14714
J. Phys. Chem. 1996, 100, 14714-14720
Direct Observation of Chloride Transfer across the Water/Organic Interface and the Transfer of Long-Chain Dicarboxylates Yuanhua Shao and Stephen G. Weber* Department of Chemistry, UniVersity of Pittsburgh, Pittsburgh, PennsylVania 15260 ReceiVed: December 13, 1995; In Final Form: May 14, 1996X
We have extended the negative side of the potential window by using the organic reference electrode Ag/ AgTPB and a low supporting electrolyte concentration in the aqueous phase. We have observed directly, for the first time, the voltammetric wave of chloride transferring across the water(W)/1,2-dichloroethane (1,2DCE) and the water/nitrobenzene (NB) interfaces. The standard potentials (and the standard Gibbs free energies of transfer) have been evaluated by consideration of half-wave potentials, the variations of the activity coefficients in both phases, and ion-pair formation. Our best estimate for the free energy of Cl- transfer to water-saturated 1,2-DCE is 45-46 kJ/mol, and for NB 38 ( 2 kJ/mol. The Gibbs free energies of transfer of a homologous series of long-chain dicarboxylates have also been obtained for the first time. They show a similar dependence on carbon number as monocarboxylates. The transfers of the singly and doubly ionized dicarboxylic acids can also be observed simultaneously when the pH of the aqueous phase is controlled in the range of 5.5-6.6. Shorter chain dicarboxylates, such as glutarate, -OOC(CH2)3COO-, cannot be transferred across either the W/1,2-DCE or W/NB interface because it is more thermodynamically uphill than the transfer of the aqueous electrolyte anion or the organic electrolyte cation. One way to overcome some of the thermodynamic barrier is to use a receptor in the organic phase that would result in facilitated transfer. Our data show that a receptor for glutarate that had a formation constant of about 103 for a receptor-glutarate complex would allow for facilitated transfer. Through use of literature data for the transfer of the neutral dicarboxylic acids and H+, we can estimate the difference in pKa values between the aqueous phase and the water-saturated nonaqueous phases. In 1,2-DCE we estimate the differences for first and second ionizations as 18.5 and 19.5, respectively, while for NB they are 13.8 and 14.4.
Introduction The transfer of cations, and their transfer facilitated by various receptors or ionophores, has been the focus in the past two decades in the field of electrochemistry of liquid/liquid interfaces.1,2 There are many fewer investigations on anion transfer, and there have been no reports on facilitated anion transfer for several reasons, such as the lack of a suitable suite of chelating agents and the pH dependence of the charge on oxyanions.3-5 Our ultimate goal is to have a sufficiently good understanding of anion transfers to be able to devise rational routes to sensors for anions, especially dicarboxylates, in the presence of likely interferences, e.g., Cl-. The transfer of a homologous series of monocarboxylates at the aqueous/organic solution interfaces has been studied by Kihara et al. by using polarography with the electrolyte solution dropping electrode.3,4 It is more difficult to observe a transfer wave for a dicarboxylate because the hydrophilicity of a dicarboxylate is significantly larger than that of a monocarboxylate. In fact there are no reports, to our knowledge, of dicarboxylate transfer. In contrast, there have been several reports on the evaluation of the Gibbs free energy of transfer of chloride across the water (W)/1,2-dichloroethane (1,2-DCE) interface with scattered data (51 kJ mol-1,6 54 kJ mol-1,7 and 46 kJ mol-1 8 all based on the tetraphenylarsonium-tetraphenylborate assumption9). There have been no direct voltammetric observations of the transfer of small, hydrophilic, inorganic anions, such as chloride, across W/1,2-DCE and W/nitrobenzene (NB) interfaces. The wider the potential window is, the larger the number of species that can be studied. There have been several reports X
Abstract published in AdVance ACS Abstracts, August 15, 1996.
