NOTES
Oct., 1956
so no appreciable error was involved in this procedure. The process of solution of a single 0.8264-g. sample of nitramide in 500 ml. of 0.001 N sulfuric acid a t 24’ was found to be endothermic by 3700 ca1.l mole. For calculation of the heat of formation of nitramide a t 24” from the elements, the following values were used. Enthalpy for the process of solution of nitrous oxide in water -5303 cal./mole (AC, between 0 and 40” +35.9 cal./OC.) as derived from the solubility data of Markham and Kobe8; heat of formation of nitrous oxide 19490 cal./mole and of liquid water -68310 as given by Rossini, et aL6 The value for the heat of decomposition of nitramide (c) to form nitrous oxide gas and liquid water was calculated to be exothermic by 28200 f 85 cal./mole. The uncertainty in this value includes that of sample purity, and that of calorimetric measurement. The heat of formation of nitramide (e) from the elements was calculated to be 20630 i 85 cal./mole (exothermic) at 24”, that for aqueous nitramide, - 16930 cal./mole. Comparison of this latter value with the heat of formation of hyponitrous acid in aqueous solution from the element,s as determined by L a t h e r and Z i m r n e r m a ~ and ~ , ~ recalculated by Rossini, et u Z . , ~ - 13700 cal./mole shows that aqueous nitramide is more stable by 3230 cal./mole than hyponitrous acid.
+
( 8 ) A. E. Markham and K. A. Kobe, J. A m . Chem. SOC.,63, 449 (1941).
THE VAPOR PRESSURE OF HC1 ABOVE NON-AQUEOUS SOLUTIONS BY J. J. FRITZ Department of chemistry, The Pennsylvania State University, Univerm’ly Park, P a . Received M a y 7 , I065
The writer and Fugetl have recently published tables of the vapor pressures of HC1 above aqueous solutions, as calculated from available cell measurements. The same methods are applicable to non-aqueous solutions. The purpose of this communication is to make available data for facilitating the calculation of vapor pressures of HC1 above non-aqueous media. In general, the vapor pressure of HCl is given by F InfHol = - (Ego - E ) RT
(1)
where E is the voltage of the cell Hz, Pt/HCl (solvent)/AgCl, Ag, (corrected to 1 atm. pressure of hydrogen); Egois the standard potential of the cell for unit fugacity of HCl. Values of Egofrom 0 t o 40’ are given by Aston and Gittler,2 and can be calculated readily for other temperatures. Some typical vapor pressures of HC1 a t 25”, so calculated, are: in water (1 m), 2.2 X 10-4 mm. Hg; 50 mole % ’ ethanol-water (1 m),1.2 X mm. Hg; ethanol (1 m ) , 0.46 mm. Hg; methanol (0.56 m),8 X mm. Hg. (1) J. J. Fritz and C. R. Fuget, Ind. Eng. Chem., to be published. (2) J. G. Aston and F. L. Gittler, J . Am. Chem. SOC., 77, 3173 (1955).
1461
By use of the standard potential for hypothetical 1 molal solution (EO)in equation 1, the standard fugacity of HC1 is obtained for each system. Table I gives some representative values of the standard fugacity a t 25”. FUQACITY OF HCl
IN
Solvent
TABLEI HYPOTHETICAL 1 MOLALSTANDARD STATEAT 25’
f” HCI, atm.
Source of f” HCl, mm. Hg cell data
4.92 x 10-7 3.74 x 10-4 Water 4.19 X 3.18 Methanol 5.06 X 38.5 Ethanol Dioxane-water“ N2 = 0.0187 1.045 X 10-6 7.93 X Nz = 0.1433 4.86 X 10-8 3.69 X l o - * N Z 0,3231 2.34 X 0.178 Na = 0.4823 1.41 X 10.7 0 Nz is the mole fraction of dioxane in the solvent. =i
3 4 4
5 5 5 5
The vapor pressure of HC1 is then given by fi
= a&
= may2&fi”
(2)
where 7~ is the mean in activity coefficient as ordinarily tabulated. The fugacity is a measure of the absolute activity of HC1 in the solution, as contrasted to the relative activity usually tabulated. As demonstrated in our analysis of the aqueous system,’ the vapor pressures obtained from cell measurements are frequently more accurate than the results of direct measurements. Where measurements are available to sufficient dilution, the vapor pressure of the solvent can, of course, be calculated by means of the Duhem equation. (3) H.8.Harned and R. W. Ehlers, ibid., 64, 1350 (1932). (4) H.8. Harned and B. B. Owen, “Physical Chemistry of Electrolytio Solutions,” Reinhold Publ. Corp., New York, N. Y.,1950, p. 336. (5) H. S. Harned, J. 0. Morrison, F. Walker, J. G. Donelson and C. Calman, J . A m . Chem. SOC.,61,49 (1939).
NUCLEATION OF COPPER METAL FROM AQUEOUS SOLUTION BY WELBYG. COURTNEY~ Chemical Construction Corporation, 6.86 West 43 Street, New York, N . Y. Received M a y 7 , 1066
Theories of nueleation can be divided into the classical “supersaturation” viewpoint2 that the size of the critical nucleus varies significantly with temperature and supersaturation (i.e., reagent activities), and the less widely accepted “constant number” viewpoint3 that the critical nucleus is essentially independent of temperature and activities. I n view of the vanishingly small solubility of metals in water, supersaturation would appear to be an uncertain concept when applied to the nucleation of metal particles by reduction of the metal ion from aqueous solution. However, the results of the following exploratory study of the nucleation of Cu metal from aqueous solution can (1) Experiment Incorporated, Richmond, Virginia. (2) M. Volmer,“Kinetik der Phasenbildung,”T. Steinkopff, Dresden
1939. (3) J. A. Christiansen and A. Nielssn, Acta Chem. Scand., 6 , 103 (1949): F. R. Duke, R. J. Bever and H. Diehl, Iowa Slate. College J. Sci., 83, 297 (1949).
