ACTIVITY COEFFICIENTS OF SILICOTUNGSTIC ACID
Dec., 1960
1867
ACTIVITY COEFFICIENTS OF SILICOTUNGSTIC ACID ; ULTRACENTRIFUGATION AND LIGHT SCATTERING’ B Y JAMES S. JOHNSON, KURTA. KRAUSilND GEORGESCAT CHARD^ C‘ontributzonfrom the Oak Ridge National Laboratory, Chemistry Division, Oak Ridge, Tenn. Received M a y 80,1880
Activity coefficients of silicotungstic acid (0.0004-0.04 M ) in aqueous solution were measured by equilibrium ultracentrifugation. The results agree with the Debye-Huckel theory for a 1-4 electrolyte, with a distance of closest, approach parameter of 7.6 A. A few ultracentrifugations of sodium silicotungstate indicate that the activity coefficients of this solute are similar. Turbidities of silicotungstic acid solutions are reported; they agree with the values predicted from ultracentrifugation results. Turbidities expected for two-component electrolyte-water systems a t low concentration are discussed. Densities and refractive indices of silicotungstic acid solutions are presented.
The class of compounds designated as heteropoly acids has attracted increasing interest in the past few years as a bridge between the solution chemistry of simple salts and that of large molecules. Silicotungstic acid (H4SiW1204~)has received special attention, since diffusion measurements3 and equilibrium ultracentrifugations4 in supporting electrolytes have indicated that it is essentially monodisperse ; molecular weight determinations by velocity ultracentrifugation,S by light scattering in supporting electrolytes, and by equilibrium ultracentrifugation in supporting electrolyte^,^ have indicated that the formula of the anion in solution (except, of course, for water of hydration) is written correctly as SiW1~040-4.The charge given for the ion (-4) indicates that four protons are ionized. This was established by acidity measurements heres and elsewhere.4.6 Further, X-ray scattering studies of concentrated solution^,^ carred out in this Laboratory, have shown that the structure of the species in solution is the same as that in the crystal. The relative wealth of information concerning silicotungstic acid makes it an interesting “known” with which to test techniques developed for large aggregates. I n this paper, a correlation of light scattering results with ultracentrifugation is presented. Activity coefficients of silicotungstic acid in aqueous solution (two-component system) were computed from the equilibrium ultracentrifugations. Since few determinations of activity coefficients of 1 4 electrolytes have been reported,8 these results 4r6
(1) This document is based on work performed for the U. S. Atomic Energy Commission a t the Oak Ridge National Laboratory, Oak Ridge. Tennessee, operated b y the Union Carbide Corporation. A preliminary report on this work wan presented a t the 138th American Chemical Society Meeting, New York, September, 1960. (2) Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts. Consultant, Chemistry Division, Oak Ridge National Laboratory. (3) M. C. Baker, P. A. Lyons and S. J . Singer, J . .4m. Chrm. Soc., 7 7 , 2011 (1955). (4) J. 9. Johnson and K. A. Kraus, Chemistry Division Annual Reports, ORNL-2386, 1957, p. 99; ORNL-2584, 1958. p. 56. (5) M. J. Kronman and S. N. Timasheff, THIS JOURNAL, 63, 629 (1959). (6) T. A. C‘arlson, unpublished results. (7) N.A. Levy, P. 4. Agron and M D. Danford. J. Chem. Phya., 30, 1486 (1959). (8) H. 9. ITarned and B. B. Owen, “The Physical Chemistry of Electrolytic Solutions.” 3rd Edition. Reinhold Publ. Corp., New York, N. Y., 1958, Appendix A ; R. A. Robinson and R. H. Stokes, “Electrolyte Solutions.” Butterworths. London (1955); R. A. Robinson J . Am. Chsm. SOC.17,6200 (1955); C. H. Brubaker, ibid., 78, 5762 (1956); 79, 4274 (1957); K. 0.Groves, J. L. Dye and C. H. Brubaker.