S0022-3654(95)03686-0 CCC: $12.00
on widening potential windows that can be classified into three categories:10-14 (a) using a bulky ion pair as the organic supporting electrolyte; in most of these cases the supporting electrolyte in the aqueous phase limits the potential window; (b) using single-hole microinterface and no supporting electrolyte in the aqueous phase; (c) the application of salting-out and salting-in effects when the supporting electrolytes in the organic phase limit the potential window. We present here some new results on the extension of the negative side of the potential window by using a silver/silver tetraphenylborate reference electrode,15 and using a low supporting electrolyte concentration in the aqueous phase. This extension has allowed us to observe directly, for the first time, the transfers of chloride and dicarboxylates across the W/1,2DCE and the W/NB interfaces. The transfers of the singly and doubly deprotonated dicarboxylic acids can also be observed simultaneously when the pH of the aqueous phase is controlled in the range of 5.5-6.6. By combining our data with literature data, the calculation of the pKa of the acids in the organic phase is possible. The free energy of transfer and pKa data obtained are used to discuss the outlook for dicarboxylate sensors. Experimental Section The circuit used for the four-electrode potentiostat is based on the work of Figaszewski,16 which in turn derives from work of Buck.17 It controls the potential difference between two reference electrodes by passing current through two auxiliary electrodes. It can compensate, by positive feedback, up to 10 kΩ of uncompensated resistance between the reference electrodes. The cell was made of glass (Figure 1). It has two side arms attached to Luggin capillaries on the inside of the cell, and vessels containing reference electrodes on the outside of © 1996 American Chemical Society
Chloride Transfer across the Water/Organic Interface
J. Phys. Chem., Vol. 100, No. 35, 1996 14715
Figure 2. Steady-state voltammogram of the cell Ag/AgTPB/1 mM BTPPATPB(1,2-DCE)//0.2 mM Na2SO4/Ag2SO4/Ag. Sweep rate 5 mV s-1. Upward-going current corresponds to the transfer of positive charge from the aqueous to the organic phase. Wave I, unknown; wave II TPP-(o) f TPB-(w).
Figure 1. Sketch of the glass cell. The bent Luggin probes are permanently positioned with their tips near the interface (dashed line). In each phase is a glass-enshrouded Pt wire auxiliary electrode.
the cell. The Luggin tips are permanently positioned. The cell, similar to that of Shao and Girault,18 has an interfacial area of 1.0 cm2. In all experiments except where mentioned, the 1,2-DCE was washed with water before use. All voltammograms are steady state voltammograms. That is, the voltammetry was run continuously for an extended period. After some period of time, depending on actual conditions, the voltammogram does not change. The interfacial region of each solvent becomes saturated in the other. The solubility of nitrobenzene in water at 20 °C is 0.19 wt %,19 1,2-DCE in water is 0.8 wt %,20 of water in nitrobenzene is approximately 0.23 wt %,19 and water in 1,2-DCE is 0.15 wt %.20 BTPPATPB (bis[triphenylphosphoranylidene]ammonium tetraphenylborate) was prepared by mixing equimolar aqueous solutions of NaTPB (Aldrich) and a methanol + water mixture (2:1) of BTPPACl (Aldrich). 1,2-DCE (Aldrich, 99+%) and NB (Fluka, >99.5%) were used without further purification except where noted. All dicarboxylic acids were purchased from Aldrich as acids, except for 1,10-decanedicarboxylate which was purchased as the diammonium salt (97%). Occasionally, and for some systems routinely, there are spikes of current on the positive current side of the negative potential end of the voltammogram. Sometimes it is possible to estimate the positive current peak potential and other times it is not. When the positions of both waves are obvious, (Ep,a + Ep,c)/2 is used as an estimate of ∆wo φ1/2. This value is compared to the ∆wo φ1/2 for an internal reference ion to give ∆∆wo φ1/2 for the ion of interest. If only one wave is observable, then the difference in peak potentials between the reference ion and the ion of interest is used to estimate ∆∆wo φ1/2. These spikes of current only occur when the interface is driven to extreme negative potentials. In fact, driving the system too far negative leads to the appearance of a precipitate or film at the interface. This has been observed before21 and probably results from the poor solubility of salts of the organic cation in water or salts of the aqueous anion in oil. The reference electrode Ag/AgTPB was made according to the literature15 and a Ag/Ag2SO4 reference electrode was made using the method for the preparation of a Ag/AgCl reference electrode. This involves electrolysis with a small current density of Ag wire (0.25 mm, Goodfellow) in 0.01 M Na2SO4 solution. A CDM 83 conductivity meter (Radiometer, Copenhagen) was employed to measure the conductivity and the temperature
