April 5 , 1958
MOLECULAR WEIGHTOF PHOSPHOTUNGSTIC ACIDS
The p H of the solutions in Table I does not change when the tetragermanate is formed. As can be seen from equation 3 the concentration of (H3Ge04)- would be small a t this pH. Removal of ( H G ~ , o ~ ~from ) ~ - the equilibrium then would produce little shift to the right and a corresponding rise in pH. Also the small amount of GeOz probe Of much duced according to equation greater importance. There was no evidence of (Ge40dz- ions in SOlUtion. The precipitate from the run SOlUtiOnS Contained a very small amount of birefringent material which could not be the acid germanate. Infrared and X-ray analyses indicated another com-
[CONTRIBUTION FROM THE
1539
pound present in small amount; howevcr, it was unidentifiable with known patterns. Since both the hydrogen germanates and tetragermanates Prepared showed no noticeable tendency to absorb moisture from the air it is presumed that the hygroscopic product described by Nowotny and Wittmanns contained residual metagermanate. Achowledgments.-The authors wish to thank Dr. Harry Knorr of the Kettering Foundation, Yellow Springs, Ohio, for his work in conducting the infrared analyses and Dr. John F. White, Geology Department, for help in optical analysis and in interpreting X-ray data. YELLOW SPRIXGS,
DEPARTMENT O F CHEMISTRY,
OHIO
CLARKSON COLLEGE O F T E C H N O L O G Y ]
The Molecular Weight of the Phosphotungstic Acids by Light Scattering1 BY MILTONKERKER,DOROTHY LEE AND ADAMCaou RECEIVED SEPTEMBER 3, 1957 The light scattering of 12-phosphotungstic and 9-phosphotungstic acids in a number of organic solvents anti water has been determined, In the organic solvents, the molecular weight calculated for the former corresponds to the monomer, H3PWI1O4,,,while that of the latter corresponds to the dimer, HsP2W18062. This is consistent with crystal structure studies by X-rays. The usual treatment is not adequate to interpret the d a t a from aqueous solutions where these acids are strong.
Since the discovery of ammonium phospho- ing of Souchay5who proposed, on the basis of cryosmolybdate by Berzelius in 1826, the heteropoly copy of the sodium salt in sodium sulfate a t its acids and their salts have provided a fruitful testing transition point, that 9-phosphotungstic acid is the ground for the theories of structural inorganic dimer, HP,P~W&~~, whereas 12-phosphotungstic chemistry. The bewildering variety of species acid is monomeric, H3PW12040. Although the structure of these acids in the solid proposed in the literature and the lack of a critical evaluation of the great amount of experimental state has been well established, the state of molecwork a t the turn of the century has necessitated a ular aggregation in solution is hardly known. This knowledge constitutes the starting point for an new look with the aid of modern structural tools.z The best characterized of the phosphotungstic understanding of the various aggregation, degradaand equilibrium phenomena encountered in acids are those with empirical formulas H ~ P W ~ Ztion 04a and H3Pb7@31, 12-phosphotungstic acid and 8- solution. I t is the purpose of this work to investiphosphotungstic acid. The complete structure for gate the molecular weight of the 12- and O-phosthese in the solid state has been elucidated by Keg- photungstic acids in solution by means of light scatgin3 and Dawson4 Dawson found that the unit tering in order t o determine whether these species cell of 9-phosphotungstic acid consists of the di- consist of monomers, dimers or higher polymers. meric ion PzWl.:lsO~z-6.This agrees with the findExperimental (1) Supported in p a r t b y U.S. Atomic Energy Commission Contract Number AT(30-1)-1801. ( 2 ) T h e s t a n d a r d treatises such a s J. W. hlellor, “A Comprehensive Treatise on Inorganic a n d Theoretical Chemistry,” Longmans, Green and Co., London, 1927-1937; J. S e w t o n Friend, “Textbook of InorRanic Chemistry,’’ Charles Griffin a n d C o m p a n y , London, 19241930; a n d “Gmelins Handbuch d e r Anorganische Chemie,” Verlag Chemie, Berlin, from 1926, summarize t h e literature t o t h e early 1930’s. T h e structural problem is stated