## Classifying reactions the order of reaction

Reactions are classified according to number of reacting species whose concentration determines the rate at which the reaction occurs, i.e. the order of reaction. We will concentrate mainly on zero-order reactions, in which the breakdown rate is independent of the concentration of any of the reactants; first-order reactions, in which the reaction rate is determined by one concentration term, and second-order reactions, in which the rate is determined by the concentrations of two reacting species.

Experimentally we can monitor the rate of breakdown of the drug either by its decrease in concentration with time or alternatively by the rate of appearance of one of the breakdown products. If we represent the initial concentration of drug A as a mol dm 3 and if we find experimentally that X mol dm 3 of the drug has reacted in time t, then the amount of drug remaining at a time t is (a - x) mol dm 3 and the rate of reaction is or

dt dt

where the proportionality constant, k, is called the rate constant. This is an example of a second-order reaction since the order of reaction is the sum of the exponents of the concentration terms in the rate equation. As we will see (section 4.4.1), many hydrolysis reactions are catalysed by H+, OH- or buffer components and so we can write equation (4.3) as, for example, dx ,

k2 is a second-order rate constant and has units of (concentration)-1(time)-1, for example (mol dm-3) 1 min-1. When the solution is buffered at constant pH, [H+] is constant and we can write equation (4.4) as dx

Notice that the term a is a constant and therefore disappears during differentiation. We will use dx/dt to describe the reaction rate in this section.

If we assume that a typical reaction between a drug molecule A and a reactant B occurs when two molecules are in collision, then we might expect that the number of collisions, and hence the reaction rate, would be proportional to the concentration of the two reacting molecules, i.e.

where k1 = k 2[H +]. Since the rate of reaction now effectively depends on one concentration term it is a first-order reaction or, more correctly in this case, a pseudo first-order reaction (see section 4.2.3). The majority of decomposition reactions involving drugs fall into this category, either because the species reacting with the drug is maintained constant by buffering or because, as in the case of uncatalysed hydrolysis reactions, the water is in such large excess that any change in its concentration is negligible.

If as well as maintaining a constant amount of water in a reaction, we also maintain a fixed drug concentration, then equation (4.3) becomes dx dt

This type of reaction, which is called a zero-order reaction, can often occur in suspensions of poorly soluble drugs. In these systems the suspended drug slowly dissolves as the drug decomposes and so a constant drug concentration in solution is maintained.

We will now examine the ways in which we can determine the rate constants for these three types of reaction.

### 4.2.2 Zero-order reactions

In this type of reaction the decomposition proceeds at a constant rate and is independent of the concentrations of any of the reactants. The rate equation is given by equation (4.6) as dt -k0

Integration, noting that x = 0 at t = 0, gives i.e.

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