was controlled at 25 ( 0.1 °C (Haake A80). All the rest of the experiments were carried out at room temperature (25 ( 2 °C). Results and Discussion We are using a technique in which the Galvani potential difference between two electrolyte phases is controlled. The convention is to state potential differences as the difference (water potential-oil potential). Thus, at more negative potentials, anions in water (and cations in the organic phase) take on a more positive free energy. When the instrumentally-applied electrostatic free energy balances the difference in free energy of solvation for an ion in two phases, then current flows across the interface as the ions are transferred. Anions going from water to oil (or cation going oppositely) are negative current. The experimental challenge to measuring the transfer of hydrophilic anions from water to oil consists of expanding the potential window to sufficiently negative potential to be able to see the relevant waves. As the limitation on the potential window is the transfer of the ions that make up the background electrolyte, one method to increase the potential window is to lower the concentration of the electrolyte.15,22 This strategy is accompanied by two problems. One is that with a low concentration of supporting electrolyte, the transference number of the solute ion under scrutiny becomes significantly different than zero, so migration as well as diffusion carries solute to the interface. Another is that it becomes more difficult to compensate for IR drop. The first problem is minimized by using as the aqueous electrolyte a sulfate salt. Sulfate with two charges carries relatively more current than an alternative, monoanionic choice of ions, e.g., F-, and it is highly hydrophilic.23 The second problem is minimized, interestingly, by using the Ag/AgTPB (TPB ) tetraphenylborate) reference electrode. Its use has improved impedance studies. Anomalous features in impedance spectra, thought to be due to the use of an aqueous reference electrode with a liquid junction to the organic phase, disappeared with the use of Ag/AgTPB.24 It is known that capacitance in the cell influences cell stability.25 Thus, while we do not really understand why this simpler reference electrode improves performance at large negative potentials, it use is beneficial. Except where noted, we have used a low concentration of Na2SO4 as the aqueous supporting electrolyte and the Ag/AgTPB reference electrode in our studies. The cell used is typically
Ag/AgTPB/1 mM BTPPATPB// 0.2 mM Na2SO4/AgSO4/Ag (cell 1) A Wave Due to an Impurity. Initial investigation of this cell showed a transfer wave at the negative side of the potential
14716 J. Phys. Chem., Vol. 100, No. 35, 1996
Figure 3. Steady-state voltammogram of the cell Ag/AgTPB/1 mM BTPPATPB//0.2 mM Na2SO4/Ag2SO4/Ag. Sweep rate 3 mV s-1. Wave I, unknown; wave II TPP-(o) f TPB-(w).
Shao and Weber
Cl-(w) h Cl-(o)
(1)
Cl-(o) + BTPPA+(o) h BTPPA+Cl-(o)
(2)
TPB-(o) + BTPPA+(o) h BTPPA+TPB-(o)
(3)
KIP1 and KIP2 are the ion-pair formation constants for eqs 2 and 3. Concentrations will be defined as Ci,p(X) where i is the species, p is the phase and X is the position in solution relative to the interface. If the notation about X is absent, the concentration refers to bulk. Let R be the degree of dissociation of the supporting electrolyte in 1,2-DCE. C1 and C2 are the total concentrations of chloride in the aqueous phase and the concentration of supporting electrolyte, BTPPATPB, in 1,2DCE, respectively. In these experimental conditions, CCl-,w , CBTPPA+,o.
KIP1 ) CBTPPACl,o/[C2R(γ(o)2CCl-,o]
(4)
KIP2 ) (1 - R)/[C2R2(γ(o)2]
(5)
where γ(o is the mean ionic activity coefficient in the 1,2-DCE phase. The Galvani potential difference, ∆wo φ, in this case, can be expressed as follows: Figure 4. Steady-state voltammogram of Cl-. The cell Ag/AgTPB/1 mM BTPPATPB//0.5 mM NaCl + 0.2 mM Na2SO4/Ag2SO4/Ag was used. Sweep rate 3 mV s-1. Wave I, Cl-; wave II TPP-(o) f TPB-(w).
