Thermal diffusion of weak electrolytes: aqueous phosphoric and iodic acids

Lij HUI AND DEREK G. LEAIST' Department of Chemistry, University of Western Ontario, London, Ont., Canada N6A 5B7

Received October 27, 1989

LO HUI and DEREK G. LEAIST. Can. J. Chem. 68, 1317 (1990). Soret coefficients of aqueous phosphoric acid and aqueous iodic acid are determined conductimetrically at 25°C. As the

molality of phosphoric acid drops from 0.05 toward 0.00 mol kg-', the enthalpy of transport jumps from 2 to 15 kJ mol-'. For iodic acid, a stronger electrolyte, the corresponding increase is smaller, from 12 to 17 kJ mol-'. Equations are developed for the enthalpy of transport of 1:l weak electrolytes. The equations are used to evaluate the reactive enthalpy of transport and the intrinsic enthalpies of transport of the ionized and molecular forms of phosphoric and iodic acids. Equating the enthalpies of transport of the acid molecules and the acid anions provides estimates of single-ion enthalpies of transport. Thermal diffusion measurements are reported for potassium dihydrogen phosphate and potassium iodate to help interpret the results.

Key words: thermal diffusion, enthalpy of transport, Soret coefficients, weak electrolytes, phosphoric acid, iodic acid.

LO HUI et DEREK G. LEAIST. Can. J. Chem. 68, 13 17 (1990). OpCrant a 25°C et faisant appel a une mCthode conductimCtrique, on a dCterminC les coefficients de Soret des acides

phosphorique et iodique aqueux. Lorsque la molalitt de l'acide phosphorique diminue de 0,05 vers 0,00 mol kg-', I'enthalpie de transport passe rapidement de 2 a 15 kJ mol-'. Pour l'acide iodique, qui est un Clectrolyte plus fort, I'augmentation correspondante est plus faible et elle passe de 12 a 17 kJ mol-'. On a dCveloppC des Cquations pour I'enthalpie de transport d'Clectrolytes faibles 1:l. On a utilist les Cquations pour Cvaluer I'enthalpie de transport reactive ainsi que les enthalpies intrinskques de transport des formes ionisCes et molCculaires des acides phosphorique et iodique. Lorsqu'on ttablit une Cquation entre les enthalpies de transport des molCcules d'acide et les anions d'acide, on obtient une bonne Cvaluation des enthalpies de transport des ions uniques. Afin d'aider dans I'interprCtation des rCsultats, on rapporte aussi des mesures de diffusion thermique pour le phosphate diacide de potassium ainsi que l'iodate de potassium.

Mots cle's : diffusion thermique, enthalpie de transport, coefficients de Soret, Clectrolytes faibles, acide phosphorique, acide iodique.

[Traduit par la revue]

1. Introduction thermostat blocks maintained at 20 or 30°C. ~ k r m a l diffusion of the

A temperature gradient applied to an electrolyte solution causes the dissolved ions to diffuse relative to the solvent ( l ,2) . The thermally-driven diffusion of strong electrolytes has been the subject of a number of studies (1-1 1). In the work reported here, thermal diffusion measurements are reported for aqueous phosphoric acid (pKa = 2.15), a "weak electrolyte (12), and aqueous iodic acid (pKa = 0.80), an "almost strong" electrolyte (13-15).

In contrast to a strong electrolyte, a weak electrolyte can diffuse in different chemical forms, e.g. HA G H+ + A-. The enthalpy of transport of a solute that exists as a mixture of rapidly-equilibrating species consists of a contribution from the intrinsic enthalpies of transport of the species and another, usually smaller, contribution from the enthalpy change of the chemical reaction (16-18). The treatment developed in the present study is used to estimate the intrinsic enthalpies of transport of the molecular and ionized forms of iodic and phosphoric acids and the reactive component of the total enthalpy of transport. To help interpret the results, thermal diffusion measurements are also reported for the potassium salts of the acids. No thermal diffusion data appear to have been reported previously for iodates or phosphates (1 1).