in modern terms in such textbooks as W. Huckel, “Structural Chemistry of Inorganic Compounds,” b y Elsevier, New York, N. Y . , 1950, p. 179; H. B. Jonassen in Bailar’s “Chemistry of t h e Coordination Compounds,” Reinhold Publ. Corp., New York, N. Y . , 1956, C h a p t e r 14; a n d A. F. Wells, “Structural Inorganic Chemistry.” Oxford, 1950, p. 348. F o r present directions in research in this field see t h e preprints of papers read a t the symposium o n “Structure a n d Properties of Heteropoly Anions,” a t t h e S a t i o n a l Meeting of t h e A . C . S . , Division of Physical a n d Inorganic Chemistry, Atlantic City, N. 7 . . September 17, 1950. ( 3 ) J. F . Keggin, Nnluue, 131, 008 (1933); 132, 351 (1933); Puoc. R o y . SOC.( L o n d o n ) , 8144, 75 (1031); J. W. Illingworth and J. 12. Keggin, J. Chena. Soc., 575 (10351, A . J . Bradley and J , W. Illingworth, Puoc. Roy. Sac. (Loizdoir), A167, 113 (1936). (4) B. Dawson, A d a Cuysf., 6 , 113 (1053).
Preparation and Analysis of Compounds. 1. 12-Phosphotungstic Acid.-The reagent grade chemical, cotnmercially available from J . T. Baker Company, n’as uscd. T h e purity was checked by analysis of P20sarid HaO content, assuming the difference was IVO,,. After conversion to the S a salt by NazC03 fusion, the usual method of precipitation of phosphate with magnesia reagent and ignition to the pyrophosphate was used. The loss in weight at 600” was assumed to correspond to the water content. T h e W/P ratio was found to be 11.7 zt 0.1. Considering the errors resulting from possible coprecipitation of \I O:i with the phosphate and t h e volatilization of P z O ~ above 250”, the above accuracy was considered satisfactory. 2. 9-Phosphotungstic Acid.-The method of S(1ucllay6 which is a modification of t h a t first reported by \Vu7 was used. One hundred g. of S a z W O j was dissolved in 850 ml. of hot water and brought to a boil. One hundred and fifty ml. of 85y0 H3P04was added slowly to the boiling solution and the whole mixture was refluxed for 5 fir. or ovcrnight (S) P. Souchay. A n n . C k i m . , [1?1 2 , 209 ( 1 9 1 7 ) . ( 6 ) P. Souchay, Ruil. S D C c h i m , 363 (1951). ( 7 ) H. \Vu, J . Bioi. Cizem., 43, 189 (1920).
whichever was convenient. The ammonium salt was precipitated with 100 g. of KHIC1. This salt was then purified by dissolving and reprecipitating with "4'21 several times. The free acid was obtained by dissolving the salt in 1 : 1 HC1 and water and then extracting with ether. T h e etherwater phase remaining after the heavy ether phase was removed was treated with more concentrated HCl and more 9-acid-ether solution was thrown down. The ether solution of the %acid was vacuum dried for several days. Two observations were made during the synthesis which are of interest. Firstly, only solid r\-€LCl will precipitate the ammonium salt of the 9-acid. Even a hot saturated solution of NH4Cl does not precipitate the ammonium phosphotungstate after cooling overnight unless a n NH4C1 crystal is added, indicating supersaturation. Secondly, reduction of the tungsten (indicated by the green-blue color) proceeded rather rapidly in the first precipitate, but with successive recrystallizations the compound became progressively more stable. This may indicate t h a t tlie purer the acid, the less easily reduced. Perhaps also, it may be t h a t the 12-acid (always a n impurity in the syntlicsis of the 9-acid) is the reducible substance. iVit1-i successive recrystallizations, the 12-acid is separated cumpletely and no reduction occurs. We were not successful in analyzing the 9-acid directly. but, as previous workers also found, had t o analyzc the ammonium salt from which the acid was derived. T h e ratio \V/P was found to be 9.02 i 0.02, using the same technique as for the 12-acid. Preparation of Solutions.