Rate Laws from Graphs of Concentration Versus Time (Integrated Rate Laws)

In order to determine the rate law for a reaction from a set of data consisting of concentration (or the values of some function of concentration) versus time, make three graphs.

The graph that is linear indicates the order of the reaction with respect to A. Then, you can choose the correct rate equation:

For a zero order reaction, | rate = k | (k = – slope of line) |

For a 1st order reaction, | rate = k[A] | (k = – slope of line) |

For a 2nd order reaction, | rate = k[A]2 | (k = slope of line) |

Examples

For a zero order reaction, as shown in the following figure, the plot of [A] versus time is a straight line with k = – slope of the line. Other graphs are curved for a zero order reaction.

For a first order reaction, as shown in the following figure, the plot of the logrithm of [A] versus time is a straight line with k = – slope of the line. Other graphs are curved for a first order reaction.

For a second order reaction, as shown in the following figure, the plot of 1/[A] versus time is a straight line with k = slope of the line. Other graphs are curved for a second order reaction.