# D36.3 Multi-step Reactions and Rate-Determining Step

A valid mechanism for a multi-step reaction has these characteristics:

• The mechanism should consist of a series of unimolecular and/or bimolecular elementary reaction steps.
• The sum of the reaction steps should agree with the overall balanced reaction equation.
• The mechanism must agree with the experimentally observed rate law.

For elementary reactions, rate laws (and reaction order) can be derived directly from the stoichiometry of the chemical equations, but this is not true for a multi-step reaction where the balanced overall equation is not an elementary reaction. For multi-step reactions, the overall rate law can be determined from experimental data.

For some multi-step mechanisms, it is possible to derive the overall rate law from the known rate laws of the individual elementary steps. If the experimentally determined rate law agrees with such theoretical rate law (derived from the mechanism), the mechanism is a plausible theory for how the reaction occurs. Other experimental data can also support the plausibility of a mechanism. For example, if an intermediate proposed in the mechanism is observed in the reaction mixture, that would support the mechanism.

Deriving rate law from a reaction mechanism can be a complex task. However, for many multi-step reactions, one elementary reaction step is significantly slower than the other steps, and this step limits the rate at which the overall reaction occurs. This slowest step in a mechanism is called the rate-determining step (or rate-limiting step), and it allows for some simplifying approximations.

As an example of a rate-determining step, consider the oxidation of iodide ions by hydrogen peroxide in aqueous solution:

2 I(aq) + H2O2(aq) + 2 H+(aq) ⟶ I2(aq) + 2 H2O(ℓ)

The currently accepted mechanism for this reaction has three steps. The third step occurs twice each time the first and second steps take place, so it is written twice.

 Step 1: H2O2(aq) + I–(aq) HOI(aq) + OH–(aq) Slow Step 2: HOI(aq) + I–(aq) I2(aq) + OH–(aq) Fast Step 3: OH–(aq) + H+(aq) H2O(ℓ) Fast OH–(aq) + H+(aq) H2O(ℓ)

The first step is labeled slow, which means that the rate constant k1 is much smaller than the other two rate constants. Steps 2 and 3 are labeled fast because rate constants k2 and k3 are much larger than k1.

Initially, steps 2 and 3 cannot occur because the concentration of one of their reactants is zero. For example, [HOI] is zero before the reaction begins because HOI is not a reactant in the overall reaction. Thus, step 2 has rate = 0 (ratestep 2 = k2[HOI][I]) until step 1 produces some HOI and raises [HOI] above zero. No matter how big k2 might be, step 2 cannot go any faster than step 1. We say that the rate of step 2 is limited by the rate of step 1. Similarly, step 3 cannot occur until steps 1 and 2 produce some OH, so the rate of step 3 is also limited by the rate of step 1. Thus, in this case, step 1 is the rate-limiting step.

Activity: Reaction Energy Diagram 