Xov., 1957
SIZEAND HYDRATION OF INORGANIC IONS
to resist removal as carbonyl by a carbon monoxide stream at 80°, while the rest of the nickel is easily so removed.’O It also has been shown that it is the larger particles of nickel which may be selectively removed in this way.ll It appears, then, that the larger over-all nickel concentrations give, on the whole, larger particles, and that these particles more readily form partial or true solid solutions with copper. The nickel in those samples with low over-all nickel concentrations is, on the other hand, less likely t o form solid solutions with copper because of the diminished accessibility to copper in the preparative stage. These conclusions are supported by the results on samples (4) and ( 5 ) . The preparation method for these samples would suggest that mechanical mixtures would be the only result. This is obviously the case. It may, in fact, be stated that no appreciable amount of the nickel is diluted with copper in these two samples. Sample (6) was studied for the express purpose of determining whether the procedure used by Best (10) G. C. A. Schuit and N. H. DeBoer, J. chim. phys., 5 1 , 9 (1954). (11) E. L. Lee, J. A. Sabatka and P. W. Selwood, J. Am. Chem. Soc., 79, 5391 (1957).
1567
and Russell was adequate to obtain a true solid solution. The result is that, while extensive dissolving has taken place, true homogeneity has not been achieved. Appreciable ferromagnetism may still be observed almost 100’ above the Curie temperature of the homogeneous alloy. In a recent paper12 it was concluded, on the basis of X-ray evidence, that the maximum deviation from homogeneity in this system could not exceed 3%. The magnetic evidence shows that Some of the alloy could deviate from homogeneity by twice this amount. On the whole the magnetic and X-ray methods are not in serious disagreement. It has been shown that the observed X-ray line broadening is probably due to some inhomogeneity rather than to lattice imperfections. In any event, it is not clear what significance may be attached to catalytic studies related to d-electron concentration in alloys unless more rigorous treatment is used to ensure homogeneity of the sample. Acknowledgment.-It is a pleasure to acknowledge the Visking Fellowship held by J.A.S. during this work. (12) (1957).
W. Keith Hall and L. Alexander, THISJOURNAL,
61, 242
SIZE AND HYDRATION OF INORGANIC IONS FROM VISCOSITY AND DENSITY MEASUREMENTS BY T. KURUCSEV, A. M. SARGESON AND B. 0. WEST Contribution from the Department of Physical and Inorganic Chemistry, University of Adelaide, South Australia Received June 17. 1967
Hydrodynamic radii and hydration numbers for several inorganic complex ions have been obtained from combined viscosity and density data. The validity of the Einstein viscosity equation for a particle size of 10 1.has been established.
The relation between hydrodynamic behavior of dilute solutions of macromolecules and their shape and size has been well defined but the lower limits of particle size for which these relationships hold are not nearly so well established. I n an effort to test the validity of the Einstein viscosity equation attention was directed to large spherical ions whose size was approximately known, ensuring the interpretation of the viscosity measurements in terms of a uniform particle size and not an average as with measurements on linear polymer solutions. The frictional resistance experienced by either macroscopic or microscopic particles is proportional to the local relative velocity of the liquid with respect to the partic1e.l However, the constant of proportionality need not be the same in the two cases, although a recent paper2 on the sedimentation and diffusion of 12-tungstosilicic acid indicates the validity of the Stokes resistance law when the diameter of the hydrodynamic unit is approximately 11A. I n the work reported here 12-tungstosilicic acid,
12-Tungstosilicic acid was prepared as described by North3 and the water content determined by igniting samples a t 500” to constant weight. The average composition of the sample was H4SiW120po:15H20. Sodium acetate-acetic acid buffer was used to dissolve the polyacid, of ionic strength 0.2 M and pH 4.60. Solutions of the acid in the buffer contain the anion [ S ~ W I ~ O ~ O J ~ - . ~ Tris-1 ,lo-phenanthrolie Iron(I1) Chloride Heptahydrate. -The complex was prepared from equivalent roportions of 1,lo-phenanthroline and ferrous chloride in aLohol, precipitated with ether and recrystallized finally from water several times, to remove all the organic material. Anal. Calcd. for FeC3BH2rN6&.7H~0:C, 54.49; H, 4.82. Found: C, 54.55; H, 4.72. Tris-Z,2’-bipyridine Iron(I1) Chloride Hexahydrate: prepared in the same manner as the phenanthroline complex.