window, which we did not expect (Figure 2), and which we thought might be Cl-. Impurities in BTPPATPB were ruled out as the source of the wave by measuring voltammograms with varying concentrations of BTPPATPB. The peak current is virtually constant. We can conclude that this wave does not arise from impurities in BTPPATPB. After extraction of 1,2DCE with deionized water, the wave at the negative side of the potential window disappears. Figure 3 shows the extended potential window that results when the washed 1,2-DCE is used with cell 1. The following electrochemical cell (cell 2) was used to study the transfer of chloride across the W/1,2-DCE interface:
Ag/AgTPB/1 mM BTPPATPB//x mM NaCl + 0.2 mM Na2SO4/Ag2SO4/Ag (cell 2) where x is from 0.1 to 0.8 mM. Figure 4 is the cyclic voltammogram of Cl- transfer across the W/1,2-DCE interface. This is the first time that a chloride voltammetric wave has been observed. The peak current, Ip, is a linear function of the concentration of chloride in the aqueous phase. The diffusion coefficient of chloride in the aqueous phase, calculated using the plot of Ip vs ν1/2, is equal to (2.25 ( 0.27) × 10-5 cm2 s-1, which is in agreement with a literature value of 2.03 × 10-5 cm2 s-1.26 If the impurity in the 1,2-DCE is Cl-, it is estimated that there may be about 0.32 mM chloride in the unwashed 1,2DCE (Aldrich, 99.0%+). The transfer of chloride across the W/NB interface has also been obtained using an electrochemical cell similar to cell 2. Determination of the Formal Potential for Cl-. There are two aspects to the problem of the determination of the formal potential of Cl-. One is the correction of the measured halfwave potential for the effects of diffusion coefficient, activity coefficient, etc., and the other is the establishment of a suitable reference potential. These are taken in turn below. The current due to chloride transfer to 1,2-DCE involves the following processes:
∆wo φ ) ∆wo φo + (RT/F) ln(CCl-,w(0)/CCl-,o(0)) + (RT/F) ln(γ(w/γ(o) (6) where ∆wo φo is the standard Gavani potential difference, and γ(p is the mean ionic activity coefficient in phase p. For eqs 1 and 2, the current can be expressed as follows,4,27-29 where K is related to a mass transfer coefficient:
I ) KDCl-,w (C1 - CCl-,w(0)) ) K(DCl-,oCCl-,o(0) + DBTPPACl,oCBTPPACl,o(0)) (7) From eqs 6 and 7, the ∆wo φ can be expressed as
∆wo φ ) ∆wo φo + (RT/F) ln(γ(w/γ(o) + (RT/2F) ln(DCl-,o/DCl-,w) + (RT/F) ln[1 + KIP1 (γ(o)2RC2(DBTPPACl,o/DCl-,o)1/2] + (RT/F) ln(Id - I)/I (8) The half-wave potential can be expressed as
∆wo φ1/2 ) ∆wo φo + (RT/F) ln(γ(w/γ(o) + (RT/2F) ln(DCl-,o/DCl-,w) + (RT/F) ln[1 + KIP1(γ(o)2RC2(DBTPPACl,o/DCl-,o)1/2] (9) The activity coefficients in each phase can be evaluated by using the Debye-Hu¨ckel equation and eq 5:
-log γ( ) AxC2R/(1 + BaxC2R)
(10)
where A, B, and a are the parameters of the Debye-Hu¨ckel theory,30 and R is the degree of dissociation. In order to calculate the standard Galvani potential difference, we have to measure or estimate the values of KIP1 and KIP2 by using conductance measurements. The 1,2-DCE (extracted with Milli-Q water) was used to prepare the organic phases and Milli-Q water was used to prepare the aqueous phases. The Shedlovsky method31 was employed to calculate the ionassociation constants. The limiting equivalent conductance, Λ°, can be obtained from the extrapolation of the straight line of of
Chloride Transfer across the Water/Organic Interface
J. Phys. Chem., Vol. 100, No. 35, 1996 14717
TABLE 1: Ion Association Constants of BTPPACl, BTPPATPB, and TBATPB in Both Phases 1,2-DCE (w)a BTPPACl BTPPATPB TBATPB
4.3 × 10 5.8 × 102 2.96 × 103
1,2-DCEb
W 2.31 × 103
2
1.35 × 103 (1.71 × 103c)
a
b
1,2-DCE extracted with double distilled water before it was used. As received. c Reference 7.
TABLE 2: Contributions from Various Terms in Eq 10a CBTPPATATPB (mM)
R
γ(
1 2.5 5 10.0
0.863 0.808 0.768 0.731
0.563 0.451 0.369 0.295
o
1b
(mV)
2c
14 20 25 30
(mV) 2 2 2 2
3d
(mV)
totale (mV)
1 2 2 3
17 24 29 35
a System: Ag/AgTPB/x mM BTPPATPB//0.2 mM Na SO + y mM 2 4 NaCl/Ag/Ag2SO4. There is very little change for γ(w when the electrolyte concentration ranges from 0.1 to 0.8 mM; γ(w is equal to 0.967 ( 0.02. b 1 ) (RT/F) ln(γ(w/γ(o)a. c 2 ) (RT/2F) ln(DCl-,o/DCl-,w). d 3 ) (RT/F) ln[1 + K (γ o)2RC (D 1/2 e IP1 ( 2 BTPPACl,o/DCl-) ]. Total ) 1 + 2 + 3.
TABLE 3: Formal Potentials and Standard Gibbs Free Energies of Chloride Transfer across the W/1,2-DCE Interface method
ref
ITIESa solubility partitioning ITIES
6 7 8 this work
a
o ∆wo φCl ∆Gto (mV) (kJ mol-1)
-528 -560 -477 -470 -475 -437
50.9 54.0 46 45.4 45.8 42.2
comments onset of wave, no voltammetric peak TBA+ as reference ion TEA+ as reference ion TPB- as reference ion
Interface between two immiscible electrolyte solutions.
