In the Classroom edited by
Applications and Analogies
Ron DeLorenzo Middle Georgia College Cochran, GA 31014
An Analogy To Help Students Understand Reaction Orders Charles J. Marzzacco Department of Physical Science, Rhode Island College, Providence, RI 02908
The rate law for a chemical reaction is an important topic in introductory chemistry courses. Students determine rate laws from sets of reactant concentrations and the associated initial rates of the reaction. Examples of zero-, first-, second-, and even third-order reactions are examined. Although this process is straightforward, many students find the mathematics behind the concept of reaction order to be difficult. Before discussing specific rate law examples, I have been using a simple analogy involving the properties of a cube that helps students learn how to work with rate law data. I begin by showing the students a cube and asking them to think about how many characteristics of the cube can be related to l, the length of the side of a cube. A cube has various characteristics, such the number of vertices, the sum of the lengths of the cube edges, the total surface area, and the volume. If these four properties are given the symbols, v, P, A and V, respectively, the following mathematical relationships exist: Number of vertices = v = 8 × l 0 = 8 Sum of the lengths of the edges = P = 12 × l Total surface area = A = 6 × l 2 Volume of the cube = V = l 3
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Clearly these four examples exemplify mathematical relationships of zero, first, second, and third order, respectively. This very concrete example nicely illustrates various ways that a dependent variable can depend on an independent variable. It should be clear to the students that the number of vertices in a cube is independent of the size of the cube. Thus, v = 8 no matter how large l is. A cube with a short edge length has the same number of vertices as a cube with long edge length. This example is analogous to a zero-order rate law. The sum of the lengths of the cube edges P shows a linear dependence on l. If one cube has an edge length that is twice as long as that of another cube, the sum of its cube edges will also be twice as large as that of the other. In other words, there is a direct proportional relationship between P and l. This example is analogous to a first-order rate law. Analogous to the way that the rate of a second-order reaction depends on the square of the concentration of the reactant, the surface area of the cube depends on the square of the edge length. In both cases doubling the value of the independent variable quadruples the associated dependent variable. Finally, the relationship between volume and length is analogous to the rate law for a third-order reaction.
Journal of Chemical Education • Vol. 75 No. 4 April 1998 • JChemEd.chem.wisc.edu
