Reaction Mechanisms, Rate-Determining Steps and Rate Laws

What actually happens, one collision at a time?

The balanced equation for a reaction tells you the starting materials and the final products. It does not usually tell you how the reaction happens. Consider the combustion of propane:

C₃H₈(g) + 5O₂(g) → 3CO₂(g) + 4H₂O(g)

If this happened in one step, one propane molecule and five oxygen molecules would all have to collide at the same instant, with the right energy and orientation. That is extremely unlikely. Even a collision of three particles at once is rare. Instead, most reactions happen through a series of simple steps, called a reaction mechanism. (Combustion of hydrocarbons involves many steps with reactive fragments called radicals.)

Elementary steps and mechanisms

An elementary step is a single collision event (or the breakdown of one particle). A reaction mechanism is the series of elementary steps that add up to the overall reaction.

• The molecularity of a step is the number of particles that react in it: unimolecular (1), bimolecular (2) or termolecular (3, rare).
• An intermediate is formed in one step and used up in a later step. It does not appear in the overall equation.
• A catalyst is used up in an early step and regenerated in a later step. It also does not appear in the overall equation.

Example: at temperatures below about 225 °C, nitrogen dioxide and carbon monoxide react through two steps:

• Step 1 (slow): NO₂(g) + NO₂(g) → NO₃(g) + NO(g)
• Step 2 (fast): NO₃(g) + CO(g) → NO₂(g) + CO₂(g)
• Overall: NO₂(g) + CO(g) → NO(g) + CO₂(g)

Adding the steps: one NO₃ appears on both sides and one NO₂ appears on both sides, so they cancel. NO₃ is an intermediate.

The rate-determining step

The overall reaction cannot go faster than its slowest step, just as a line of people cannot move through a door faster than one at a time. The slowest step is called the rate-determining step. Speeding up a fast step makes little difference; speeding up the slow step speeds up the whole reaction.

On a potential energy diagram, the rate-determining step is usually the step with the highest activation energy (the biggest climb from the valley or level before it).

Rate laws

Experiments show how the rate depends on concentration. The result is written as a rate law:

rate = k[A]ᵐ[B]ⁿ

• k is the rate constant. It is constant at a given temperature and gets larger when temperature increases or a catalyst is added.
• m and n are the orders of the reaction with respect to A and B. They are usually 0, 1 or 2, and they must be found by experiment. They are not simply the coefficients of the overall balanced equation.

What orders mean: if a reactant is first order, doubling its concentration doubles the rate. If it is second order, doubling its concentration multiplies the rate by 2² = 4. If it is zero order, changing its concentration has no effect on the rate.

The link to mechanisms: for a single elementary step, the rate law can be written from the step itself, because the rate depends on how often those particles collide. For the step A + B → products, rate = k[A][B]; for 2A → products, rate = k[A]². So the rate law of the rate-determining step usually gives the rate law of the whole reaction. For NO₂ + CO, step 1 (NO₂ + NO₂) is slow, so:

rate = k[NO₂]²

This is exactly what experiments find: the rate does not depend on [CO] at all (CO is zero order), because CO only takes part in the fast step.

Mechanisms in the atmosphere

In the stratosphere, chlorine atoms released from chlorofluorocarbons (CFCs) by ultraviolet light destroy ozone through a two-step mechanism:

Step 1: Cl(g) + O₃(g) → ClO(g) + O₂(g)

Step 2: ClO(g) + O(g) → Cl(g) + O₂(g)

Overall: O₃(g) + O(g) → 2O₂(g)

The chlorine atom is a catalyst (regenerated in step 2), and ClO is an intermediate. Because each chlorine atom is regenerated, a single atom can destroy many ozone molecules before it is removed by other reactions. Understanding this mechanism led to the Montreal Protocol (1987), an international agreement signed in Montréal to phase out CFCs. The ozone layer is slowly recovering.

A Canadian contribution

John Polanyi, a chemist at the University of Toronto, studied the energy of molecules formed in individual elementary reactions by detecting the faint infrared light they give off. He shared the 1986 Nobel Prize in Chemistry with Dudley Herschbach and Yuan T. Lee for their contributions to understanding the dynamics of elementary chemical processes. Work like this tests the ideas in this lesson, such as how energy and orientation determine whether a collision leads to a reaction.