2. Experimental The solutions were prepared from BDH reagent grade materials and

distilled deionized water. The phosphoric acid solutions were analyzed by potentiometric titration against standard alkali.

Conductance methods for the determination of the Soret coefficients of electrolytes are well developed (1-8). The cells used in the present study were of the pattern described by Agar and Turner (3). The cells held short columns of solutions (height 0.9-1.2 cm) between copper

'TO whom correspondence should be addressed.

ions was followed by measuring changes in electrical resistance across pairs of small platinum electrodes at fixed levels near the top and bottom of the solution column. Details of the equipment and procedure have been reported (1 9).

Published densities (20, 21), cqnductances (13, 15, 20-23), and isothermal diffusion data (24-27) were used to evaluate the Soret coefficients from the measured resistance changes. Since no diffusion coefficients appear to have reported for aqueous HI03 or KI03, a few isothermal diffusion measurements were made on these electrolytes. A simplified version of Harned's conductimetric procedure was employed (24).

3. Results Thermal diffusion in a convection-free solution leads to a

steady state in which the diffusion of solute driven by the temperature gradient is balanced by ordinary diffusion back down the thermally-induced concentration gradient. The Soret coefficient defined by (1, 2)

gives the relative change in solute molality per degree at steady state. Positive a values indicate thermal diffusion to the colder parts of the solution.

The enthalpy of transport of an electrolyte is related to its Soret coefficient by the following identity (1, 2)

v + and v- give the number of moles of cations and anions per mole of fully dissociated electrolyte, m is the total electrolyte molality, and y, is the stoichiometric mean ionic activity coefficient. The enthalpy of transport may be interpreted as the heat absorbed to keep the solution at constant temperature when solute diffuses out of a volume element of solution (1, 2).

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1318 CAN. 1. CHEM. VOL. 68, 1990

Soret coefficients were determined conductimetrically at molalities from 0.001 to 0.2 mol kg-' at the mean cell tempera- ture 25°C. The results are given in Tables 1-5. The reported u values represent average values from two or three runs at each composition. The values of u were reproducible within 2-4%, except at the lowest molalities where the reproducibility was poorer, about 5%. Published activity coefficient data (12, 13, 28-33) were used to calculate enthalpies of transport (H *) from the measured Soret coefficients, as listed in Tables 1-5 and plotted against the square root of the ionic strength I in Fig. 1.

KHz Po4 A short extrapolation to zero ionic strength gives 4.3 kJ mol- '

for the limiting enthalpy of transport of aqueous KH2P04. If C1- is arbitrarily assigned conventional enthalpy of transport 0 kJ mol-' at ionic strength 0.01 mol kgp1, the conventional (1, 4-6, 11) ionic enthalpies of transport of K+ and H2PO4- are, respectively, 2.0 and 1.4 kJ mol- ' .

In addition to K+ and H2PO4- ions, aqueous KH2P04 solutions contain traces of H+, HPO~'-, and molecular H3PO4 species due to the equilibria H2PO4- H+ + HPO~'- (K2 = 6.2 x lo-') (34, 35) and H3PO4 & H+ + H2PO4- (K1 = 7.14 x 1 OW3) (1 2). These minor species may be neglected here because their concentrations are very small. This simplification is supported by the observation that the limiting slope dH */dl 'I2

agrees qualitatively with the value - 10.8 kl kg1'' m ~ l - ~ ' ~ expected for a simple 1: 1 electrolyte (1 1). Moreover, previously measured (27) isothermal diffusion coefficients of aqueous KH2P04 extrapolate co~~ect ly to the limiting Nernst value for a strong 1 : 1 electrolyte.

