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.