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a solvent containing Co(T(p-CH,O)PP)B. To test this hypothesis, methylene chloride solutions of tetrabutylammonium hexafluorophosphate (TBAH) were prepared and dioxygen uptake of Co(T(p-CH30)PP)(py) in each solution was determined at -34.6 “C. The dioxygen sensitivity of the complex increased from log KO, = -2.24 mm-’ with no electrolyte present in the solution and reached a maximum at 0.02 M TBAH where log KO,= -2.06 mm-’. From 0.02 M to higher electrolyte concentrations, the dioxygen uptake ability of the complex remained nearly constant. The results of a dilution conductivity study based on the Onsager equation32and methods published by Boggess and Zatko indicate that TBAH is a weak electrolyte in methylene chloride and it is interesting to note that the point a t which the equivalent conductivity of the solution ceases to change is near the point of which dioxygen uptake levels off. The small change in the dioxygen uptake ability of the complex in salt solutions is consistent with a small change in 2 values. Unfortunately, the 2 values of the TBAH solutions are unknown.
Conclusion The dependence of reversible dioxygen uptake of Co(T(p-CH30)PP)Bcomplexes on solvents is determined by a number of complex variables related to an intricate in(32) Boggess, R. K.; Zatko, D. A. J. Chem. Educ. 1975,52,649.
terplay of properties of solvent and solute molecules. The gross effects are accounted for by analyzing the dependence of log KO and AHoz on the dielectric constant of the medium and the electrophilic solvating power of the solvents using a* and ET(30) values as a guide. The intercepts of polarity plots and “gas-phase values” calculated from ET(30) plots are similar and suggest both functions measure similar solute-solvent properties. The constants obtained from the intercepts of polarity plots and “gas-phase” values deduced from ET(30) plots may contain a small contribution (log KO,, 5 0.3 mm-’; AHo, 5 0 . 3 kcal/mol) from the polarizability function. Deviations from the general trend can be explained on the basis of the physical and chemical properties of the solute and/or solvent and the thermodynamics of the system. It was found that enthalpy and entropy changes were off-setting terms in the AH,-,, and log KO,trends for reactions in chlorobenzene and N,N’-dimethylformamide. Thus, an analysis of the intricate details of dioxygen uptake indicated that entropies do change somewhat, rather than remaining constant as has previously been suggested. Acknowledgment. We thank the Research Corporation, the donors of the Petroleum Research Fund, administered by the American Chemical Society, and the Foundation of the University of North Carolina at Charlotte for support.
Activity Coefficients of Mixed Electrolytes from Liquid-Liquid Partitioning Measurements John M. Kennlsh and David K. Roe’ Environmental Sciences and Resources-Chemistry Department, Portland State University, Portland, Oregon 97207 (Received: Ju/y 2, 1982; In Final Form: February 25, 1983)
Distribution of an uncharged metal chelate between aqueous and nonaqueous solutions is shown to depend upon, inter alia, the activity coefficient of the metal ion when the distribution ratio is small. From this dependence, mean ionic activity coefficients may be determined of metal salts in the presence of nonreactive electrolytes. Experimental results are given for copper(I1) salts in the presence of three different strong electrolytes and the resulting activity coefficients are compared with ion selective electrode measurements and with calculated activity coefficients based on three different theories of mixed electrolytes. Further variations on the method and application to biological and environmental studies are discussed.
Introduction Methods for the determination of activities of dissolved electrolytes at low and trace levels in the presence of relatively large concentrations of other solutes are of interest in environmental chemistry, biology, and the theory of electrolyte solution. An approach is described here which is of rather general applicability and results are presented for copper(I1) salts in the presence of several common electrolytes. This method relies on the partitioning of an uncharged chelate of the metal ion of interest between an aqueous solution and an immiscible solvent. Thus, it is amenable to those metal ions which form stable complexes and the major electrolytes present must be inert to the same reaction. It is also clear that proton activity in the solution is important since suitable chelate ligands are universally weak acids. In other respects, liquid-liquid partitioning is quite analogous to other methods which have been used for the determination of activities of solutes; the commonality is that some intensive property of
a phase in contact with the solution under study is measured as a function of solute concentration or ionic strength. Liquid-liquid partition equilibrium (LLPE) has been recognized’ to have promise for the measurement of chemical potentials, but thus far applications have been made to only two systems involving ion-pair formation. In the first: ionic activity coefficients of uranyl nitrate in the presence of various concentrations of sodium nitrate were obtained by equilibration with a solution of uranyl nitrate in ether. The idea was based upon the concept of “isoactive” solutions. In practice, a series of solutions was prepared containing uranyl nitrate and sodium nitrate, and one reference solution of uranyl nitrate alone. In ether the uranium salt dissolves as an uncharged molecule. Thus, (1)R. A. Robinson and R. H. Stokes, “Electrolyte Solutions“, Butterworths, London, 1968. (2)E. Glueckauf, H.A. C. McKay, and A. R. Mathieson, J . Chem. SOC.,S299 (1949).