K2HP04 Thermal diffusion measurements were made on aqueous

K2HP04 solutions to provide additional information about aqueous phosphates. As the molality drops to 0.001 mol kg-', the slope of H * against is increasing, and it exceeds the limiting value -32.4 kJ kg 'I2 m ~ l - ~ ' ~ suggested by theory for a 1:2 strong electrolyte (1 1). This behaviour may be due to the dissociation of KHP04- ion pairs, or to the hydrolysis reaction HPO~'- + H20 =S H2PO4- + OH- (Kh = 1.6 X lo-'). It was not possible to estimate the limiting value of H * reliably.

No attempts were made to measure thermal diffusion of K3PO4. Since this salt hydrolyzes extensively, its diffusion is a complicated ternary process involving coupled transport of K+ + OH- (26).

KI03 Table 3 gives the Soret coefficients for the potassium salt of

iodic acid. Extrapolation leads to the value 6.2 kJ mol-' for the salt's limiting enthalpy of transport. The conventional enthalpy of transport of the 103- ion has the value 4.2 kl mol-I. For comparison, the conventional enthalpies of transport of the ions 104- and C104- are 1.5 and -0.8 kJmol-', respectively (11). Table 3 includes the values of the isothermal diffusion coeffi- cient D that were obtained for aqueous KI03 solutions. The limiting value of D, 1.393 x m2 s-', was calculated by using the Nernst relation DO = 2D+D-/(D+ + D-) and the limiting ionic diffusion coefficients D+(K+) = 1.958 x lop9 and D-(103-) = 1.081 x m2 s-'. The ionic diffusion coefficients were calculated from the limiting ionic conduc- tances (15) A+' = 0.007354 and A-O = 0.004060 S mP2 mol-' by using the identity Di = RTA?/F~Z~'.

TABLE 1. Soret coefficients and enthalpies of transport of aqueous KH2P0, at 25°C

rn/mol kg-' 1 0 3 u / ~ - ' H */kJ mol-' 1 + d In y ,/d In m

"Extrapolated value.

TABLE 2. Soret coefficients and enthalpies of transport of aqueous K2HP04 at 25°C

rn/mol kg-' 1 0 3 u / ~ - ' H */kJ mol-' I + d In y ./d In rn

phosphoric acid are given in Table 4. Both the Soret coefficient and the enthalpy of transport of the acid increase sharply as the concentration drops toward zero. This behavior is not surprising in view of the large intrinsic enthalpy of transport of the H+ ions (1 1) that are produced by dissociation of the dilute acid.

The sharp curvature of the plot of H * against I 'I2 (Fig. 1) makes the direct extrapolation of H * highly unreliable. (Similar difficulties are encountered in the extrapolation of the acid's molar conductivity to the limiting value.) A better approach is to estimate the limiting enthalpy of transport of the dissociated acid by appealing to the additivity rule (1-6), and extrapolating the enthalpy of transport of the hypothetical fully dissociated electrolyte H+ + H2PO4- estimated from strong electrolyte data as follows: H *(H+ + H2P04-) = H *(KH2P04) + H*(HCl) - H *(KC]). The extrapolation of H * (H+ + H2PO4-) estimated from the measured enthalpies of transport of KH2F'04, HC1 (lo), and KC1 (6) is shown in Fig. 1 -(lower dashed curve). This procedure gives 15.4 kJ mol- ' for the limiting enthalpy of transport of phosphoric acid. This value is based on neglect of the second and third stages of dissociation of the acid.

HIO~ The Soret coefficient and enthalpy of transport of HI03

(Table 5) are less sensitive to changes in concentration than for H3PO4 because the former is almost fully ionized at the concentrations used in the present study. As the molality of the acid drops from 0.05 toward 0.00 mol kg- ' , for example, the degree of dissociation, a, of HI03 increases from about 0.83 to 1.00 (1 3), whereas a for H3PO4 changes from 0.35 to 1 .OO (12). Extrapolation of H *(HCl) + H * (KI03) - H *(KCl) (upper dashed curve in Fig. 1) leads to the value 17.3 kJ mol-' for the limiting enthalpy of transport of HI03.

