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Anal. Chem. 1990, 62,2270-2274
(77) Wieringa, J. H.; Stratling, J.; Wynberg, H.; Adams, W. Tetrahedron Lett. 1972, 169-172. (78) Schuster, G. 6.; Turro, N. J.; Steinmetzer, H.-C.; Schaap, A. P.; Faier, G.; Adam, W.: Lui, J. C. J. Am. Chem. SOC. 1975, 9 7 ,
7110-7118. (79)Schaap, A. P. Personal communication. (80) Richardson, W. H.; Montgomery, G. C.; Yeivington, M. 6.; O'Neai, H. E. J . Am. Chem. Soc 1974, 9 6 , 7525-7532. (81) Koo, J.-Y.; Schuster, G. B. J. Am. Chem. SOC. 1977, 99,
6107-6109. (82) Schuster, G. 6.; Dixon, 6.; Koo. J.-Y.; Schmidt, S. P.; Smith, J. P. Photochem. Photobio/.1979, 30, 17-26. (83) Handley, R. S.;Stern, A. J.; Schaap, A. P. Tehahedron Lett. 1985, 3183-3 186. (84)Schaap, A. P.; Gagnon, S. D.; Zakka, K. A. TetrahedronLett.1982. 2943-2946. (85)Lee, C.: Singer, L. A. J. Am. Chem. SOC.1980, 102, 3823-3929. (86) McCapra, F.; Beheshti, I.; Burford, A.; Hann, R. A,; Zakilka, K. A. J. Chem. Soc., Chem. Commun. 1977, 944-946. (87)McCapra, F. J. Chem. SOC.. Chem. Commun. 1988, 155-156. (88)Turro, N. J.; Lechtken, P.; Schuster, G.; Oreli, J.; Steinmetzer, H.-C.; Adam, W. J. Am. Chem. SOC.1974, 96, 1627-1629. (89) Schaap, A. P.; Gagnon, S. D. J . Amer. Chem. SOC. 1982, 104, 3504-3506. (90) Schaap, A. P. Photochem. Photobiol. 1988,47S, 50. (91) Schuster, G. B.; Schmldt, S. P. Adv. Phys. Org. Chem. 1982, 18, 187-238.
(92) Adam, W.; Cueto, 0. J. J. Am. Chem. SOC. 1979, 101, 6511-6515. (93) Edwards, 8.; Sparks, A.; VOyta, J. C.; Bronstein, I . J . Bblumih. Chemiilumin. 1990, 5 , 1-4. (94)Bronstein, I.; Voyta, J. V.: Edwards, B. J. Eiolumin. Chemilumin. 1988, 2 , 186. (95) Ribi, M. A,; Wel, C. C.; White, E. H. Tetrahedm 1972, 26,481-492. (96) Wilson, T. Int. Rev. Sci.: Phys. Chem., Ser. Two 1976, 9 , 265-322. (97) Wilson, T.; Landis, M. E.; Baumstark, A. L.; Bartiett, P. D. J. Am. Chem. SOC.1973, 95, 4765-4766. (98) Bartiett, P. D.; Baumstark, A. L.; Landis, M. E. J. Am. Chem. SOC. 1974, 96, 5557-5558. (99)Tizard, R.; Cate, R. L.; Ramachandran, K. L.; Wysk, M.; Voyta, J. C.; Murphy, 0. J.; Bronstein. I. Proc. Natl. Acad. Sci. U . S . A . 1990, 8 7 , 4514-4518. (100) Hauber, R.; Geiger,
51 1-514.
R. J. Clin. Chem. Clin. Biochem.
1987, 2 5 ,
(101)Hauber, R.; Geiger, R. Nucl. Ac& Res. 1988, 76, 1213. (102)Richterich, P. Thesis, Universlt&t Konstanz, FRG, 1990. (103) Genius : non-radiwctive DNA labeling and detection kit, Application Manual; Boehringer: Mannheim, 1989. (104) Kissinger, C.; Dunne, T.; Beck, S.;Koster. H. Unpublished results. (105) Bronstein, I.; Kricka, L. J. Am. Clin. Lab. JanlFeb 1990, 33-37. (106) Schaap, A. P.; Akhavan-Tafti, H. Personal communication. (107) Schaap, A. P.; Akhavan-Tafti, H.; DeSilva, R. Personal communication.