Λ (equivalent conductance) vs the square root of the concentration of salts when they are less than 1 mM. The results are listed in Table 1. For eq 9, DCl-,o/DCl-,w ) 1.149 (Walden rule). KIP1 ) 4.3 × 102 and DBTPPACl,o/DCl-,o = 0.3.27 The mean activity coefficients in the aqueous and 1,2-DCE were calculated with the ion-size parameter a ) 0.3 or 0.9 nm (for aqueous and organic phases, respectively). Equations 5 and 10 are needed for the evaluation of γ( and R; they are solved iteratively. The contributions of the different terms in eq 10 are listed in Table 2 for a range of concentrations of the organic supporting electrolyte. There is very little dependence on the Cl- concentration over the experimental range used (0.1-0.8 mM). The effect on the ∆wo φo from ion association is quite small. The experimentally determined values of ∆wo φ1/2 or peak potential from cell 2 were corrected by the amount listed in Table 2 (17 mV for 1 mM supporting electrolyte) to arrive at a value of ∆wo φo. It remains to determine the difference between this value and that of a suitable reference ion. Because of potential complications from changes in the equilibria that influence Cl- activity, we used three internal reference ions in our study, namely tetrabutylammonium (TBA+), tetraethylammonium (TEA+), and tetraphenylborate (TPB-). The values of their formal potentials based on the TATB assumption are well established. Table 3 shows the Cldata in the literature and data from the current experiments. We estimate the random error to be no more than 5 mV. The potential inaccuracy in our results from using TPB- as the reference ion (influencing ion pair equilibria) is perhaps responsible for the difference between that measured value
Figure 5. Steady-state voltammogram of a dicarboxylate, Ag/AgTPB/1 mM BTPPATPB//0.15 mM-OOC(CH2)12COO- + 0.2 mM Na2SO4 + NaOH, pH 10.10/Ag2SO4/Ag. Sweep rate 20 mV s-1. Wave I, dicarboxylate (w) f dicarboxylate (o).
TABLE 4: Formal Potentials and Standard Gibbs Free Energies of Chloride Transfer across the W/NB Interface method
ref
o ∆wo φCl (mV)
∆Gto (kJ mol-1)
partitioning partitioning ITIES
32 33 this work
-308 -399 -383.6
29.7 38.5 37.0
-414.6
40.0
comments
TBA+ as internal reference ion TEA+ as internal reference ion
(-437 mV) and the other two (-470 and -475 mV). We tend to put more weight on the latter two values. The results show excellent agreement with the results from partitioning.8 We note that results from this work and that from refs 6 and 8 are lower than the result from ref 7. A contributor to that difference is the presence of water in the organic solvent in all of the methods except the solubility method.7 As ref 6 used the onset of current as the signal for ion transfer, this result is perhaps less well-defined than the others. A best estimate of the transfer free energy of Cl- from water to water-saturated 1,2-DCE is in the range of 45-46 kJ/mol. The standard potential of chloride transfer across the W/NB interface, ∆wo φo, is equal to -384 and -415 mV with TBA+ and TEA+ as reference ions, respectively (see Table 4). These data are in agreement with one of the published values. The range of likely values for the transfer free energy is 38 ( 2 kJ/mol. Transfers of Di- and Monocarboxylates of Dicarboxylic Acids. Because of the wider potential window, it is now possible to try to observe the transfers of some of the dicarboxylates -OOC(CH2)nCOO- which have an impact on our investigations of possible potentiometric sensors for dicarboxylates using artificial receptors.34 The acid dissociation constants K1 and K2 of sebacic acid are 3.39 × 10-5 and 2.6 × 10-6, respectively. The K’s for longer chain dicarboxylic acids are similar. The dianion predominates when the pH is greater than 7. The transfer of the dicarboxylates has been studied as a function of the number of methylene groups, n, for n ) 8, 10, 12, 14. A wave for the dicarboxylate with n equal to 12 can be obtained clearly (see Figure 5) with cell 3:
Ag/AgTPB/1 mM BTPPATPB//x mM H2A + 0.2 mM Na2SO4 + NaOH/Ag2SO4/Ag (cell 3) where x is 0.05-0.4 mM and H2A is HOOC(CH2)12COOH. The pH of the aqueous phase is ca. 10.50. In order to obtain the ∆wo φo, 0.5 mM TBATPB was added to the organic phase in cell 4. The wave for the TBA+ was used as an internal reference ion. The Gibbs free energies for the
14718 J. Phys. Chem., Vol. 100, No. 35, 1996
Shao and Weber SCHEME 1 Kwa
w
RCOOH
o
RCOOH
RCOO– + H+
RCOO– + H+ Koa
mograms of mono- and dicarboxylate ion transfers.
Ag/AgTPB/1 mM BTPPATPB//x mM H2A + 0.2 mM Na2SO4/Ag2SO4/Ag (cell 4) The pH of the aqueous phase was controlled by addition of NaOH and H2SO4. Figure 7 shows a cyclic voltammogram from one such cell. As there is undoubtedly rapid exchange of protons in aqueous solution, one must consider that the following scheme represents the actual occurrences contributing to the first wave: Figure 6. Free energies of transfer for organic acids and their conjugate bases. The set of data plotted are (from the top down) dicarboxylates into 1,2-DCE (O), into NB (0); singly ionized dicarboxylic acids into 1,2-DCE (O), NB (0); monocarboxylates4 into 1,2-DCE (O), NB (0); dicarboxylic acids into octanol (]);41 monocarboxylic acids into octanol (+).35 The x-axis label should be interpreted literally; thus, for 1-propionic acid, n ) 1. Vertical arrows represent free energies which, to an additive constant, are equal to the free energy of dissociation of R-COOH in water-saturated solvent. In the upper left, the horizontal line represents the catholic limit of the voltammetric experiment for a dianion, while the dashed (- - -) line represents the regression of the data for dicarboxylates into NB (0). The vertical arrow represents how much more favorable the transfer free energy of glutarate must be to observe a wave.
