Anal. Chem. 1999, 65, 1443-1460
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Measurement of Water-Hexadecane Partition Coefficients by Headspace Gas Chromatography and Calculation of Limiting Activity Coefficients in Water Jianjun Li' and Peter W. Carr University of Minnesota, Department of Chemistry, Smith and Kolthoff Halls, 207 Pleasant Street Southeast, Minneapolis, Minnesota 55455
A very simple and easy method for measuring water-hexadecane partition coefficients (Pw,16) of J~ from -2.7 a wide range of solutes (log P Wranging to 4.4) by headspacegas chromatography has been developed. This method requires no standard solution of the solute and no calibration of the detector. It only requires that the solute bevolatile enough to be measurable in the headspace of the water-hexadecane two-phase system and the detector be linear. The precision of measurement is often better than 2% in log Pw,16. From the measuredwater-hexadecane partition coefficient and gas-hexadecane partition coefficient (log&), a gas-water partition coefficient and hence the limiting activity coefficient (7") in water can be calculated. The 7" values obtained this way compare very favorably (ca. 5%) to those directly measured by other techniques such as direct headspace gas chromatography and inert gas stripping. This method should be equally applicable to the measurement of partition coefficients between other immiscible solvent systems. INTRODUCTION Lipophilicity,often expressed as the logarithm of apartition coefficient (log P),is a physicochemical property which describes the partition equilibrium of solute molecules between water and an immiscible organic solvent.' The most commonly used immiscible organic solvents are octanol and saturated hydrocarbons. Water-octanol partition coefficients have been widely used in quantitative structure-activity relationships (QSAFb) in medicinal and pharmaceutical chemistry.2~3 The success of water-saturated octanol as a model for such systems, e.g., biological membranes, has been attributed to its lipophilic-hydrophilicbalance which results from the n-octyl chain, the hydrogen-bonding ability of the hydroxy group, and the relatively high water content of watersaturated octanol (at equilibrium, octanol contains 1.7 mol/L water and water contains 4.5 X 10-3 mol/L Odan~l).~ The last point has been supported by new experimental evidence5 which shows that water saturation of n-octanol has only a small although real effect on the chemical properties of
* Current address: The Procter & Gamble Co., Miami Valley Laboratories, P.O. Box 398707, Cincinnati, OH 45239. (1)Tayar, N. E.; Testa, B.; Carrupt, P.-E. J. Phys. Chem. 1992, 96, 1455. (2) Hansch, C.; Leo,A. Substituent ConstantsforCorrelation Analysis in Chemistry and Biology; Wiley-Interscience: New York, 1974. (3) Leo, A. J. Chem. SOC.,Perkin Trans. 2 1983,825. (4) Miller, M. M.; Wasik, S. P.; Huang, G.-L.; Shiu, W.-Y.; Mackay, D.Enuiron. Sei. Technol. 1985, 19, 522. (5) Dallas, A. J.;Carr, P. W. J. Chem. SOC.,Perkin Trans. 2 1992,2155. 0003-2700/93/0385-1443$04.00/0
n-octanol. Water-hydrocarbon partition coefficients, on the other hand, have been used in other QSARs where the hydrocarbon may be used to model a lipophilic system in which there are no hydrogen-bonding interactions between the solute and solvent.6~~For example, Franks and Lieb7 used water-hexadecane partition coefficients to test for hydrophobic binding sites in the enzyme luciferase. The most common procedures for the direct measurement of lipophilicity are the "shake flask"b11 and "generator c01umnn12J3methods. In these methods, the solute concentration in each phase of the equilibrated water-immiscible organic mixture is determined by spectrophotometric8 or chrornatographicg-l1methods, in which equilibration and analysis can be time-consuming and tedious. Although indirect methods based upon correlations with gas14 and liquid15J6 chromatographic retention parameters have been developed for such determinations, deviations in these correlations still necessitate the occasional evaluation of partition coefficients by the traditional, direct techniques. Indirect17 and direct18 methods of using centrifugal partition chromatography (CPC)for the determination of wateroctanol partition coefficients have been reported. Recently, Abrahamlg and Martire13920 reported almost simultaneously an indirect method for determining waterhexadecane partition coefficients. The method is based on the fact that the mutual solubility of water and hexadecane is very low (the solubility of water in hexadecane is 2 X 10-3 mol/dm3 and that of hexadecane in water is 4 X 10-4 mol/ dm3);19 the water-hexadecane system can be regarded as a system containing two pure solvents. Hence water-hexadecane partition coefficients (Pw,16) can be determined indirectly using eq 1,where Kwand K16 are the respective gas-solvent partition coefficients (note that K16 is the same as L16, the symbol we and others previously used in gas-liquid equilibrium studies by gas-liquid chr~matography).l~*~~*~~ [solutel, (6) Finkelstein, A. J. Gen. Physiol. 1976, 68, 127. (7) Franks, N. P.; Lieb, W. R. Nature (London) 1978,274,339.
