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 dmg A as a mol dm and if we find experimentally that x mol dm of the drug has reacted in time t, then the amount of drug remaining at a time f is (a - x) mol dm and the rate of reaction is 

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 dmg 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. 

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

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