d
P.~
In m
= [ M ( 1 - Ep) w2/2BT] d(x2) (1)
in its integrated formlo
where d P = pwz x dx
( 2)
I n these equations, a = a*” is the activity of the solute; m is its concentration in moles/1000 g. HzO; ?* is the mean (molal) ionic activity coefficient; M is molecular weight of the solute; v is number of moles of ions per mole solute; R, gas constant; T , absolute temperature; 2, radius; w , angular velocity (2, times revolutions/sec.) ; P is pressure: p, solution density; subscripts a! and P indicate quantities a t radii xa and xp; and 7 ? ~is the partial specific volume of the solute a t r n ~ . ’ O For an exact solution, the partial volume should be known as a function of pressure. If this information is available or if values measured at one atmosphere pressure are an acceptable approximation, activity coefficient ratios may be computed from the equilibrium concentration distribution. If z p is the radius of the meniscus, the activity coefficient ratios will be for “bench-top” conditions. As infinite dilution is approached, the activity (9) See e.%. R. J. Goldberg, THISJOURNAL, 67, 194 (1953). (10) T. F. Young, K. A. Kraus and J. 5. Johnson, J. Chem. Phys., 22, 878 (1954).
J. S.JOHNSON, K. A. KHAUSAND GEORGESCATCHARD
1868
coefficient term disappears and measurement of the concentration distribution gives M / v , the number average molecular weight of the ions. 2. Light Scattering.-For a two-component system, showing no dissymmetry in scattering, the turbidity AT (in excess of solvent scattering) may he written" AT
=
H ' V ( dn/bm)Zm ( b In a / d In m)
where H' = (32n3n2/3NX4)
In equation 3, 72 is refractive index; V , volume of solution containing 1000 grams of solvent; N , Avogadro's number; and h is the wave length of light. In these partial derivatives, pressure and temperature are constant; with this restriction, partial derivatives with respect to molality are, in a two-component system, equivalent to total derivatives. For an electrolyte, it is customary to write the activity as an ion pioduct, and hence ( 3 In a / b In m ) = ( d hi m * ~ : ~ y /Inb m) = v[l ( 3 In r i b In m)l
+
(4)
If the correct value of v is selected, the activity coefficieiit term will approach zero as the concentration is lowered. From Equations 3 and 4 we obtain
or
As the concentration is lowered, the term ( 3 In y * / b In m) = ( b In y*/b In w) in Equation 6
becomes smaller, and a number average weight of the ions, M / v , is approached,12 i.e., the same result which is found by ultracentrifugation without supporting electrolyte. The equations given here for the light scattering of electrolytes are valid only as long as electroneutrality "is seriously violated only for regions with dimensions small compared to the wavelength of light."" In solutions so dilute that electroneutrality is violated for dimensions large relative to the wave length of the light, one expects the term I/ in the equations to be replaced by unity if scattering by the small ions is negligible. The matter has been treated quantitatively by Herm a n ~ 'on ~ the basis of interference scattering theory. In his equations, the distances in question enter in terms of the ratio ( K ~ / c J ~ ) = (m/q), in which K is the Debye-Huckel reciprocal length and u = (4n/h) sin(O/2), e being the angle between incident and deflected light. From his equations 10 and 11, we obtain for v', the apparent number of moles of ions/mole of solute, with neglect of scattering contributions by small ions
For a 1-4 electrolyte and wave length 436 mp, v = 5 and q = 4 X Although the equation is somewhat approximate, it should allow a good estimate of the lower concentration limit for the light scattering equations presented here. Experimental
where H = H'V(bn/bw)'/1000, and w = Mm/1000 is the weight of solute per gram of solvent. Equation 5 may also be written
Thus, one obtains from light scattering of a solute of known molecular weight (with supplementary measurements of refractive index increments) the slopes, d la y*/d hi m, which can, after appropriate integration, he used to obtain activity coefficients, just as with the ultracentrifuge. A direct experimental comparison between light scattering and ultracentrifugation results may be made if (bnlbm) is independent of' pressure and if the terms (a In a / b In m) of Equations 1 and 3 are equal (ie., if e does not vary under the conditions of the experiment). One then obtains from these equations where A = N ( 1 - iip)w2/2RT. The comparison is particularly straightforward when the ultracentrifugation is carried out with schlieren optics, in which case the experimentally obtained quantity is directly proportional to dn/dlr. If different wave lengths of light are used in the two methods, comparison may nevertheless be made by multiplying the right side of Equation 8 by the appropriate ratio of refractive index increments. (11) FT. 11. P t o c k i n a g e i , J
Chefn P h ~ a 18, , 58 (1'350).
