Kinetics Studies of the Bleaching of Food Dyes >> Background Step 2

Kinetics Studies of the Bleaching of Food Dyes

Background Step 2 - Getting information from a kinetic trace

Finding the order of the reaction with respect to dye.

We will consider three possible orders for the reaction:

which may be simplified to:

Integrating these differential equations gives the dye concentration as a function of time:

The following plots show how [dye] changes with time for each of these cases.

For zeroth-order reaction, the rate of the reaction is independent of dye concentration, so we get a straight line with slope k'.

For a first-order reaction, the rate is proportional to [dye], so the rate decreases as the reaction proceeds and [dye] decreases.

For a second-order reaction, the rate is proportional to [dye]², and the decrease in rate as the reaction proceeds is more rapid than for the first order reaction.

A useful technique for identifying first order reactions is to plot ln([dye]) versus time:

Note that only the first order reaction gives a straight line.

If we plot 1/[dye] versus time, only the second order reaction gives a straight line:

This leads to a useful means to identify the order of reaction. Given a kinetic trace, we compare the following three plots:

For this data, the plot of 1/[dye] versus time gives a straight line. This indicates that the reaction is a second order reaction and the rate law is:

Suppose the kinetic trace you measured in the lab led to the following three plots:

Which of the following is the rate law for the reaction?

The description above explains how to use this plotting technique to determine the order of a reaction. To understand why it works, please see the explanation of "integrated rate laws" in the textbook and your class notes.