The values of the isothermal diffusion coefficients for H3po4 aqueous HIO3 are listed in Table 5. The limiting value of D

The results of the experiments and calculations on aqueous was calculated according to Nernst's equation using D(H+) =

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TABLE 3. Soret coefficients, enthalpies of transport, and isothermal diffusion coefficients of aqueous KI03 at 25'C

m/mol kg-' 1 0 9 ~ / m 2 s-' 103u/K-' H */kJ mol-' 1 + d In y ,/d In m

0.000 1.393" 4.2b 6.2b 1 .000 0.002 1.35 3.86 5.57 0.976 0.005 1.34 3.72 5.30 0.963 0.010 1.32 3.62 5.08 0.950 0.020 1.29 3.57 4.92 0.933 0.030 1.26 3.58 4.88 0.922 0.050 1.21 3.61 4.83 0.905 0.100 1.13 3.72 4.83 0.879 0.200 1.04 4.11 5.14 0.846

"Nernst value. 'Extrapolated value.

----____ KIO tHCI-KC1 ------------- L----------

KH2P04 + HCI -KC! ----- --------_--_ ----- ----

lo\ H103

-

\ K2HP04 1 I

A k A - - A -

K l O j

5 - .-. \ .-. - .- KH2P04 e-• - - e-

lo' HjP04

FIG. 1. Plot of measured enthalpies of transport against the square root of the ionic strength for aqueous HIO3, H3PO4, K2PO4, UO3, and KH2P04 at 25°C. The dashed curves give the enthalpies of transport estimated for the hypothetical fully dissociated acids H+ + 103- and H+ + H2PO4-.

TABLE 4. Soret coefficients and enthalpies of transport of aqueous H3P04 at 25°C

m/mol kg-' 103u/K-' H */kJ mol-' 1 + d In y. /d In m - -

0.000 10.4" 15.4" 1 .000 0.001 7.50 9.89 0.892 0.005 5.68 6.35 0.756 0.010 4.72 4.67 0.670 0.030 3.24 2.99 0.624 0.050 2.66 2.35 0.597

"Extrapolated value.

9.317 X and D(I03-) = 1.081 X lop9 m2 s-' (15). Previous studies (25, 36-39) have shown that diffusion data for dilute weak acids can be analyzed to estimate the diffusion coefficient of the molecular form of the acid, Do. But in this case, only a small portion of dilute aqueous iodic acid diffuses

in molecular form. As a result, it was not possible to obtain a reliable value of Do. It is likely, however, that the value of Do for the molecular HI03 species is close to 1.08 1 X m2 s- ', the diffusion coefficient of 103-. (The diffusion coefficients of H2PO4- and the structurally similar molecular H3P04 species, forexample, are0.86 x 1OP9and0.87 x m2 s-' (25,40).)

4. Discussion Polymeric species, such as H(H2P04)- or H(103)2-, compli-

cate the properties of concentrated solutions of phosphoric and iodic acids in water (12, 13). But a negligible proportion of the total acid exists as these secondary species provided the acid molality is kept below about 0.05 mol kg-'. For the purposes of the present study, dilute aqueous solutions of phosphoric acid or iodic acid will be treated as simple weak electrolytes subject to the single equilibrium reaction HA G H+ + A-.