(8)Rekker, R. R. The Hydrophobic Fragmental Constant; Elsevier: Amsterdam, 1977. (9) Grunewald, G. L.; Pleiss, M. A.; Gatchell, C. A,; Pazhenchevsky, R.: Raffertv. M. F. J. Chromatom. 1984.292. 319. '(10) Xi; T. M.; Hulthe, B.; Fhestad, S. Chnosphere 1984,13,445. (11) Haky, J. E.; Leja, B. Anal. Lett. 1986, 19, 123. (12) Tewari, Y.B.; Miller, M. M.; Wasik, S. P.; Martire, D.E. J. Chem. Eng. Data 1982,27,451. (13) Schantz, M. M.; Martire, D.E. J. Chromatogr. 1987, 391, 35. (14) Valko, K.; Lopata, A. J. Chromatogr. 1982,252,77. (15) McCall, J. M. J. Med. Chem. 1975,18, 549. (16) Haky, J. E.; Young, A. M. J. Liq. Chromatogr. 1984, 7, 675. (17) Berthed, A.; Armstrong, D.W. J . Liq. Chromatogr. 1988,11,547. (18)Gluck, S. J.; Martin, E. J. J. Liq. Chromatogr. 1990,13, 2529. (19) Abraham. M. H.: Grellier. P. L.: McGill. R. A. J . Chem. Soc.. Perkin Trans. 2.1987, 797. (20) Schantz, M. M.; Barman, B. N.; Martire, D.E. J. Res. Natl. Bur. Stand. (U.S.) 1988, 93, 161. (21) Zhang, Y.; Dallas,A. J.; Carr, P. W. J. Chromatogr., in press. (22) Li, J.; Zhang, Y.; Dallas, A. J.; Carr, P. W. J. Chromatogr. 1991, 550, 101. Q 1993 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 65, NO. 10, MAY 15, 1993 pw.16
= K,$K, = [solutell~[solutel,
K, = [solutel,/[solute],
(1)
(3)
denotes the equilibrium concentration of the solute in the phase x [ x = gas (g), water (w), or hexadecanel.16 Both Abrahamlg and Martire13s20have shown that values of Pw,16 obtained indirectly via eq 1are virtually identical with directly measuredPw,16 values. Since the valuesof K16 can be measured with reasonable accuracy by a gas chromatographic method using hexadecane as the stationary phase19321*22or by direct headpsace gas chromatography (HSGCLZ3K, or p w , 1 6 can be interchangeably calculated once one of the other quantities is known. Abraham used K, values that were determined from various techniques (but mainly from aqueous solubility J ~ eq l.24 data) and obtained a large data base of P W via The purpose of the present work is twofold. First we sought to develop a method for the direct measurement of waterhexadecane partition coefficients for a wide variety of compounds by headspace gas chromatography. Second was to obtain gas-water partition coefficients via eq 1 by using accurately measured K16 data from gas-liquid chromatography or headspace gas c h r ~ m a t o g r a p h y ~and ~ , ~the ~ -p~w ,~1 6 values obtained in this work. Infinite dilution activity coefficients in water can then be calculated from the gaswater partition coefficients by eq 4, where p~ is the density
of water at 25 "C, MW1 is the molecular weight of water, p i is the solute vapor pressure, R is the gas constant, and T is the absolute temperature. Since the limiting activity Coefficients of sparingly water-solublesolutes are of particular interest to us,25 our focus is on such compounds.
