Firstorder Reactions

In first-order reactions, the rate of transformation of a substrate is proportional to the substrate concentration. The rate of change of substrate S with time is

The decrease in the concentration of the substrate with time t is dependent on the rate constant k times the concurrent concentration S of the substrate. After integration, we obtain the equation

where St is the concentration of the substrate remaining at any time t. The rate constant k involves some expression per unit time (e.g., h-1, day-1, or year-1).

To calculate the time required to transform one-half the initial substrate (St = S0/2), we start with ln(V2)

kt1/2

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