law showing second-order dependence on the NO2 concentration, and the sum of the two equations gives the net overall reaction.

In general, when the rate-determining (slower) step is the first step in a mechanism, the rate law for the overall reaction is the same as the rate law for this step. However, when the rate-determining step is preceded by a step involving a rapidly reversible reaction the rate law for the overall reaction may be more difficult to derive.

A reversible reaction is at equilibrium when the rates of the forward and reverse processes are . Consider the reversible elementary reaction in which NO dimerizes to yield an intermediate species N2O2. When this reaction is at equilibrium:

This expression may be rearranged to express the concentration of the intermediate in terms of the reactant NO:

Since intermediate species concentrations are not used in formulating rate laws for overall reactions, this approach is sometimes necessary.

Source:

Flowers, P., Theopold, K., Langley, R., & Robinson, W. R. (2019). Chemistry 2e. Houston, Texas: OpenStax. Accessed for free at https://openstax.org/books/chemistry-2e/pages/1-introduction