Francesco
Malatesta
*,
Chiara
Fagiolini
and
Roberto
Franceschi
Dipartimento di Chimica e Chimica Industriale dell’Università di Pisa,
via Risorgimento 35, 56126, Pisa, Italy. E-mail: franco@dcci.unipi.it; Fax: +39 050 2219260; Tel: +39 050 2219258
First published on 1st December 2003
An experimental method is illustrated, which opens up an effective line of attack in the fundamental and practically unexplored field of not-necessarily-dilute, not-necessarily-low-charge, multiple electrolytes. The method is based on the idea that ions of a sufficiently enhanced hydrophobic character (typically, charged metal complexes and organic or partially organic ions) can be studied by means of liquid membrane cells without undergoing any interference by highly hydrophilic ions such as SO42−, OH−, H+, Mg2+, La3+, etc. Proofs are given for hexacyanocobaltate(III) and tris(ethylenediamine) cobalt(III) salts. As a first application, the method is used to find otherwise unknown activity coefficients of trace electrolytes in swamping ionic bulks – the typical situation encountered in equilibrium, kinetic constant, and standard potential determinations. Observed salt effects do not prove in any case to be trivial, and in particular, the activity coefficients of 3:3 salts in 2:2 and 3:2 ionic bulks are found to be completely different from expectations.
When introducing the method of liquid membrane cells, which solved the problem of high-charge single electrolytes, Malatesta and Carrara maintained that their liquid membranes were intrinsically unable to make any selection between ions of the same sign, and therefore, that the measurements were only feasible for single electrolytes.4 However they were wrong, as they had forgotten that aqueous phases, unlike organic membranes, are always ion-selective bulks. As indifferent as the organic phase may be to the substitution of some ions for others of the same sign, the different water–ion interaction energies can lead a membrane to be permeable to only one ion of the aqueous solution, the less hydrophilic one among those of the right sign.
We shall demonstrate that these conditions are actually met in several cases, and therefore, liquid membrane cells make it possible to determine the activity coefficients of a variety of electrolytes in mixed solutions. Results are examined for K3[Co(CN)6] in K2SO4 and KOH, tris(ethylenediamine)cobalt(III) chloride–[Co(en)3]Cl3– in HCl, MgCl2, and LaCl3, and finally for [Co(en)3][Co(CN)6] and [Co(en)3][Fe(CN)6] in MgSO4 and La2(SO4)3, particularly interesting because of the cations and anions all carrying high charges. In this first approach, aimed at introducing the method, the experiments have been limited to identifying, for each mixed solution, the activity coefficients of one electrolyte of nearly null concentration in a varying concentration of the other. However, all desired mixing patterns are equally well allowed, e.g. changing the ratio of concentrations at a constant ionic strength, or the ionic strength at a constant concentration ratio, etc.
Structure of cells and membrane electrodes have already been described in papers devoted to single electrolytes,2,4 the only (although fundamental) difference consisting in the solutions examined, which contain two electrolytes instead of one single electrolyte. Additional information concerning salt preparation and apparatus is provided in the ESI sections 1 and 2.†
(−) Ag, AgCl |KCl (m0) |K+| KxX (m1) |Xx−| MaXb(m),CcYd(m′) |Mz+| MClz(m2) |AgCl, Ag (+) | (cell 1) |
E![]() ![]() ![]() ![]() ![]() ![]() ![]() | (1) |
The problem is whether it is really possible to obtain an |Xx−| membrane so insensitive to Yy−, and an |Mz+| membrane so insensitive to Cs+, for eqn. (1) to hold over a wide range of concentration ratios. (The original considerations that led us to believe this problem to be resolvable, are discussed in the ESI section 3.†) Closely related to this problem, is how to demonstrate that such a condition has really been met. We reached a sound proof for Xx−=
[Co(CN)6]3− matched with Yy−
=
SO42− or OH−, and for Mz+
=
[Co(en)3]3+ matched with Cs+
=
H+, Mg2+, and La3+. (Only one case is discussed in outline hereafter, the others being treated in the supplementary information.)
Consider a variant of (cell 1),
Ag, AgCl | KCl(m0)
|K+| K3[Co(CN)6](m1)
|[Co(CN)6]3−| …K3[Co(CN)6](m), K2SO4(m′)… |K+| KCl (m0) | AgCl, Ag | (cell 2) |
ϕleft![]() ![]() ![]() ![]() ![]() ![]() | (2) |
E![]() ![]() ![]() ![]() ![]() ![]() | (3) |
![]() | ||
Fig. 1 The cell's emf (E′![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
By developing the cell equation at m′ no longer constant and sufficiently high m/m′ ratios for Q to be neglected, one has:
E![]() ![]() ![]() ![]() ![]() ![]() | (4) |
E![]() ![]() ![]() ![]() ![]() ![]() ![]() | (5) |
The membrane electrodes for [Co(CN)6]3− or [Fe(CN)6]3− and [Co(en)3]3+, practically unresponsive to SO42−, OH−, H+, Mg2+, and La3+ respectively, make a first group of interesting mixed solutions available. Like [Co(CN)6]3− or [Fe(CN)6]3− and [Co(en)3]3+, all ions whose charge is shielded by a hydrophobic shell-or counterbalanced by a hydrophobic tail-are predictably accessible to examination in the presence of more hydrophilic species. Besides, no particular difference in hydrophilic character is expected between Mg2+ and Ca2+ (or Sr2+ or Ba2+), or between sulfate and carbonate or phosphate, or between H+ and Li+ or Na+, thus expanding the set of allowable supporting electrolytes. Not all electrolyte combinations thus obtained will probably enjoy selectivity properties as favorable as those examined in the present paper, but sufficient for less extreme m/m′ ratios. (The criteria to be adopted in such cases are discussed in the ESI section 5).
Consider a mixed stock solution where m≪
m′ and where the activity coefficients of K3[Co(CN)6] no longer vary on further diminishing m–thus proving indistinguishable from the limit for m
=
0 in m′
(the Fig. 1 solutions obey this condition). On diluting such a solution, one obtains the relative activity coefficients for vanishing concentrations of K3[Co(CN)6] at decreasing concentrations of K2SO4, down to the extreme limits allowed by the liquid membrane cell. Extrapolation to ionic strength zero-to transform the relative activity coefficients into real activity coefficients-is unnecessary, since the activity coefficients found are linked to that of the stock solution, which is linked in turn (viaE‡, eqns. (4) and (5)) to pure K3[Co(CN)6] in water, whose activity coefficients are already known. Likewise, the activity coefficients of trace amounts of K3[Co(CN)6] in KOH, [Co(en)3]Cl3 in HCl, [Co(en)3]Cl3 in MgCl2, [Co(en)3]Cl3 in LaCl3, [Co(en)3][Co(CN)6] in MgSO4, [Co(en)3][Co(CN)6] in La2(SO4)3, and finally, [Co(en)3][Fe(CN)6] in MgSO4 and [Co(en)3][Fe(CN)6] in La2(SO4)3, are determined. The results (Figs. 2, 3, and 4; the full details and source data are available in the ESI) deserve some discussion, since they are not so obvious. In particular, for [Co(en)3][Co(CN)6] in MgSO4 the results appeared to be so discordant from expectations, as to suggest repeating a second series of measurements for [Co(en)3][Fe(CN)6]. (The results fully corroborated those of [Co(en)3][Co(CN)6], thus proving that the experiments were right and that the theory has to adapt oneself to allow for such effects.)
