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SOTES
Previous investigattions of thermodynamics of ionization of aqueous ca,rboxylic acids in which there is no possibility of zwitterion formation indicate that entropies of ionization can be expected to be about -20 cal./deg. mole. Thle entropy of ionization of benzoic acid, which should be comparable to that of the pyridine monocarboxylic acids in the form YRCOOH, is - 18.9 cal./deg. mole.8 Entropies of ionization of amino acid zwitterions are considerably less negative, often being about - 110 cal./deg. m ~ l e . ~ J ~ Entropies of ionization reported in Table IV are clearly less negative than expected for S R C O O l l species and therefore support the work of Jaff6’ and Green and Tong4 which led them to conclude that the pyridine monocarboxylic acids exist largely in the zwitterion form +HXRCOO- in aqueous solution: The entropy of ionization of picolinic acid is considerably more negative than A S ” values for nicotinic and isonicotinic acids, which indicates that the charges in the zwitterion of picolinic acid are so close together that, from the point of view of nearby water molecules, there is only a little difference between +HRKCOOand RNCOOH. Acknowledgment. We are grateful to the National Institutes of Health for support of this research. (8) L. P. Fernandez and L. G. Hepler, J . P h y s . Chem., 63, 110 (1959). (9) R. N. Diebel and D. jF. Swinehart, ibid., 61, 333 (1957). (10) J. T. Edsall and J. Wyman, “Biophysical Chemistry,” Vol. I , Academic Press, Inc., New York, N. Y . , 1958.
A Steady-State at Initial Concentration Method of Studying Reaction Rates
by Homer Jacobson a:nd Herbert Dubno Department of Chemistry, Lliooklyn College, City University of N e w Y o r k , Brooklyn 20, N e w York (Received J a n u a r y I?’, 1964)
This communication describes a method of measur-. ing reaction rate kinetics in a stirred-flow system with a steady state which does not vary from the initial condi-. tions. Known methods using flow systems to study kinetics in the gas pharsel or in ~ o l u t i o n ~give - ~ a steady state within the reaction chamber. Where there is a longitudinal flow path, the steady state will vary along it; in the stirred-flow reaction methods, the steady state is substantially constant, once attained, but cannot be specified in advance and must be measured by
“freezing” the reaction and analyzing aliquots from the flow, The recent development of servo-controlled buret^^,^ has allowed measurement of reaction rates as a function of the flow rate of the reactant (typically H+) added (or of H + product removed by addition of OH -), I n the described method, the entire reaction mixture is rigidly maintained in a steady state determined in advance, at concentrations initially put into the system. The reaction rate is determined by measuring the flow rate of input reactants, as needed to maintain the steady state. A servo device is basic for attainment of correct flow rate to keep the steady state. A careful adjustment of the relative quantities of reactants, as determined by reaction stoichiometry, and of concentrations of added reactants, and, if desired, an overflow device to keep the volume of the system constant (the flow rate will otherwise increase exponentially with the volume) constitute, in principle, the requirements of the steady state at initial concentration, or SIC, kinetics method. Any servo system which responds t o a null device primarily activated by a change in concentration of one component of the mixture can suffice to adjust the reaction rate. The pH-Stat, responding t o changes in [H+], is frequently convenient and commercially available. Let such a reaction including proton transfer for study be represented in generalized form by the equation aA
+ bB + h H + +
CC
+ dD
(generalization to proton-producing reactions, using OH- instead of H + in the compensating buret, is entirely analogous and needs no separate treatment). Let the initial concentration of reactant or product Y be designated [Yi]. At the reaction rate needed to match an input of reactants, reaction stoichiometry demands a mole ratio of a : b :h : c : d for the reactants added and products produced, respectively. The servo system needed t o maintain the match must supply these reactants in compensation in the mole ratios a :b :h. We define the generalized compensatory concentration [XI such that the servo burets supply A, B, and H + in concentrations of a [ X ] ,b [ X ] ,and h[X], respectively. I n addition, however, a supply of solutions of the reagents must also compensate for their ~~
~
(1) M. Bodenstein and S.Wolgast, 2. physik. Chem., 61,422 (1908). (2) K. G. Denbigh, Trans.Faraday Soc., 40, 352 (1944). (3) H. H. Young and L. P. Hammett, J . Am. Chem. Soc., 72, 280 (1950). (4) J. Saldick and L. P. Hummett, ibid.,72, 283 (1950). (5) J. J. Lingane, A n a l . Chem., 21, 497 (1949).
