446
IRVIN BACHMAN
Also, all these materials were found to occlude varying amounts of an amorphous material, essentially silica. 3. Hydrous silica is not necessary for the stabilization of the complex compounds. 4. Reasons are discussed to explain the formation of such a compound rather than the copper silicate to be expected in such a reaction. The authors are indebted to Dr. Harvey A. Seville, Head of the Department of Chemistry and Chemical Engineering of Lehigh University, for his valuable criticism of their paper. REFERENCES (1) BINDER:Ann. chim. 6,337-409 (1936). (2) DOELTER:Handbuch der Mineralchemie, Vol. 11, pp. 775-9. Theodor Steinkopff, Dresden and Leipeig (1914). (3) HANAWALT, RINN,A N D FREVEL: Ind. Eng. Chem., Anal. Ed. 10, 457 (1938). (4) JORDIS AND HENNIS:J. prakt. Chem. [21 77, 238-61 (1908). ( 5 ) MELLOR:Treatise o n Inorganic and Theoretical Chemistry, Vol. 111, p. 261. Longmans, Green and Co., London (1923). (6) NEVILLEAND OSWALD:J. Phys. Chem. 36, 60-72 (1931). (7) POSNJAK A N D TUNELL:Am. J. Sci. [51 18, 1-34 (1929). (8) STERICKER:Chem. Met. Eng. 26, 61 (1921). (9) WEISER:Inorganic Colloid Chemistry, Vol. 111, p. 369. John Wiley and Sons, Inc., New York (1938).
CONVERGENCE OF TIE LINES I N TERNARY LIQUID SYSTEMS IRVIN BACHMAN
U.S. Industrial Chemicals, Inc., Fairfield, Maryland Received J u n e 20, 1959
Tie lines connecting compositions of conjugate solutions on ternary liquid diagrams appear to converge to a point on the extension of the base of the triangle. Tarasenkov and Paul’sen (2) have attempted to locate this point mathematically by writing an equation for tie lines, but these authors failed to take into account the fact that compositions ona ternary chart must be translated to the rectangular system of coordinates before substituting such compositions in the equation. These authors, moreover, concluded that tie lines converge to a common point. The mathematical method of the present article corrects the error made by Tarasenkov and Paul’sen and presents data to show that tie lines for less concentrated solutions have no common focal point.
447
CONVERGENCE OF TIE LINES IN TERNARY LIQUID SYSTEMS
Referring to figure 1, we observe that any point, such as PI,representing a ternary mixture of components A, B, and C, may be located on a C
B
''
Y
FIG.1. Location of ternary compositions on rectangular coordinates TABLE 1 Points o j intersection o j tie lines with eztended base o j triangle
I
!
*The numbers refer to the system numbers of table 2.
12.0 36.5 11.8 36.7
448
IRVIN BACHMAN
system of rectangular coordinates of which the x-axis is an extension of the base of the ternary diagram and the y-axis passes through vertex A. The ordinate of PI, or yl, is identical with its content of component C. The abscissa of P I , or xl, is given by the line SP1. From the geometry of the figure it is evident that SPi
=
SM
+ MPI
where CI and B1 are the C and B content, respectively, of the point Pi. Consequently,
TABLE 2 Systems investigated IVzXPDBATWBI
BE?mENCB
‘C.
Benzene-alcohol-water Benzene-alcohol-water Toluene-alcohol-water Cyclohexane-alcohol-water Benzene-acetic acid-water Chloroform-acetic acid-water Acetone-chloroform-water Benzene-alcohol-water
20 25 20 25
25:
25 25 25
The general equation of a straight line passing through two points is Y 2
- Y2 - Y1 - Y2 - 2 2 z1 - zg
Letting y = 0 to obtain the intercept of the l i e upon the z-axis, we have Z(Y1
- Y2)
=
z2y1
- y8zl
If, now, we substitute in this equation the coordinates of the points PI and P2 we obtain the abscissa of the point where the extended tie line crossea the z-axis. This expression reduces to
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). D. N., AND PAUL’SEN,I. A.: J. Gen. Chem. (U. 5. S. R.) 8, 76(2) TARASENKOV, 82 (1938). (3) TAYLOR, S. F.: J. Phys. Chem. 1, 401 (1897). (4) VARTERESSIAN, K. A , , AND FENSKE,M. R.: Ind. Eng. Chem. 28,928 (1936). (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:
