Characterization of Lithium Sulfate as an Unsymmetrical-Valence Salt

The transference numbers t of lithium sulfate in acetoni- trile/water and methanol/water solvent mixtures have been studied by measuring the emfs of s...
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Anal. Chem. 1998, 70, 2589-2595

Characterization of Lithium Sulfate as an Unsymmetrical-Valence Salt Bridge for the Minimization of Liquid Junction Potentials in Aqueous-Organic Solvent Mixtures Cristiana L. Faverio, Patrizia R. Mussini, and Torquato Mussini*

Department of Physical Chemistry and Electrochemistry, University of Milan, Via Golgi 19, I-20133 Milano, Italy

The transference numbers t of lithium sulfate in acetonitrile/water and methanol/water solvent mixtures have been studied by measuring the emfs of such transference cells as Pb(Hg)|PbSO4|Li2SO4 (m2)||Li2SO4 (m1)|PbSO4| Pb(Hg), Hg|Hg2SO4|Li2SO4 (m2)||Li2SO4 (m1)|Hg2SO4|Hg, and LixHg1-x|Li2SO4 (m1)||Li2SO4 (m2)|LixHg1-x, in view of characterizing Li2SO4 as an unsymmetrical salt bridge for the minimization of liquid junction potentials in potentiometric applications. In water, Li2SO4 is nearly as good a salt bridge as the popular KCl one. Its effectiveness has been verified through the operational pH-metric cell using various aqueous pHS standards. In acetonitrile/water solvents of 0.09 mass fraction of acetonitrile at 298.15 K, Li2SO4 shows exact ionic equitransference, obeying the general condition t+/z+ ) t-/|z-|. The Li2SO4 salt bridge can be used either for simple insertion between two different electrolyte solutions to minimize the intervening liquid junction potentials, as the outer component of a double-bridge arrangement of any commonly available reference electrode, or, obviously, for structural incorporation in sulfate-reversible reference electrodes as the appropriate supporting and bridge electrolyte. The operational potential of the Hg| Hg2SO4|2 m Li2SO4 reference electrode in aqueous solutions is 0.6326 V at 298.15 K. The necessary practice of inserting a “concentrated equitransferent” salt bridge between the sample solution and the reference electrode solution in the operational cells for pH and p(ion) measurements to minimize the intervening liquid junction potentials was amply motivated and analyzed earlier.1-6 Inappropriate selection or improper use of the salt bridge would cause high * To whom correspondence should be addressed. E-mail: pmussini@ imiucca.csi.unimi.it. (1) Guggenheim, E. A. J. Am. Chem. Soc. 1930, 52, 1315-1337; J. Phys. Chem. 1930, 34, 1758-1766. (2) Ives, D. J. G.; Janz, G. J. Reference Electrodes-Theory and Practice; Academic Press: New York, 1961; pp 54-56. (3) Covington, A. K. In Ion Selective Electrodes; Durst, R. A, Ed.; NBS Special Publication 314; Washington, DC, 1969; p 107 and literature cited therein. (4) Bockris, J. O’M.; Reddy, A. K. N. Modern Electrochemistry, Vol. 1; Plenum Press: New York, 1970; pp 406-410. (5) Bates, R. G. Determination of pH-Theory and Practice, 2nd ed.; Wiley: New York, 1973; pp 311-313. (6) Mussini, T. J. Chem. Educ. 1988, 65, 242-243. S0003-2700(98)00014-6 CCC: $15.00 Published on Web 05/09/1998

