1816
The Journal of Physical Chemistty, Vol. 83, No. 14, 1979
R. C.
Johnston, C. 0. Lobdell, and G. E. Janauer
Cation Exchange in Mixed Solvent Media. 2. Alkali Ion and Solvent Self-Diffusion in Dowex 50W-Dimet hyl Sulf oxide-W atet Robert C. Johnston,+ Charles 0. Lobdell, and Gilbert E. Janauer" Department of Chemistry, State University of New York at Binghamton, Binghamton, New York 13901 (Received November 13, 1978; Revised Manuscript Received March 20, 1979) Publication costs assisted by Azon Division, Defiance-Azon Corporation
Self-diffusion coefficients, D,for Na+, Rb+, and Me2S0 have been measured in poly(styrenesu1fonate) resins over a wide range of solvent compositions in aqueous Me2S0,a system previously shown to ensure high resin solvent uptake with very little solvent selectivity up to 70 mol % Me2S0 with alkali resinates of Dowex 50W resins. External self-diffusion coefficients, D, were also determined in corresponding binary mixtures under conditions identical with those prevailing in the presence of the ion-exchange resins. Both DNaand DMezso pass through shallow minima in the intermediate composition range of the binary system reflecting essentially the pronounced viscosity maximum encountered in MezSO-water at 33 mol % Me2S0. In the resins, on the other hand, a very steep, continuous drop of effective &a was observed when MezSO content was increased from 0 to 70 mol %. The value for apparent DMeaSO showed a similar drop from 0 to 33 mol % Me2S0, but then leveled off and remained virtually constant beyond that point. Allowing for tortuosity in the resins according to the simple Mackie-Meares model we can explain these results by the interplay between strong, stoichiometric MezSO-water association and increasing difficulty for fulfilling the solvation needs of counterions and fixed anions. As the mole fraction of MezSO increases (total internal solvent molality rapidly drops) in the binary mixture the electrostatic ion pairing is strongly enhanced in the resin phase. This situation is illustrated by comparison of corrected Stokes radii calculated for the diffusing entities. Additional supporting evidence is provided by activation energies for self-diffusion, ENaand ENa, obtained from the temperature dependence of D and D for Na+ and MezSO, and by measurements of &,+and D R ~at+ selected compositions.
Introduction Starting with the original work of Boyd in 1947, diffusivity studies in ion-exchange resins have contributed greatly to our understanding of the ion-exchange process. Development of radio tracer techniques1v2opened possibilities for kinetic studies under conditions of chemical equilibrium, Le., no change in chemical composition of the resin or external solution during the course of the experiments. That diffusion is the controlling step in the overall exchange rate was established in the first kinetic s t u d i e ~ Thus . ~ ~ ~diffusion coefficients are measured directly by the overall exchange rate. Computer-aided solutions have been found for the mass transfer equations resulting from the application of Ficks laws to the boundary and terminal conditions in ion exchange in spherical beads. Following is the solution for the general case in which diffusion within the bead, as well as in the external solution to and from the spherical resin surface, contributes to the overall rate:4#5 6027-A~ sin2 (M,ro) 1- f ( t ) = exp(-DMn2t) :r n=i M,4
c
(1)
where f ( t ) is the fractional attainment of equilibrium, D the diffusion coefficient in the adherent (Nernst) film and in the external solution (cm2s-l), D the diffusion coefficient in the resin bead (cm2 s-l), t is the time after start of diffusion (s), ro the radius of beads (cm), C the concentration-of diffusing species in the external solution (mol ~ m - ~C) the , concentration in resin bead (mol ~ m - ~6 )the , thickness of Nernst film (cm), 8 = CD/CDS (cm-l), and where M,, are the nonzero roots of the equation: Mnro= (1 - Or,) tan M,ro, A , = M,2r: (Or, - 1)2/M,2r02+ (Or, - 1)6ro.
+
t Azon Division, Defiance-Azon Corporation, P.O. Box 290, Johnson City, N.Y. 13790.
