258
STANLEYBUKATA A N D JACOBA. MARINSKY
12.66 and 3.35 cal./(mole OK.), respectively, for pentaerythrityl fluoride. A sum of the two transitions in each of these substances gives the disorder present above their common lattice energy. Subtracting this sum for the fluoride from that of the alcohol gives 26.0 - 16.0 = 10.0 cal./(mole OK.). This is well within experimental error of the 10.1 cal./(mole O K . ) calcu-
lated by Westrum and Payne and, as such, is further evidence for the proper choice of mechanism for the observed transitions. Acknowledgment. This work was performed under the auspices of the United States Atomic Energy Commission. The authors are indebted to Dr. Elfreda Chang for assistance in the evaluation of the data.
Job’s Method of Continuous Variations with Ion Exchange for the Study of Complexes in Solution
by Stanley Bukata1f2 and Jacob A. Marinsky3 Department o j Chemistry, State University o j A’ew York at Buffalo, Buffalo, New York (Received J u n e 18, 1963)
The use of ion-exchange properties for determining the nature of complex species in solution by Job’s continuous variations method has been developed. The CU+~-EDTA,Caf2EDTA, and Ca+2-citrate systems were studied to demonstrate the method. The results obtained were in agreement with the results of earlier investigations of these systems.
Introduction Job’s method of continuous variations4 of isomolar solutions has been used frequently for the study of complexes in solution. Solution properties, which are linear functions of the concentrations of the species involved, are analyzed in applying the method. Some properties which have been employed are refractive index15heat of mixing6 densityI7dielectric constantI8 and light a b s o r p t i ~ n . ~A ~ ’solution ~ property adaptable to ,Job’s method and not previously discussed in the literature is ion exchange. The discussion below is given for cation exchange but would be similar for anion exchange. 1st mixtures be made by the addition of z ml. of B to (VT - t) ml. of A when both solutions are a t a concentration of 114 moles/l. The symbol VT corresponds to the total volume of the mixtures which is presumed to be essentially constant in the absence of appreciable volume change on mixing. Allow these isomolar solutions to undergo cation exchange with a suitable The Journal of Physical Chemistry
resin. Assume that A and B react to form a single complex according t o A
+ nB
AB,
(1)
Further, assume A undergoes cation exchange according to the equation
(1) (2)
(3) (4)
(5) (6)
Union Carbide Predoctoral Fellow, 1961-1962. This paper is based on a portion of a dissertation submitted by S. Bukata in partial fulfillment of the requirements for the degree of Doctor of Philosophy. Correspondence t,o be addressed to this author. P. Job, Ann. Chem., 9 , 113 (1928). G. Spacu and E. Popper. Bul. soc. stiints Cluj.. 7,400 (1934) M. M. Chauvenet, P. Job, and G . Urbain, Compt. rend., 171,855 (1920).
(7)
(8) (9)
Y. Wormser, Bull. aoc. chim. France, 15, 395 (1948). N. Q. Trinh, Compt. rend.. 226, 403 (1948). W .C. Vosburgh and G . R. Cooper. J . Am. Chem. SOC..63, 437 (1941).
(10)
R. K. Gould and W. C . Vosburgh, ibid., 64, 1630 (1942).
CONTINUOUS VARIATIONS WITH IONEXCHANGE
where the subscripts S and R refer to the solution and resin pha,se, respectively. The cation Pi must not form a complex with B and B and AB, are expected to be excluded from the resin, being anionic or neutral entities. In the presence of excess N, the ion exchange may often be represented by a linear equation
AR
k~As
=
(3)
where An is the concentration of A in the resin phase at equilibrium and A S is the concentration of A in the solution phase. At equilibrium, eq. 1, 2, and 3 must be satisfied simultaneously. Let Ci
=
(As)
(4)
=
(B)
(5)
(AB,)
(6)
C2
C3
=
where the parentheses signify millimolar concentration. Then for any mixture
c1 := M(VT - x)
- c3 -- kDCl
C2 = Mx - nC3 C1C2"
=
KC3
259
Thus, where C3 is a maximum or a minimum, n can be determined by use of eq. 17. In general, C3is not measured directly; instead use is made of the ion-exchange property of the solution to evaluate C3. Letting Y equal the difference between the observed removal from solution of A by exchange with N and by complexing with B (M(VT- x) - kDC1 - C,) and the calculated removal of A without complex formation { r n ( ~ T- x) - kDCl] then
in a concentration region in which eq. 3 holds. ferentiating eq. 18 with respect to x dY 1 dC3 1 k~ dx dx
+
(7) (8) (9)
where K is the equilibrium constant for reaction 1. The condition for a maximum or a minimum in the curve of C3 plaltted against x is dC3 -=o dx Differentiating eq. 7, 8, and 9 with respect to x
Experimental Several aqueous systems in which the complex species were already well defined were studied to test the above treatment. Dowex-50-4x in the sodium form was used throughout. The concentration regions studied werle where the ion exchange was governed by a linear rela-
0.7
=
(19)
where dCsdx = 0, dY/dx = 0, a plot of Y us. x will have a maximum or a minimum with Ca and eq. 17 continues to be valid.
0.8
At dCs/dx mum
Dif-
i
0, the position of the maximum or mini-
z 0.6 -'
a 0.5 0.4
and
0.3
dCz _- M dx substituting these values into (13) and using eq. 7, 8, and 9
0.2 0.1
0
Figure 1. Cu +2-EDTA system, Job's plot.
Volume 68, Number 2
February, 1964
260
STANLEY
4.0
BUKATA AND JACOB A. MARINSKY
1 4.0
*0 . 3
3.0
X h
2.0
1.0
” 10
20 30 40 60 X , ml. of EDTA.
Figure 2. Ca+LEDTA system,Job’s plot.
0
10
20
30
40
50
X , ml. of citrate.
tion. Constant ionic strength was maintained in the solutions. The total volume of solutions used was 50 ml.
Results Job’s plot for the CU+~-EDTAsystem is given in Fig. 1. Cupric nitrate (0.01 M) and the disodium salt of ethylenediaminetetraacetic acid (Na2H2EDTA) (0.01 M) were used. An ionic strength of 0.52 was maintained by means of sodium nitrate. The maximum occurs a t x = 25 corresponding to n = 1 in agreement with the literature. Figure 2 is Job’s plot for the Ca+2-EDTA system a t an ionic strength of 0.62; n = 1 in agreement with the literature. Job’s plot for the Ca+z-citrate system a t a pH of 6.6 to 7.2 is given in Fig. 3. Sodium citrate solutions were used as the source of ligand. A maximum occws where n = 1 but as x increases, the curve does not drop as ’
The Journal
of Physical Chemistry
Figure 3. Ca+2-citrate system, Job’s plot.
sharply as would be expected for the existence of just one complex species. We attribute this behavior to the presence of more than one complex. The existence of two calcium-citrate complexes has been noted in the literature. l 1 The results obtained are in agreement with the literature. The treatment given is limited to systems where only one predominant complex is formed. The method should be useful for those systems where other functions of the concentration are not linear or involve large experimental difficulties or costly equipment. Acknowledgment. Financial support through Contract No. AT(30-1)-2269 with the U. s.Atomic Energy Commission is gratefully acknowledged. (11)
J. Schubert and J. W. Richter, J . Phga. Colloid Chem., 5 2 , 350 (1948).