ARTICLES Dissociation of Tetrahexylammonium Picrate Ion Pairs Adsorbed at the Chloroform-Water Interface Lawrence Amankwa and Frederick F. Cantwell*
Department of Chemistry, University of Alberta, Edmonton, Alberta, Canada T6G 2G2
Two membrane phase separators, made of porous Teflon and of paper, are used to measure isotherms for adsorption of tetrahexyiammonium picrate (OP) at the chloroform-water interface in a rapidly stirred liquid-liquid dispersion. The ion-pair species OP and the cation 0' are both surface-active but the picrate anion P- is not. I n the presence of a large excess of P- dissociation of the adsorbed species QP is suppressed. Its adsorption follows a Langmuir isotherm. Without a large excess of P- present, the adsorbed QP dissociates appreciably on the interface. The ion-pair dissociation constant is Km,w = (1.2 f 0.1) X lo5 moVL. Aspects that are peculiar to ion-pair dissociation at an interface, as opposed to ion-pair dissociation tn bulk solution, are discussed and quantified. These include competitive adsorption between Q+ and OP as well as the presence of an electric charge on the interface as a result of adsorbed Q+.
Experiments employing a rapid-stir apparatus with a porous Teflon membrane phase separator previously have been used to measure adsorption isotherms for ion pairs at the chloro0003-2700/90/0362-2270$02.50/0
form-water interface. Langmuir adsorption isotherms have been observed for interfacial adsorption of ion pairs formed between cationic metal-ligand complexes and simple anions (1) and for the ion pair tetrahexylammonium bromothymol blue (QHB) (2). For the latter system not only does the ion pair adsorb but also both the constituent ions, Q' and HB-, adsorb. Competitive adsorption between HB- and QHB was characterized. Analytically,bromothymol blue is an important reagent anion used in the photometric determination of cations by ion-pair extraction ( 3 ) . An even more important reagent for this purpose is picrate, P- ( 3 , 4 ) . Picrate differs from bromothymol blue in that it does not adsorb at the chloroform-water interface. In the present paper it is shown that this difference leads to a significant difference in the properties of interfacially adsorbed tetrahexylammonium picrate ion pair (QP)compared to QHB in the same concentration range. Adsorbed Q P is involved in a dissociation equilibrium into Q+, which is adsorbed, and P-, which is in the aqueous phase. Use of a paper membrane phase separator allows direct measurement of the concentration of P- in the aqueous phase during stirring. The ionpair dissociation of QP a t the interface is quantitatively characterized. 1990 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 62, NO. 21, NOVEMBER 1, 1990 2271
EXPERIMENTAL SECTION Reagents. Water was demineralized, distilled, and finally distilled over alkaline permanganate. Aqueous phosphate buffer at pH 6.5 was prepared from sodium hydrogen phosphate and sodium dihydrogen phosphate at an ionic strength of 0.050. Reagent grade chloroform was washed with water shortly before use. A 1 X lo4 M solution of reagent grade tetrahexylammonium bromide (Eastman Kodak Co., Rochester, NY) was prepared in chloroform. Reagent grade picric acid (Matheson, Coleman and Bell, Ltd.) was used as received to prepare a 1 X 10” M aqueous solution in pH 6.5 phosphate buffer. Chloroform solutions of the ion-pair QP were prepared in the concentration range 2.0 x lo4 to 2.0 x M as follows: An aqueous solution of QBr and an aqueous solution of pH 6.5 picric acid, containing at least a 5-fold stoichiometric excess of picric acid, were pipetted into a separatory funnel containing 60 mL of chloroform. After the funnel was shaken for about 5 min and the phases allowed to separate, the chloroformextract was transferred into a second separatory funnel and washed with 20 mL of fresh aqueous buffer. The chloroform phase was then transferred into a 100-mL volumetric flask and diluted to volume with chloroform. Apparatus. The rapid-stir extraction apparatus incorporating the porous membrane phase separator and photometric detector interfaced to an IBM-XT microcomputer has previously been described in detail (2,5). A porous Teflon membrane was used as a phase separator when the chloroform phase was being monitored and a paper membrane was used when the aqueous phase was being monitored. In all experiments 100.0 mL of both of the chloroform and aqueous phases were combined in the rapid-stir cell a t 20 f 1 O C . Stirring was at a constant speed of 2300 rpm and the pumping rate was 1.0 mL/min. In some experiments absorbance of the separated phase was measured by flowing it through the on-line spectrophotometer, while in other experiments absorbance was measured on a collected portion of the separated phase in a Model 8451A diode m a y spectrophotometer (Hewlett-Packard). Measurements of pH were made with an Accumet Model 525 pH meter (Fisher Scientific) with a combination electrode. Interfacial tensions