© 1998 American Chemical Society

residual liquid junction potentials, which are known to be the primary cause of impairment of the accuracy of the above measurements, both in aqueous media and in aqueous-organic solvent mixtures. As a matter of fact, one of the mandatory conditions for the reliability of such measurements is that the reference electrode solution and the sample solution (or the standard solution) be in the same solvent, a condition which is all too often infringed. For applications in purely aqueous solutions, a number of salt bridges, all of them superior to the familiar potassium chloride, have been characterized quite recently,7-9 cesium chloride and rubidium chloride being those that most closely behave as the ideal salt bridge. Conversely, the availability of salt bridges for use in nonaqueous solvents or aqueous-organic solvent mixtures is very poor.10-14 This situation prompted us to start a program of systematic investigation of the ionic transference properties of binary salts in aqueous-organic solvent mixtures,14 parallel to the determination of standards for pH measurements in such solvents,13 high priority being assigned to unsymmetrical-valence salts, which were hitherto neglected. Indeed, in review, it seems that all of the salt bridges hitherto duly characterized are alkali metal chlorides or nitrates, i.e., symmetrical 1:1 valent electrolytes, which more or less closely approach their theoretical equitransference condition tC ) tA ) 0.5, a condition implying equality of the transference numbers tC and tA of the cation C and the anion A, respectively. Mussini6 recently showed that, for the general salt bridge Cν+z+Aν-z-, the equitransference condition required for zeroing the liquid junction potential was not expressed by tC ) tA but by (7) Mussini, P. R.; D’Andrea, F.; Galli, A.; Longhi, P.; Rondinini, S. J. Appl. Electrochem. 1990, 20, 651-655. (8) Mussini, P. R.; Rondinini, S.; Cipolli, A.; Manenti, R.; Mauretti, M. Ber. Bunsen-Ges. Phys. Chem. 1993, 97, 1034-1037. (9) Buizza, C.; Mussini, P. R.; Mussini, T.; Rondinini, S. J. Appl. Electrochem. 1996, 27, 337-341. (10) Mussini, T.; Covington, A. K.; Longhi, P.; Rondinini, S. Pure Appl. Chem. 1985, 57, 865-876. (11) Rondinini, S.; Mussini, P. R.; Mussini, T. Pure Appl. Chem. 1987, 59, 15491560. (12) Rondinini, S.; Longhi, P.; Mussini, P. R.; Mussini, T. Pure Appl. Chem. 1987, 59, 1693-1702. (13) Mussini, P. R.; Mussini, T.; Rondinini, S. Pure Appl. Chem. 1997, 69, 10071014. (14) Mussini, P. R.; Mussini, T.; Perelli, A.; Rondinini, S. J. Chem. Eng. Data 1995, 40, 862-868.

Analytical Chemistry, Vol. 70, No. 13, July 1, 1998 2589

tC/zC ) tA/|zA|

LixHg1-x|Li2SO4 (m1)||Li2SO4 (m2)|LixHg1-x

or, equivalently,

uC/zC ) uA/|zA|, or νCtC ) νAtA, or τC ) |τA|

(1)

where the z’s are ionic charge numbers with pertinent signs, the u’s are ionic mobilities (in terms of velocity attained by the ion under unit potential gradient), and the t’s are transference numbers in the usual “electric” definition (i.e., fraction of charge transferred by the pertinent ion), whereas the τ’s are corresponding transference numbers defined in terms of moles of species transferred per faraday of charge inside the cell from anode to cathode. This latter definition is applicable to both charged species (ions) and uncharged species (solvents): the solvent transference number τZ will be used specifically in eqs 6, 7, 13, and 14 for the interpretation of emfs of transference cells. Equation 1 implies that the ideal 1:1 valent bridge must have tC ) tA ) 0.5, but a 1:2 valent bridge must have tC ) tA/2 ) 0.333, a 2:1 valent one must have tC/2 ) tA ) 0.333, and so on. Limiting ionic conductance data in aqueous medium15 would indicate that Li2SO4 might sufficiently approach the pertinent equitransference condition tC ) tA/2 ) 0.333, but no such data are available for Li2SO4 in nonaqueous or aqueous-organic solvent mixtures. Therefore, since in the case of some incompatibility it would be important to have at hand an alternative (albeit unsymmetrical) salt bridge having SO42- as characteristic anion instead of the traditional Cl- or NO3- ones, in the present work the characterization of Li2SO4 as a salt bridge has been carried out in methanol/water as well as in acetonitrile/water solvent mixtures Z. Of course, this characterization hinges on the systematic determination of the transference numbers of Li2SO4 in the relevant solvents Z. The effectiveness of Li2SO4 as a salt bridge incorporated in mercury(I) sulfate reference electrodes has here been assessed by multistandard calibrations in pH-metric operational cells. METHODOLOGY The methodology adopted here is the same as applied recently17 and lends itself best for obtaining accurate transference numbers over extended Li2SO4 molality ranges and in various mixed solvents.16,17 It is based on electromotive force (emf) measurements of the following concentration cells with transference:

where Pb(Hg) denotes two-phase lead amalgams and LixHg1-x flowing dilute lithium amalgam electrodes with lithium at mole fraction x. The emfs of cells 2 and 3, whose electrode pairs are reversible to the SO42- anion, are here denoted by EA, have the same Nernstian expression for EA, and are directly related to the cation transference number tC. Conversely, the emf of cell 4, whose electrode pairs are reversible to the cation Li+, is denoted by EC and is directly related to the anion transference number tA. The Li2SO4 molality m1 is fixed, whereas m2 is varied within the required molality range in the (aqueous or aqueous-organic) solvent Z. The pertinent cell emfs must be combined with the emfs EMAX of the corresponding double cell 5 without transference:

