NOT ’ES
286
Experimental Materials.-The %-pentanewas Phillips Pure Grade 99 per cent. pure. The diborane was analyzed by infrared absorption, and it contained 2.1 mole per cent. ether, 3.5 mole per cent. ethane and 94.4 mole per cent. diborane. Procedure .-The stainless steel cylinders were attached t o a vacuum system and 10.00 cc. of n-pentane was distilled into each one. The number of moles of diborane added to each cylinder was measured by filling a vacuum system of known volume to a given and condensing the diborane in the cylinder wit a li%uid nitrogen bath, The cylinders were then warmed to 0.0 and thoroughly agitated to ensure equilibrium, and this process was repeated for each succeeding higher temperature. Pressures were read on ordinary gages as received with no special calibration.
+
7
Vol. 58
where K i is the dissociation constant of the complex, E is the potential difference between the electrodes, A%+ is the concentration of the reference silver solution, N is the number of ligand molecules per silver ion in the complex, Lfis the concentration of free ligand, and A g L N + is the concentration of the complex ion formed. I n the region of amine concentration where the maximal codrdination number attains equation 1can be recast in the form pKi
E - log y Agr+ - N
0.06016
log y’(Lt N Agt+) log Y” Agt+ (2)
+
where L t is the total ligand concentration, Agt+ is the total silver ion concentration in the amine solution, and y, y’ and y” are the respective molar activSILVER ETHYLAMINE COMPLEXES I N ity coefficients. ALCOHOLIC SOLUTIONS Values of N were assumed and constancy of p K i BY HANSB. JONASSEN, THOMAS F. FAULEY, C. C. ROLLAND as calculated from equation 2 noted. A plot of -E/0.06016 versus - N logy’ (Lt - N Agt+) log AND P. C. YATES y” Agt+ gave a straight line with a slope of 1.0 for Richardson Chemistr Laboratory of Tulane University, A, Orleans, La. N = 2. Received October 85, 1065 I n addition, conductance titrations run over the Introduction.-Silver (I) occupies a relatively concentration range employed in the e.m.f. studies unique position among the transition elements. point to the validity of the choice of 2 for N . After the method of BjerrumJ6 silver nitrate Although it is commonly supposed that it exhibits a stable coordination number of two in its complex and the complex compound in the alcoholic media ions, there are numerous cases1 in which observed were considered as weak electrolytes. Bjerrum’s data can best be explained in terms of a coordina- theory allows the calculation of the association tion number of three or four or even six. Theoreti- constant of such ion-pairs, but the solution of the cally, there should be little difference in the relative equations depends on the value assigned to the stabilities of the two and four coordinated statesn2 parameter “II,” which in turn depends on the efThis investigation was undertaken in order to ex- fective radii of the ions in solution. Crystalloamine some of the factors which would influence graphic radii were used for the ions involved. In the formation of silver(1) complexes with a coordin- the case of the complex ion Ag(C2H6NH2),*, where ation number higher than two. It has been noted x is any integer, Fischer-Hirschfelder models were elsewhereS that one of the principal contributions used to decide the statistically most probable shape to the stability of complex ions lies in the dielectric of the ethylamine molecule and its effectivelength constant of the solvent medium. Thus, on the calculated from covalent radii. When added to basis of electrostatics, a lower dielectric constant of the value for Ag+, this yielded 4.48 A. for the effecthe solvent should serve to increase the effective tive radius of the complex ion. This value should polarizing power of the cation in question, and so be independent of the number of ethylamine moleenhance the stability of the higher coordinated cules attached to the silver ion, since the ion formed could be viewed as spherical in any such case. state. The values of the association constanb K-l calTheoretical.-The method employed to determine the dissociation constants of the complexes culated for isopropyl alcohol solutions at 30’ were studied is a modification of the potentiometric 489.3 for AgN03 and 116.3 for the complex Agmethod of Bodlander4 and Koch.6 In this, the (C2HsNH2)zNOa.For ethanol solution at 30°, the values are 142.4 for AgNOs and 39.73 for the comNernst expression for the cell plex. Ag, Ag+ + ligand (I Ag+ The mean molar activity coefficient of the ionAg is related to the mass action expression for the pairs, y*l was expressed as a function of a the dedissociation of the complex ion formed in the left gree of dissociation, by use of the “extended” Dehand half-cell. For a one-electron change a t 30°, bye-Hiickel equation and the resulting equation the resulting equation is used to evaluate (Y by successive approximations. The molar activity coefficient for the uncharged ionE PKr = -log& - - log Agr+ pair, y12,was assumed to be unity. This is not ’ - 0.06016 without precedent? N log Lf+ log AgLN+ (1) Furthermore, in the actual calculation of PKi (1) AgCl4-*, W. Erber and A. SchUhly, J . prakt. Chem., 168, 176 (1941); AgsBrc-4, W. Erber, 2. altorg. Chem., a 4 4 32, 36 (1941); values, it was necessary to assign a value of unity Ag(OAc)a-a, I. Leden, Suensk. Kem. Tid.,68, 129 (1946). for the activity coefficient of ethylamine in the al(2) L. P a u l i g , “The Nature of the Chemical Bond,” 2nd Edition, cohols, This procedure was primarily due to the Cornell University Press, Ithaca, N. Y.,1948, pp. 81-89.