Recently, Agar and Lin (18) developed the thermodynamic theory for thermal diffusion of a solute that exists in two

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CAN. J . CHEM. VOL. 68, 1990

TABLE 5. Soret coefficients, enthalpies of transport, and isothermal diffusion coefficients of aqueous HI03 at 25°C

mlrnol kg-' D/ rn2 s- a/ K- H*/kJrnol-I l + d l n y , / d l n m

"Nernst value. bExtrapolated value.

rapidly-equilibrating forms: nA A,. Adapting their results to the problem under discussion leads to the exact expression

for the enthalpy of transport of a 1: 1 weak electrolyte. Ho* and H,* stand for the intrinsic enthalpies of transport per mole of the molecular (HA) and ionized (Ht + A-) forms of the electrolyte. to and t, are transport numbers which give the fractions of the total electrolyte transported as HA or H+ + A- (by definition, to + t+ = 1). H,*, the reactive contribution to the enthalpy of transport, is given by

where A,H is the enthalpy change of the dissociation reaction HA = H+ + A-, m, = a m is the molality of the ionized portion of the electrolyte, and dm,/dm measures the change in the ionized electrolyte molality with the total electrolyte molality, under equilibrium conditions. If t, is greater than dm,/dm, diffusion tends to remove ions faster than they are produced by dissociation; the subsequent dissociation required to maintain local equilibrium then makes a contribution to the enthalpy of transport of the same sign as the enthalpy of dissociation. Conversely, H * and H,* will have opposite signs if t, < dm,/dm.

The generally accepted value of the enthalpy of dissociation of dilute aqueous phosphoric acid is -7.9 kJ mol-' at 25°C (41). The value of A,H for iodic acid is somewhat uncertain; calorimetric (14), conductance (15), and solubility measure- ments (42) lead to the discordant values -2.8, -4.6, and - 10.0 kJ mol-', respectively. Without obvious reasons to dis- miss any of these careful determinations, the simple arithmetic mean value -5.8 kJ mol-' will be naively adopted.

Values of t, and dm,/dm are also required to estimate the reactive enthalpy of transport. dm,/dm was calculated from the extents of dissociation recommended by Pitzer and Silvester (12) (for phosphoric acid) and by Pethybridge and Prue (13) (for iodic acid). The transport numbers were evaluated by using the dilute-solution transport equations (43-45)

for the flux densities of H+, A-, and molecular HA species (designated by subscripts +, -, and 0 respectively). ci and Vfii are the concentrations (in moles per unit volume) and the gradients in the electrochemical potential of the species. The conditions of electroneutrality ( j + = j - ) and local chemical equilibrium (Po = fi+ + fi-) may be used to show that the

TABLE 6. Reactive enthalpy of transport of aqueous H3PO4 at 25°C

mlrnol kg-' ci f ? dm. /dm H,*/kJ rno1-'

TABLE 7. Reactive enthalpy of transport of aqueous HI03 at 25°C

mlrnol kg-' ci f ? dm. /dm H,*/kJ rno1-'

fraction of electrolyte transported in ionic form is given by

(An approach similar to the one used here has been used to analyze the reactive enthalpy of transport of aqueous sulfuric acid (19) subject to the bisulfate/sulfate equilibrium.)

Tables 6 and 7 list the estimates of the reactive enthalpy of transport together with the supplementary values of t,, dm, /dm, and a. The calculations indicate negative reactive enthalpies for both phosphoric and iodic acids. Iodic acid has larger reactive enthalpies of transport because its enthalpy of dissociation is larger. The magnitude of H,* for each acid passes through a maximum at a molality near K-', where similar amounts of the associated and dissociated forms of the acid are present (1 8).

Study of Tables 6 and 7 indicates that the fraction of acid transported in the ionized form is less than the fraction of total acid that is dissociated, i.e. t, < a. This behavior stems from the relatively low mobility of the dissociated electrolyte: the motion of H+ and A- through the solvent meets greater frictional resistance than the motion of the single associated species HA (25, 36-39).

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HUl AND LEAIST

FIG. 2. Intrinsic enthalpy of transport of aqueous phosphoric acid and iodic acid plotted against the transport number of the ionized form of the acid.