Pb(Hg)|PbSO4|Li2SO4 (m2)|LixHg1-x-LixHg1-x| Li2SO4 (m1)|PbSO4|Pb(Hg) (5) Recently, the theory of these cells has been revised,7,14,18 and, for such a 1:2 valent electrolyte as Li2SO4, it now hinges on the thermodynamic eqs 6-10:

dEA/dEMAX ) tC(APP) ) tC - 2τZMZm

(6)

dEC/dEMAX ) tA(APP) ) tA + 2τZMZm

(7)

dEA + dEC ) dEMAX, and EA + EC ) EMAX

(8)

EMAX ) (3k/2) ln(m2γ2/m1γ1)

(9)

tC(APP) + tA(APP) ) tC + tA ) 1

(10)

where 2τZMZm is the solvent-transfer function described earlier,7,18 tC(APP) and tA(APP) are the apparent ionic transference numbers (viz., not cleared of the solvent transfer contribution), and tC and tA are the true ionic transference numbers of Li2SO4; τZ is the transference number of the solvent Z; k ) RT/F, where R is the molar gas constant, F is Faraday’s constant, and T is the absolute temperature; γ1 and γ2 are mean molal activity coefficients of Li2SO4 at molalities m1 and m2, respectively: the required γ values are available from a recent work.19 tC and tA comply with the Stokes-Robinson equation,20,21

tC ) tLi+ ) [λ°Li+ - B2xm/(1 + a0Bxm)]/

Pb(Hg)|PbSO4|Li2SO4 (m2)||Li2SO4 (m1)|PbSO4|Pb(Hg) (2)

Hg|Hg2SO4|Li2SO4 (m2)||Li2SO4 (m1)|Hg2SO4|Hg (3) (15) Robinson, R. A.; Stokes, R. H. Electrolyte Solutions, 2nd rev. ed.; Butterworth: London, 1965; pp 463-465. (16) Spiro, M. Physical Methods of Chemistry, Vol. I, Part IIA. In Electrochemical Methods: Determination of Transference Numbers; Weissberger, A., Rossiter, B. W., Eds.; Wiley-Interscience: New York, 1971; pp 284-285. (17) Spiro, M. Physical Methods of Chemistry, Vol. 2. In Electrochemical Methods; Chapter 8: Conductance and Transference Determinations; Rossiter, B. W., Hamilton, J. F., Eds.; Wiley-Interscience: New York, 1986; and literature cited therein.

2590 Analytical Chemistry, Vol. 70, No. 13, July 1, 1998

(4)

[Λ°Li2SO4 - 3B2xm/(1 + a0Bxm)] 1

) /3 + [t°Li+ - 1/3]/ {1 - B2xm/[(1 + a0Bxm)Λ°Li2SO4]} (11) (18) Mussini, P. R.; Longhi, P.; Mussini, T.; Rondinini, S. J. Appl. Electrochem. 1990, 20, 645-650. (19) Faverio, C. L.; Mussini, P. R.; Mussini, T. Thermodynamics of the amalgam cell {Li(Hg)|Li2SO4 (m)|Hg2SO4|Hg} in water, (methanol+water) and (acetonitrile+ water) solvent mixtures. J. Chem. Thermodynamics, in press. (20) Stokes, R. H. J. Am. Chem. Soc. 1954, 76, 1988-1990. (21) Reference 16, pp 155-157.

Table 1. Electromotive Forces EMAX and EA of Cells 5 and 2 (or 3), Respectively, as a Function of the Molality m2 of Aqueous Li2SO4 at 298.15 K, with Fixed m1 (Also Quoted Are the Pertinent Mean Molal Activity Coefficients γ)a m2/(mol‚kg-1)

γ2b

EMAX/V

EA/Vc

0.001 0.002 0.0025 0.0035 0.007 0.01 0.02 0.02 0.03 0.03 0.04 0.05 0.05 0.05 0.06 0.07 0.07 0.1 0.1 0.15 0.15 0.2 0.2 0.2 0.3 0.3 0.5 0.5 0.5 0.7 0.7 1 1 1 1.5 1.5 2.0 2.0 2.0 2.5 2.5 2.9 2.9 2.9