![]() | ||
Fig. 2 Activity coefficients of trace amounts of K3[Co(CN)6] in solutions of KOH (mole ratio 1∶110) and K2SO4
(mole ratio 1∶103) compared with the corresponding smoothed values in water (bold line) and IPBE predictions for an infinitely diluted 1:3 salt in a 1:1 salt solution (a![]() ![]() ![]() ![]() |
![]() | ||
Fig. 3 [Co(en)3]Cl3 in HCl (concentration ratio 1∶117), in MgCl2
(concentration ratio 1∶204), and in LaCl3
(concentration ratio 1∶130) solutions, compared with the smoothed activity coefficients of [Co(en)3]Cl3 in water (bold line) and the IPBE predictions for a 3:1 salt at zero concentration in a 1:1 (a![]() ![]() ![]() ![]() ![]() ![]() |
![]() | ||
Fig. 4 [Co(en)3][Co(CN)6] and [Co(en)3][Fe(CN)6] in MgSO4 and in La2(SO4)3 compared with pure [Co(en)3][Co(CN)6] in water and the IPBE predictions. The IPBE calculations refer to a 3:3 single electrolyte (a![]() ![]() ![]() ![]() ![]() ![]() |
The activity coefficients of K3[Co(CN)6] in K2SO4 and KOH are slightly but perceptibly lower than those of pure K3[Co(CN)6] of an equal ionic strength (I, mol kg−1), and very similar to one another. The results are compared with simulation curves obtained by solving the unmodified exponential form of the Poisson–Boltzmann equation (numerical integration method IPBE)7 for trace amounts of 1:3 electrolytes dissolved in 1:2 or 1:1 electrolytes (in the ESI a copy of the IPBE algorithm is available). We assumed a single value for the distance of closest approach a of the ions, since IPBE, like the Debye–Hückel theory, does not consistently admit the use of different values of a for different ions of the same solution.3 Lower values of a correspond to stronger interactions and vice-versa. According to Brønsted's principle of specific interaction, the principal interactions that condition the excess free energy of infinitely diluted K3[Co(CN)6] in K2SO4 are those between the target cations K+ and bulk anions SO42−
(as encountered in pure K2SO4, a=
0.34 nm) and target anions [Co(CN)6]3− and bulk cations K+
(as in pure K3[Co(CN)6]; a
=
0.42 nm). Therefore, one expects that the most appropriate average value for a has to be between 0.34 and 0.42 nm. As a matter of fact, a is actually found to hold ca. 0.37 nm (Fig. 2). Likewise, the expected value for K3[Co(CN)6] in KOH is between 0.42 nm (as in pure K3[Co(CN)6]) and 0.47 nm (pure KOH; deduced by applying IPBE to the KOH data from ref. 8) and the empirical value that best reproduces the experimental data is really 0.43–0.44 nm.
Activity coefficients of [Co(en)3]Cl3 in MgCl2 and LaCl3 do not differ appreciably from those of the pure electrolyte at equal ionic strength, while HCl lowers the values. The different interaction strengths can be evaluated from the IPBE values of a to be used for the corresponding single electrolytes. HCl (principal interactions, H+–Cl−) requires a=
0.54 or 0.55 nm;9 MgCl2
(Mg2+–Cl−), 0.55 nm; LaCl3
(La3+–Cl−), 0.51 nm; [Co(en)3]Cl3
([Co(en)3]3+–Cl−), 0.37 nm (for dilute regions) or 0.35 nm (an empiric adjustment that covers a wider range of ionic strengths).2 These values suggest that the distance of closest approach needed to simulate the activity coefficients of [Co(en)3]Cl3 should be intermediate between 0.55 and 0.35 nm both in HCl and MgCl2, and between 0.51 and 0.35 nm in LaCl3. On the contrary, the values actually requested are all lower than expected, ca. 0.37 nm in LaCl3, 0.35 nm in MgCl2, and still less (0.33–0.34 nm) in HCl, thus diagnosing stronger than expected interactions not easy to rationalize.
A much more complex and unexpected behavior is observed for [Co(en)3][Co(CN)6] and [Co(en)3][Fe(CN)6], two salts characterized by strong ionic interactions. Thus, unlike e.g. K3[Co(CN)6] or [Co(en)3]Cl3 whose single solutions do not display negative deviations from the limiting law, [Co(en)3][Co(CN)6] and [Co(en)3][Fe(CN)6] do so. The behavior of these 3:3 salts in water is consistent with the IPBE approximation for a population of 3+ and 3− charged spheres with a value of a of ca. 0.46 nm.10 If the corresponding ions are dispersed in a more concentrated supporting electrolyte whose ions are not so highly charged, e.g. MgSO4 or La2(SO4)3, the negative deviations are expected to decrease, and actually do. However, lanthanum sulfate would also be expected, owing to the higher charge, to cause larger negative deviations than magnesium sulfate at equal ionic strength. On the contrary, the experiments said no, and no mistakes are possible in the experiments since the same results have been independently obtained for both [Co(en)3][Co(CN)6] and [Co(en)3][Fe(CN)6].