between previously equilibrated chloroform and aqueous solutions were made by the drop-volume technique as previously described (2). Liquid-Liquid Distribution. The distribution isotherm for tetrahexylammonium, added as tetrahexylammonium bromide, QBr, between chloroform and aqueous bulk-liquid phases was measured by a batch equilibration experiment, as previously described (2). Interfacial Adsorption. Interfacial adsorption isotherms between the chloroform-water interface and the bulk-liquid phases were measured for tetrahexylammonium and for the ion-pair QP using the rapid-stir cell. Details of the measurement of the adsorption isotherm for tetrahexylammonium have previously been presented (2). For QP, interfacial adsorption was measured as follows: A pH 6.5 aqueous buffer and a chloroform solution of QP were combined and stirred to achieve distribution equilibrium. While stirring, and with the aid of the Teflon membrane phase separator, the concentration of QP was measured in the chloroform phase using the absorbance at 372 nm. The stirrer was then shut off and, after the phases completely coalesced, the concentration of QP was again measured in the chloroform phase. The amount of QP adsorbed at the interface was calculated from the difference in concentrations with the stirrer off and on. Repeating the experiment with different initial concentrations of QP yields the adsorption isotherm. In a second set of experiments, to demonstrate the effect of NaP on adsorption of QP, the procedure was repeated but with excess NaP added to the aqueous phase. In a third set of experiments, the procedure was again repeated, without added Nap, but using the paper phase separating membrane instead of the Teflon one and measuring the absorbance of picrate ion in the aqueous phase at 362 nm. RESULTS AND DISCUSSION Distribution of Q’. Both the liquid-liquid distribution and the interfacial adsorption previously have been studied for tetrahexylammonium bromide (2). The species adsorbed a t the interface is the cation Q’ with electroneutrality near
3
z
I
2-
0
1
2
3
4
5
6
7
8
9
Figure 1. Adsorption isotherms for tetrahexyhmmnium picrate at the chloroform-aqueous interface. Points are experimental. Curve A is in absence of added Nap, line calculated with eq 10. Curve B is in presence of 4.0 X M Nap, line calculated with eq 4. Constants = 1.60 x IO-”, K ~ ~ , = , , 1.2 x used: K,, = 2.75 x io4, rop,snT M are of interest. Only data up to C,p,o,8 = 6 X
the positively charged interface provided by an equivalent surface excess of negative charge in the diffuse part of the electrical double layer in the aqueous phase (6, 7). Distribution of P-.In aqueous solution a t p H 6.5 picric acid is fully dissociated to picrate ion. Previous studies have shown that NaP does not extract into chloroform (8). Furthermore, neither Pnor NaF’ adsorbs a t the chloroform-water interface. This is revealed both by the fact that the concentration of P- in the aqueous phase is the same whether the stirrer is on or off and by the fact that the “Gibbs isotherm”, which is a plot of interfacial tension versus the logarithm of the concentration of sodium picrate (not shown) (9), is essentially horizontal (slope 0.15 f 0.06). Distribution of QP. The ion-pair extraction constant for QP between chloroform and water is about 4 X 1O’O ( I O - I Z ) , so that there is virtually none of this component present in the aqueous phase a t the concentrations employed in this work. Also at these concentrations, dimerization and higher aggregation of the ion pair in chloroform are negligible (3,IZ). The dissociation constant of QP in chloroform has not been measured but is expected to be about lo-’ (2,3,13,14). Thus, dissociation of QP in chloroform may or may not occur to some extent a t concentrations as low as lo4 M. However, since concentrations of tetrahexylammonium picrate in chloroform were measured spectrophotometrically against a calibration curve of absorbance versus concentration, the measured concentrations are correct, independent of whether any ionpair dissociation occurs in chloroform. (Incidently, the calibration curve was linear with zero intercept.) The total moles of tetrahexylammonium adsorbed a t the interface, nADS, is calculated from the expression where CQp,ois the analytical concentration of tetrahexylammonium picrate in the chloroform phase, V , is the volume of the chloroform phase, and the subscripts “s” and “ns” refer to “stirring” and “no-stirring”, respectively. Two interfacial adsorption isotherms for tetrahexylammonium picrate are shown in Figure 1. These isotherms are plots of r versus CQp,o,s. Interfacial concentration (i.e. surface excess) in units mol.cm-2 is given by The interfacial area, A , has the value 3.9 X lo-* cm2, as measured in this apparatus at 2300 rpm (2). Curve A in Figure 1 was measured with no excess sodium picrate (Nap) added to the aqueous phase while curve B was measured with 4.0 x M NaP added to the aqueous phase.