0.886 0.845 0.830 0.805 0.745 0.710 0.636 0.636 0.589 0.589 0.555 0.529 0.529 0.529 0.508 0.490 0.490 0.449 0.449 0.406 0.406 0.377 0.377 0.377 0.340 0.340 0.301 0.301 0.301 0.279 0.279 0.262 0.262 0.262 0.251 0.251 0.250 0.250 0.250 0.257 0.257 0.267 0.267 0.267

-0.151 32 -0.126 39 -0.118 49 -0.106 70 -0.082 97 -0.071 08 -0.048 65 -0.048 65 -0.035 97 -0.035 97 -0.027 16 -0.020 43 -0.020 43 -0.020 43 -0.014 99 -0.010 43 -0.010 43 0 0 0.011 13 0.011 13 0.019 96 0.019 96 0.019 96 0.031 62 0.031 62 0.046 54 0.046 54 0.046 54 0.056 70 0.056 70 0.067 98 0.067 98 0.067 98 0.081 88 0.081 88 0.092 92 0.092 92 0.092 92 0.102 56 0.102 56 0.109 73 0.109 73 0.109 73

-0.049 55 -0.041 22 -0.039 00 -0.035 13 -0.025 97 -0.023 61 -0.017 22 -0.015 64 -0.011 81 -0.011 19 -0.008 26 -0.006 49 -0.006 38 -0.006 71 -0.004 29 -0.003 69 -0.002 69 0 0 0.003 38 0.003 40 0.006 00 0.006 06 0.006 80 0.009 34 0.010 81 0.013 68 0.014 20 0.013 04 0.016 55 0.016 94 0.019 68 0.019 93 0.019 99 0.023 02 0.024 24 0.025 85 0.027 60 0.026 97 0.028 42 0.029 02 0.029 84 0.030 36 0.030 25

t°Li+

0.3266 ( 0.0001

(m1)FIXED ) 0.1 mol‚kg-1. (γ1)FIXED ) 0.449, interpolated from ref 19. Interpolated from ref 19. c In italics, measured EAs of cell 2; in regular type, measured EAs of cell 3; in bold, EAs from conversion of measured ECs of cell 4 using eq 8. a

such electrodes. The same article also describes the preparation of the mercury|mercury(I) sulfate|sulfate ion electrodes of cell 3, a cell that functionally parallels cell 2. Cells 2 and 3 are thermodynamically equivalent, but cell 2 can sense activities of aqueous sulfate ion lower by about 1 order of magnitude than those sensed by cell 3, on account of the values of the activity solubility product constants of PbSO4 and Hg2SO4, respectively.22 The lithium amalgam electrodes appearing in cell 4 were of the flowing dilute amalgam type23 and were prepared electrolytically, by lithium deposition on mercury cathode from methanolic 1 mol‚kg-1 LiOH solution, using a cell of the same design as described earlier.24 An important factor for accuracy and repeatability of results proved to be the homogenization of such lithium amalgams by storage overnight at 323 K with efficient stirring and under ultrapure N2 flow before transfer to the two-capillarytube amalgam dropper for the cell 4 emf measurements. Of course, the same amalgam was fed to the working lithium amalgam electrode pair. All solutions were prepared by mass from redistilled deionized water, reagent-grade acetonitrile and methanol, and other chemicals. The emfs were measured by a type 619 Keithley digital electrometer at Li2SO4 molalities approximately up to the solubility limit in each solvent mixture considered, a solubility which decreases rapidly with increasing proportion of the organic component in the solvent mixture. The thermostatic apparatus was described in an earlier paper.24 RESULTS AND DISCUSSION Tables 1-3 report the EA and EMAX values as a function of the molality m2 of Li2SO4 for different solvent compositions, with appropriate reference of symbols to cells 2, 3, and 4. The form of the EA vs EAX plots is that of a straight line at low and intermediate molalities which becomes a flat curve at higher molalities, i.e., it really has an oblique asymptote (cf. example in Figure 1, referring to the mixed solvent of mass fraction 0.1 of acetonitrile), analogously to that observed in several other cases studied earlier with different alkali halides.14,19 For the reasons explained earlier,14,19 we interpret the EA vs EMAX relationships in terms of the following equation:

EA ) a + bEMAX + c exp(EMAXd) ) bEMAX + c[exp(EMAXd) - 1]