(1) J. G. Kirkwood, J. Chem. Phgs., 14, 180 (1946). (2) M. C. Baker, P. A. Lyons and 8. J. Singer, J. Am. Chem. Soc., 77, 2011 (1955).
(3) E. 0. North in “Inorganic Syntheses,” Vol. I, John Wiley and Sons,Inc., New York, N. Y ., p. 129.
tris-1,lO-phenanthrolineiron(I1) chloride heptahydrate, tris-22’-bipyridine iron(I1) chloride hexahydrate, and tris-(bis-ethylenediamine-cobalt(II1)p-diol)-cobalt(IJ.1) chloride tetrahydrate were subject,ed t o density and viscosity measurements over a series of concentrations to obtain an estimate of the size and hydration number of the large ions contained therein. Experimental
T. KURUCSEV, A. M.SARGESON AND B. 0. WEST
1568
TABLE I COEFFICIENTS O F THE JONES AND DOLE EQUATION AND
PARTIAL
Vol. 61
SPECIFIC VOLUMES A T 30’
Concentration
cm%7h
Solvent
[Fe(bipy)al Cd [Fe(phen)al CL Hexol Cle H4SiWlzO40
Water Water Water Acetate buffer
0.013-0.132 .015- .090 .003- .090 .012- . l o 2
VI9
A
B
0 0 0.09 0
1.27 1.75 1.26 1.39
cm.l/g.
.6744 .6522 .4746 .1431
TABLE I1 CALCULATED VALUESOF HYDRODYNAMIC VOLUMES AND RADII,IONIC VOLUMES AND HYDRATION NUMBERS vi (A.8) vi (A.9 Solvent
a
[Fe(bipy)al 4 + Water [Fe(phen)da+ Water Hexole+ Water SiWl~0~~4Acetate buffer n‘ given to the nearest water molecule.
Vhyd
(A*’)
846 1165 845 740
R hyd (A. 5.9 6.5 5.9
5.6
(Darmois’ scale)
(Eucken’s scale)
593 655 496 715
584 647 470
n‘a
9 17 22 1
Anal. Calcd. for FeCsoHztNaClz.6HzO: C, 51.23; H, by the ionic volumes, has been related to the indi5.16. Found: C,51.80; H,5.12. vidual ions by Gurney6according to the equation Tris-( bis-ethylenediamine-cobalt(II1)-@-diol)-cobalt( 111) B = EniBi Chloride Tetrahydrate (Hexol).-Cobalt nitrate hexahydrate (45 g.) was dissolved in water (150 ml.) and treated The value of B i is then a measure of the volume of with 10% aq. ethylenediamine solution (300 ml.). Onvigorous stirring the solution acquired a deep red-brown color; the hydrated ions and in addition accounts for the i t was then filtered and allowed to stand in an evaporating effect of the dissolved ions on the solvent strucbasin. After two days crystals of the hexol nitrate trihy- ture.7~8 drate separated out, which were filtered, washed with a little Euckeng has estimated quantitatively the contricold water and recrystallized from warm water. A saturated aqueous solution of the nitrate was then bution of the “solvent effect,” ABS,to the value of poured through a Deacidite FF column (2“ X 2’) charged B i , by a consideration of a disturbance in the existwith chloride ion and the procedure repeated six times. ing equilibrium between the 1-, 2-, 4- and 8- water The hexol chloride was then crystallized by careful addition polymers as a result of the hydration of the ions. of alcohol to the solution. showed that the magnitude of ABS was of the Anal. Calcd. for C O ~ C I Z H ~ ~ N I Z O & C, ~ ~ ~14.87; ~ H ~ O He : Since A B S is small, as a first