R. S. Perkins Un~versit~ of Southwestern Lou~siana Lafoyette, 70501
In an elementary reaction, the rate law depends on the stoichiometry of the reaction. For the reaction mA + nB -products, the rate law is
Rate
-
~[A]~[B]" Discussions justifying why the powers in the rate law are the same as the coefficients in the reaction equation are often vague or absent or are in terms of collision theory. B, the And as has been pointed out for the reaction 2A rate does not depend on [AI2 hut approaches this for large numbers of particles.' Application of one equation gives the correct concentration dependence for all elementary reactions and gives the B. The equacorrect behavior for such reactions as 2A tion is the equation for combination of n things taken r at a time
-
Rate Laws for Elementary Chemical Reactions
Therefore, for any numher of nA atoms, Rate = k ' n ~= kP1. A+B-C
The rate here will be proportional to the numher of ways n ~atoms, , taken one at a time, can he combined with n~ atoms also taken one a t a time. Therefore
-
Rate
=
k'nAnB = k[A][B]
A+B+C-D
Proceeding as in the previous case
Rate o n ~ n ~ n c and it is applied through the use of particle interactions. Equation (1) is a fundamental equation of probability and its derivation and examples of use can he found in most elementary books on Mosteller, Rourke, and Thomas2 treat the equation in an especially detailed and understandable way.
Rate 2A
=
k[Al[BI[Cl
+ B-C
The rate of this reaction will be proportional to the numher of ways n~ atoms, taken two a t a time, can be combined with ne atoms taken one a t a time. Therefore
2A-B
For reaction to occur, two A atoms must collide or interact. For a set of nA atoms in a constant volume, the numher of bimolecular collisions will he proportional to the number of possihle bimolecular collisions. The number of possihle bimolecular collisions is also the number of combinations of nAatoms taken two at a time. Therefore
For a large numher of nA atoms, Rate = k'nA2. Since we are dealing with a constant volume, nA is proportional to [A] and Rate = k[AIZ. 3A
-
B
For this reaction the rate will he proportional to the number of possihle termolecular interactions. This number is the same as the numher of combinations of nA atoms taken three at a time. Therefore
k[AI3 For a large number of n~ atoms, Rate = k ' n ~= ~ A-B
Although bimolecular collisions are involved in this reaction, according to the Lindemaun mechanism the rate depends on decomposition of activated molecules by transfer of energy to a particular vihrational mode of motion. Considering such a transfer as a self interaction, the rate of reaction will depend on the number of possihle unimolecular interactions. This number is the same as the number of combinations of nA atoms taken one at a time. Therefore 254
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Journal of Chemical Education
For a large numher of particles Rate = k'npns
=
k[AP[B]
Surface Reaction Summarizing from above, if a reaction involves three A B, the rate of reaction depends on atoms such as 3A the number of possible three particle interactions. For 2A B, bimolecular interactions are considered. For A B, unimolecular or self interactions are considered. For A + S B where A is strongly absorbed on the surface S, the rate of reaction depends only on the surface and therefore depends on zero A particles interacting.
-
-
-
Therefore, Rate = constant and the rate is zero-order with respect to A. Teaching certain elementary reactions based on the above approach should give students in freshman courses a clearer understanding of the relationships derived. For both freshman and upper division courses, the use of eqn. (1) emphasizes the role of probability in reaction rates, and this will correlate with the use of probability in other aspects of chemistry such as entropy, kinetic theory, and statistical mechanics. 1 Glasoe, Paul K.,
J. CHEM. EDUC., 48,390 (1971).
ZMosteller, Frederick, Rourke, Robert E. K., and Thomas, George B., Jr., "Probability with Statistical Calculations," 2nd Ed., Addison-Wesley,Reading, Mass., 1970, pp. 49-55.