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ANALYTICAL CHEMISTRY, VOL. 62, NO. 21, NOVEMBER 1, 1990 3
?
0
1
2
3
4
5
6
7
8
9
Flgure 2. Adsorption of tetrahexylammoniumpicrate in the absence of added Nap. Curve A is the identical adsorption isotherm as curve A in Figure 1. Curve C is a plot of To calculated from experimental values of [P-1, using eq 6. Solid line in curve C is empirical fit. Only M are of interest. data up to Cw,o,s= 6 X
Briefly, these adsorption isotherms involve the adsorption of the species QP from chloroform onto the interface and the partial dissociation of this adsorbed ion-pair according to the reaction
(QP)i+ (Q+)I
+ (P-)a
(3)
in which the surface-active cation Q+ is adsorbed at the interface but the non-surface-active anion P- enters the aqueous phase. Addition of sodium picrate to the aqueous phase shifts the equilibrium in eq 3 to the left, suppressing the ion-pair dissociation (Le Chatelier's principle). A picrate concentration of 4.0 X lo4 M is sufficient to quantitatively suppress ion-pair dissociation so that curve B in Figure 1 is the adsorption isotherm for the species QP, alone. The details and justification for this model are presented below. The data in curve B, up to about CQp,o,s= 6 X M, conform to the Langmuir adsorption equation ( 6 )
rQp(curveB) =
~QPSATKQPCQP,~,~
1+ KQPCQP,~,~
(4)
in which rQp(curveB) is the surface excess of the species QP, I'Qp,SAT is the surface excess a t monolayer saturation by the species QP, and K Q p is the equilibrium constant in L/mol for the adsorption of the species QP. It can be demonstrated that the data in curve B up to about CQp,o,s= 6 x M conform to Langmuir behavior by the fact that a plot of c ~ p , ~ , ~ ( r Q p (curve B))-l versus CQp,o,s is linear for the first six data points (8). The line has a slope of (0.62 f 0.10) X 10" cm2/mol and an intercept of (2.3 f 0.3) X lo6 cm2/L. The value of K Q p is calculated from the ratio slope/intercept to be (2.7 f 0.6) X lo4L/mol and the value of rQp,SAT is calculated from (slope)-' to be (1.6 f 0.3) X lo-" mol/cm2. The solid line in curve B of Figure 1 was calculated via eq 4 using the above reported values of K Q p and rQp,SAT. The data up to CQp,o,s= 6 x M are well represented by the line, but above that concentration the data (seventh point) exhibit a marked upward deviation from Langmuir behavior. The general shape of the overall isotherm is a familiar one, having been designated as a type I1 BET isotherm in gassolid adsorption (15)and as a type L3 or perhaps L4 isotherm in liquid-solid adsorption (16-19). Nearly always, this type of upward deviation from Langmuir behavior is the result of interactions between adsorbed solute molecules coming into play when they become crowded together as monolayer coverage is approached (15, 16). Specifically, it may be due to reorientation of the molecules which allows tighter packing or to multilayer formation (18-20). In the present case, where we are interested in studying dissociation of the ion-pair QP,
we shall deal only with data in the Langmuir region, at C Q ~ , ~ , ~ 5 6 x IOT5M, in order to avoid complications introduced by interactions between ion pairs on the interface. Comparing curves A and B in Figure 1,it is proposed that the difference between these two curves is due mainly to dissociation of Q P via eq 3. This proposition can be tested by measuring the concentration of picrate ion in the aqueous phase. In the absence of added Nap, it is found that there is no P- in the aqueous phase with the stirrer turned off but that P appears in the aqueous phase when the stirrer is turned on (curve C, Figure 2). This evidence confirms the Occurrence of ion-pair dissociation at the interface. A further question is whether the dissociation shown in eq 3 can be quantitatively expressed in terms of the equilibrium dissociation quotient predicted from the law of mass action