--All solvents were distilled, filtered under nitrogen pressure through a fine fritted glass filter apparatus and stored. Prior to a run the solvent was refiltered into a light scattering cell and its turbidity measured. This solvent was used to make up the solution by pouring directly into a 25-ml. volumetric flask containing a neighed amount of acid. T h e solution was then filtered directly into the light scattering cell, using the first 5 ml. of filtrate for rinsing. T h e cell was covered at all times except cyhile emptying the rinse solution. The ethanol solutions of the 12-phosphotungstic acid tended to undergo photoreduction. In order to avoid this a trace of nitric acid was added. I n the case of the aqueous solutions, elimination of dust was the most difficult problem. iVe found that adding a few crystals of common alum, KA1(SO1)*, to the solution and then filtering twice eliminated most of the dust. Any effects of the added nitric acid or alum was incorporated in the properties of the solvent. Optical Measurements.-Light scattering measurements were made with the American Instrument Campany light scattering microphotometer, using the 4360 A. line of the mercury spectrum. The scattering cell was 2.4 X 2.4 X 7.0 cm. T h e instrument was calibrated with Ludox by tlie method of Maron and Lou.8 hlaron and Loug h a w given factors for correctirig the turhidity for solvents with refractive index different from water. These factors depend upon the design of the light scattering instrument. Oilr instrument was the same as theirs and we have used their expression for C,' which corrects for the spreading of the light rays on leaving the scatteying cell. \Ve disagree slightly with their expression for C, which corrects for the volume of the aolrition observed by the phototube and have used equation (1) instead
The rcfractive index of n-ater and the solvent for which t h e correction is t o be applied are n , and n , respectively. The distances V I , ~ 2 Y:, and 1 , shown in Fig. 1, are 1.4,2.0, 1.5 and. 0.28 crn., respectively. The correction factors for the solvents we have used are presented in Table I. S o n e of the solutions investigated showed any depolarization beyond that exhibited by the solvent itself. The difference in refractive index between solution and solvent was measured with a Brice-Phoenix Ilifferential In a l l c:iscs the differential reRefr:ictorueter a t 4200 .L\ fractive index remained constant wit11 cnticcntration. Tlic values rif the tiiffercntial refracture intlcs, dn/dc, are listctl in Tnhle 11. ( 8 ) S . I1 >Taron a n d 11 l.ou, J . P o l y . Sri , 1 4 , 20 (1904) (9) S . H. h l a r o n a n d R. Lou, ibzii., 14, 273 (1954).
TABLE I FACTORS FOR CORRECTING THE TL-RBIDITY IN NON-AQUEOUS SOLVENTS Cn ' Cv ' C"'C,' Acetic acid 1.04 1.01 1.05 Allyl alcohol 1.09 1.03 1.13 Ethanol 1.03 1.01 1.04 1-Propanol 1.04 1.03 1.07 TABLE I1 VALUESOF n, dn/dc A N D 15 AT 436 mp Acid
Solvent
n
dn/dc
12 12 12 12 9 9
Acetic acid Allyl alcohol Ethanol b'ater Ethanol I-Propanol Water
1.372
0.125 .lo2 .112
9
1.413 1.365 1.334 1.365 1.385 1.334
x lot 4.49 3.18 3.56
I1
.lo3
2.87
,128 .122 .119
4.62 4.33 3.82
T h e solutions of 9-phosphotungstic acid were light yellow so that it was necessary to correct for the attenuation of both incident and scattered radiation due to absorption. Since the loss due to true absorption mas large compared to scattering, the absorption coefficient could be obtained by determining the optical density in a Beckman spectrophotometer and the attenuation of the beam in the light scattering cell was calculated from this. The Beer-Lambert law held over the range of concentration and path lengths applicable. T h e PH of the various aqueous solutions was adjusted by addition of HC1. For Rayleigh scatterers, the excess turbidity due to concentration flurtuations is given bylo 3 2 d M , c n * (dit/dc) ( 2) " = 3X4Nopi( - d In ji/dc) \v h er c X = wave length of light in oucuc ? o ' -- Avogadro's number AIl = molecular weight of solvent c = weight concn. (g./ml.) ?z = refractive index of s o h . pi = density of solvent ,f1 = fugacity of solvent I n dilute solutions of non-electrolytes for which the estended van't Hoff law is obeyed A
lcading to
nhere for a given solvent and n a v e length, H is a lumped constant. I'alues of H a r e listed in Table 11. The procedure used to determine the molecular \I eight nf the solute ma4 to plot the quantity I l c / r , against the conccntration c. The intercept a t c = 0 gives the reciprocal of the molecular neight.
