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American Chemical Society
with which has been incorporated the
American Chemical Journal
(Founded by Ira Remsen)
[CONTRIBUTION FROM THE PHOENIX PHYSICAL LABORATORIES, COLUMBIA UNIVERSITY. ] A CALORIMETRIC PROCEDURE FOR DETERMINING THE HEATS OF SLOW REACTIONS.
I. THE ANALYSIS OF PARTIALLY CONCURRENT HEAT EFFECTS.
Received February 2, 1920.
The reaction heats of slow chemical changes have not as yet been measured with dependable exactness. The closest approach so far made toward the satisfactory calorimetry of such processes is, without doubt, the very careful work of Brown and Pickering on the heats of mutarotation of glucose and fructose,' and on the heats of hydrolysis of starch and sucrose by enzymes. In these investigations Brown and Pickering did not attempt the calorimetry of the whole process; but only that of a part of it, determined in each instance by the change in optical rotation which simultaneously occurred. They thus offered a method of attack which was neither completely general nor wholly calorimetric; and since, when their measurements were made, calorimetric procedure had not yet been developed beyond the stage to which Berthelot had carried it.
'Brown and Pickering, J. Chem. Soc., 71, 756 (1897).
* Brown and Pickering, ibid., 71, 783 (1897). For Berthelot's earlier but unsuccessful attempt to measure the heats of mutarotation, see Compt. rend., 120, 1019 (1895); see also Brown and Pickering's remarks upon this work (loc. cit.,  pp. 757759); and Nelson and Beegle's criticism (THIS JOURNAL, 41, 571 (1919)).
their work, though admirable for its ingenuity, precision and caution, must have been affected by very considerable error.1 Their method, none the less, is clearly applicable to many, if not all, of those slow changes which do not involve an appreciable heat of mixture, and their calorimetric errors could now be materially reduced. It is regrettable that their work has not been followed up. As a consequence of this and similar neglect, we still lack dependable knowledge concerning the internal energy relations of all those reactions, the speeds of which are measureable. The obvious effect of such ignorance in limiting the scope and coördination of physicochemical and of physiological research points clearly to the high desirability of developing general and easily adaptable procedures adequate for the precise calorimetry of slow processes.
It was the primary purpose of this investigation to develop such a procedure, more general than that of Brown and Pickering, which should permit the calorimetric examination of complete reactions of various thermochemical character in liquid systems, whether or not these were accompanied by a heat of mixture; and which should be sufficiently exact in principle to make its gradual improvement to the limit of calorimetric precision, defined by minimal thermometric error, not impossible. In order that these conditions should be met, there was chosen for examination and experimental test a reaction of considerable complexity; that, namely, of the complete inversion of sucrose by hydrochloric acid. This reaction possessed many advantages for the purposes in view. Like the greater number of those changes which occur in liquid systems, it is always accompanied by a heat of mixture, that of dry sucrose in acid, or that of acid in sucrose solution, neither one of which can be separately determined; the heat of inversion itself requires, under safe and convenient conditions of temperature and concentration, more than 5 hours for its complete development; and the process as a whole, involves both endothermal and exothermal changes. To measure the heat of this reaction, therefore, it was necessary at the outset to devise means for overcoming the three greatest difficulties likely to be encountered in the calorimetry of
1 For example, Brown and Pickering remark (loc. cit.,  p. 787) that in the determination of the heat of hydrolysis of starch by amylase, the most protracted measurement of which occupied 30 minutes, the correction for thermal leakage was "generally much larger than the actual rise of temperature to be measured."
2 Brown and Pickering, in their measurements on mutarotation made correction for its progress during dissolution; but their procedure, which is not described in detail, was empirical and probably (in relation to present calorimetric precision) approximate (loc. cit.,  p. 759).
3 The current practice of calculating these heats of reaction from heats of combustion, or otherwise by inference from thermodynamical generalizations characteristically inexact, is confessedly a makeshift procedure which yields uncertain, or at best roughly approximate results. See, for instance, the remarks of Brown and Pickering on this point (loc. cit.,  pp. 783, 784).
protracted processes, which are: the simultaneous determination of two partially concurrent heat effects; the exact maintenance of a negligible or precisely measurable thermal interchange between calorimeter and environment during a long period of time; and the facile adjustment of such control continuously for rising and falling temperatures.
Anticipating the results of work yet to be described, these difficulties, it is believed, have been satisfactorily met, within a margin of error largely determined by the uncertainties of mercury thermometry. The present paper describes a method devised for the analysis of the concurrent heat effects of the sucrose inversion. A second communication will describe the calorimetry of this reaction, and the application of the formulations here developed to the results of actual measurement.
The following analysis will be found applicable to many concurrent effects other than that with reference to which it is developed. The discussion must, therefore, be interpreted as illustrated by, rather than as restricted to, the phenomena of sucrose inversion.
Thermal Effects in the Inversion of Sucrose by Acid Catalysis.
For the determination of any heat of reaction which is accompanied by heat of mixture, two alternative procedures will in general be possible, since the mixture may be accomplished in two ways. For reasons that will soon be apparent,' it was decided in actual measurement to initiate the reaction by dissolving dry sucrose in acid, rather than to mix acid with sucrose solution.
The dissolving of sucrose in dilute acid is an endothermal process; the reaction of inversion is exothermal. When, therefore, dry sucrose is mixed with acid there is at first a considerable fall in temperature, which is succeeded almost immediately by a slow rise, the rate of which gradually diminishes as time goes on. If the temperature change in this process be plotted in rectangular coördinates against the time, we have a curve typical of this sort of reaction. Such a curve, drawn from the results of measurement, and divided for convenience into segments marked by the time intervals I, II and III, is shown in Fig. 1. During Period I the dominant effect is the negative heat of solution; in Period II, the positive
1 See page 1302.
REACTION CURVE FROM DETERMINATION No3