Vol. 64
*
Ultracentrifugations were carried out a t 25.0 0.1" with a Spinco Model E Ultracentrifuge, equipped with the temperature control standard with the machine. I n the lorn concentration range, interference optics and a five cell ilnalytical G rotor (cells 12 mm. thick in light path) were used; higher concentrations were followed by schlieren optics with a two cell (30 mm. in light path) Analytical E rotor. Light of 546 mp, isolated with a Baird interference filter, was employed. Details of experimental procedure have been given previ~usly.'~ A Brice-Phoenix photometer was used in light scattering measurements, with dissymmetry cells standard with this instrument. Calibration was effected by use of the opal glass diffuser provided with the instrument. The constants for the diffuser given by the manufacturer had been earlier checked with Cornel1 Standard polymer in toluene.'6 Solutions were clarified by filtration through ultrafme sintefed glass. Freedom from dust was checked by visual inspection of a Tyndall beam and by dissymmetry in scattering. Two measurements of the scattering of each solution were made, with a second filtration intervening, and the average of these is reported. Densities were measured with a 25-cc. pycnometer, and refractive indices with a Brice-Phoenix differential refractometer. Chemicals were reagent or C.P. grade. Distilled (12) Confusion on this point seems to have crept into the literature. perhaps in part because Doty and Edsall (P. Doty and J. T. Edsall, Adi'ancrs in Protein Chemistry, Volume V I , 35 (1951)) tacitly limit the discussion of two component systems (p. 61) t o un-ionized solutes, for which Y is equal t o unity. (13) J. J. Hermans, Rec. trau. chim.. 68,859 (1949). In this discussion, posaible supporting electrolyte effects arising from impurities or ionization of solvent are neglected. (14) J. S. Johnson, K. 4 . Kraus and T. F. Young, J. Am. Chem. Soc., 76, 1436 (1954); J. S. Johnson, G . Scatchard and K. A . Kraus, J . P h y s . Chem. 6S, 787 (1959). (15) Performed b y Dr. E. W. Anacker Montana State College, Oak Ridge National Laboratory Sumnier Participant, 1957.
Dec., 1960
ACTIVITY COEFFICIENTS OF SILICOTUNGSTIC ACID
water deionized by passage through a mixed bed ion exchanger was used in preparation of solutions. Concentrations of all but two of the solutions used in centrifugation were determined by gravimetric analysis or computed from weight dilution of an analyzed stock (uncertainty of composition, about 1 0 . 3 % ) . I n the two exceptions, poor checks between separate analyses were obtained, and an average concentration based on density, refractive index, and analyses was used. (Volumes and refractive indices of these two solutions are not reported in Table I, because 01 uncertainties in the composition, about 1Yc). Analysis of silicotungstic acid (the solid contains a variable quantity of water) was usually by precipitation with cinchonine,’E followed by ignition, expulsion of silica with HF, and weighing as Wo3. In some cases, a simple evaporation of solvent was substituted for precipitation by cinchonine; in some, SiOzwas not expelled, and the analysis was based on the weight of oxide as SiOz,12W03. Neither of these modifications of the procedure affected the results significantly. Concentrations of solutions employed in light scattering were computed from their densities. Computations of the ultracentrifuge results were performed with the ORACLE, the ORNL digital computer. Corrections were made for the effect of differences in pressure on the refractive indices of solution and solvent.’* These corrections amounted to about 0.3Yc in ratios of activity coefficients. Possible changes of the apparent molal volumes of the solutes with pressure were neglected. The maximum pressure in the centrifugations was 60 atmospheres.
1869
n : i 7% /
Fig. 1.-Experimental slopes from ultracentrifugation. Solid curves computed from Debye-Huckel theory (equation 10) with indicated values of a‘. (Dee,sodium silicotungstate; other symbols, silicotungstic acid. Symbols refer to same centrifugations as in Fig. 2 and 3.