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Activity Coefficients of Mixed Electrolytes
the series of solutions could be equilibrated by circulation of an ether solution, a condition which meant that the chemical potential of uranyl nitrate in each solution was the same as a consequence of transport by the ether. From independent measurements, activity coefficients of uranyl nitrate solutions were known so that analysis of the solutions for uranyl allowed activity coefficients to be calculated for the solutions containing added sodium nitrate relative to the reference solution. Several assumptions were necessary and these were addressed in a subsequent series of publication^.^-^ Perhaps the most important assumption was that the activity of the salt was unaffected by mutual solubility of the solvents. The importance of this effect was investigated for a number of organic solvents and found to be rather small in most cases. Empirically, the percent change in electrolyte activity due to the presence of organic solvent was about twice the solubility of the solvent in the aqueous electrolyte, expressed as percent by weight. By suitable choice of organic phase, the error may be held to 1%or less, according to these results. In the other study of ion-pair extraction, activity coefficients of aqueous solutions of methylene blue perchlorate (M13C104)in the presence of added urea9 and electrolyteslO were obtained by partitioning with an organic phase. The procedure used was termed “isoextraction” since potassium perchlorate was added to each aqueous solution until the concentration of the dye salt reached a reference level in the organic phase, as measured spectrophotometrically. Instead of extrapolating to zero ionic strength, the mean ionic activity coefficient of methylene blue salt was assumed to be unity at 0.4 mM in 1mM hydrochloric acid. In addition to these two examples, LLPE has been employed to measure solvent activities11J2and nonelectrolyte activities, both organic13 and inorganic.14 Extraction of uncharged metal chelate complexes into nonpolar solvents is a widely recognized analytical technique of considerable versatility and specificity.lk20 Application to activity and activity coefficient determinations is indeed possible, as will be shown, provided that con(3) H. A. C. McKay and A. R. Mathieson, Trans. Faraday SOC.,47,428 (1951). (4) E. Glueckauf, H. A. C. McKay, and A. R. Mathieson, Trans. Faraday Soc., 47,437 (1951). (5) A. W. Garner, H. A. C. McKay, and D. T. Warren, Trans. Faraday SOC.,48, 997 (1952). (6) A. W. Gardner and H. A. C. McKay, Trans. Faraday SOC.,48,1099 (1952). (7) H. A. C. McKay, Trans. Faraday SOC.,48, 1103 (1952). (8) I. L. Jenkins and H. A. C. McKay, Trans. Faraday SOC.,50, 107 (1954). (9) P. Mukerjee and A. K. Ghosh, J . Phys. Chem., 67, 193 (1963). (10) A. K. Ghosh and P. Mukerjee, J. Am. Chem. SOC.,92,6413 (1970). (11) Y. Hasegawa and T. Sekine, Bull. Chem. Sot. Jpn., 38, 1713 (1965). (12) Y. Hasegawa, Bull. Chem. SOC.Jn., 42, 1429 (1969). (13) John E. Gordon, ‘The Organic Chemistry of Electrolyte Solutions”, Wiley, New York, 1975. (14) H. Reinhardt and J. Rydberg in “Solvent Extraction Chemistry”, D. Dyrssen, J. 0. Libjenzin, and J. Rydberg, Eds., Proceedings of the International Conference on Solvent Extraction Chemistry, Goteborg, North-Holland Publishing Co., Amsterdam, 1967. (15) E. B. Sandell, ‘Colorimetric Determination of Traces of Metals”, 3rd ed., Interscience, New York, 1959. (16) G. H. Morrosion and H. Freiser, “Solvent Extraction in Analytical Chemistry”, Wiley, New York, 1957. (17) J. Stary, “Solvent Extraction of Metal Chelates”,Pergamon Press, London, 1964. (18) A. K. De, S. M. KhoDkar. and R. A. Chalmers. “Solvent Extraction of Metals”, Van Nostrand-Reinhold, London, 1970. (19) Y. A. Solotov, “Extraction of Chelate Compounds”, Ann Arbor Science Publishers, Ann Arbor, MI, 1970. (20) T. Sekine and Y. Hasegawa, “Solvent Extraction Chemistry; Fundamentals and Applications”, Marcel Dekker, New York, 1977.