Figure 7. Steady-state voltammogram of singly and doubly deprotonated acids in weak acid solution using cell 5.
transfer of dicarboxylates with n ) 8, 10, 12, and 14 have been evaluated for both W/1,2-DCE and W/NB systems. Figure 6 shows the relationship between n and the Gibbs free energies of transfer for several species. The slopes for the dicarboxylate are -2.88 kJ mol-1 per CH2 unit for the W/1,2DCE and -3.5 kJ mol-1 for the W/NB systems which are similar to the results obtained by Kihara et al.4 for n-alkyl monocarboxylates (-3.6 kJ mol-1). A similar linear relationship was reported for alkylcarboxylic acids from water to n-heptane and from water to octanol systems with slopes of -3.4 and -3.08 kJ mol-1, respectively.35,36 These linear relationships reflect the constant free energy transfer of the -CH2- group within a particular solvent/solute system. At a pH of 5.6, the concentrations of singly- and doublyionized acids are about the same. It is possible to observe the transfer of both forms of them at the same time. The following electrochemical cell (4) was used to record the cyclic voltam-
Aw2- + H2Aw h 2HAw-
(11)
HAw- h HAo
(12)
Thus, the first wave represents more than simple monoanion transfer, and its peak potential will not be identically equal to the value for a simple ion transfer. However, as the amount of H2A is at most 20% of the total, we assume that reaction 11 plays a small role and that the measured peak potential for the process in eq 12 reflects the free energy for that process. Figure 6 also has the plot of ∆G vs n for these species. Slopes are -3.15 and -2.69 kJ/mol/CH2 for W/NB and W/1,2-DCE, respectively. Implications for Sensor Design. There are many worthwhile analytes that have at least one carboxylate group and one other polar functional group. Such species as lactate, phosphate, succinate, glutarate, adipate, R-oxoglutarate, glutamate, aspartate, and N-acetylaspartyl glutamate are examples of highly polar, anionic analytes for which liquid membrane potentiometric sensors do not exist. The challenge lies in overcoming the large affinity for water that these species have. This section defines this problem quantitatively for carboxylates. There are some general comparisons that can be made which will serve as a check of our data. From the vertical displacement of the line for ∆G (-OOC-(CH2)n-COO-) and ∆G (CH3(CH2)n-COO-), we obtain the difference between the ∆Gt for -COO- and -CH3. The ∆Gt for acetate can then be estimated by adding to this 2× the ∆Gt of -CH3 (-8.8 kJ/mol37) (i.e., ∆Gt,CH3COO- ) ∆Gt,-COO- - ∆Gt,-CH3 + 2∆Gt,-CH3). The results are nearly the same for both solvents, averaging 55 kJ/mol. Extrapolation of Kihara’s data to nCH2 ) 0 (acetate) yields 54 and 46 kJ/mol for 1,2-DCE and NB, respectively. Other values for this free energy are not in the literature; however, there are data38 for non-HBD solvents (in kJ/mol) dimethylformamide (66), dimethylacetamide (70), acetonitrile (61), dimethyl sulfoxide (50). Thus, the value for acetate extrapolated from our data is in reasonable agreement with published values. We can use our data in combination with those of others to determine values for pKa of the carboxylic acid group in NB and 1,2-DCE. Scheme 1 shows that the acid dissociation constant for a carboxylate is determinable from the partition coefficient of the neutral acid, the single ion transfer free energies of the carboxylate and of the proton, and the acid dissociation constant in water. The difference of pKa values between organic and aqueous phases is
Chloride Transfer across the Water/Organic Interface
pKoa - pKwa ) ∆wo pKa )
J. Phys. Chem., Vol. 100, No. 35, 1996 14719 TABLE 5
s,wfo s,wfo s,wfo + ∆Gt,RCOO (∆Gt,H + - - ∆Gt,RCOOH)/2.303RT (13)