The discrepancy is surprising, since the experimental results do not seem to be the logical extension of the known behaviour of the component single salts. In both La2(SO4)3 and MgSO4 supporting electrolytes the interactions trace cation – bulk anion are the same, [Co(en)3]3+–SO42−, while the interactions trace anion – bulk cation are different, [Co(CN)6]3−–La3+ or [Co(CN)6]3−–Mg2+. The interactions between [Co(CN)6]3− and La3+ involved in the first case are the same also present in La[Co(CN)6], which displays considerable negative deviations, while conversely, the interactions between [Co(CN)6]3− and Mg2+ are the same as in Mg3[Co(CN)6]2 – which only displays very moderate negative deviations. Hence, the larger negative deviations are reasonably predicted for [Co(en)3][Co(CN)6] in La2(SO4)3 and not in MgSO4. However, the prediction is wrong. Alternatively, one can observe that IPBE, when applied to a simulated mixture of a 3:3 salt (trace amounts) and 2:2 salt, or 3:3 salt and 3:2 salt (the same concentration ratios as in the experiments), is able to reproduce the experimental results fairly well, provided a is properly adjusted as an empirical parameter. The proper values are 0.54 nm in La2(SO4)3 and 0.41 nm in MgSO4. Comparison of such values with those referring to the pure electrolytes in which the same cation-anion interactions occur, reveals that 0.54 nm is not far from the mean value between 0.38 nm and 0.66 nm found in [Co(en)3]2(SO4)3 and La[Co(CN)6] respectively. However, the value of a for Mg3[Co(CN)6]2 is 0.67 nm, nearly the same as for La[Co(CN)6]; thus, one would expect that the proper value of a for [Co(en)3][Co(CN)6] in MgSO4 should again be ca. 0.54 nm, and not 0.41 nm. Identical considerations apply to the corresponding solutions of the hexacyanoferrate (III) salt.
The failure of IPBE is probably the consequence of intrinsic limitations of the Poisson–Boltzmann original equation form; thus it is possible that other, more advanced theories solve the problem of the strange behavior observed.§ However, as far as we know, no electrolyte theory has so far predicted similar facts. On the other hand, such occurrences have so far been unknown, since it has been utterly impossible to detect them by other experimental methods.
The method can further be improved by taking advantage of ion selective reliable electrodes such as the glass membrane electrode for H+, lanthanum fluoride membrane electrode for F−, etc., to trace also hydrophilic ions. Thus, for instance, the activity coefficients of both HCl and [Co(en)3]Cl3 can be determined in the respective mixed solutions. Although such a possibility was unimportant in the present study (the extreme concentration ratios examined lead the activity coefficients of HCl to be the same as those, already known, of the corresponding pure solutions), in the usual mixed solutions, the ability to determine activity coefficients of different components is highly desirable.
The experimental determinations presented, though restricted to a limited set of mixed electrolyte solutions all of the same type (a target electrolyte of negligible concentration inside a supporting electrolyte of variable concentration) have already revealed some unexpected peculiarities of the multicomponent systems containing high-charge ions, which deserve thorough theoretical examination, and will probably lead to a critical revision of current ideas. It is easy to prophesy that the extended opportunity of determining activity coefficients in mixed solutions will produce a much higher level of insight into real ionic medium effects, with a significant impact both on the field of electrolyte theory, and on the study of equilibrium and kinetic aspects of chemical reactions involving ions.
Footnotes |
† Electronic supplementary information (ESI) available: (Part A) 1. Apparatus and reagents. 2. Modus operandi. 3. Ion selectivity and water-induced ion selectivity. 4. Tests for ion selectivity (Tables S1–S5). 5. Less demanding checks. 6. Mixed electrolytes with (and without) ions in common. 7. Revised activity coefficients of [Co(en)3][Co(CN)6] in water at 298.15 K (Table S6). 8. Activity coefficients of reference mixed solutions (Tables S7–S15). 9. Activity coefficients of trace electrolytes in supporting electrolytes of variable concentration. (Tables S16–S24). 10. Ion hydration effects. (Part B). The IPBE algorithm: how to use the computation program; the source program IPBE. See http://www.rsc.org/suppdata/cp/b3/b311624g/ |
‡ Particular forms to be used for electrolytes with ions in common, are reported in the ESI section 6.† Corrections needed to allow for the change in the free energy arising from the water molecules that escort the ions that enter the membranes, are neglected in eqn. (1) for simplicity (for the exact forms see ESI section 10; the differences are negligible in dilute solutions). |
§ C. W. Outhwaite has informed the authors of a theoretical paper on electrolyte mixtures which he, B. Hribar Lee, V. Vlachy, L. B. Bhuiyan, and M. Molero, have recently published.11 It is possible that their theoretical models are able to rationalize our results. |
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