0022-3654/79/2083-1816$01.00/0
Self-diffusion of counterions in ion-exchange resins in aqueous medium has been extensively studied.6-8 As a result, the effect of variables such as pore size, crosslinking, ionic charge, and hydration is now understood. Rate studies in mixed solvent systems have been much less frequent, and systematic self-diffusion measurements have not been reported. Most studies have been motivated by the need to optimize conditions for analytical separations in organic or mixed solvents. Interpretation of results in terms of a model has been difficult or impossible because of the large number of new variables introduced with the additional solvent. Differential swelling of the resin, preferential absorption of the solvents, and substantial differences in dielectric constants of the imbibed and external solvent mixtures lead to complex variations during the course of individual kinetic experiments which were difficult to interpret. We have conducted self-diffusion measurements in poly(styrenesu1fonate) cation exchange resins in mixed solvent systems with a view to eliminating or minimizing these variables and therby providing data more amenable to mechanistic i n t e r p r e t a t i ~ n . ~The J ~ solvent system we chose was dimethyl sulfoxide (Me2SO)-water. The sodium and rubidium forms of the resin show little preferential solvent absorption in this system and the degree of resin swelling remains reasonably high over the entire composition range as shown by Van Wart and Janauer.'l The bulk dielectric constants of Me2SO-water mixtures vary nearly linearly from 78 to 48,12values sufficiently high to ensure complete dissociation of salts of strong acids and bases. Specifically, we have measured self-diffusion coefficients of sodium and rubidium ions in poly(styrenesu1fonate) resin beads of 8 and 4% divinylbenzene cross-linking by varying the solvent mixture from 0 to 70 mol % Me2S0. We have made parallel measurements of diffusivity of the two ions in 0.1 M external solutions of their chlorides in mixtures of the same solvents. In addition, we performed 0 1979 American Chemical Society
Cation Exchange in Mixed Solvent Media
self-diffusion measurements of Me2S0in the same aqueous MezSO mixtures both in the poly(styrenesu1fonate) resins and in the external solutions. A feature of the MezSO-water system, significant for our purpose, is the strong interaction of these solvents. Much evidence points to the existence of a 2:l water-MezSO complex, likely prevailing as an nmer. Raman ~pectroscopy‘~ and neutron inelastic scattering data of Safford14 suggest strong H bonding between MezSO and water; Tommila16 has proposed that one water is bonded by dipole-dipole interaction between water 0 and Me2S0 S; the kinetic data of Fuchs16and the thermodynamic data of Lindbergll give evidence that water-MezSO bonding takes precedence over water association in mixtures of the two liquids. Maxima and minima in many properties, occurring in the 33 mol % Me2S0 region, support the existence of an adduct which MoreP has termed a “privileged complex”. The negative enthalpy of mixing17 shows a maximum a t 33 mol 70 MezSO, as does the vi~cosity.’~ The solubility of H2 and the entropy and enthalpy of solution of Hzin Me2SO-water mixtures show maxima at 33 mol % MezS0.20 A number of multivalent metal ion equilibrium distribution coefficients were determined earlier,21122and univalent cation exchange equilibria were studied here23 and elsewhere.24 Maxima in selectivity quotients, QHM, were found in all cases between 30 and 50 mol % Me2S0. These maxima were strongly temperature dependentz3as is the viscosity maximum found at 33 mol 70Me2S0 in the Me2SO-water system.lg Maxima were also observed in that same composition range for the selectivity quotients, within three homologous series (alkali, alkaline earth, and tetraalkylammonium ions) where M2 is the ion having the greater ionic radius than M1. The results of that work and of an extensive study of solvent uptake by alkali resinates of the same type of poly(styrenesulfonate) resins from aqueous MezSO medial1 all supported the hypothesis that counterion solvation in the resin, and in the external solution where applicable, and MezSO-water interaction in the external solvent mixture, are the two main controlling factors.
Experimental Section We have employed the radioisotope thin-bed technique of Boydl for self-diffusion measurements of the alkali metal ions within the resin. In this method a solution of the appropriate electrolyte is passed continuously through a thin bed of spherical ion-exchange resin beads in the corresponding ionic form with trace amounts of radioactive counterion. The external solution is thus maintained at zero concentration of tracer ion. The equilibrium concentration within the resin is similarly zero. The apparatus used is indicated schematically in Figure 1. The capsule “a” contained the thin bed of resin beads between two polypropylene screens in a cylinder of the same material. Approximately 100 beads of largest diameter were chosen from a batch of Biorad AG50 W-X8 16-20 mesh beads. These were checked under a low-power laboratory microscope for spherical shape and freedom from fractures. The diameters of the individual beads in sodium form were measured with a Hamilton micrometer. The average diameter was checked by pycnometric measurements. Changes in diameter of the beads with the composition of the binary solvent mixture and with the change from sodium to rubidium resinate were calculated from changes in bed volume. Before each experiment the beads were immersed in NaCl or RbCl solutions tagged respectively with 23Na+or ssRb+.