(5) in which [P-lais the picrate ion concentration in the aqueous phase and rQis the surface excess of the adsorbed species Q'. By analogy with ion-pair dissociation in solution, it might seem that the value of r Q p to be used in eq 5 when no excess picrate is present should be equal to r Q p (curve B) from eq 4, obtained in the presence of a large excess of P-. However, this reasoning is not necessarily correct for species adsorbed at the interface. For example, it has clearly been demonstrated for the ion-pair tetrahexylammonium bromothymol blue (QHB) that both of the Langmuir adsorption parameters (rQHB,SATand KQHB) are decreased by the presence of an excess of one of the constituent ions (e.g. HB-) as a result both of competitive adsorption and of changes in the chemical character of the interface ( 2 ) . Also, it has been found in the picrate system that addition of a large excess of tetraalkylammonium bromide quantitatively prevents adsorption of the tetraalkylammonium picrate ion pair because of adsorption of Q+ (21). Therefore, in the current system it is anticipated that the presence of adsorbed Q+, which is present as a result of dissociation of adsorbed &PImight reduce rQp,SAT and K Q p for the remaining undissociated QP to values lower than those measured for curve B. If this happens then r Q p to be used in eq 5 , when no excess picrate is present, will not be equal to 1'Qp (curve B) obtained in the presence of a large excess of picrate. In any event, whether or not this is true, the correct value of r Q P to be used in eq 5 can be obtained in the following manner. First, from the stoichiometry of eq 3 it is seen that in the absence of added P-
Shown as curve C in Figure 2 is a plot of [P-],V,A-' versus C Q ~ , ~Curve , ~ . A in Figure 2 is the same as Curve A in Figure 1. Next, according to the proposed model I'(curve A) = rQp rQ (7)
+
Therefore, r Q p can be calculated by rearranging eq 7 and substituting for rQfrom eq 6 rQp
= r(curve A) - [P-],V,/A
(8)
A plot of repobtained from eq 8 versus r Q p (curve B) obtained from eq 4 is approximately linear with zero intercept but, instead of having a slope of I, it has a slope of 0.52 f 0.04. While the linearity of this plot is fortuitous, the fact that the values of r Q p from eq 8 fall well below the Langmuir values of I'QP (curve B) demonstrates that the adsorbed Q+, arising from dissociation of the ion pair, does in fact decrease rQp,sAT and/or K Q p to values below those that they have in curve B. Furthermore, the magnitude of this effect is in the range that would be predicted by analogy with the QHB system (2) for the values of rQinvolved. The alternative explanation, that either the Teflon membrane or the paper membrane might not be measuring the true bulk-phase equilibrium concen-
ANALYTICAL CHEMISTRY, VOL. 62, NO. 21, NOVEMBER 1, 1990 n, ".J
I
Table I. Parameters Related to Electrical Double Layer Theory and to the Thermodynamic Ion-Pair Dissociation Constant (See Text for Details)
I
v
*,, v
YP.rb
exp(+FQ,/RT)
0.0059 0.0083 0.0096 0.0110 0.0149 0.0154 0.0206 0.0209 0.0241 0.0244
0.0021 0.0030 0.0034 0.0039 0.0053 0.0055 0.0074 0.0075 0.0086 0.0087
0.74 0.73 0.73 0.72 0.71 0.71 0.69 0.69 0.68 0.68
0.60
40,
(r (Curve A) - [P-I,
2273
0.250 0.450 0.594 0.775 1.463 1.575 3.225 3.375 5.00 5.20
b] x 1011(mol/cmZ) A
0.064 0.069 0.073 0.076 0.086 0.087 0.101 0.102 0.111 0.112
YPJ2
0.60 0.61 0.61 0.62 0.62 0.63 0.63 0.64 0.64
Figure 3. Plot based on eq 9 to evaluate the ion-pair dissociation quotient KW,* The points are experimental and the line is from linear regression.