apH, 6.52; N, 16.99; C1,21.39. Found: C, 14.66; H, 6.36; order 0 -+ -0.25. N, 17.10; C1, 21.64. proximation we may assume that the values B i for Solution viscosities were determined with a British Stand- the large ions are a measure of the hydrodynamic ard No. 0 Ostwald viscometer at 30 f 0.005” and the den- volumes only. Application of the Einstein equasity measurements were carried out at 30 f 0.005” with 10- tion ml. calibrated pycnometers. qr - 1 = 2 . 5 ~
Discussion Viscosity.-The concentration dependence of the relative viscosity of strong electrolytes in dilute aqueous solution has been shown by Jones and Dole4 to obey the equation
where y is the volume concentration in %, leads to Vhvd
= 400Bi/N~
where qr = q/qo is the relative viscosity of the solution, c is the concentration in moles/liter, and A and B are constants whose values for the systems under discussion are given in Table I. The coefficient A represents the contribution to the viscosity of the resistance to shear by the ionic atmosphere.6 Its value depends on the radius of the ionic atmosphere, the charge of the ions and the ionic strength of the solution. Here, the only system where A # 0, within the limits of accuracy of the viscosity measurements, was the hexol in water. The unusually high value of A for this system compared with other strong electrolytese is probably explained by the high charge density on the surface of the cation. The coefficient B, a contribution to the viscosity
where NA is Avogadro’s number. Here Ohyd, the hydrodynamic volume according to Ogston,lo includes in addition to the volume of the unhydrated ion, water carried by “viscous interaction,” “chemical or physico-chemical interaction” and “physical entrainment.” Bi values for the ions were calculated using the values B260C1- = -0.007, B 2 5 0 ~=+ +0.070, B3O”cl- = -0.002,6.9 giving values of Vhyd and the hydrodynamic radii R h y a shown in Table 11. Density.-The apparent specific volume of each compound was found constant in the concentration region under investigation. In this respect the substances approached ideal behavior. I n order to separate the partial specific volumes into their ionic constituents, Darmois’l (also Bernal and Fowler’) assigned the value 37 A.a to the ionic volume of the chloride ion in aqueous solution by separating the apparent molecular volume of cesium chloride into ionic volumes in approximate
(4) G. Jones and M. Dole, J. A m . Chem. Soc., 61, 2950 (1929). (5) H. Falkenhagen, “Electrolytes,” Clarendon Press, Oxford, 1934. (6) R. W. Gurney, “Ionic Proceases in Solution,” McGraw-Hill Book Co., Inc., 1953. p. 159.
(7) J. D. Bernal and R. H.Fowler, J . Chem. Phys., 1, 515 (1933). (8) E. Asmus, 2. Naturforsch., 4A,589 (1949). (9) A. Eucken, Z.EEektrochem., 51, 6 (1948). (IO) A. G. Ogston, Tram. Faraday Soc., 49, 1481 (1953). (11) E. Darmois, J. phys. radium, a; 2 (1941).