The Journal of Physical Chemistry, Vol. 83, No. 14, 1979
1817
I t waste
- _ _ _ _ Figure 1. Apparatus used for determination of selfdiffusion coefficients in Na+ and Rb’ resinates as described in the text: (a) capsule containing resin beads; (c) NaI crystal probe; (d) valve; (e) vessel containing solvent; (f) vessel containing 0.1 M salt solution; (9) air vents; (i) valve; (j)flow meter; (k) pump; (I) valve; (p) lead brick.
The activity in the capsule was monitored by the thallium-doped sodium iodide scintillation counter “c” and the total count displayed on a Nuclear Chicago manual lab scaler Model 8775. At the start of the experiment the valve “d” is switched to draw the 0.1 M NaCl solution through the bed, initiating the self-exchange process. The total count was read at 6-s intervals and the self-exchange rate calculated and plotted against time as percent attainment of equilibrium. The diffusion coefficient was calculated from the attainment-of-equilibrium curve by means of eq 1,utilizing a suitable computer program. Since values for 6‘ were not known, D values a t several times for each of several 6’ values were calculated. The 6’ value giving D values most nearly constant with time was taken as the true 0 for the particular experiment. The average of the most-nearly-constant D series was taken as the D for the experiment. A precision of &5.070 (standard deviation) was found in five replicate experiments. The value of 1.82 X lo4 cm2 s-l for Na ion in X8 resin compares with a value of 1.4 X lo4 cm2s-l for the same ion under similar conditions found by Pika1 and Boyd.25 The Nernst film thickness, 6, was calculated to be 8 X cm for the X8 resin at 0 mol % MezSO. This low value implies that under experimental conditions the flow rate was adequate to minimize the contribution of film diffusion to rate control. Diffusion coefficients (D)for Na+ and Rb+ in 0.1 M solutions were determined by the open-end capillary technique of Wang.26 Uniform bore capillaries were loaded with 0.102 M solution of the NaCI- or RbC1-containing radioactive tracer and immersed in a gently stirred 0,100 M solution of the same salt. The small difference in concentration minimized any convective effect. Activity remaining in the capillaries was determined after 2-3 days and compared to that in capillaries loaded in the same manner but from which no material was allowed to diffuse. Fractional attainment of equilibrium was between 0.3 and 0.6. Precision, as determined by five replicate determinations, was &5% (standard deviation). Our value for DNa+ in pure water of 1.38 X cm2 s-l compares with a value of 1.31 X cm2 s-l found by Wang.26 Self-diffusion coefficients of Me2S0 within the resin were determined by using trace amounts of 35Slabeled
1818
The Journal of Physical Chemistry, Vol. 83, No. 14,
1979
R. C. Johnston, C. 0. Lobdell, and 0. E. Janauer
I Ln I
0
rl
X 0.1
2
VI
0 rl
X el
2
\' ' '. , ,
I 0
IO
20
30 40 MOLE % DMSO
50
60
70 VI I
0
rl
Flgure 2. Self-diffusion coefficients of Na+ and dimethyl sulfoxide in Na+ Dowex 50W-X8 and in free (external) solution as a function of
X 0
solvent composition. Dotted line shows bb+ after correction by using eq 2.
2
MezSO placed in the sample resin beads. The sample capsule and sample preparation were similar to that for ionic self-diffusion measurements. A solution of the appropriate solvent mixture containing only unlabeled MezSO was pumped through the sample capsule a t a uniform rate. The effluent was collected in a sample collector and the 0activity at 0.167 MeV of each fraction was measured in the presence of an Aquasol liquid scintillation cocktail in a Mark I scintillation counter. Since infinite volume conditions prevailed in these experiments as well as in the ionic diffusion measurements, the treatment of the data thus obtained-was similar. Five replicate determinations of DMezSO at 2.8 mol % MezSO had a standard deviation of f4.0%.