Ionic strength of the bulk aqueous phase is c, = 0.050. Ionic activity coefficient in the bulk aqueous phase is ~ p = , 0.77 ~ from D-H limiting law.
tration, has already been ruled out (22). Thus, the important conclusion here is that the values of r Q p to be used in eq 5 to fit the data in curve A should be calculated with eq 8 rather than being calculated with eq 4. Combining eq 5, 6, and 7 and rearranging yields the expression
calculated line is within experimental error, considering that the relative uncertainty in the calculated line is about 10% and that in the points is about the same. Effect of Interfacial Charge. When surface-active ions are adsorbed at a liquid-liquid interface, an electrical potential difference is developed between the charge-surface containing the charges of these ions and the bulk aqueous solution (6). The existence of a potential can be demonstrated by microelectrophoresis (23)or potentiometry (24). In the simplest case, the interfacial potential, qo,can be calculated from rQ by using the Gouy-Chapman equation to describe the "electrical double layer" (6,25,26). As a consequence of this potential, ions, including P-, have a different concentration in the aqueous phase near the interface than they have in the bulk aqueous phase, and the degree of this difference is greater at higher potentials. For this reason one might have expected that KDis,Qpin eq 5 would not have been a constant. However, it is shown below that at the low potentials involved a constant value for KDis,Qpis consistent with theory. The thermodynamic dissociation constant of Q P a t the interface is
Shown in Figure 3 is a plot of this equation with the data taken from curves A and C. The points are calculated a t values corresponding to the data points in curve A. The solid line in Figure 3 is the linear regression line. The fact that this plot has a zero intercept (-0.9 f 1.5) X and is linear (r = 0.97) validates eq 5 with KDis,Qp as a constant. From the slope of this line (0.49 f 0.05) the interfacial ion-pair dissociation quotient is found to be Kuj,Qp= (1.2 f 0.1) X loi, mol/L. The scatter of the points in Figure 3 reflects, among other things, the fact that the term (r(curve A) - [P-],V,/A) is the difference between numbers of similar magnitude and also the fact that [P-]: is the square of a measured concentration. It can be calculated from eq 5, and it can be observed graphically from the closeness of curves A and C in Figure 2, that in the absence of added excess P- adsorbed tetrahexylammonium picrate is extensively dissociated at surface concentrations below about 2 x lo-" mol/cm2 (i.e. below Cw,04 =6 x M at the present stirring rate). Furthermore it can also be calculated from eq 5 that in the presence of 4.0 X 10" M excess P- dissociation of adsorbed QP is never greater than about 3%, justifying the assumption that the isotherm in curve B is that of the ion-pair only. It should be noted that the evaluations of rQp,r Q , [P-I,, and KDls,Qp,described above, utilized data only from curves A and C and did not employ curve B. Nevertheless, it is worthwhile trying to express curve A in terms of curve B in order to develop an expression relating curve A to the solution concentration, CQp,04.The key to doing this is the relationship between rQpand r Q p (curve B) which is empericdy expressed by the slope of a plot of these two quantities, i.e. 0.52 (see above). Combining this relationship with eqs 5, 6, and 7 gives the expression IYcurve A) = Va O.52r~p(CUrVeB) + KDia,QP-(0.52)rQp(curve B)
Y1=
( A (10) in which rW(curve B) is calculated via the Langmuir equation, eq 4. The line in curve A in Figures 1 and 2 was calculated by using eq 10. The agreement between the points and the
