TABLE I THERMODYNAMIC &UANTITIES 1200 Kn, -AFno, -AHnQ and A S n o INVOLVED I N THE RE.4CTION 30 AND 40' AND IONIC STRENGTH 0 OF sEVER.ZL RIVALEEUT hfCTAI, I O N 5 WITH IIICT\\IIUT:
VALUES FOR THE
AT
10, 20,
-f
Ion
n
log Kn 200
100
500
400
100
H+
1 10.35 f 0.01 10.01 f 0 . 0 1 9.70 f 0.01 9 . 4 0 f 0 03 13.4 2 6.83 f .02 6.05 f .01 5.87 f .02 5.60 f .03 8 . 1 C u t + 1 10.25 f .01 9.82 f .01 9.50 f .01 9.12 f .02 13.3 2 7.02 f .04 6.69 f .02 6.45 f .02 6.20 f .03 9 . 1 Ni++ 1 7.36 f .05 7.03 f .03 6.77 f .05 6.06 f .04 9 . 5 2 5.43 f .05 5.22 f .03 5.01 f .02 4.85 f .02 7 . 0 3 3.39 f .06 3.20 f .04 3.25 f .09 3.20 f .04 4 . 4 C o t + 1 5 . 5 2 & .02 5.16 f .02 5.08 f .02 5.01 f .05 7.15 2 4.01 f .01 3.77 f .03 3.76 f .03 3.63 f .03 5 . 2 C d + + 1 5.12 f .02 4.83 f .02 4.80 f .01 4.54 f .05 6 . 6 2 3.60 f .03 3.40 f .05 3.39 f :02 3.25 .08 4 . 7
strength of the sigma bond in the chelation process so that ratios higher than those for simple diamines should indicate stabilization other than by sigma bonding (presumably by a-bonding). Similar ratios computed from formation constant data for histamine, 4-(2-aminoethyl)-imidazole, are presented here. The stabilization is even greater than for 2-(2-aminoethyl)-pyridine. Previous work on histamine-metal ion systems was done in 0.1 M KC1 a t only two temperatures and did not include Cd ++. 3--6 Experimental and Results The preparation of solutions of metal ions, measurements and calculations were performed as described previously. Solutions of histamine were prepared from the hydrochloride by means of anionexchange The results are given in Table I. Discussion Acid Dissociation Constants.-For histamine the values of p K 2 (for BH+) and pK1 (for BHzz+)are both greater than those for 2-(2-aminoethyl)pyridine-the former is almost equal to that for 1,3-propanetliamine. Formation Constants.-The complexes of histamine are more stable than those of 2-(2-aminoethyl)-pyridine as would be expected of a stronger base.' The comparison in Table I1 shows that the stabilization of complexes of a 4-(2-aminoethyl)imidazole due to the heterocyclic nitrogen is slightly greater than that of 2-(2-aminoethyl)-pyridine. TABLE I1 STABILIE4TION D U E TO
Histamine
1 2 2-(2-Arninoethyl)1 pyridine 2 1,3-Propanedi,Lmine 1 2 (3) J. Z. Hearon, D. Burk
DOUBLY-BONDED NITROGEN
0.62 .5G
.51
0.44 .32 .38 .24 .33 .23
0.66 .57 .51
0.47 .35 .47 .27 .38 .30
and A. I,. Schade J . Natl. Cancer Inst., 9, 337 (1949). (4) A. Albert, Biochem. J., SO, 693 (1952). ( 5 ) B. L. Mickel and 8. C. Andrews, J . Am. Chem. Sac., 7 7 , 323, 5291 (1955). (6) C. R. Rerlsch, W. C. Fernelills and R. P. Block, J . P h y s . Chem., 6.2,444 1'19.58). ( 7 ) R. J. Bruehlrnsn and F. €1. Verhoek, J. Am. Chem. Soc., 70, 1401 (1948).
20"
-A P o 80
40"
1 3 . 1 13.4 1 3 . 5 8 . 0 8.05 i 0 13.2 1 3 . 2 13 1 8.9 9.0 S 9 9.4 9.4 9.4 6.9 7.0 6.9 4.3 4.5 4.6 7.2 6.9 7.0 5.2 5.1 5.2 6.5 6 . 5 6.65 4 7 4.6 4.7
-Ailno 10-400
13 4 10.1 15.5 11.0 10.9 8.2
2.3 6.9 4.8 7.4 4.4
AS,,CI
30'
0 -i -1 -0
-5 -4
7 -1 16
-3 1
THE CALCULATION O F LIQUID MOLE FRACTIONS ASD ACTIVITY COEFFICIEKTS FROM ACTIVITY DA4T:I BY SHERRIL D. CHRISTIAN, EDWARD NEPARKO,HAROLD E. AFFSPRUNG AND FRANK GIBSARD Department of Chemistry, The University of Oklahoma, Norman, Oklahoma Received October 84, 1960
A previous paper' described a method for determining activity coefficients of components in binary liquid mixtures from measurements of vapor density and total vapor pressure. Liquid phase compositions were not measured, directly but were calculated from the expression 2,
= d In a z / ( dIn a2
- d In a,)
(1)
where a1 and a2 are the activities of components 1 and 2, respectively, and x1 is the mole fraction of component 1 in the liquid phase. Equation 1 is derived from the const'ant temperature, constant pressure form of the Gibbs-Duhem equation. The vapor density method referred to above yields activity values directly, but it is necessary to curve-fit az as a function of al in order to calculat'e liquid composition and activity coefficients. Therefore, it was decided to develop a computer program for calculating activity coefficients and liquid mole fractions from tables of values of a2 and a1 for binary systems at constant temperature. In using the equilibrium still, and a number of other activity methods, values of a2 and a1 are obtained as a function of xl,and it is often desirable to check these data for self-consistency with the Gibbs-Duhem equation. A computer program which makes possible the calculation of 21 from tables of a2 and a1 values should prove useful for this purpose. It was proposed that such a program be developed and tested on several sgst>ems for which az, a1 and x1 have all been measured directlv. A comparison between calculated and experimental a2 2's. x1 and al 1's. x1 curves would provide an indication of the applicability and accuracy of the computational method. (1) S. Christian, E. Neparko and 11. Affsprnng, J. Phys. Chem., 64, 43? (InGo).
NOTES
June, 1961
Method of Calculation
1049
1.0
Equation 1 may be rearranged to give the expression x1 = 1/(1 - azdal/aldaz)
0.8
(2)
Using this relation, if a1 is known as a function of a2, z1may be calculated for any given value of ul. The function f = (a1 az - l ) / a z (3) proved very useful for curve-fitting purposes. For all of the systems studied, f varied slowly and uniformly as al changed from 0 to 1. For an ideal solution f = 0 for all values of a1 and a2. I n the case of solutions deviating positively from ideality, 0 < f < 1, and for negatively deviating solutions,
+
. 0.6 .-,x +
.3
4
0.4
f
