BARBITURIC ACID DISSOCIATION CONSTANTS
449
The above equation has been applied to data taken from the literature for ternary liquid systems. Table 1 gives the distances thus calculated under the columns headed “abscissa distances”. In columns adjacent to the abscissa values of table 1 the corresponding values of the average concentrations of the consolute components are given (average C = (C, C2)/2). With increasing concentrations the value of average C approaches the per cent C at the critical point. The abscissa distances in the upper part of table 1, corresponding to tie lines for the less concentrated solutions closer to the base of the ternary diagram, are definitely not constant. The abscissa distances in the lower part of table 1, applying to the more concentrated solutions, show less variation, yet even in this region there is considerable deviation from constancy. These findings are in line with D. B. Hand’s (1) empirical equation, which holds for concentrated ternary mixtures but falls down for those mixtures very dilute with respect to either component A or component B. For several of the systems investigated a graph of abscissa distance versus concentration of the consolute component shows a trend of the abscissa values toward a maximum point.
+
REFERENCES (1) HAND,D. B.: J. Phys. Chem. 34, 1981 (1930). (2) TARASENKOV, D. N., AND PAUL’SEN,I. A.: J. Gen. Chem. (U. 5. S. R.) 8, 7682 (1938). (3) TAYLOR, S. F.: J. Phys. Chem. 1, 401 (1897). K. A , , AND FENSKE,M. R.: Ind. Eng. Chem. 28,928 (1936). (4) VARTERESSIAN, (5) WRIGHT, C. R. A., THOMPSON, C., AND LEON,J. T . : Proc. Roy. Soc. (London) 49, 174 (1891).
T H E EFFECT OF VARIATION I N IONIC STRENGTH AND TEMPERATURE ON THE APPARENT DISSOCIATION CONSTANTS OF THIRTY SUBSTITUTED BARBITURIC ACIDS M. E. KRAHL The Lilly Research Laboratories, Indianapolis, Indiana, and the Marine Biological Laboratory, Woods Hole, Massachusetts Received August 30, 1999
Although it has long been known from the work of Wood (12) that barbituric acid and certain of its mono- and di-substituted derivatives behave in aqueous solution as weak acids, little attention has been devoted to the determination of the degree of electrolytic dissociation of these substances in solutions of varying salt content and temperature. Such data are now of biochemical interest for two reasons:
450
M. E. KRAHL
First, as pointed out by Michaelis (9) for 5 ,5-diethylbarbituric acid, the disubstituted barbituric acids and their salts may be used as buffers to cover the range from pH 6 to pH 9, where the number of other substances available for buffers is relatively small. Secondly, the di- and tri-substituted barbituric acids are now widely used as hypnotic agents in medicine and physiology, and as such become partially dissociated in physiological media into hydrogen ions and barbiturate anions. From the preliminary experiments of Clowes and Keltch (3) it appears that certain of the barbituric acids penetrate living cells more readily as undissociated molecules than as anions. During a more extensive investigation of the factors bearing on the penetration and anesthetic action of these substances (4),it became necessary to determine, with some accuracy, to what degree each of a large number of barbituric acids would dissociate when dissolved in sea water. The present study was undertaken in an effort to provide data to meet this need and, a t the same time, to provide data and equations from which the approximate degree of ionization of any of the commonly used barbituric acids could be calculated for solutions of any salt content and temperature within the biological range of interest. THEORETICAL
In aqueous solution a t constant temperature the dissociation of a monobasic acid, HA, may be expressed as the reaction HA(aq.) F? Hf
+ A-
(1)
for which the equilibrium expression is the equation
In equation 2, [A-] and [HA] are the molar concentrations of anion and 1 undissociated acid molecule respectively; pH is equal' to log - ; pK', an+ the negative logarithm of the apparent dissociation constant, is related to the true thermodynamic dissociation constant, K, by the equation pK' = pK
+ log'x
(3)
YEA
For salt concentrations and temperatures in the physiological range it is assumed that yHa,the activity coefficient of the undissociated molecules, 1
1 pH, rather than paH, is used here t o represent log - for the reasons discussed
by Clark (2, footnote pp. 479-81).
a=+
BARBITURIC ACID bISSOC1ATION CONSTlYNTB
451
may be taken as unity. Under the same conditions yA-, the activity coefficient of the monovalent anion, is dependent on the ion content and temperature of the solution, according to the modified Debye-Huckel (5) equation:
- log 7.4-
=
1
+A Ba&4
(4)
In equation 4,A and B are independent of the acid used and are dependent on the dielectric constant and the temperature of the solution; a is an empirical constant which depends on the nature of the anion.' The ionic strength, p , of a solution is defined as one-half the sum of the products of the concentration of each ion present in the solution multiplied by the square of its valence.a According to Lewis and Randall (7, page 294), the thermodynamic dissociation constant, IC, for reaction 1 is related to the standard free energy change, A P , and the absolute temperature, T , by the equation:
AP
=
-RThK
(5)
where R is the gas constant having a value of 1.9864 calories per degree. Equation 5 may be put into the following form, which is more favorable for me here: = 2.3RT pK
A P varies with temperature (7, page 172), according to the equation
In equation 7, As" is the entropy change for reaction 1 under the same standard conditions as those for which K is determined. The numerical value of AS" is the slope of the line obtained by plotting experimental values of A P against 7'. For the purpose of the present discussion AS" may be regarded as independent of the salt content of the solution.
* Values of A and B , along with a discussion of the significance of a, are given by Clark (2, p. 500). Both y and p were originally defined for molal concentrations, which are expressed in terms of grams of solute per 1000 grams of solvent. The highest concentration of total salt (sodium chloride) used in the present experiments was 2 molar. From the specific gravity of a 2 molar sodium chloride solution, i t may be calculated that a t this concentration of sodium chloride the substitution of molar for molal concentrations results in a value for
AND
S. W. GRINNELL*
Department of Chemistry, Stanford University, California Received June 27, 1999 I. INTRODUCTION
Objects Our object in this paper is to obtain in general and exact form the thermodynamic laws of galvanic cells subject to external gravitational fields. In attaining this object we shall make use of a therniodynamic 1 The contents of this paper are taken largely from the dissertation submitted by S. W. Grinnell to the Faculty of Stanford University in partial fulfillment of the requirements for the degree of Doctor of Philosophy, 1938. * Shell Research Fellow, Stanford University, 1937-38.