where superscript s is for a particular solvent. Taking s,wfo as 55.1 (s ) 1,2-DCE) and 32.5 (s ) NB) kJ/mol,39,40 ∆Gt,H + w DCE ) 17.08 ( we estimate ∆wo pKNB a ) 11.61 ( 0.12 and ∆o pKa 0.09. The errors (95% conf. inf.) represent the slight differences in the slopes of the lines in Figure 5 and thus are to represent more the range of values to be found for n ∼ 0-14 rather than being the result of experimental uncertainty. For diprotic acids, we have for the first proton s s,wfo s,wfo ) (∆Gt,H + ∆Gt,HOOC(CH ∆wo pKa,1 + 2)nCOOs,wfo )/2.303RT (14) ∆Gt,HOOC(CH 2)nCOOH
and for the second proton s s,wfo ) (∆Gt,H + ∆Gt,s,wfo ∆wo pKa,2 + -OOC(CH2) COO- n s,wfo )/2.303RT (15) ∆Gt,HOOC(CH 2)nCOO-
There are data in the literature41 for the partition coefficient of HOOC(CH2)nCOOH for n ) 2, 4, and 7 from water to octanol. We have regressed the values against n and found that the slope of the line is considerably different from the slopes of the lines of the other carboxylates and dicarboxylates (-2.5), so we are reluctant to extrapolate the line too far. For n ) 8, we have carried out the calculations in eqs 14 and 15. These values for ∆wo pKa are found in Table 5. We would have expected a similarity between ∆wo pKa for the monocarboxylic acids and ∆wo pKa,1 for the dicarboxylic acids. They are, in fact different by ca. 2.5 units. One also expects ∆wo pKa,1 to be roughly equal to ∆wo pKsa,2, and in fact they are satisfying close to each other. Figure 5 shows a composite plot of our data and literature data for transfer free energies of a variety of linear, aliphatic carboxylic acids and carboxylates. On Figure 5 there are three estimates related to the free energy of ionization of a carboxylate. They are based on the difference between Tanford’s monocarboxylic acid data and Kihara’s monocarboxylate data (38 kJ/mol); Collander’s dicarboxylic acid data and our hydrogendicarboxylate data (49 kJ/mol); our hydrogendicarboxylate and our dicarboxylate data (51 kJ/mol). In each case, the average of the 1,2-DCE and NB data were used. It seems that, from both this perspective, and the related values of ∆wo pKa, Kihara’s numerical values may be somewhat too negative. Our best estimates for the pKa values of diprotic acids (n ≈ 8) in water-saturated NB and 1,2-DCE are on the order of 19 and 20 for first and second protons (NB) and 24 and 25 (1,2-DCE). A potentiometric sensor for carboxylates or dicarboxylates will operate based on a molecular receptor. Polar dicarboxylates such as glutarate (n ) 3) do not have observable waves in the ITIES experiment. If an ITIES wave cannot be seen for a given ion, then with the same two-phase system, that ion cannot depolarize the interface, and it is impossible to use the interface in a potentiometric sensor.2 From current data, we can predict what the formation constant for a glutarate-receptor complex must be in order to see a wave. Figure 5 shows where the limit for an observable wave for a dianion is. The predicted wave position for glutarate is about 17 kJ beyond that limit. As a result, a formation constant of only 103 is required to see a wave. In any real sample in which potentiometric sensors are expected to determine glutarate, interferences will be present. Chloride is a likely interferent. If we want the glutarate wave
∆wo pKas (25 °C) s ) 1,2-DCE
s ) NB
16.0 18.5 19.5
11.5 13.8 14.4
monocarboxylic acid dicarboxylic acid, first dissociation dicarboxylic acid, second dissociation
to occur 100 mV less negative than the Cl- wave, then the formation constant for the complex between receptor and the dicarboxylate needs to be much higher, on the order of 107. We note that simple, hydrogen-bond based receptors for glutarate have been prepared for which the complex formation constant is >105 in a competitive solvent (DMSO).42 The formation constant will be larger in less competitive solvents such as the plasticizers used for ISEs. Another attribute of the receptor, if it is a Brønsted acid, is its pKa. Clearly the carboxylate is a good base in the nonpolar solvents. If the receptor is a proton donor, the protonation of carboxylates may occur (see eqs 16 and 17). This does not preclude the observation of a response, but it may decrease the molecular selectivity. When the receptor and