Some measurements also are reported for the sodium salt of silicotungstic acid, obtained by neutralization of the acid. To avoid difficulties from possible decomposition of the silicotungstate ion a t low acidities, l7 neutralization was carried only to the composition Naa.sHo.~Wlz040.The average TABLE I values 0.137 cc./g. obtained for the apparent VOLUMES A N D REFRACTIVE INDEX INCREMENTS specific volume and 406 cc./mole for the apparent dpparent specific molal volume are considered less certain than the Moles/l. (An/c)firs volume (An/c)ras corresponding values for the acid since fewer exH4SiWlzOlo periments were carried out and since solution 0.03216 0.1448 0.305 0.287 composition was not known with as high a degree .02511 ,289 .1455 ,304 of accuracy. As with the acid, the apparent vol,02002 ,289 ,1447 ,307 umes for the sodium salt were sufficiently inde.01604 ,286 .1444 ,306 pendent of concentration to permit their use as par.01255 ,289 .1445 ,308 tial volumes. ,00774 ,289 ,142 .305 Solution densities are needed in Equation 1 and .I42 .307 .00500 ,287 for conversion between moles/l. (c scale) and moles/ .140 .307 ,287 .00386 1000 g. HzO (m scale). Densities a t the concen,00251 .147 .306 ,288 trations in question here could be represented .00249 ,289 .143 ,314 within +=0.00005(average deviation, 0.00003) by Weighted av. ,288 .1444 .306 the relationship r\’a3.sHo.&iWlzO40 0.135 0.312 .138 ,313 .144 ,314 ,137 ,313
P
= ps
+ kc
where ps is the density of solvent; c, concentration in moles/l.; and k = 2.463 for H4SiW12040 and 2.559 for Na3.8H~.2SiW12040. The refractive index increments (on a c scale) also show no significant change with concentration. Results Average values of An/c = 0.288 a t 546 mp and 1. Molal Volumes and Refractive Index Incre- 0.306 a t 436 mp were obtained for the acid by ments.-Results of measurements of apparent weighting the individual values according to conspecific volumes and refractive index increments centration; for the sodium salt, the corresponding are summarized in Table I. Measurements on values are 0.294 and 0.313, respectively. These solutions at concentrations lower than 0.002 M are values may be compared with the increment 0.3065 not included; their precision is low. Since no f0.0040 (436 mp) reported by Kronman and Timasignificant change was found in appaient specific sheff,6 presumably for the acid. Increments were volumes of silicotungstic acid over more than a ten converted t o the appropriate quantities on the m fold range of concentration, an average value scale through the density data. 2. Activity Coefficients by Ultracentrifugation. weighted according to concentration was used for the partial volume in computations with Equations -We have carried out seventeen centrifugations of 1 and 8. This was 0.144 cc./g. (or 414 cc./mole) silicotungstic acid involving fifteen solutions of and compares well with 0.141 cc./g. earlier re- concentrations from 0.0006 to 0.032 mole/liter, a t speeds from 16,200 t o 24,630 r.p.m. Activity ported for H4SiW12040 in acetate b ~ f f e r . ~ coefficients were computed with Equation la (v (16) W. F. Hillebrand, G. E. F. Lundell, H. A. Bright and J. J. = 5). Average values for the slopes, d In r*/d Hoffman, “Applied Inorganic Analysis,” John Wiley and Sons, Ino., 0.01000 .005997 .00200 Weighted av.
New York. N. Y., 2nd Ed., 1953, p. 689.
0.294 ,294 ,298 ,294
(17) L. Malaprade. Ann. ahim. ( P a r i s ) , [IO] 11, 159 (1829).
J. S. JOHNSON, K. A. -us
1870
+O*O'O
t
AND
Vol. 64
GEORGE SCATCHARD
1
a'=2.25
~
I
+
n
I
-0.010
h"
L
11
t
ut=2.50
- +0.005
a
I
-4
cn
z 0 L
a > w
n
1
i
a'=2.75 0
I
0
0
L - , . L L l L L A L J - '
- 3.5
-3 0
- 2.5
-2.0
1
I
i
I 1 _A -1.5
log m . Fig. 2.--Deviations of experimental activity coefficients of silicotungstic acid from values cornputcd with DebyeIIuckel theorv (equation 11). iipproviniate spwds of rotation (r.p.m.): 24,630, A, E, 0 , *, V (every 2nd fringe), x (every 3rd fringe); 19,160, o (every 2nd fringe), o (every 2nd fringe), A (every 3rd fringe, same solution as x); 16,200, v, v, 0, 0 , a, A , e (same solution as +), 0,0,A, +, 0 Schlieren; all others, interference.
