D30.1 Multi-step Reactions and Rate-Determining Step

We now know how to experimentally measure the reaction orders and determine the value of k, which also informs us about activation energy and the frequency factor, but how do we use the experimentally determined rate law to assess whether a proposed reaction mechanism is likely to be correct?

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 that are plausible based on our knowledge of chemical bonding and interactions between molecules.
  • For example, if a step in a proposed mechanism involves three reactant species, it is very unlikely that this would be an elementary reaction, and therefore the mechanism is likely incorrect.
  • If a reaction step involves breaking a very strong bond, then it is unlikely to have a small enough activation energy to occur fast enough to make the mechanism work.
• The sum of the reaction steps should agree with the overall balanced reaction equation.
• The mechanism must agree with the experimentally observed rate law.

Let us consider the last point in more detail.

For some multi-step mechanisms, it is possible to derive the overall rate law from the known rate laws of the individual elementary steps (which can be derived directly from the stoichiometry of the chemical equations). If the experimentally determined rate law agrees with the theoretical rate law derived from the mechanism, the mechanism is a plausible theory for how the reaction occurs. If the mechanism predicts a rate law that is not the same as the experimentally observed rate law, then the mechanism must be incorrect. Other experimental data can further 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 the 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:

The currently accepted mechanism for this reaction has three steps. The third step occurs twice: each time the first step takes place and each time the 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 conveys the idea that the rate constant k₁ is much smaller than the other two rate constants. Similarly, steps 2 and 3 are labeled “fast” to communicate that rate constants k₂ and k₃ are much larger than k₁.

However, keep in mind that the actual reaction rate of each step also depends on the concentrations of their reactants. Initially, steps 2 and 3 do not occur (rate = 0) because the concentration of one of their reactants is zero. For example, [HOI] = 0 M initially because HOI is not a reactant in the overall reaction. Thus, step 2 (rate_{step 2} = k₂[HOI][I^–]) cannot proceed forward 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.