sF-l=A&+Bc
THERMODYNAMICS OF THE Ti-Ti203 SYSTEM
Nov., 1957
proportion to the cube of the respective crystallographic ionic radii. Euckenlg however, used cesium iodide as th,e reference substance and obtained a volume of 41 A.3 for the chloride ion. Ionic volumes based on both scales are given in Table 11. Eucken considers four terms contribute t o the partial ionic volumes, vi: (a) the volume occupied by the unhydrated ion; (b) the “solvent effect” or the volume change due t o structural changes of the solvent, AVI; (c) “electrostriction” which is the decrease in volume of the solvent molecules attached to the ion; (d) a volume increase due t o the formation of a second diffuse hydration layer around the ions. For ions of relatively large size and small surface charge factors (c) and (d) are negligible. Further, neglecting the “solvent effect” as a first approximation,’l the difference vhyd
- vi
may be considered as the volume of water contained in the hydrodynamic volume of the ion. The approximate hydration number, n‘, calculated in this way is given in Table 11. The ‘(solvent effect” may be taken into account by using the equationsg AB8 = n2.75( D8/55.5) Avl = nl.8( D s / N * )
where n is the number of hydrated water molecules per ion, D Sthe change in mole fraction of the water8-polymer per mole fraction of hydrated water molecules, and substituting these values in nu0 = { 4 0 0 ( B i - A & ) ) / N A
- ( v i - Av,)
where vo is the volume of a water molecule. Then, using the value of n’ obtained by Darmois’ approxi-
1569
mation, a self-consistent method of calculation may be applied to compute a constant value of the hydration number n. The self-consistent hydrodynamic ionic volume is then obtained from the term Bi - ABs. Since Da values are only tabulated between n = 4 -+ 15, the Eucken correction could only be carried out for t,he bipyridine complex, leading to a hydration numbgr n = 11 and a hydrodynamic radius Rg cor. = 6.1 A., the corrected values not being significantly different from those obtained by parmois’ approximation, n’ = 9 and R h y d = 5.9 A. Conclusion The diameter of the 12-tungstosilicic acid anion was found to be 11.2 A. and was of the same magnitude as that obtainedofrom the sedimentation and diffusion studies2(11 A.) and fzom the X-ray analysis of the solid (unit cell 12.1 A.). This would seem to indicate that the Einstein viscosity equation is valid for aqueous solutions where the particle size is of the order 10 A. diameter. The sizes obtained for the hexol, phenanthroline and dipyridylcations 11.8,13.0 and 11.8W.diameter1 respectively, would also seem to support this conclusion, since these were the results expected from a consideration of the individual bond lengths and scale models (Catalin) of the substances, a slight increase in value being attributed to the hydration of the ions. Acknowledgments,-The authors are indebted to Professor D. 0. Jordan for helpful criticism and suggestions. One of the authors (T.K.) wishes to express his gratitude to the Commonwealth Scientific and Industrial Research Organization for a Postgraduate studentship.
THERMODYNAMICS OF THE Ti-Ti20s SYSTEM AND THE DISSOCIATION ENERGY OF Ti0 AND TiOzl BY J. BERKOWITZ, Department of Physics, University of Chicago, Chicago, Ill.
w. A. CHUPKA AND Argonne National Laboratory, Lemont, Ill.
MARKG. INGHRAM Department of Physics, University of Chicago, Chicago, Ill. Received June 86, 1867
The concentration of gaseous species in equilibrium with various compositions of the solid Ti-Ti02 system has been studied employing mass spectrometric analysis of the vapor effusing from a Knudsen cell. The gaseous species observed were Ti, TiO, and TiOz. A thermodynamic treatment of ion intensities yields TiO(s) 4TiO(g), AH&,* = 139 5 kcal./ mole; TiOr(s) 4 TiOz(g)? A H L 7 146 & 5 kcal./mole. Combining these values for the heat of sublimation with other well known thermodynamic data yields 6.8 and 13.5 e.v., respectively, for the atomization energies of T i 0 and TiOz.
Introduction The heats of sublimation of T i 0 a n d “ioz have been determined by Groves, Hoch and Johnston,2 using the Knudsen effusion cell technique. They ( 1 ) Sponsored jointly by t h e Office of Ordnance Research, U.S. Army and the National Science Foundation, (2) W. C. Groves, M. Hoch and H. L. Johnston. THISJOURNAL, 69. 127 (1955).
determined the vapor pressures from the weight loss of the cell after a known period of operation a t a known temperature. The Composition of the Vapor was inferred from X-ray diffraction studies of the condensate. This is a rather indirect method and leaves uncertainty concerning the identity Of the species in the gaseous phase* In order to eliminate this uncertainty, the experiments
