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ON UNIMOLECULAR REACTIONS AND RADIOACTIVE TRANSFORMATIONS GEORGE ANTONOFF Department of Chemistry, Fordham L‘niversity, New Yark, NEWYOTE Received March 22, 1946
Following the publication by the author of an article on unimolecular reactions (l),there ensued an exchange of letters; ultimately two letters were published by Luder (5, 6) and one by Glasstone (4), the latter of whom invited the readers to
disregard the author’s statements on unimolecular and first-order reactions. In view of the highly confused state of the subject, the author wishes to make the following statement. He finds it difficult to teach kinetics because in most textbooks the definitions are different, if they are given a t all, and to his knowledge he is not alone, many other people complaining about the confused state of the subject. In his paper the author took the same view as expressed by Lind in his article on radioactivity in Taylor’s Treatise on Physical Chemistry (7, page 1724). The well-known exponential expression used in radioactivity, according to Lind, “is the ordinary equation for unimolecular reaction, and in fact, represents the most perfect case, and, as is sometimes maintained, may represent the only true case of unimolecular change.” In the following, the theory will be discussed as the author understands it. It should be mentioned that, for reasons which will be explained later, he uses in this paper the terms “unimolecular reaction” and “first-order reaction” indiscriminately. It is a well-known fact that when the student of physical chemistry approaches the treatise on rate he is informed that the expression for first-order reactions is
-dC-- KC dt
\There C is the concentration, t is time, and Zi is a constant. The popular definition of a first-order reaction is so worded that it involves concentration; hence the above mathematical expression is the logical result. When he investigates radioactive decay, he is informed that the rate is given as
where N is the number of particles reacting, and that here the rate is independent of concentration. If he investigates further he learns that, strictly speaking, volume is not a necessary factor in expressing first-order reactions, and that it would seem more precise to express the rate in terms of number. The question then arises in his mind, “Why have two expressions for identical phenomena? Why treat a first-order reaction and radioactive decay separately?”
5 14
GEORGE ANTOSOFF
I t is our content,ion that the expression -&V/dt could very well substitute for both reactions and more clearly express their rate. We contend that -cW/dt is the simpler expression and that all others can be reduced to it by cancellations of unnecessary terms on both sides of equation 1 . The above expression (equation 2 ) in integrated form mill be
.V
= Noe-kl
where S o is the number of particles initially present, and N their number at a time t. The exponential equation will be equally well satisfied if we write C = Coe-”, where Co is the initial concentration, and C is the concentration at time t . One could also write G = G 0 c k 8where , Go is the number of grams initially present, and G the number a t time t . The latter expression can be written
N X 1.65 X lo-’‘ X -11 =
X 1.65-2dX III X e--ki
where N and NOare as above, 1.65 X lo-?‘ is the mass of the hydrogen atom in grams, and M is the molecular weight. If one divides both sides by V , the volume, the equation is then expressed in concentrations. In all cases, on cancellation, what remains is always:
-V = AVoe-kt ,It is the fundamental equation and its rate, -dS/dt, is the velocity of it reaction having a definite physical meaning, and is independent of concentration. All other expressions, such as -dC/dt or -dCo/dt, can be regarded only as multiples of it, and should be used only with special care. Expression 1 is objectionable because it conveys the idea to a student that the velocity of the reaction depends upon concentration, whereas in reality it does not. That much the student can understand, but the theory upheld by Luder and Glasstone is too contradictory to be taught, as can be seen from the following: Both of them cite in their respective letters (4,6) the textbooks of the latter (3) but do not specify any pages. In the index the heading “Unimolecular reactions” refers to page 1028. One iinds there actually the word “unimolecular” mentioned more than once but without any definition or explanation. On page 1031 in the section on pseudo-unimolecular reactions there is the sentence “. . . each act of decomposition involves one molecule only.” This might be regarded as a suitable definition of a unimolecular reaction but it is not clear whether it is intended to mean that, because the reaction 25206
+ 2N20r
+
0 2