The intrinsic enthalpy of transport can be evaluated by subtracting the reactive enthalpy of transport from the measured total enthalpy of transport: toHo* + t?H,* = H * - H,*. In Fig. 2, the intrinsic enthalpies of transport obtained in this manner are plotted against t + , the transport number of the dissociated form of the acids. A linear extrapolation to t+ = 0 for phosphoric acid gives the value - 1.0 kJ mol-' for Ho*, the enthalpy of transport of the molecular H3PO4 species. The corresponding extrapolation for iodic acid is long and unreliable due to the larger values of t, for this "almost strong" acid. It appears, however, that the extrapolation for iodic acid runs parallel to the extrapolation for phosphoric acid, but is shifted upwards by 2-4 kJ mol-'. This observation leads to the tentative value 2 + 1 kJ mol-' for the enthalpy of transport of the molecular HI03 species.

It is intriguing that the difference between the enthalpies of transport of the H3PO4 and HI03 molecules appears to mirror the difference in the enthalpies of transport of the &Po4- and 103- ions [ H *(H2PO4-) - H *(103-) = H *(KH2P04) - H * (KI03) at low ionic strength (see Fig. I)].

The comparison provides circumstantial evidence, but not proof, that the enthalpies of transport of the anion/molecule pairs H2P04-/H3P04 and IO3-/HIo3 are nearly identical. This suggestion is not unreasonable on physical grounds since the acid anions and the acid molecules are structurally very similar. Moreover, the relatively low charge densities of the H2PO4- and 103- anions would tend to reduce the distortion of the structure of the nearby solvent.

If the enthalpies of transport of the acid molecules and anions are indeed nearly identical, it is then possible to evaluate single-ion enthalpies of transport. Adopting - 1 .O kJ mol-' for the enthalpy of transport of H2PO4- and molecular H3PO4 species, for example, leads to the corresponding values 16.4, 5.3, and 0.9 kJ mol-' for the limiting enthalpies of transport of the ions H+ , K+ , and 103-.

The quoted single-ion enthalpies of transport are speculative and remain to be checked by thermal diffusion measurements on other ion/molecule pairs. Nevertheless, progress along these lines may provide a practical scale of single-ion enthalpies of transport that is acceptably close to the true value of these elusive but theoretically-important quantities.

Acknowledgment The authors thank the Natural Sciences and Engineering

Research Council for financial support of this work.

1. J. N. AGAR. Advances in electrochemistry and electrochemical engineering. Edited by P. Delahay and C. W. Tobias. Inter- science, New York. 1963. Chap. 2.

2. H. J. V. TYRRELL. Diffusion and heat flow in liquids. Butter- worths, London. 1961.

3. J. N. AGAR and J. C. R. TURNER. J. Phys. Chem. 64, 1000 (1960).

4. J. N. AGAR and J . C. R. TURNER. Proc. R. Soc. (London) A255, 307 (1960).

5. P. N. SNOWWN and J. C. R. TURNER. Trans. Faraday Soc. 56, 1409 (1960).

6. P. N. SNOWWN and J. C. R. TURNER. Trans. Faraday Soc. 56, 1812 (1960).

7. N. H. SAGERT and W. G. BRECK. Trans. Faraday Soc. 57, 436 (1961).

8. A. D. PAYTON and J. C. R. TURNER. Trans. Faraday Soc. 58, 55 (1962).

9. L. G. LONGSWORTH. J. Phys. Chem. 61, 1557 (1957). 10. J. LIN, J. A. BIERLEIN, and J. G. BECSEY. J. Solution Chem. 3,

827 (1974). 11. N. TAKEYAMA and K. NAKASHIMA. J. Solution Chem. 17, 305

(1988). 12. K. S. PITZER and L. F. SILVESTER. J. Solution Chem. 5, 269

(1976). 13. A. D. PETHYBRIDGE and J. E. PRUE. Trans. Faraday Soc. 63,

2019 (1967).

Can

. J. C

hem

. Dow

nloa

ded

from

ww

w.n

rcre

sear

chpr

ess.

com

by

132.