Results In Figs. 2 and 3 is plotted I1c/re against concentration for 12-phosphotungstic acid and !+phosphotungstic acid in various solvents. According to equation 4, the interrept a t zero concentration is the reciprocal of the inolecular weight. There is a definite difference between the results in organic solvents from those in water. We will discuss the latter shortly. I n ethanol and allyl alcohol, the molecular weight of 12-phosphotungstic acid is 2600 and 2900, re(IO) G Oster, Cheni R c s , 43 319 (1948)
April .?, Inq%
nfOLECULAR W E I G H T O F PIIOSPHOTUNGSTIC
ACIDS
1341
IL - - L - - - I
0
0.04
os
C.
Fig. 1-Schematic diagram of optical path in light scattering photometer showing the distances r , , 72, rl and 1. N, incident nose piece; C, scattering cell; I, collimated incident light beam: AB, receiving nose piece; L, photomultiplier tube.
spectively, which compares reasonably well with the empirical formula weight of 2880 for the monomer, H3PW12040. We estimate the uncertainty in our experimental values of the molecular weight to be about 10%. We did not extrapolate the H c / T curve ~ for acetic acid to zero concentration because, due to the steepness of the curve a t low concentrations, relatively small errors in the turbidity produce considerable uncertainty in the intercept. Of course, the light scattering data are also least precise in this low concentration range. However, i t is apparent from Fig. 2 that the acetic acid data are consistent with the results obtained in ethanol and allyl alcohol. The molecular weight of the 9-phosphotungstic acid in ethanol and propanol was determined to be 4700 and 4400, respectively, which agrees with a formula weight of 4370 for the dimer, H6P2W18065.
Fig. 3.-Hc/7, for %phosphotungstic acid a:. copceiitration c (g./ml. solution) in water (A), ethanol ( B ) and 1-propanol (C).
The aqueous solutions of the 12-phosphotungstic acid were only stable when the pH was maintained in the neighborhood of from 1 to 2. Figure 4 depicts the increase in turbidity with time of a solution containing 0.152 g. of 12-phosphotungstic acid per ml. of distilled water. This suggests light scattering as a sensitive tool with which to investigate the kinetics of this decomposition. Aqueous solutions of 9-phosphotungstic acid were stable both in neutral and moderately acid solutions.
-s
8
X c
6
I
3
3
1
I
I
0.04
0.08 C.
Fig. 2.-Hc/7.
I
40 00 Time (min.). Fig. $.--The change of excess turbidity re with time for 0.153 g. of phosphotungstic acid per ml. distilled water.
for 12-phosphotungstic acid tu.concentration c (g./ml. solution).
The molecular weight of the acid calculated from the turbidity of the aqueous solutions was much lower than in the organic solvents and also lower than the empirical formula weights. This is not surprising in view of the fact that the procedure for calculating the molecular weight is dependent upon the solute being a nearly ideal non-electrolyte. The phosphotungstic acids are actually strong electrolytes. In the case of the 12-phosphotungstic acid, the molecular weight obtained varied with pH. At pH of 2, i t was 1700 and a t pH of 1, it was 2100. This
1542
JAMES
/(I/ t ti I
KINGAND NORMANDAVIDSON
Vol. 80
We are now engaged in determining d In a*/dc for 12- and 9-phosphotungstic acids from measurements of cells with transference, transference number and dissociation constants. We will report on this work in a subsequent communication.
