Concentration Dependence of Kinetics

The measurement of rates of reactions under various conditions gives several different kinds of mechanistic information [8]. The concentration dependence of rates can give information on the number of steps in a mechanism and the species involved in reaction collisions. Eor these purposes, other variables such as temperature and choice of solvent are kept constant. 

Experimentally, a solution of known concentration of starting material A is prepared, and then as the reaction proceeds, the concentration of A and/or B is measured repeatedly. In this simple reaction, A continually decomposes without coreactants or catalysts. When the supply of A reaches half the original concentration, the rate should be half the initial rate. If the rate at any point in time is divided by [A] at that point, the quotient should be a constant k, sometimes called the rate constant or specific rate (Eq. 4.8). The constant k is expressed in reciprocal seconds, s , and is simply the rate of the reaction when [A] = 1, even though it may have been determined at much lower concentrations than 1 molar. 

The determined value of k is a fundamental property of the reaction, independent of the concentration of A. Since by Equation 4.7 the rate is proportional only to the concentration of one component to the first power, this is called a first-order reaction. A simple first-order reaction mechaifism involves only collisions of reactant with unreactive solvent 

FIGURE 4.5 Linear plot of kinetic data for a first-order reaction. 

Dimerization reactions (Eq. 4.10) give a different kinetic result. Here a collision between two A molecules is necessary therefore, as the concentration of A decreases, the rate drops faster than that found for Equation 4.6. At half the initial concentration, collisions would be only one-fourth as frequent. Division of the rate by [A] gives a constant for this reaction (Eq. 4.11). Since the rate is proportional to the concentration of A squared, it is called a second-order reaction. 

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