Mar., 1954
685
OTES
layer was more than twice as large. For comparison, we may also mention that the heat of hydration of anhydrite, CaS04, to gypsum, CaSO4.2Hz0 is 2000 cal./mole of waterlo; the heat of hydration of pseudowollastonite, a-CaSi03, to the monohydrate is 2600 cal./mole; and the heat of hydration of wollastonite, p-CaSi03, to the monohydrate is 1300 cal./mole. Acknowledgments.-We wish to acknowledge our great indebtedness to Dr. L. E. Copeland
for generously supplying us with most of the materials used in these experiments; to Mr. C. L. Ford and his associates, Mr. E. E. Pressler, Mr. E. LaBonde, Mr. W. G. Hime, and Miss Helen E. McMillen for the very fine analytical work performed on the materials; and to Mr. T. C. Powers, Dr. L. E. Copeland, Dr. H. H. Steinour, Mr. G. J. Verbeck and Dr. D. L. Kantro for the helpful discussions and suggestions contributed to this work.
NOTES T H E APPROXIMATE SOLUBILITY OF DIBORANE I N PENTANE’ BY L. V. MCCARTY AND JOHNGUYON Research Laboratory. Uenerol EkClr%’C Company, Scheneclady, N . Y. Received October 19, 1965
The solubility of an impure sample of diborane gas is calculated from pressure measurements of the gas in equilibrium with normal pentane solutions at various temperatures. A number of assumptions have to be made for lack of a detailed knowledge of this system. Raoult’s law is applied to the solutions, and all vapors are treated as ideal gases. The molar volume of diborane in solution is ignored in the calculations, but this should not cause an error of more than 3% in the concentration of diborane in the liquid phase a t the highest, concentrations. The coefficient of expansion of normal pentane2 is used up to 55” even though it is given for the 0-30” temperature range only. The vapor pressure of n-pentane is taken from Stull’s table^.^ The data recorded in the table under “B2Hapressure” are obtained by subtracting the vapor pressure of n-pentane from the “observed pressure.” The equilibrium constants for the system B*Hs(g) = B ~ H (in B pentane solution), K
=
SJP
are recorded in Table I. S is the solubility expressed as mole per cent. diborane in solution, and P is the partial pressure of diborane in atmospheres. The solubility of diborane in n-pentane is somewhat less than observed for ethyl ether.4 Calculations based on the diborane vapor pressure equation of H. L. Johnston,s et al., indicate that Rnd t ’ s law applies very well to the system diboranen-pentane. The observed partial pressures of diborane in equilibrium with a n-pentane solution in the temperature range 0-55 are reproduced by the equation This work was done for A r m y Ordnance Contract TU1-2000A. ( 2 ) M. P. Doss. “Physical Constants of the Principal Hydrocarbons,” The Texas Company, 1943. (3) D. R. Stull. I n d . Eng. Chem, 89, 517 (1947). (4) J. R. Elliott, W. L. Roth. G . F. Roedel and E. M. Boldeburk. J . Am. Chem. Soc.. 74, 5211 (1952). (5) “Condensed Gas Calorimetry.” E. B. Rifkin, E. C . Kerr and
The heat of solution is -2500 cal./mole which is somewhat less than observed for ethyl ether as the solvent . TABLE I
EQUILIBRIUM PRESSURES
DIROR.4NE
IN
PENTANE
cc.
Observed pressure, p s i . abs. m
1 ,
OC.
0.0 10.2 19.G 30.7 39.0 54.8
10.4 13.2 15.8 20.5 24.6 35.6
... 18.4 22.0 27.1 32.1 44.7
23.7 27.8 32.2 38.2 43.9 57.0
34.2 30.5 45.2 53.2 60.2 75.4
50.2 56.5 63.7 72.2 80.2 98.2
B2Ha pressure, atm. 0.0 10.2 19.6 30.7 39.0 54.8
0.466 .507 .532 .588 .653 .G93
... 0.802 0.958 1.041 1.103 1.245
1.37 1.51 1.66 1.81 1.91 2.09
2.09 2.31 2.56 2.85 3.05 3.42
3.20 3.45 3.84 4.17 4.45 5.03
Rlole % B2& in liquid 0.0 10.2 19.G 30.7 39.0 51.8
1.59 1.49 1.47 1.31 1.15 1.15
.., 2.83 2.53 2.37 2.28 1.98
4.50 4.12 3.74 3.42 3.27 2.98
7.32 G . N 6.5G 6.07 5.85 5.32
11.25 11.04
9.95 9.65 9.24 8.10
ii = S / P (mole % B2€16/atm. of &€I6) (Av. K )
(1)
H. 1.. Johnston, Tech. Report No. 5, Project RB-309,The Ohio State Univ. Research Foundation.
FOR
MmolesBzHB 5.84 3.26 9 . 8 1 12.68 24.0 Mrnoles CSH,2 8 5 . 4 85.4 85.4 85.4 85.4 Cylinder vol., 100.8 101.8 104.7 7 3 . 5 101.0
0.0 10.2 19.6 30.7 39.0 51.8
(3.4) (3.0) (2.6) (2.2) (1.9) (l.G)
3.4 2.9 2.8 2.2 1.8 1.7
...
3.3 2.G 2.3 2.1 1.G
3.3 2.7 2.3 1.9 1.7 1.4
3.5 3.0 2.6 2.1 1.9 1.6
3.5 3.2 2.6 2.3 2.1 l.G
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.
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 E - log y Agr+ - N log y’(Lt pKi 0.06016 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 effective length 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 CY 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 values, it was necessary to assign a value of unity (1941); AgsBrc-4, W. Erber, 2. altorg. Chem., a 4 4 32, 36 (1941); 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.
+
7
+
+
-
(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.