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ditions are chosen so that only a small fraction of the metal species of interest is partitioned, rather than analytically extracted in the usual sense.
Relation between Activity Coefficient and Distribution Ratio Expressions for solvent extraction of neutral metal chelates have been derived in a number of For the present purpose, it is only necessary to include activity coefficients in the usual equations and rearrange to the desired relations between experimental quantities and the mean activity coefficient of the aqueous metal ion salt. Certain conditions must be met: (a) activities of all species in the aqueous phase are unchanged by saturation with the organic solvent, or the change is small and constant under all experimental conditions; (b) the only extractable species in the aqueous phase is the uncharged metal complex, ML,, and no self-association of this species occurs in the orgnic phase (although the treatment could be extended to include this complication); (c) activity coefficients of the protonated ligand, HL, and the metal complex, ML,, in the organic phase are constant with moderate changes of concentration at low levels. These conditions are most easily realized by selection of a nonpolar solvent of low solubility in water and a chelating agent with a very large partition constant so that the aqueous concentration is very small. Indeed, the concentration may be so low that from a practical viewpoint the reaction of HL with the metal ion may occur only in the interfacial region. Finally, it will be necessary to choose experimental conditions such that only a very small fraction of the metal ion is partitioned and the resulting concentration of ML, in the organic phase is low. While these statements are qualitative, it can be expected that the conditions will be met in the millimolar concentration range and that they are experimentally verifiable. Thermodynamic equilibrium constants are defined in terms of the following reactions in which the activity of a solute in a given solvent is referred to infinite dilution in that solvent: HL(aqueous) = HL(organic) KHL= ~ H L W / ~ H L
(1)
HL = H+ + L-
k~ = ~
H ~ L / ~ H L
(2)
Mn+ + nL- = ML, Pn
=
aML,/
[aM(adn1
(3)
ML,(aqueous) = ML,(organic)
KD= ~
M L J ~ ~ M L ,
(4)
To simplify notation, only the organic phase is identified in the expressions for Km and KD; reactions 2 and 3 occur exclusively in the aqueous phase. Activities are noted by U N for the species N. The distribution ratio
D = [ML,(o)l/C[misl
(5)
is an experimental quantity and it is based upon molar concentrations indicated by brackets. The denominator stands for the sum of metal ion species in the aqueous phase. Usually, the concentration in the organic solvent is measured and the denominator terms is obtained by difference. The total amount (molarity) of metal ion species before partitioning may be known, as in the ex(21) H. A. Laitinen and W. E. Harris, “Chemical Analysis”, McGrawHill, New York, 1975.
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periments reported here, or may be found by any suitable total concentration analysis. There is a dependence of D on the activity of Mn+as can be seen by substitution for the numerator of eq 5 from eq 4 and using eq 1-3 to cast the expression in terms of reactants:
KA~HLW K & ~ M
D =
(s
)yMLn(o)x[misj
(6)
If, at equilibrium, the term representing the sum of metal ion species in the aqueous phase is substantially equal to [Mn+]though appropriate choice of conditions, then YM = aM/[Mn+],the activity coefficient of the metal ion on the molar scale, may be substituted into eq 6. By introducing the activity coefficient of the anion, yx, into the numerator and the denominator and noting that the mean molar activity coefficient is y* = ( y ~ y ~ ~ ) l lfor ( ~the + l )salt of interest and for the acid of the same anion, yaHx = ( y ~ t y ~ )(assuming l/~ X is univalent), eq 6 becomes
Application of this expression is quite straightforward in a classical ionic strength study in which the metal ion salt of interest is at low concentrations and an inert electrolyte is used to change ionic strength. From suitable concentration measurements, values of D are determined as a function of ionic strength, I. In view of the DebyeHuckel equation, a plot of log D vs. Ill2 is expected to become linear as Ill2approaches zero and the intercept value, D', pertains to a reference solution for which activity coefficients are unity, by convention. A direct calculation for ya at each ionic strength is most easily made from ratios of D to D'since all constant terms cancel. Also, if a large excess of ligand is employed, the ratio C I H L ( ~ ) / ~ ' H L (is~ )adequately approximated by the known concentration ratio after equilibrium. The ratio Y M L , ( ~ ) / Y ' M L ~ ( ~can ) be set equal to unity if the final concentrations of ML, in the organic phase are kept very low, i.e., small values of D. Restricting D to be