Results and Discussion Diffusion coefficients resulting from these measurements are presented in Tables I and I1 and graphically in Figure 2. Though the diffusion coefficient for Na+ in the external solution shows a decrease with increasing Me2S0 content, Stokes radius calculations show a decrease in radius of the kinetic unit from 3.3 A at 0 mol % MezSO to 2.8 A at 33 mol %. The calculation, based on the Einstein-Stokes relationshipz7 is, of course, not strictly applicable to nonspherical particles, but the relative calculated size of the diffusing species is nevertheless probably significant. The decrease in size of solvated Na+ ion may be explained by the competition of increasing amounts of MezSO for the water available to the Na+ ion for hydration. The water tends to be stripped from the Na+ ion, which may then diffuse faster than it would otherwise in the more viscous medium. Self-diffusion coefficients for MezSO in MezSO-water mixtures (0.1 M in NaCl), shown in Table 11, indicate that the MezSO kinetic unit actually increases in size over the
d ?;
x x x
P
F
x x x
F
00
0
rid
rl
x x
x
mt-
d
2: 2
Cation Exchange in
Mixed Solvent Media
The Journal of Physical Chemistty, Vol. 83, No. 14, 1979
1819
TABLE 11: Me,SO Diffusion Coefficients (cm2/s)
-
25 "C pure solvent mixture
53 'C, pure solvent mixture
38 'C, pure solvent mixture
0.1 N NaCl
I
mol % Me,SO
resiE 1070
external 1 0 5 ~
resi: 1070
external
2.8 6.0 20.0 33.5 50.5 69.5 100.0
4.13 4.09 1.50 0.39 0.13 0.097 0,099
1.06 0.75 0.51 0.36 0.44 0.57 0.80
4.12
0.93
0.38 0.15
0.34 0.49
105D
same range of solvent mixtures. In the region above 33 mol % MezSO the apparent size of the Na' kinetic unit increases. This probably reflects solvation of Na+ by Me2S0, replacing water at higher Me2S0 concentrations. On the other hand, the MezSO unit, calculated from the data in Table 11,tends to decrease in size. This is of course reasonable since above the 33 mol % Me2S0 level a higher proportion of Me2S0 molecules will travel in a nonhydrated condition. Comparison of self-diffusion coefficients within the resin with the above data in the external solution reveals interesting differences. As would be expected, resin coefficients are considerably smaller. One obvious reason is the tortuous path an ion or other entity must follow within the resin. Mackie28has given an equation relating resin void volume to relative path length:
where ( D / D ) , is the Mackie tortuosity factor and E the fractional pore volume. We have calculated (DID), at several mole fractions of Me2S0 by using solvent uptake data obtained by Van Wart and Janauer" in a similar system. The dashed curve in Figure 2 represents D values, corrected for tortuosity according to the Mackie equation. I t is clear that there are factors other than tortuosity retarding the cation in the resin, particularly as the Me2S0 content becomes appreciable. Since the reasons usually given for a slower rate of ion exchange in mixed solvent Le., pronounced resin deswelling and low dielectric constant, are de-emphasized in our system, it is necessary to look further for an explanation of the much-more-rapid drop in D with increasing Me2S0 as compared to that for D. It seems reasonable to suppose that the rapid loss of mobility of Na+ in the resin with increasing Me2S0 results from the competition between Me2S0 and Na+ for water of hydration. With diminished hydration the Na+ is increasingly bound to the fixed ion sites of the resin. In the region above 33 mol % Me2S0 energy for site dissociation might be supplied by solvation of Na+ by Me2S0.30 However Me2S0 has little tendency to solvate the fixed sulfonate anions3I and it is thus lack of anion solvation which may cause ion pairing in the resin in the region above 33 mol % Me2S0. In any case, with increasing Me2S0 content, the total number of solvent molecules per Na+ becomes small (see Table 111). It appears that even a t 10 mol % Me2S0, if we assume that each Me2S0 molecule effectively captures 2 water molecules, there remain only 4 water molecules for hydration of each sodium and fixed anion in our system. At 70 mol % MezSO there are only 2.7 molecules of either solvent present for the solvation needs of cation and fixed anion. It is not
resig 1070
external 105D
resic 1070
external 1050
6.26 6.43 2.41 0.90 0.25
1.71 0.90 0.68 0.58 0.61 0.88 1.37
10.34 12.53 4.32 2.15 0.84 0.31 0.35
1.70 1.67 1.42 1.05 1.14 1.09 1.60
0%
0.22
TABLE 111: Solvent/Ion Mole Ratio in Biorad AG 50W X8 Resin, Na' Form mol % Me,SO 0 5.9 9.8 14 20 27 50 70
