Photodissociation by UV radiation is not the only possible fate of NO₂ in urban air. An ordinary decomposition reaction, in which NO₂ reacts to form NO and O₂, is also possible. This reaction was studied at 370°C by a student, and the following data were obtained:

Based on these data, determine the order of this reaction and the rate constant.

Strategy The available data are the reactant concentration as a function of time for a single experiment, so we will need to use graphical techniques to determine the order of the reaction. There are three possibilities we can explore using the integrated rate laws we’ve examined. The reaction could be zero order, first order, or second order with respect to NO₂. We will need to manipulate and plot the data in various ways to determine whether there is a good fit with any of these models. (Other orders are also possible, so we should be aware that all three tests could conceivably fail.) With a spreadsheet or a graphing calculator, such manipulation of data is easy. For this example, first we will calculate all of the data needed for all three plots and then make the appropriate graphs to find the linear relationship and determine the rate law.

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Time (s) 0.0 5.0 10.0 15.0 20.0 25.0 30.0 [NO₂] (mol L-¹) 3.00 x 10-1 1.97 x 10-2 1.00 × 10-² 7.00 × 10-³ 5.20 × 10-³ 4.10 x 10-3 3.50 x 10-3