# Chapter 3. Basics of the reaction kinetics

Chemical kinetics studies the speed with which a chemical reaction occurs and the factors that affect this speed. This information is especially useful for determining how a reaction occurs. Let’s consider the following chemical reaction:

 . (3.1)

Here letters A, B, C, and D represent chemical species involved in the chemical transformation. νa, νb, νc, and νd are the stoichiometric coefficient for the given reaction.

The speed of a reaction is the rate at which the concentrations of reactants and products change. The term rate of reaction (r) occurring in a closed system under isochoric conditions, without a build-up of reaction intermediates can be written in the form (Atkins, 1997):

 , (3.2)

where ci is the concentration and is the stoichiometric coefficient of reactants and products, respectively. (Note: The rate of a reaction is always positive. Stoichiometric coefficients for products are positive and for reactants are negative in reaction kinetics. Moreover, stoichiometric coefficients are not always cardinal numbers.)

The effect of concentration on the rate is isolated as

 , (3.3)

where the specific rate k, called reaction rate coefficient, is independent of concentration but does depend on temperature, catalysts, and other factors. The law of mass action states that the rate is proportional to the concentrations of the reactants and has a form

 . (3.4)

Here exponents α, β are empirical and identifies the order of the reaction, and they can be determined from reaction kinetics measurements. Importantly, they are identical with the stoichiometric coefficients when the stoichiometric equation truly represents the mechanism of reaction i.e. the reaction is an elementary reaction.

## 3.1. Differential rate law

In many reactions, the rate of reaction changes as the reaction progresses. Initially the rate of reaction is relatively large, while at very long times the rate of reaction decreases to zero (at which point the reaction is complete). In order to characterize the kinetic behaviour of a reaction, it is desirable to determine how the rate of reaction varies as the reaction progresses. A rate law is a mathematical equation that describes the progress of the reaction (3.4). In general, rate laws must be determined experimentally as we discuss earlier. Unless a reaction is an elementary reaction, it is not possible to predict the rate law from the overall chemical equation. There are two forms of a rate law for chemical kinetics: the differential rate law and the integrated rate law.

The differential rate law relates the rate of reaction to the concentrations of the various species in the system. Differential rate laws can take on many different forms, especially for complicated chemical reactions. Each rate law contains the reaction rate coefficient. The units for the rate coefficient depend upon the rate law, because the rate always has units of mole L−1 s−1 and the concentration always has units of mole L−1. There are some examples of different differential rate laws.

First-Order Reaction:

For a first-order reaction, the rate of reaction is directly proportional to the concentration of one of the reactants. Differential rate law: r = k cA; the rate coefficient, k, has units of s−1.

Second-Order Reaction:

For a second-order reaction, the rate of reaction is directly proportional to the square of the concentration of one of the reactants. Differential rate law: r = kcA2; the rate coefficient, k, has units of L mole−1 s−1.