Problem 12-51

Finding the order of a reaction:

The dataset in this table is the original dataset that has been modified to show how the concentration of a species (reactant) changes over time for different reaction orders.

If these data are presented graphically, it is possible to determine the order of the reaction, based on [NO₂], according to the integrated rate law:

time [NO2] ln[NO2] 1/[NO2] 0 0.500 -0.693 2.000 1.2x103 0.444 -0.812 2.252 3.00x103 0.381 -0.965 2.625 4.50x103 0.340 -1.079 2.941 9.00x103 0.250 -1.386 4.000 1.80x104 0.174 -1.749 5.747

• [NO₂] vs time = linear : order zero
• Ln [NO₂] vs time = linear : order one
• 1/[NO₂] vs time = linear : order two

From these graphs, the linear trend is obtained for 1/[NO₂] as a function of time, indicating that it is a second-order reaction.

This question may require the use of Excel.
It can also be solved by performing a linear regression analysis with your calculator.
Because this question is time-consuming, it is rarely asked in exams.
However, the three graphs can be presented to the student to identify the rate law of the reaction (see question 12-57).