NOTES
1462
be adequately interpreted by the constant number theory. Experimentally, the nucleation of Cu metal by the disproportionation of Cu(1) was studied a t 25 f 1” by noting the induction period, r , for a Tyndall effect to appear in an unstirred aqueous solution containing initial concentrations ’ of 0.00077-0.0015 M CU(I), 0.2-6 M H+, 0.02-2 M NH4+and 0.0001-0.01 M Cu(II), all as the sulfates. Runs were made by pouring together with rapid shaking 2-20 ml. of [Cu(NH3),]zS04 and 10-100 ml. of H2S04 stock solutions in a test-tube or 250ml. erlenmeyer flask. The Cu(1) stock solution was prepared from recrystallized CuS04.5H20, excess 99.95% Cuo powder (- 325 mesh) and NHs in 10-fold molar excess over the expected final Cu(1) concentration. Conversion to Cu(1) was practically complete in 48 hours when agitation was used. A Nz atmosphere protected all solutions. The final CuO product from a nucleation run was composed of 5-10 micron flocs of 0.5-1 u polyhedral particles. Figure 1 plots typical results showing the de~ the initial Cu(1) molar conpendence of l / upon centration, co, at a constant 1M H + concentration.
- 2.9
I
-3.1
If T is interpreted as essentially resulting from nucleation kinetics only,4 it can be shown theoretically, following the constant number theory, that CO
- cs
= Kc~QT
(2)
where co and c, are the molar concentrations of Cu(1) a t times zero and r , K is a temperaturedependent constant which includes thermodynamic and kinetic factors, and p is the total number of Cu(1) ions involved in nucleation, ie., in the ratedetermining step plus any prior equilibria. Linearity of the experimental plot of log(l/T) vs. log co suggests that (a) the data can be adequately interpreted by the constant number theory, and (b) co - cT is both very small and essentially constant for the experimental metal sols, Therefore, the observed slope of 10 in Fig. 1 may be identified with p in equation 2. A possible nucleation mechanism would be the prior equilibrium formation of a cluster of four metal atoms, or fast (Cuo)4 4Cu(II) fast (Cu0)4 Cu(1) = (Cuo)&u(I) “adsorption” slow (CuO)a.Cu(I) Cu(1) +(CUO)S Cu(I1) fast (CUO)~--+- microscopic particle growth
+
8Cu(I)
+
+
(3)
+
This mechanism is somewhat supported by the conclusion of Taylor, et U Z . , ~ on quantum mechanical grounds that the 5-atom Cuo cluster is thermodynamically the least stable of small Cuo clusters which are in contact with CuO vapor. Thus, if the growth of Cuo clusters of different sizes involves similar kinetics, then in the extreme case the formation of the least stable cluster would be the rate-determining step in particle formation. The author is pleased to acknowledge the advice of Drs. H. M. Hulburt and F. A. Schaufelberger and the assistance of Messrs. P. B. Eng and J. J. Shaw.
s ,O -3.0
Vol. 60
1
-3.2 -2 -3 -4 log W T ) . Fig. 1.-Variation of induction period ( 7 ) with initial Cu(1) molar concentration (co) for constant H + ion concentration equal to 1 M ; see equation 1. 7 was measured in seconds. -1
A slight but uncertain effect of H + upon T was noted, but further work on this problem had to be indefinitely postponed. T was independent of (NH4)2S04 and CuS04 in the concentration ranges used here. The data a t H+ equal to 1 M corresponded to 10-27.9
e
(1)
Precision in r appeared t o be limited by subjective error only, being independent of the order of mixing of reagents, a 1000% variation in the volumes of solutions, and a 200y0 variation in concentrations in the stock solutions. It is therefore concluded that T is a t least, partially related t o nucleation kinetics.
(4) If T is attributed to both nucleation and growth kinetics, it can be shown, following R. A. Johnson and J. D. O’Rourke IJ. A m . Chem. Soc., 7 6 , 2 1 2 4 (1954)]that the Cuo nucleus would involve 18 to 20 metal atoms. Such a number would seem remarkably large unless unknown trace impurities give an “organiser” mechanism where a polymeric complex of metal ions and impurity reacts to form a metal nucleus [J. Turkevitch, R. C. Stevenson and J, Hillier, Disc. Faraday Soc., 11, 55 (1951)l. ( 5 ) H. S. Taylor, H. Eyring and A. Sherman, J . Chem, Phys., 1, 68 (1933).
BROMINE PENTAFLUORIDE. FREEZING AND BOILING POINTS, HEAT OF VAPORIZATION AND VAPOR PRESSURETEMPERATURE RELATIONS BY MAX T.ROQERS A N D JOHNL. SPEIRS Contribution from Kedzie Chemical Laboratory, Michigan State University, East Lansing, Michigan Received M a y Q, 1968
As part of a program investigating the physical properties of the halogen fluorides, we have redetermined certain physical properties of bromine pentafluoride originally reported by Ruff asci
4