1
Appendix The correction factor CV' which is the volume seen by the photomultiplier tube in non-aqueous solvents compared to that in water may be derived with the aid of Figs. 1 and 5.
r,
-+-
r,
--
Fig 5 -Didgram of optical system used in derivation of expression for C,
may be due to the common ion effect. The lower pH favors the formation of more undissociated acid and the system thus approaches the conditions for which the light scattering treatment is valid. For the 9-phosphotungstic acid, the pH has no effect, the turbidity in pure water and a t pH of 2 being identical. This probably is due to the fact that the 9-phosphotungstic acid is so strong that the additional hydronium ion does not produce sufficient undissociated acid to affect the turbidity. In order to relate the light scattering of a nonideal substance to the molecular weight, it is necessary to revert to equation 2 . By utilizing the Gibbs-Duhem relation XI d lnf, + NZd 1n.f~ = 0 (5 ) and N z are mole fractions, it can be shown where that in dilute solutions
Thus the determination of the molecular weight requires in addition to the turbidity, knowledge of d In a*/dc. This relation is perfectly general in moderately dilute solutions.
[COXTRIBUTION No. 2260
where RV = ratio of volume PW to the actual volume seen by the photomultiplier tube in the presence of a liquid with refractive index n. When the angle m is sufficiently small so that sin m % tan nz, it can be shown that
and z p = z
It follows that
(a+:+
rl
+ w/2
n.\/ll+;;i>
(9)
The light radiated by the excess volume is only half as intense as that radiated by the volume L2w.l1 The ratio of the light scattered by the volume 1% to the total volume seen by the photomultiplier tube is
and the correction factor for non-aqueous solvents becomes
(11) C. I. C a r r a n d B. H. Zimm, J. Chem. Phyr., 18, l G l O (1950).
POTSDAM, N. Y .
GATESAND CRELLINLABORATORIES OF CHEMISTRY, CALIFORNIA IXSTITUTE OF TECHNOLOGY ]
FROM THE
Kinetics of the Ferrous Iron-Oxygen Reaction in Acidic Phosphate-Pyrophosphate Solutions B\'
JAMES
KING.4ND
xOR?riAN
DAVIDSOS'
RECEIVED OCTOBER 15, 1957 T h e rate law for the ferrous iron-oxygen reaction in acid solutions (PH -1-2) containing phosphate and pyrophosphate anions is - d ( F e + + ) / d t = kl(Fe++)(HnPOn-)2Po, k2(Fe++)(H2P;07-)Po, where k l = 1.08(+0.06) X atrn.-'mole-? liter2 sec.-1 a n d kz = 2.13(=!~0.05) X 10-2 atm.-l mole-' liter set.- a t 30" ( p = 1.0-1.1 mole/liter, SaC104). T h e activation energies are aH1* = 21( 1) a n d AH2* = 6( +1) kcal. T h e rate law a n d the values of k l and k? both show that H&'?07and HzP04-are independent catalysts a n d that the unusual quadratic dependence on (HzPO,-) is not due to the equilibrium 2 H z P 0 4 - F? HZP207- HiO. T h e mechanism of the reaction presumably involves a s the rate-determining step either the one electron transfer process FeII 0 2 Fe"' 0 2 - or the two-electron process Fe" 0 2 + FeIv 02=, with iron in the transition state stabilized by the complexing phosphorous anions.
+
+
+
+
-.f
+
+
+
Cher and Davidson2 found that the rate law for the oxygenation of Fer*in phosphoric acid solution
is -d(Fe++) 'dt = kl(Fe++)Pop(€12P01-)2.The quadratic dependence on (H2POI-) is somewhat
(1) We are indebted t o t h e Atomic Energy Commission for support of this research under Contract A T ( l l - l ) - 1 8 8 ; a n d to t h e Danforth Foundation and t h e General Education Board for fellowships to one
of us ( J . K . ) . T h i s paper was presented in p a r t a t t h e 129th National Meeting of t h e A. C . S., Dallas, April, 1956. ( 2 ) M. Cher and N. Davidson, THISJ O U R N A L , 77, 793 (1955).