(12)

b

where λ°Li+ and Λ°Li2SO4 are the limiting (infinite dilution) molar conductivities of Li+ and Li2SO4 in the solvent Z, respectively, t°Li+ ) 2λ°Li+/Λ°Li2SO4 is the limiting transference number of the cation Li+, a0 is the ion size parameter, and B2 and B are classical constants of the Debye-Hu¨ckel-Onsager theory. EXPERIMENTAL SECTION The two-phase lead amalgam|lead(II) sulfate|sulfate ion electrodes of cell 2 were constructed and operated exactly as described in a recent article22 concerning the redesign and reassessment of (22) Fusi, P.; Mussini, P. R. J. Solution Chem. 1997, 26, 337-353.

where, by definition, EA ) 0 and EMAX ) 0 when m2 ) m1, which implies a ) -c. Therefore, from eqs 12 and 6, we obtain

dEA/dEMAX ) tLi+(APP) ) tLi+ - τZMZm ) b + cd exp(EMAXd)

(13)

and, using eq 9 for EMAX, we can write

dEA/dEMAX ) tLi+(APP) ) tLi+ - τZMZm2 ) b + Q(m2γ2)3kd/2

(14)

(23) Mussini, T.; Longhi, P.; Rondinini, S. Pure Appl. Chem. 1985, 57, 169179. (24) Mussini, T.; Pagella, A. J. Chem. Eng. Data 1971, 16, 49-52.

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Table 2. Electromotive Forces EMAX and EA of Cells 5 and 2 (or 3), Respectively, at 298.15 K, as a Function of the Molality m2 of Li2SO4 but with Fixed m1, in Methanol/Water Solvent Mixtures of Mass Fraction wORG of the Organic Component of the Mixtures (Also Quoted Are the Pertinent Mean Molal Activity Coefficients γ) wORG ) 0.15a

wORG ) 0.3b

m2/(mol‚kg-1)

γ 2c

EMAX/V

EA/Vd

0.001 0.002 0.005 0.01 0.02 0.02 0.03 0.05 0.05 0.07 0.07 0.1 0.1 0.15 0.15 0.22 0.22 0.3 0.3 0.4 0.4 0.55 0.55 0.8 0.8 1.1 1.1 1.4 1.4

0.872 0.828 0.752 0.681 0.602 0.602

-0.148 49 -0.123 79 -0.092 19 -0.067 66 -0.047 33 -0.047 33

-0.047 32 -0.039 02 -0.028 73 -0.021 51 -0.015 21 -0.015 31

0.491 0.491 0.451 0.451 0.411 0.411 0.368 0.368 0.331 0.331 0.305 0.305 0.283 0.283 0.262 0.262 0.242 0.242 0.229 0.229 0.221 0.221

-0.020 30 -0.020 30 -0.010 10 -0.010 10 0.000 00 0.000 00 0.011 60 0.011 60 0.022 10 0.022 10 0.031 10 0.031 10 0.039 00 0.039 00 0.048 60 0.048 60 0.059 20 0.059 20 0.069 90 0.069 90 0.077 90 0.077 90

-0.006 08 -0.006 09 -0.002 61 -0.003 14 0 0 0.003 95 0.003 58 0.006 77 0.006 56 0.009 65 0.009 07 0.011 42 0.011 37 0.014 78 0.014 19 0.017 05 0.016 08 0.019 50 0.019 60 0.021 42 0.021 43

t°Li+

0.3169 ( 0.0001

γ2c

EMAX/V

EA/Vd

0.508 0.444 0.444 0.404 0.404 0.363 0.363 0.321 0.321 0.286 0.286 0.260 0.260 0.239 0.239 0.219 0.219 0.199 0.199

-0.033 52 -0.018 99 -0.018 99 -0.009 68 -0.009 68 0.000 00 0.000 00 0.010 87 0.010 87 0.021 09 0.021 09 0.029 42 0.029 42 0.037 25 0.037 25 0.046 10 0.046 10 0.056 89 0.056 89

-0.009 38 -0.005 02 -0.005 60 -0.002 32 -0.001 98 0 0 0.003 52 0.003 95 0.006 72 0.006 08 0.008 88 0.008 27 0.010 51 0.010 6 0.013 44 0.012 00 0.016 53 0.014 29