[Me,SO], mol/mol Na +
[water], [tot solvent], mol/mol molecules/ Na' counterion 10.2 7.7 6.5 5.5 4.4 3.5 1.7 0.8
0 0.5 0.7 0.9 1.1 1.3 1.7 1.9
10.2 8.2 7.2 6.4 5.5 4.8 3.4 2.7
TABLE IV: Activation Energies for Self-Diffusion of Sodium Ion (25-54 "C) X8 resin E, Ea, A[~*s*/RI (ext soln), mol % kcal/mol ( l o *c m ) kcalimol Me,SO 0 2.8 6.0 33.3 50.5 a
6.2 7.1 7.4 10.6 12
7.2 11.6 12.5 44 90
4.8a 2.8
From data of Boyd and Soldano.6
surprising that the exchange rate becomes extremely slow under these conditions and the effective self-diffusion coefficient becomes very small indeed although the total solvent volume in the resin remains high. The low D values for Na+ at high Me2S0 concentrations contrast with the relatively high D values for Me2S0 in this solvent composition range. The greater mobility of the MezSO molecule may be explained by the fact that, as a neutral species, it is free to migrate without restriction due to ion pairing, such as affects the counterion. Eyring's application of his absolute reaction rate theory to diffusion32has been applied by Boyd2 to diffusion of cations within a cation exchange resin. Table IV presents the calculated energies of activation for the diffusion of Na+ in X8 resin at several MezSO levels calculated from the temperature dependence of D for Na+. The entropy term is calculated from the Eyring relationship
D=
x ~kT -~AS*/R~-E/RT
h
(3)
where X is the distance between equilibrium positions of diffusing molecule, AS* the standard entropy change for the activation process, k the Boltzmann constant, T the absolute temperature, R the gas constant, and E the observed energy of activation, calculated from D = Ae-E/RT. The increase in energy of activation is consistent with our picture of a more weakly solvating environment within the resin as the MezSO content increases. It would be
1820
The Journal of Physical Chemistry, Vol. 83, No. 14, 1979
expected that energy of activation would increase as less of the energy required for dissociation can be supplied by solvation. The entropy term, X[e~p(S*/R)ll/~, increases from 7.2 X cm in water to 44 X cm at 33 mol % Me2S0. It is not possible to distinguish between the effect of an increase in A, the Eyring “jump” distance, and of an increase in the exponential entropy factor. It might be expected from our model that X would increase to the distance between the fixed sites as ion pairing becomes an important consideration. Taking a typical value of 1.5 A for X in water as derived by Wang33and an average intersite distance of 7 A for an X8 resin, we can show that much of the increase in h [ e ~ p ( S * / R ) ]might ~ / ~ be explained by the increase in A. If the environment within the resin is unable to provide for the solvation needs of the ions for dissociation one might expect the intrinsically less solvated Rb’ ion to be less retarded by a change in solvent from water to a 50 mol % Me2SO-water mixture, than is the Na’ ion. That this is actually the case may be seen from the data in Table I. Rb+ is retarded by a factor of 203 by the change from water to 50 mol 70’ MezSO while Na+ is retarded by a factor of 281. As is to be expected, Rb+ has a higher diffusion coefficient under all conditions, than does Na’, reflecting its smaller solvated size. In the X4 resin the change in medium from water to 50 mol % MezSO results in retardation of Na+ by a factor of only 84 as compared to 281 in the X8 resin. It seems clear that this reflects the lower concentration of sites and thus the availability of more solvent per site in the X4 resin.
Conclusion The experimental data for self-diffusion of Na+ in a cation exchange resin in water-Me2S0 media may be interpreted in terms of the solvating ability of the medium for the sodium ion. The competition for water of hydration between Me2S0 and Nat in the lower Me2S0 region explains the transport behavior of both Na+ and Me2S0 in the external solution and in the resin. Scarcity of solvent to supply solvation energy for dissociation likewise accounts for the diffusion behavior of counterions in the resin a t higher Me2S0 levels. Acknowledgment. The authors thank George E. Boyd, Friederich G. Helfferich, and Henry Eyring for helpful
R. C. Johnston, C. 0. Lobdell, and G. E. Janauer
discussions. The kind assistance of H. D. Sharma and M. E. Starzak in providing computer programs is gratefully acknowledged. This work was supported in part by a National Science Foundation Grant (GP 9416).