(6) C . F. Jacobsen and J. Leonis, Compt. rend. trau. Lab. Carlsberg: Ser. Chim., 27, 333 (1951).
Volume 68, Number 11
,Vovember, 1964
YOTES
3438
dilution of the reaction mixture by the solvent present, This means that the additional concentrations of [A,], [B,], and [H,'] must be added t o the compensatory concentrations above, since addition of solutions a t the same concentration will not dilute, making the corrective concentrations of the three reactants equal to [A,] a [ X l , [B,] b[X], and [HI+] h[X], respectively. There are further constraints, if absolute constancy of conditions is desired. There is ordinarily likely to be a buildup of products, and certainly so if none are present in the initial reaction mixture. This buildup can be prevented if products are initially added to the system, taking advantage of the diluting action of the solvent in the added reactant solutions, using a prescribed initial concentration of products, Le., [C,] and [D,],in the mole ratio of c : d . If, nom, [C,] and [D,]are taken equal to c [XI and d [XI, then the conversion of reactants to products can be simply shown to be exactly matched by a sufficient addition of solvent to keep the concentration of products the same. We have described the addition of the compensatory reactants as though a single such solution were added. Such a solution would, of course, be unstable, and in practice the material must be added with a t least two separate burets to prevent reaction. The concentrations given for compensation above would have, for instance, to be doubled if added in two equal but separate solutions from two burets. Reactions other than proton transfer can, of course, be studied by the SIC method. A separate electrode system, sensitive to changes in any other reactant or product concentration, e.g., an oxidation-reduction electrode, or one more or less specific for a given reactant or product ion, used with the pH-Stat electronics and burets, will give the same kind of compensation. Reaction rates cannot be obtained by the full SIC method for solutions without some products initially present, as well as reactants. Where the reverse reaction or presence of products plays no role, a partial SIC can be used, with the ratio of [XI to product concentrations arbitrary. Where the reverse reaction is important, however, the minimum amount of initial product concentrations present is determined by how low [XI can go practically. At low enough values, the ratio of [XI to the initial reactant concentrations is so small that setting the compensation by the concentrations in the buret becomes inaccurate. Moreover, the rate of the reaction may become large compared with the mixing and diffusion rate at low values of [XI. Unreacting substances whose effect on the kinetics of the reaction of interest, such as salts or variable solvent, can be simply present at one constant concentra-
+
+
The Journal of Physical Chemistry
+
tion in the initial solution and in all compensating burets. Comparison of the SIC method with the stirred-flow methods of Hammett and c o - ~ v o r k e r sshows ~ ~ ~ the advantages of avoidance of any sampling or measurements on the system other than that implicit in the null device, furnishing of data directly on a linear plot or record, estimation of the accuracy of the determined rate and the freedom from side reactions from the linearity of the plot, lack of waste of reactants during the almost instantaneous setting up of the steady state, and, above all, determination of the rate of reaction at an unchanging and previously set group of concentrations. It shares the disadvantage with stirred-flow methods of giving only a single point on a kinetics curve per run, although the variable of the null device can be changed during the measurement if desired; in addition, the demand for clean and known reaction stoichiometry and the requirement that mixing be rapid relative to the reaction rate measured place limits on the type of reaction which can be studied by the SIC method. I n the variation of Saldick and Hammett, in which continuous titration of the efluent of the stirred reactor is made, one sees something very close to the discovery of the SIC method (the Saldick-Hammett work was unknown to the authors prior to this). The simple switching of the titrator to the input of the reactor would have, along with the compensatory concentrations demanded, given the essence of SIC. Acknowledgment. We acknowledge with support from N.I.H. on Grant GMS-09023.
thanks
Reaction of Hydroxylamine with Thiolesters
by R. Bruce Martin and Laura P. Henkle Cobb Chemical Laboratory, University of V i r g i n i a , Charlottesuille, V i r g i n i a (Receised J u n e 19, 1964)
Two studies of the reaction of hydroxylamine with thiolesters a t room temperature have given apparently conflicting results. The reaction of hydroxylamine with acetylthioglycolic acid has been found to be first order in hydroxylamine at p H 5.4.l On the other hand, a second-order reaction in hydroxylamine has been reported for the reaction of hydroxylamine with butyl thiolacetate a t pH 5.4-7.5.2 In this note further (1) L. H. Soda, S.A. Kuby, and H. A. Lardy, J. Am. Chem. SOC., 75, 913 (1953). (2) T.C . Bruice and L. R. Fedor, ibid., 8 6 , 738 (1964).