involves two molecules according to Luder, with whom Glasstone agrees completely, and they both call it unimolecular. On page 1085Glrtsstone (3) says, “For unimolecular changes, or more explicitly for those of first order, the time taken to reduce the concentration of reactant by a
UNIMOLECULAR REACTIONS AND RADIOACTIVE TRANSFORM.1TIONS
515
definite fraction is independent of that concentration; for a given mass of gas, the amount decomposed in unit tame, Le., the rate of reaction,‘ will, thereforc, be independent of the volume.” Here the rate of reaction as he defines it would be, in our notation: dG -_ dt
In his letter (4)the rate is: dC -_ dt
On page 1024, in a footnote, he saya that the rate, velocity, and speed are used indiscriminately and should be regarded as synonymous, but surely two different cxpressions used for the rate by the same author are not synonymous. Want of convention and of clear-cut definitions leads in the hands of some other writers to such inaccuracies as the following: -dC/dt is described as the rate, and the rate is said t o be proportional to the amount of mattei reacting. In our notation it n-ould mean:
-which is inconsistent with both equations 1 and 2. ’rheie is another puint difficult to understand. Luder says that radioactive decay is not a first-order process in concentration. Glasstone agrees with him completely, and yet on page 1027 he says, “The decay of a radioactive element may be regarded as a first-order process.” Thus it appears that the order depends on the. letter used in the equation. If it is written with N , it is not first order; if for the same process C is used, it is t,he other way about. It should be added that Luder does not read rightly the exponential equation used in radioactivity. It is not stated in terms of weight, as he says, h i t number. Besides, it is expressed in terms of the number present at any t:rne, and not decomposed, as Luder says. In view of the above, the author cannot recognize as valid the method of Glasstone and Luder for discriminating between unimolecular and first-order reactions. CONCLUSIOX
The coefficient -d.V/dt is the only proper expression for the velocity of firstorder reactions. Radioactive changes and first-order reactions must be classed together, being subject to the same law, as stated in the article by Lind (7, page 1724). Want of proper definitions in chemical kinetics is the cause of the confused state of the subject. 1
Italics inserted by the author.
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GBORGE WTONOFF
Indiscriminate use of the expressions “speed,” “velocity,” and “rate” without giving definition t o these terms 1eads.to confusion, of which the theory upheld by Luder and Glasdtone is a manifestation. REFEREKCES (1) ANTONOFF,G.: J. Chem. Education 21, 420 (1944). (2) ANTONOFF,G.: J. Chem. Education 22, 98 (1946). (3) GLASSTONE, S.: Tezt-book of Physical Chemistry. D . Van Noatrand Company, Inc., New York (1940). (4) GLASSTOHE,S.:J. Chem. Education 22, 201 (1945). (5) LUDER,W. F.: J. Chem. Educstion21, 559 (1944). (6) LUDER,W. F.: J . Chem. Education 23,201 (1945). (7) TAYLOR, H . S.: A Treatise on Phgsical Chemistry, 2nd edition, Vol. 11. D . T-an Sost r a n d c o m p s n y , Inc.,NewYork (1931).
ISOTONIC SOLUTIONS : OSMOTIC AND ACTIVITY COEFFICIENTS OF LITHIUM AYD SODIUM PERCHLORATES AT 25°C.’ JAMES HOMER JONES Department of Chemistry, Indiana University, Bloominglon, Indiana
Received September 3,1946
The activity coefficients of lithium and sodium perchlorates up to 1 molal have been determined from freezing-point measurements by Scatchard and coworkers (4). No measurements a t 25°C. are available in the literature. The present investigation determines the osmotic and activity coefficients of the two salts a t 25’C. and over a much wider concentration range-about 0.2-6.5 molal for sodium perchlorate and 0.2-4.5 molal for lithium perchlorate. The method used is the familar isopiestic vapor-pressure measurement developed by Robinson and Sinclair and perfected by Robinson (3). The reference salt is sodium chloride, the activity and osmotic coefficients of which have been tabulated by Stokes and Levien (5). The apparatus, except for some modification, has been described previously (1). An all-brass desiccator about 8 in. in diameter and 6 in. deep replaced the one previously used, and a new rocking device was installed. This furnished a much superior heat reservoir and helped to moderate the effect of small fluctuations of temperature in the thermostat. EXPERIMENTAL
Purijicatim of materials c. P. anhydrous sodium perchlorate was recrystallized from isobutyl alcohol, washed with anhydrous ether, and dried a t 100OC. The material was then crushed in an agate mortar, dried a t 250°C., and stored in a vacuum desiccator over anhydrone. The lithium perchlorate \vas made according t o the method 1 Presented before the Division of Physical and Inorganir Chemistry at the 110th meeting of the American Chrmical Soriety, Chicago, Illinois, September, 1946.