A2- + RH2 h A2-‚‚‚H2‚‚‚R
(16)
A2- + RH2 h AH2 + R2-
(17)
substrate form a complex (16) the molecular recognition phenomenon dictates that there will be some size/shape selectivity in RH2’s preference for various species. On the other hand, the proton transfer reaction (17) would seem to involve no such recognition. Acknowledgment. We are pleased to acknowledge the financial support of the NSF through grant CHE-9403450. References and Notes (1) Girault, H. H. In Modern Aspects of Electrochemistry No. 25; Bockris, et al., Eds.; Plenum Press: New York, 1993; pp 1-62. (2) Senda, M.; Kakiuchi, T.; Osakai, T. Electrochim. Acta 1991, 36, 253. (3) Kihara, S.; Suzuki, M. Maeda, K.; Ogura, K.; Matsui, M. J. Electroanal. Chem. 1986, 210, 147. (4) Kihara, S.; Suzuki, M.; Sugiyama, M.; Matsui, M. J. Electroanal. Chem. 1988, 249, 109. (5) Dietrich, B. Pure Appl. Chem. 1993, 65, 1457. (6) Sabela, A.; Marecek, V.; Samec, Z.; Fuoco, R. Electrochim. Acta 1992, 37, 231. (7) Abraham, M. H.; Danil de Namor, A. E. J. Chem. Soc., Faraday Trans. 1 1976, 72, 955. (8) Czapkiewicz, J.; Czapkiewicz-Tutaj, B. J. Chem. Soc., Faraday Trans. 1 1980, 76, 1663. (9) Gru¨nwald, E.; Baughman, G.; Kohnstan, G. J. Am. Chem. Soc. 1960, 82, 5801. (10) Osaka, T.; Kakutani, T.; Nishiwaki, Y.; Senda, M. Anal. Sci 1987, 3, 499. (11) Stewart, A. A.; Shao, Y.; Pereira, C. M.; Girault, H. H. J. Electroanal. Chem. 1991, 305, 135. (12) Geblewicz, G.; Kontturi, A. K.; Kontturi, K.; Schiffrin, D. J. J. Electroanal. Chem. 1987, 217, 261. (13) Alemu, H.; Solomon, T. J. Electroanal. Chem. 1987, 237, 113. (14) Osborne, M. D.; Shao, Y.; Pereira, C. M.; Girault, H. H. J. Electroanal. Chem. 1994, 364, 155. (15) Clarke, D. J.; Schiffrin, D. J.; Wiles, M. C. Electrochim. Acta 1989, 34, 767. (16) Figaszewski, Z.; Koczorowski, Z.; Geblewicz, G. J. Electroanal. Chem. 1982, 139, 317. (17) Buck, R. P.; Eldridge, R. W. Anal. Chem. 1965, 37, 1242. (18) Shao, Y.; Girault, H. H. J. Electroanal. Chem. 1990, 282, 59. (19) Davis, H. S. J. Am. Chem. Soc. 1916, 38, 1166. (20) Durans, T. H. Solvents; Chapman & Hall Ltd.: London, 1971; p 190. (21) Bronner, W. E.; Melroy, O. R.; Buck, R. P. J. Electroanal. Chem. 1984, 162, 263.
14720 J. Phys. Chem., Vol. 100, No. 35, 1996 (22) Shao, Y.; Girault, H. H. J. Electroanal. Chem. 1992, 334, 203. (23) Marcus, Y. Z. Naturforch 1995, A50, 51. (24) Silva, F.; Moura, C. J. Electroanal. Chem. 1984, 177, 317. (25) Britz, D. J. Electroanal. Chem. 1978, 88, 309. (26) Bockris, J. O’M.; Reddy, A. K. N. In Modern Electrochemistry; Plenum: New York, 1970; p 296. (27) Wanklowski, T.; Marecek, V.; Samec, Z. Electrochim. Acta 1990, 35, 1173. (28) Hundhammer, B.; Solomon, T.; Dhawan, S. K.; Zerihun, T.; Tessema, M. J. Electroanal. Chem. 1994, 369, 275. (29) Hundhammer, B.; Solomon, T.; Zerihun, T.; Abegaz, M.; Bekele, A.; Graichen, K. J. Electroanal. Chem. 1994, 371, 1. (30) MacInnes, D. A. The Principles of Electrochemistry; Dover: New York, 1961; pp 137ff. (31) Shedlovsky, T.; Kay, R. J. Phys. Chem., 1956, 60, 151.
Shao and Weber (32) Rais, J. Collect. Czech. Chem. Commun. 1971, 36, 3253. (33) Abraham, M. H.; Liszi, J. J. Inorg. Nucl. Chem. 1981, 43, 143. (34) Shao, Y.; Weber, S. G., manuscript in preparation. (35) Smith, R.; Tanford, C. Proc. Natl. Acad. Sci. U.S.A. 1973, 70, 289. (36) Abraham, M. H.; Chadha, H. S.; Whiting, C. S.; Mitchell, R. C. J. Pharmaceutical Sci. 1994, 83(8), 1085. (37) Tanford, C. The Hydrophobic Effect, 2nd ed.; Wiley: New York, 1980. (38) Marcus, Y. Pure Appl. Chem. 1983, 55, 977. (39) Tan, S. N.; Girault, H. H. J. Electroanal. Chem. 1992, 332, 101. (40) Markin, V.; Volkov, A. G. Electrochim. Acta 1989, 34, 93. (41) Collander, R. Acta Chem. Scand. 1951, 5, 774.
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