+,
In m, were estimated for the individual experiments The curve for a' = 2.50 (d = 7.6 B.)fits the and are presented in Fig. 1. Curves for the deriva- measurements with reasonable precision. It tive should be emphasized that neither the determination of the experimental slopes, d In r*/d In m, d in y* -(4)(2.303)(0.5097).\/F d In m from the individual ultracentrifugations nor the 2(1 a'dii)* use of Equation 10 for computation of this quantity of the slightly modified Debye-Huckel equation depend in any way on extrapolation t o zero concentration. - log y* = 4(0.5097)v'i 1 a'.\/; Figure 2 shows the detailed deviations of experifor a' = 2.25, 2.50 and 2.75 are also exhibited in mental activity coefficient ratios this figure, where p is the ionic strength, 2mi2i2/2 A log Yt = 1% (?'*/Y*Msn)exp. - log ( Y i / Y i & f e n ) o a m p . e (here p = 10 m ) ; and a' is a parameter proportional t o the distance of closest approach 8. from values computed with the Debye-Huckel -I
+
+
+
ACTIVITYCOEFFICIENTS OF SILICOTUNGSTIC ACID
Dee., 1960
> w
n
1871
2
+o.o1r
u ’ =2 . 7 5
0.00_-
- 0 01 I--
I I
L
I-
-30
-
-
J
-
~
I
_
~
1
1
- 2.5
-
-
---
-
---
----20
-
1
log m e Fig. 3.-I>eviations of experimental activity coefficients of sodium silicotungstate from values computed with DebyeHiickel theory (equation 11). All centrifugations with interference optics. Approximate speed of rotation (r.p.m.): 24,630, 0 e ; 14,290, e.
equation 11, where the subscript~“Men”refers to the meniscus, and e is so selected that the sum of average deviations for a given run is zero. The individual points represent fringe positions in the experiments carried out with interference optics (only every second or third point is plotted in some cases t o avoid excessive crowding) or readings a t 0.05 cm. radial intervals with schlieren optics. If agreement were perfect, all points for a given experiment would lie on a horizontal line, of zero ordinate. From this figure, the lower precision of the results a t low concentrations is evident; the values of the slopes, d In y*/d In m, given in Fig. 1, for this range are correspondingly uncertain. The insensitivity of these slopes t o changes in a’ at low concentration is also illustrated. No significant difference is noted between results for different speeds of rotation; this indicates that the assumption of constancy of V with pressure is valid within the accuracy of the present results. We have also carried out a few activity coefficient measurements 011 the sodium salt of silicotungstic acid (neutralized with NaOH to an average formula Naa.aHo.zSiWltOea). The interpretation assumed a two-component system with solute having the average formula ; differences in equilibrium distribution between the sodium salt and the small amount of acid present affect the results to only a minor extent. The results are shown in Fig. 1, and the deviation plots in Fig. 3. Equations 10 and 11 with a’ = 2.50 also represent these results
satisfactorily. Within experimental uncertainty, the activity coefficients of the acid and of the sodium salt appear to be the same. 3. Light Scattering.-Turbidity measurements have been made on silicotungstic acid solutions in the concentration range c = 0.005 t o 0.04, and the results are recorded in Table 11. TABLE I1 COMPARISON OF EXPERIMENTAL TURBIDITIES WITH TURBIDITIES COMPUTED FROM ULTRACENTRIFUQATIONS WITH SCHLIEREN OPTICS x 10‘A Tern. 10 ‘A roomp. (Ea.8 ) 436 2.51 2.63 546 0.90 0.93 .0310 436 1.92 1.89 546 0.71 0.67 .0196 436 1.25 1.28 546 0 45 0.46 .00973 436 0.60 0.62 546 0 21 0.22 .00494 436 0 31 546 0.10 No centrifugations with schlieren optics carried out a t this concentration. m
0.0404
A direct comparison is also presented in this table with turbidities computed from values of dn/dx obtained by ultracentrifugations with schlieren optics (Equation 8). The agreement is particularly gratifying since in this comparison
187’2
.J.
s. JOHNSON, I