75.8

0.18

3 on

12/

08/1

4Fo

r pe

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1322 CAN. 1. CHEM. VOL. 68, 1990

14. E. M. WOOLLEY, J. 0 . HILL, W. K. HANNAN, andL. G. HEPLER. 29. J. M. STOKES. Trans. Faraday Soc. 41, 685 (1945). J. Solution Chem. 7, 385 (1978). 30. C. W. CHILDS, C. J. DOWNES, and R. F. PLATFORD. Aus~. J.

15. L. E. STRONG and A. D. PETHYBRIDGE. J. Solution Chem. 16, Chem. 26, 863 (1973). 841 (1987). 31. E. A. GUGGENHEIM and J. C. TURGEON. Trans. Faraday Soc. 51,

16. B. BARANOWSKI, A. E. DE VRIES, A. HARING, and R. PAUL. 747 (1955). Adv. Chem. Phys. 16, 101 (1969). 32. K. S. RTZER. J. Phys. Chem. 77,268 (1973).

17. J. C. JOHNSON and A. L. BEYERLEIN. J. Phys Chem. 82, 1430 33. K. S. RTzERandG. MAYORGA. J. Phys. Chem. 77,2300 (1973). (1978). 34. A. K. GRZYBOWSKI. J. Phys. Chem. 62,555 (1938).

18. J. N. AGAR and J. LIN. J. Solution Chem. 16, 973 (1987). 35. R. G. BATES and S. F. ACREE. J. Res. Natl. Bur. Std. (U.S.) 34, 19. D. G. LEAIST. J. Solution Chem. 18, 651 (1989). 373 (1945). 20. E. W. WASHBURN (Editor). International critical tables. McGraw 36. G. T. A. M ~ ~ L L E R and R. H. STOKES. Trans. Faraday Soc. 53,

Hill, New York. 1929. 642 (1957). 21. C. M. MASON and J. B. CULVERN. J. Am. Chem. Soc. 71,2387 37. L. A. DUNN and R. H. STOKES. Aust. J. Chem. 18,285 (1965).

(1 949). 38. E. L. HOLT and P. A. LYONS. J. Phys Chem. 69,2341 (1965). 22. M.-C. JUSTICE, R. BURY, and J.-C. JUSTICE. Electrochim. Acta, 39. V. VITAGLIANO and D. A. LYONS. J. Am. Chem. Soc. 78, 4538

16, 687 (1971). (1956). 23. R. M. Fuoss and C. A. KRAUS. J. Am. Chem. Soc. 55, 476 40. M. SELVARATNAM and M. SPIRO. Trans. Faraday Soc. 61, 360

(1933). (1965). 24. 0 . W. EDWARDS and E. 0 . HUFFMAN. J. Phys Chem. 63, 1830 41. D. P. WAGMAN, W. H. EVANS, V. B. PARKER, I. HALOW, S. M.

(1959). BAILEY, and R. H. SCHUMM. Natl. Bur. Stand. (U.S.) Tech. 25. D. G. LEAIST. J. Chem. Soc. Faraday Trans. 1,80,3041 (1984). Note 270-3. Government Printing Office, Washington. 1968. 26. D. G. LEAIST. J. Solution Chem. 14, 709 (1985). 42. R. W. RAMETTE and D. A. PALMER. J. Solution Chem. 13, 637 27. R. A. NOULTY and D. G. LEAIST. J. Phys. Chem. 91, 1655 (1984).

(1987). 43. A. R. GORDON. J. Chem. Phys. 5 , 522 (1937). 28. S. GOLDMAN, R. G. BATES, and R. A. ROBINSON. J. Solution 44. W. H. STOCKMAYER. J. Chem. Phys. 33, 1291 (1960).

Chem. 3, 593 (1974). 45. D. G. LEAIST. J. Chem. Soc. Faraday Trans. l ,78,3069 (1982).

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