Rate Expression for Activated Complexes To the Editor: In the July, 1972 issue of this Journal there appeared an article "Activated Complex Theory of Bimolecular Gas Reactions" by Dr. C. L. Arnot (J. CHEM. EDUC., 49,480 (1972)). In this article Dr. Arnot attempts to clarify activated-complex theory by suggesting an alternative approach to the problem. Unfortunately, his exposition is marred by a serious error which leads him to conclude that the usual rate expression
should in fact be multiplied by a factor of two. As in other treatments1-3 Dr. Arnot semegates the acti. . \fated complexes into two kinds: those, X I q that , are passing from reactants into prnducts, and those, X,', that are from products &to reactants. He then makes the error of supposing that the concentration of X i * can he calculated, in terms of the concentrations of reactants A and B, by the statistical-mechanical formulation of the equilibrium constant. This, however, is not so; when the reactants and products are a t equilihrium i t is the total concentration of complexes, [Xi ] + [X,*], that must he calculated by the statistical-mechanical formulation. The true concentration of xi*is thus half of this-that is, half of what is supposed by Dr. Amot. Aside from the logic of this argument, a variety of other approaches to rate theory-simple collision theory, more refined collision theories, classical dynamical treatments, quantum-mechanical dynamical treatments, and stochastic theories-all lead to a formulation consistent with that of activated-complex theory,3 with no suggestion of the factor of two which Dr. Arnot claims to have unearthed. K. J. Laidler University of Ottawa Ottawa, Canada, KIN 6N5 Glasstone, S., Laidler, K. J., and Eyring, H., "The Theory of Rate Processes," MeGraw-Hill Book Company, New York, 1941. ZBishop, D. M., and Laidler, K. J., J Chen. Phys., 42, 1688 (1965). 3Laidler, K. J., "Theories of Chemical Reaction Rates," McGraw-Hill Book Co., New York, 1969.
To the Editor: Dr. Laidler states that I make "the error of supposing that the concentration of xi* can he calculated, in terms of the concentrations of reactants A and B, by the statistical formulation of the equilibrium constant." The approach in my article was to express the rate constant, k,, for the formation of X,* in terms of the equilihrium constant, rather than to express the rate of reaction as the rate of crossing through the transition state. It followed that if the rate constants for dissociation of Xi* and Xb* are identical, the steady state concentration of Xi* will be that given by equilibrium theory. Dr. Laidler does not state whv this sueeestion is in error. He asserts "it is the total c¢raii& of complexes [Xit] .IXPI. - .. that must be calculated hv the statistical-mechanical formulation." I would agree Lf the purpose is to arrive
+
a t the usual expression for the bimolecular rate constant. However, as Dr. Laidler has stated in several texts,l "activated complexes are transient species passing from initial to final state and unable to turn back." Therefore, an equilibrium between activated complexes and reactants does not exist. I t is my contention that at overall chemical equilihrium there are simultaneous steady states of Xi* and Xb*, and, for the reasons given in my article, their total concentration .[Xr*l , . + ~Xh*l. . . . will not he eiven bv the statistical-mechanical theory oiequilihrium. The (lerivatinn of the usual exprr.sii11nfor the rate constant from other theories does n i t seem relevant to a discussion of activated-complex theory. C. L. Arnot Bishop's University, Lennoxville, Quebec, Canada 'Laidler, K. J., "Theories of Chemical Reaction Rates," McGraw-Hill Book Co.. New York. 1969. o. 44. Laidler. K. J.. "Chemical Kinetics," (2nd Ed.), ~ c ~ r & ~ Book i l l c;., N& Yark, 1965, p. 75. Identifying Colors To the Editor: I read with interest the Note hv A. Lasis on "The Prohlems of Descrihmy and identifying Colors and a I'hilatclic Solurion." 1.1. CIlE.\1. EDI'C.. 30, 355 r1973,l. 1 s u s ~ e c t that ~ r . ' ~ & is i sunaware of the major advances that have been made in the national and international standardization of color names and the description and identification of colors. I would very much like to have seen him recommend a "Universal Color Language" for the further use of chemists, asindeed one is used by many chemists, other scientists in a wide variety of disciplines, designers, architects, artists, business men, etc. Such a language, using descriptive color names understood even by those not trained in color, was developed some years ago by the Inter-Society Color Council and adopted by the National Bureau of Standards. It is descrihed, and its terms are related to those of many specialized, less readily comprehended, and less widely accepted "color guides" in NBS Circular 553, "The ISCC-NBS Method of Designating Colors and a Dictionary of Color Names," available from the Government Printing Office for a few dollars. For about the same price one can order a chart of about 250 internationally accepted color guide samples designated in the ISCC-NBS universal language, as Standard Reference Material No. 2106, from the National Bureau of Standards. Fred W. Billmeyer, Jr., Secretary Inter-Society Color Council Rensselaer Polytechnic Institute Troy, New York 12181
Practical Slides lor Professional Meetings. I I To the Editor: Sigred Lanoux has descrihed [J. CHEM. EDUC., 50, 476 (1973)l a quick, inexpensive way to make lantern slides, using rub-off letters. Let me submit an even quicker and less expensive way. Buy from your local artists' supply shop a yard or two of 8-mil matte acetate, and with a paper cutter chop it into rectangles the size of Polaroid slides, namely 70 mm X 96 mm. With scissors cut '14 in. off the lower right hand corner of each. You can write or draw directly on the matte side of one of these blanks with ordinary pencil. I like to use 6B penVolume 50, Number 1 7 , November 1973
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