0.2933 ( 0.0004

a (m ) -1 b -1 1 FIXED ) 0.1 mol‚kg . (γ1)FIXED ) 0.411, interpolated from ref 19. (m1)FIXED ) 0.1 mol‚kg . (γ1)FIXED ) 0.363, interpolated from ref 19. Interpolated from ref 19. d In italics, measured EAs of cell 2; in regular type, measured EAs of cell 3; in bold, EAs from conversion of measured ECs of cell 4 using eq 8.

c

where, at a given temperature, Q ) cd(m1γ1)-3kd/2 ) constant. At infinite dilution (m2 ) 0, γ2 ) 1), we have τZMZm2 ) 0 for the solvent transfer term, and the limiting slope gives the limiting transference number (t°Li+) of Li+:

(dEA/dEMAX)m)0 ) b ) t°Li+(APP) ∝ t°Li+

(15)

The t°Li+ results are quoted with the respective standard errors at the bottom of Tables 1-3. Their dependence on the mass fraction of the pertinent organic component of the mixture is illustrated in Figure 2. From this, it is evident that Li2SO4, which in water is as discrete a salt bridge as the popular KCl, upon addition of acetonitrile to water does become exactly equitransferent (in terms of eq 1) at an acetonitrile mass fraction close to 0.09. On the contrary, addition of methanol to water progressively worsens the equitransference level of Li2SO4. A tentative explanation for this effect of mobility increase of one ion with respect to its partner upon varying the mixed solvent composition can be put forward in the following terms. With increasing proportion of acetonitrile (a solvent of linear structure and of dipole moment greater than twice that of water), a preferential solvation of the cation Li+ occurs (wherein the negative end of the acetonitrile dipole, i.e., the N atom, is attracted by the high-density-charge Li+ cation), causing progressive replacement of H2O molecules (susceptible to promoting hydrogen bonding) of the Li+ hydration 2592 Analytical Chemistry, Vol. 70, No. 13, July 1, 1998

shell by acetonitrile molecules (notoriously unable to produce hydrogen bonding). Thus, the outer solvation shell would become more and more structure-breaking, with a resulting effect of favoring the Li+ mobility (thus increasing the transference number) with respect to that of SO42-. Instead, for the observed opposite case of increase of transference number of the anion SO42- with respect to that of the cation Li+ upon increasing proportion of methanol, too many factors overlap, and, on account of the present lack of data on primary solvation numbers of SO42in aqueous-alcoholic mixtures, no simple explanation seems available. After the above chacterization of the transference parameters of Li2SO4 solutions in different solvent mixtures, a verification of the effectiveness of Li2SO4 salt bridges has been performed in aqueous media through parallel emf measurements of the operational pH-metric cells 16 and 18 described below:

Hg|Hg2SO4|Li2SO4 (2 m)|| pHS standards|glass electrode (16) The emf expression pertinent to cell 16 is

E16 ) E°[glass] - (ln10)k′pHS {E° [Hg|Hg2SO4] - (k/2) ln(mSO4γSO4) + EJ} ) E°[glass] - (ln10)k′pHS - EREF[Hg|Hg2SO4]

(17)

Table 3. Electromotive Forces EMAX and EA of Cells 5 and 2 (or 3), Respectively, at 298.15 K, as a Function of the Molality m2 of Li2SO4 but with Fixed m1, in Acetonitrile/Water Solvent Mixtures of Mass Fraction wORG of the Organic Component of the Mixtures (Also Quoted Are the Pertinent Mean Molal Activity Coefficients γ) wORG ) 0.1a

wORG ) 0.2b

m2/(mol‚kg-1)

γ2c

EMAX/V

EA/Vd

γ2c

EMAX/V

EA/Vd

0.001 0.003 0.01 0.03 0.05 0.05 0.07 0.07 0.1 0.1 0.15 0.15 0.22 0.22 0.3 0.3 0.4 0.4 0.55 0.55 0.8 0.8 1.1 1.1 1.4 1.4

0.879 0.807 0.695 0.569 0.507

-0.149 59 -0.110 56 -0.069 89 -0.035 46 -0.020 01

-0.050 78 -0.036 48 -0.022 27 -0.011 81 -0.006 75

0.467 0.467 0.426 0.426 0.383 0.383 0.345 0.345 0.318 0.318 0.295 0.295 0.274 0.274 0.253 0.253 0.240 0.240 0.233 0.233