References and Notes (1) G. E. Boyd, J. Schubert, and A. W. Adamson, J. Am. Chem. SOC., 69, 2818 (1947). (2) G. E. Boyd, A. W. Adamson, and L. S. Myers, Jr., J . Am. Chem. Soc., 69, 2836 (1947). (3) G. Schulze, 2. Phys. Chem., 89, 168 (1915). (4) L. R. Ingersoll, 0. J. Zobel, and A. C. Ingersoll, “Heat Conduction”, McGraw-Hill, New York, 1948. (5) J. J. Grossman and A. W. Adamson, J. Phys. Chem., 56, 97 (1952). (6) G. E. Boyd and B. A. Soklano, J. Am. Chem. SIX., 75, 6091 (1953). (7) M. Tetenbaum and H. P. Gregor, J. Phys. Chem.,58, 1156 (1954). (8) H. D. Sharma, R. E. Jervis, and L. W. McMiilen, J . Phys. Chem., 74, 969 (1970). (9) R. C. Johnston, Ph.D. Thesis, State University of New York at Binghamton, 1975. (10) C. 0. Lobdell, Ph.D. Thesis, State university of New York at Binghamton, 1976. (11) H. E. Van Wart and G. E. Janauer, J. Phys. Chem., 78, 411 (1974). (12) de MM. G. Douheret and M. Morenas, C. R . Acad. Sci. Paris, Ser. C,264, 729 (1967). (13) J. R. Scherer, M. K. Go, and S. Kint, J. Phys. Chem., 77, 2108 (1973). (14) G. J. Safford, P. C. Schaffer, and P. S. Leung, J. Chem. Phys., 50, 2140 (1969). (153 E. Tommila and M. L. Murto, Acta Chem. Scand., 17, 1947 (19633. (16) R. Fuchs, G. E. McCrary, and J. J. Bloomfield, J. Am. Chem: SOC., 83, 4281 (1961). (17) J. J. Lindberg and J. Kenttamaa, Suomem Kem., 833, 104 (1960). (18) J. P. Morel, Bull. Soc. Chim., 1456 (1968). (19) J. M. G. Cowie and P. M. Toporowskl, Can. J . Chem., 39, 2240 (1961). (20) E. A. Symons, Can. J. Chem., 49, 3940 (1971). (21) G. E. Janauer, Mikrochlm. Acta, 1111 (1968). (22) G. E.Janauer, H. E. Van Wart, and J. I. Carrano, Anal. Chem., 42, 215 (1970). (23) G. E. Janauer, H. E. Van Wart, N. Hokschmldt, R. C. Johnston, and R. Fox, unpublished results. Abstracts 160th National Meetlng of the American Chemical Society, Chicago, Ill., Sept 1970 (Symposium on the Physical Chemlstry of Ion Exchange). (24) R. Smits, D. L. Massart, J. Juilliard, and J. P. Morel, Anal. Chem., 48, 458 (1976). (25) M. J. Pika1 and G. E. Boyd, J . Phys. Chem., 77, 2918 (1973). (26) J. H. Wang, J. Am. Chem. Soc., 73, 510, 4181 (1951). (27) R. A. Robinson and R. H. Stokes, “Electroiyte Solutions”, Butterworths, London, 1959, p 43. (28) J. S. Mackie and P. Meares, Proc. R . SOC.London, Ser. A , 232, 498 (1955). (29) Y. Marcus in “Ion Exchange and Solvent Extraction”, J. A. Marinsky and Y. Marcus, Ed., Marcel Dekker, New York, 1971, Chapter 1. (30) J. L. Wuepper arid A. I. Popov, J. Am. Chem. Soc., 92, 1493 (1970). (31) A. J. Parker, Q . Rev. Chem. Soc., 16, 163 (1962). (32) S. Glasstone, K. J. Laidler,and H. Eyrlng, “Theory of Fate Processes”, 1st ed, McGraw-Hill, New York, 1941. (33) J. H. Wang, J. Am. Chem. Soc., 73, 4181 (1951).