where [P-jXis the molar concentration of picrate in the aqueous phase at a distance x-cm away from the charge surface and yp,* is the ionic activity coefficient of picrate ion at distance x. It is assumed in eq 11 that yQs for the adsorbed ion Q+, which protrudes into the aqueous phase, is also equal to ~ p and , that ~ YQP,~ for the adsorbed neutral ion pair is equal to 1. The distance x is the location of the plane of closest approach to the charge surface by nonpaired picrate ions. It is taken to be the sum of the radius of the Q' ion (9 A) and the radius of the hydrated P- ion (5 A), on the assumption that ions closer than a hydrated radius will be ion paired with Q'. Ionic radii were measured from space-filling molecular models. The charge-surface of Q+ ions is probably located at or very close to the chloroform-water interface. This is because Q' is spherically symmetrical, unlike ions such as dodecyltrimethylammonium for which the charge surface is said to be located a few angstrom units away from the interface (6,25, 26). At the low goand ionic strength involved the Debye-Huckel approximation can be used to simplify the Gouy-Chapman equation (27). The interfacial potential is given by the express ion in which F is the Faraday constant and c, is the ionic strength
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ANALYTICAL CHEMISTRY, VOL. 62, NO. 21, NOVEMBER 1, 1990
in the bulk aqueous solution (i.e. 0.050). The potential at distance x is given by $,
2=
$o exp((-3.29
x 1O’)c’k)
(13)
in which x = 14. x cm, as discussed above. The concentration of P- a t x is related to its measured concentration in bulk solution by the Boltzmann equation
Substituting for [P-1, in eq 11 from eq 14 yields
ponent adsorbed is similar to the effect of HB- concentration, though for a different chemical reason; picrate affects the degree of dissociation while HB- exercises its effect by competitive adsorption. Two analytical techniques in which immiscible liquid phases are used under conditions where the ratio of interfacial area to bulk liquid volume is large are segmented flow (e.g. solvent extraction/ flow injection analysis ( 4 ) ) and liquid-liquid partition chromatography (e.g. “extraction chromatography” (32)).The latter is popular in radioanalytical chemistry. An insufficient excess of reagent ion could lead to a nonlinear calibration curve in the former technique and to asymmetric chromatographic peaks in the latter technique.
LITERATURE CITED from which it is seen by comparison with eq 5 that KDis,QP
= KoDis,QP
[
YP,x
( Ti)]
exp +-
For consistency the ionic activity coefficient should culated from the Debye-Huckel limiting law (28) yP,, = antilog ( - 0 . 5 1 ~ ~ ’ ~ ~ )
since the Debye-Huckel approximation was used in deriving eqs 12-14. The ionic strength, c x , at distance x includes contributions from Na+, H2P0,, and HPOZ- ions, all of whose concentrations at x are different from those in bulk solution but can be calculated via the appropriate forms of the Boltzmann equation (27) and from the Q’ ion. The concentration of Q+ at x was calculated as (r,$l103) mol/L. Shown in Table I are the values of c,, $, $x, yP,,, and yp,z2 exp(+F+,/RT), calculated to correspond with the data points in Figure 3. Two features of this table should be noted. The first is that, as a result of the small surface-charge densities, the interfacial potentials are small. The second is that the quantity yp,x2exp(+F$,/RT) is essentially constant (0.62 i 0.01). The constancy of this term explains why the dissociation quotient, KDis,QP, in concentration units, turns out to be a constant. It is the quotient of two constants, KoDk,Qp and y P 2 exp(+F$,/RT) as seen in eq 16. Other Considerations. Interfacial tension or pressure measurements (29-31) and zeta potential measurements (23) have previously been used as qualitative evidence to suggest that ions adsorbed at the liquid-liquid interface undergo some ion-pair formation with counterions from solution. The present work provides an alternative experimental approach in which a large ratio of interfacial area to bulk solution volume is employed. I t provides direct measurement of concentrations in both bulk phases and indirect measurement of the amount of solute adsorbed at the interface. Interfacial equilibria are readily evaluated quantitatively, making this an attractive alternative or complementary approach to conventional surface chemical techniques. The analytical consequences of the dissociation of interfacially adsorbed ion pairs are similar to those described for the ion pair tetrahexylammonium bromothymol blue ( 2 )because the effect of a varying, low excess reagent concentration of P- in the aqueous phase on the amount of cationic com-
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RECEIVED for review April 25,1990. Accepted June 29, 1990. This work was supported by the National Sciences and Engineering Research Council of Canada and by the University of Alberta.