-0.010 21 -0.010 21 0 0 0.011 46 0.011 46 0.022 24 0.022 24 0.031 02 0.031 02 0.039 27 0.039 27 0.048 61 0.048 61 0.060 02 0.060 02 0.070 23 0.070 23 0.078 39 0.078 39

-0.002 93 -0.002 82 0 0 0.004 18 0.003 26 0.007 09 0.006 41 0.009 60 0.009 22 0.012 60 0.012 22 0.014 94 0.014 07 0.019 05 0.017 40 0.020 91 0.020 45 0.023 17 0.021 68

0.869 0.792 0.672 0.538 0.474 0.474 0.432 0.432 0.390 0.390 0.345 0.345 0.307 0.307 0.279 0.279 0.257 0.257 0.236 0.236

-0.146 56 -0.107 85 -0.067 74 -0.034 17 -0.019 20 -0.019 20 -0.009 77 -0.009 78 0 0 0.010 93 0.010 93 0.021 18 0.021 18 0.029 52 0.029 52 0.037 38 0.037 38 0.046 30 0.046 30

-0.050 85 -0.038 90 -0.022 92 -0.011 84 -0.005 66 -0.005 65 -0.002 94 -0.002 60 0 0 0.003 28 0.003 09 0.006 48 0.007 11 0.009 28 0.009 63 0.010 85 0.011 80 0.013 99 0.014 90

t°Li+

0.3344 ( 0.0001

0.3480 ( 0.0001

a (m ) -1 b -1 1 FIXED ) 0.1 mol‚kg . (γ1)FIXED ) 0.426, interpolated from ref 19. (m1)FIXED ) 0.1 mol‚kg . (γ1)FIXED ) 0.390, interpolated from ref 19. Interpolated from ref 19. d In italics, measured EAs of cell 2; in regular type, measured EAs of cell 3; in bold, EAs from conversion of measured ECs of cell 4 using eq 8.

c

Figure 1. Dependence of the emf EA (of the Li2SO4 concentration cells 2 or 3) on EMAX (cell 5) in acetonitrile/water solvent mixture at acetonitrile mass fraction 0.1, described by eq 12, at 298.15 K; the limiting slope gives the transference number t°Li+ of Li2SO4. Symbols: b, EA of cell 2; 0, EA of cell 3; 4, EC of cell 4 converted to EA of cell 3 through eq 8.

where E° denotes the standard potentials and EREF the operational potentials, respectively, of the parenthesized electrodes acting as reference electrodes; k ) RT/F is the theoretical Nernstian factor, whereas k′ e k is the practical factor (“slope factor”). As shown by eq 17 and in compliance with Bates’s terminology,25,26 at a given

temperature T, EREF consists of the sum of a (constant) standard potential and a (constant) ionic activity term plus a liquid junction potential EJ whose ill-defined but presumably negligible value (25) Reference 5, pp 61-66. (26) Reference 2, pp 157-161.

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Table 4. Multistandard Calibration of Glass Electrodes through the Emfs E at 298.15 K of the Parallel Operational pH-Metric Cells 16 and 18 with Different Reference Electrodes and Comparing the Newly Proposed Li2SO4 Salt Bridge with the KCl and CsCl Ones (Also Quoted Are the Least-Squares Parameters for the Pertinent Linear Relation, E ) U - (ln10)k′pHS) type of glass electrode Ingold reference electrode salt bridge

Mettler

Hg|Hg2SO4 2 m Li2SO4

Hg|Hg2Cl2 4.8 m KCl

-0.1314 j -0.2235 -0.2562 -0.2873 -0.4225 -0.4538 -0.5492 -0.6073

U/V ln k′/V

Hg|Hg2SO4 2 m Li2SO4

Hg|Hg2Cl2 4.8 m CsCl

0.2697 0.1581 0.1319 0.0914 -0.0352 -0.0679 -0.1715 -0.2210

-0.1376 j -0.2381 -0.2654 -0.3003 -0.4315 -0.4630 -0.5630 -0.6170

0.2597 0.1484 0.1228 0.0829 -0.0446 -0.0771 -0.1795 -0.2316

-0.0159 ( 0.0055

0.3680 ( 0.0005

-0.0287 ( 0.0033

0.3586 ( 0.0011

0.05875 ( 0.00080

0.05880 ( 0.00008

0.05852 ( 0.00047

0.05877 ( 0.00016

pHS standardsa 1.679b 3.557 c 4.005 d 4.718 e 6.865 f 7.413 g 9.180 h 10.012 i

E/V

a Cf. ref 27. b 0.05 m potassium tetraoxalate. c Saturated potassium hydrogen tartrate. d 0.05 m potassium hydrogen phthalate. e 0.01 m acetic acid + 0.01 m sodium acetate. f 0.025 m Na2HPO4 + 0.025 m KH2PO4. g 0.03043 m Na2HPO4 + 0.008695 m KH2PO4. h 0.01 m disodium tetraborate. i 0.025 m NaHCO + 0.025 m Na CO . j Not included in the regression. 3 2 3