+
-
(3) H. B. Jonassen, Record of Chemical Progress, 18, 136 (1952). (4) a. Bodlander, r e cited in S. Glasstone, “Textbook of Physiosl Chemistry,” 2nd Ed., D. Van Nostrand Co., Inc., New York. N. Y., 1946,
pp.
972-974.
( 5 ) F K. V. Koch, J . Chem. Soc., 2053 (1930).
(6) N. Bjerrum, a8 oited in H. S. Harned and B. B. Owen, “The Physical Chemistry of Electrolytic Solutions,” 2nd Ed.. Reinhold Publ. Corp., New York, N. Y . ,PP. 42-45. (7) D. A. MacInnes, “The Principles of Electrochemistry,” Reinhold Publ. Corp., New York, N. Y., 1939, p. 372.
Mar., 1954
287
NOTES TABLE I1 ISOPROPYL ALCOHOL logy Agrf = -2.05
lack of available data, and while not entirely justifiable, the error introduced should certainly lie within the limits of other necessary approximations. Experimental.-All chemicals employed were of C.P. grade. Ethanol was dried according to the method of Lund and Bjerrums and suitable precautions were employed throughout the measurements to prevent its exposure to moisture. The isopropyl alcohol contained 0.50% water. The dielectric constant of the ethanol was taken as 24.2 at 30°, from the data of “International Critical Tables.”g The dielectric constant of the isopropyl alcohol was determined by a resonance circuit methodlo and found to be 19.2 a t 30”. The alcoholic A NO3 solutions were standardized against NaCl. The ethyfaamine solutions were standardized potentiometrically against aqueous hydrochloric acid. The silver electrodes were prepared after the method of MacDougall and Peterson.ll The measurements were made using two half-cells containing silver nitrate solutions of the same concentration, connected through an agar salt bridge (saturated with KNOs) to a standard potentiometer set-up The e.m.f. values were measured for concentration increments of amine reagent, and pKi’s were calculated for each as shown by a few re resentative calculations for the two solvents in the Table ?(ethanol) and Table I1 (isopropyl alcohol). The average pK1 value for the complex in ethanol was 8.22 and in isopropyl alcohol as a solvent was 8.50. TABLEI I ETHYL ALCOHOL log y Ag,+ = -1.92
.
Amine, ml. E/O ,06016 Apt Lt 2 log Lf or-Complex -log (COLI --log u”.. pKi +
7.00 6.757 0.04599 0.3088 1.328 0.759 1.457 0.320 8.23
8.02 6.862 0.04556 0.3363 1.221 0.760 1.461 0.319 8.22
8.98 6.953 0.04615 0.3617 1.133 0,760 1.465 0.318 8.22
10.00 12.00 7.028 7.183 0.04474 0.04394 0.3882 0.4388 1.050 0,910 0.761 0.763 1.468 1.475 0.317 0.316 8.21 8.22
(8) H. Lund and J. Bjerrum, Ber., 64B,210 (1931). (9) “International Critical Tables,” Vol. VI, MoGraw-Hill Book Co., Inc., New York, N. Y., 1929,p. 85. (10) The authors wiah to thank Dr. F. Boylan (formerly of these laboratories) who determined this value for u. (11) P. H. MaoDougall and 1. Peterson, THISJOURNAL, 61, 1346 (1947).
Amine, ml. 20.00 22.00 24.00 26.02 28.02 9.391 8.285 8.339 E/O.O6O16 8.125 8.215 Apt 0.03616 0.03515 0.03420 0.03329 0.03243 0.9170 0.9642 0.8187 0.8689 Lt 0.7656 0.1408 0.0942 -21og Lf 0,3182 0.2517 0,1933 0.685 0.687 a-Complex 0.678 0.681 0.683 1.642 1.652 1.622 1.632 -lOg(ca) 1.611 0.378 0.384 0.381 0.386 -logy’* 0.389 8.50 8.50 8.50 8.51 PKi 8.49 +
Discussion.-Even though in a strict sense direct comparison is invalidated by the fact that each complex ion is referred to a different solvated ion, one must note the increase in stability of the Ag(Et”&+ complex with a decrease of dielectric constant of the solvent. The inclusion of the value for the aqueous system as determined by Carlson, et aE.,layields the following table for this complex. Solvent
Dielectric constant
Water Ethanol Isopropyl alcohol
76.7 24.2 19.2
PK~
7.14 8.22 8.50
At high concentrations of amine, Le., at mole ratio of amine to Ag+ of 30, the assumption of a coordination number of 3 gives a constant pKi value of 8.42 for ethanol solution. This constancy may be illusory since a t such high amiiie concentrations the quantity (Lt - NAg+) is practically constant and relatively insensitive to the value of N chosen. Furthermore, the constancy of the p K i values at these high concentrations may be a reflection of significant departures of the activity coefficient of the free amine from unity. Acknowledgment.-The authors are indebted to the Office of Naval Research for the sponsorship of this and continuing investigations. (12) C. A. Carlson, J. P. McReynolds and F. R. Verhoek, J . Am. Chem. Soc., 67, 1334 (1945).
