Chemical Kinetics

A rate equation is a mathematical expression used in chemistry to link the rate of a reaction to each reactant and their various orders. The following represents a generic, three-reactant rate equation.

r_A = k[A]^a[B]^b[C]^c

Where r_A is the rate of reaction which standardly has the units mol dm^-3 s^-1. k is the rate constant, a constant of proportionality, the units depend upon the order of reaction. A, B and C are the reactants, where the square brackets denote concentration, the units are mol dm^-3. a, b and c are indices which indicate the order relevent to the corresponding reactant. The sum of the indices gives the order of reaction.

Not all reactants in a chemical equation are necessarily in the rate equation, this is due to fast reacting molecules not having an effect on the rate of reaction. Thus, the rate of reaction reflects the slowest step of a reaction, the rate-determining step.

Example

For the reaction 2 H₂(g) + 2 NO(g) → N₂(g) + 2 H₂O(g)

The rate equation is r_A = k[H₂][NO]² - H₂, having no index is first order; NO is second order, according to the index.

As can be seen, the rate equation does not simply reflect the reactants - the steps must be looked at, this reaction has three:

1. 2 NO ↔ N₂O₂ (fast equilibrium, K)
2. N₂O₂ + H₂ → N₂O + H₂O (slow, k₂)
3. N₂O + H₂ → N₂ + H₂ (fast, k₃)

It is the slowest reaction that is reflected in the rate equation: number 2.