On Unimolecular Reactions GEORGE ANTONOFF Fordham University, New York City
HERE is no clarity in the chapters on unimolecular Treacbons . ' in . textbooks of physical chemistry and this can be traced to the time when physical chemistry began its existence as a separate science. If one takes, for example, the textbook of Nernst,' in one of the earlier editions one finds unimolecular reactions defined as those in which as a result of a reaction "only one category of molecules undergoes a substantial change in concentration." According to this definition a reaction
should be regarded as unimolecular, and yet i t is a dimolecular reaction. Besides, in a unimolecular reaction the concentration of the product or products undergoes a change in concentration. Thus his definition shows itself utterly unsatisfactory. According to some present-day textbooks a reaction is unimolecular if "one molecule reacts a t a time." If one has only a few molecules in a system one can well imagine a case in which one molecule will react a t a time. But if we have, say, 6.06 X loz3molecules in a system, i t is obvious that a great many of them will react a t any given moment. Thus, if we have a reaction of the type
it will be a unimolecular reaction irrespective of whether only one molecule reacts a t a time or millions of them. The essential point is that there should be only one molecule on the right-hand side of the equation. Such a definition is quite satisfactory, but i t may be not the only one possible. For example, one can say that a unimolecular reaction is one in which the transformation takes place within each reacting molecule. Thus the reaction ought not to be influenced by other molecules and should be independent of concentration. This subject has been clarified by the late Lord Rutherford. Of course, he was not a chemist and would never have tackled this problem as such. But the object of his interest was radioactive transformations, which follow the type of unimolecular reactions, and thus his work indirectly is a substantial contribution to chemical kinetics. The radioactive transformations are independent of concentration and the atom reacts without being influenced by the neighboring a t m s . Rutherford expressed the velocity of these transformations by the equation - -DN = dl
KN
(1)
Theoretische Chernie, Verlag van Ferdinand Enke, Stuttgart. 1921, p. 631.
where N is the number of atoms present a t a given time and K is a constant. It stands to reason that the velocity of the reaction will be the same irrespective of the volume in which the N molecules are concentrated. A unimolecular chemical reaction diiers from a radioactive reaction in that the molecules rather than the atomsreact, but it followsthe samelaws and therefore its velocity must be independent of concentration. The present-day theories, however, attribute certain &ects to collisions between the molecules, so that the chemical reactions, or some of them, may not be unimolecular in a strict sense of the word, but they will be considered as such if they take place according to equation (1). The present-day textbooks express the velocity of unimolecular reactions in terms of concentration
It follows from the above that the use of the equation (2) is not altogether justifiable, especially because i t conveys the idea that the velocity of a reaction will be diierent in different dilutions. Thus in principle the use of equation (2) is not justified, because i t introduces an unnecessary parameter, restricting the number of molecules to a given volume. However, in the practical sense it is harmless, because
where C is the concentration and V is the volume. The equation (2) can be expressed as dN --= -
Vdt
KN
V
where the unnecessary parameter V cancels, and equation (2) shows itself identical with (1). Both lead to the result that the reaction rate K and the half period t,,, are connected by the equation
and are therefore independent of concentration. CONCLUSION
Thus, a unimolecular reaction is one in which the veloaty of the reaction is proportional to the number of molecules of the reactant (there is only one reactant) irrespective of dilution. The molecules do not react with one another and the change takes place within each reacting molecule. This is tantamount to the statement that in a unimolecular reaction there must be only one molecule a t the left-hand side of the eauation.