Figure 2. Variation of the cation transference number t°Li+ of Li2SO4 with the mass fraction wORG of the organic component in acetonitrile/water and methanol/water solvent mixtures at 298.15 K.

depends on the standard pHS solution in contact with the same salt bridge. The other, comparative pH-metric cell is

Hg|Hg2Cl2|KCl or CsCl (4.8 m)|| pHS standards|glass electrode (18) whose emf expression is

E18 ) E°[glass] - (ln10)k′pHS {E°[Hg|Hg2Cl2] - k ln(mClγCl) + EJ} ) E°[glass] - (ln10)k′pHS - EREF[Hg|Hg2Cl2]

(19)

The same glass electrode was tested in both cells 16 and 18 at 298.15 K, by measuring the parallel emfs E16 and E18 on the pHS standards quoted in Table 4, which cover the range 1.5 < pH < 2594 Analytical Chemistry, Vol. 70, No. 13, July 1, 1998

10. Then a second such run was performed with another glass electrode of a different type. If the Li2SO4 salt bridge is as effective in “zeroing” EJ as are the CsCl and the KCl bridges, then parallel straight lines E ) U - (ln10)k′pHS should be displayed as predicted by eqs 17 and 19, which is excellently confirmed by the values of least-squares slopes (ln10)k′ in Table 4. In this context, it is interesting to note that the “zero point” of the emf of the pH-metric cell 18 (that comprising the calomel reference electrode) lies approximately at pH midscale, whereas that for cell 16 (which instead comprises the mercury sulfate reference electrode) is close to pH ) 0. The experimental slope factor turns out to be 99.3% of the theoretical one for all of the four sets of data in Table 4, except for that concerning the Mettler electrode combined with the Hg2SO4 reference electrode, where the percentage is slightly lower (98.9). Considering the E16 and E18 values measured on the pHS ) 4.005 standard (i.e., the potassium hydrogen phthalate buffer, which is the “reference value standard” for the pH scales in the IUPAC nomenclature27), from eqs 17 and 19, we have

EREF[Hg|Hg2SO4] ) EREF[Hg|Hg2Cl2] - (E16 - E18) (20) and, since the operational potential EREF[Hg|Hg2Cl2] of the calomel reference electrode with incorporated 4.8 m KCl salt bridge is known to be 0.2444 ( 0.0005 V at 298.15 K,25,26,28 inclusive of the negligible EJ contribution,25,26,28 the corresponding value for the mercury(I) sulfate electrode with incorporated 2 m Li2SO4 bridge can be evaluated from eq 20 as EREF[Hg|Hg2SO4] ) 0.6326 ( 0.0010 V. The mercury(I) sulfate electrode with Li2SO4 salt bridge has a simple design, wholly analogous to that of the popular calomel electrode with KCl bridge, and essentially the same mode of operation. A parallel and useful sulfate-reversible electrode (27) Covington, A. K.; Bates, R. G.; Durst, R. A. Pure Appl. Chem. 1985, 57, 531-542 and literature cited therein. (28) Reference 5, p 327.

configuration, that of the lead amalgam|lead(II) sulfate electrode, has a more complex design and mode of operation, as described in a recent paper.22 In conclusion, the Li2SO4 salt bridge constitutes a useful acquisition to the electroanalyst, and can be employed (i) for simple insertion between two different electrolyte solutions to minimize the intervening liquid junction potentials, (ii) as the outer component of a double-bridge arrangement of any commonly available reference electrode, or, obviously, (iii) for structural incorporation in sulfate-reversible reference electrodes as the appropriate supporting and bridge electrolyte. As indicated by

the present results, extension of this investigation to other suitable aqueous-organic solvent mixtures appears desirable and overdue and will be soon undertaken in these laboratories. ACKNOWLEDGMENT The financial support granted by Italy’s National Research Council (CNR) is gratefully acknowledged. Received for review January 6, 1998. Accepted March 19, 1998. AC980014B

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