THEORY The basic idea behind the present method is to measure the change of the concentration of a solute in a vapor phase that is in equilibrium with a dilute solution of that solute in water upon addition of a known volume of hexadecane (method I). Conversely, one can measure the change of the concentration of a solute in the vapor phase that is in equilibrium with a dilute solution of that solute in hexadecane upon addition of a known volume of water (method 11). This change is directly related to the partition coefficient of the solute between water and hexadecane. Headspace gas chromatography is used as a tool to determine the solute concentration in the vapor phase. Due to the very wide range in Pw.16, it is sometimes best to use method I. With other species method I1 is preferred. One uses that method which gives the greatest change in signal. The first is applicable to solutes that have large water-hexadecane partition coefficients, that is, for those solutes where partitioning into hexadecane is much more favorable than partitioning into water. For these systems, an initial aqueous solution is made and the solute peak area is measured and then a known (small) volume of hexadecane is added and the solute peak area is again measured. From the measured change (ratio) of the solute peak areas and knowledge of the volume of added hexadecane, the partition coefficient of the solute between water and hexadecane can be calculated. The second (23) Dallas, A. J. Ph.D. Thesis, University of Minnesota, 1992. (24) Abraham, M. H.; Whiting, G. S.; Fuchs, R.; Chambers, E. J. J. Chem. SOC.,Perkin Trans 2 1990,291. (25) Li, Jianjun Ph.D. Thesis, University of Minnesota, 1992.
approach is for solutes that have small water-hexadecane partition coefficients, Here an initial hexadecane solution of the solute is made, and water is then added to the hexadecane solution. Similarly, the water-hexadecane partition coefficient of the solute can be calculated from the change in the solute peak area and the volume of water added. Large Pw,le Systems. We start with a closed system of a dilute solution of a solute in water. In this system, the volume of water is v",mL, the volume of the gas phase is V,, and the total amount of solute is no mol. Because the solute partitions between water and the gas phase, when a sample of vapor is analyzed by GC, a solute peak, whose peak area is denoted A, will be obtained. In principle, this peak area will be proportional to the solute concentration in the gas phase. That is
A = +[solute], (5) where is the response factor of the solute. If the amount of solute in the gas phase is small compared to no,then
+
[solute] ,= no/v",
(6)
Upon substituting eq 6 in eq 3, we get eq 7 and then substitution of 7 into 5 leads to eq 8, where Ao is the solute peak area of the initial aqueous solution. [solute], = no/(VJ,)
(7)
A' = +no/( V&,)
(8)
Now, if we add a known volume of n-hexadecane then the solute will partition into the n-hexadecane phase (the amount being n16). If we still neglect the amount of solute that partitions into the gas phase and assume that K, is independent of the presence of hexadecane, then
no = n, no =
+ n16
solute], + V16[solute]16
solute], + V16~~,16[solute],
(9)
(10)
From eq 10, we get
solute^, = no/(VO,+ v16pw,16) substitution of eq 11 into eqs 3 and 5, leads to
(11)
Af = $no/[(v", v16pw,16)Kwl (12) where Af is the solute peak area after adding n-hexadecane. If we take the ratio of Ao to A', we obtain Ao/Af= 1 + (pw,16/v",)VI6 (13) From eq 13, we can see that the ratio of the solute peak area before and after adding n-hexadecane is linearly proportional to the volume of n-hexadecane ( VI61 added. If we add different volumes of n-hexadecane, and measure the different ratios of AO/Af,and then plot AO/AfvsVIS, the intercept of this plot will be 1 and the slope will be equal to PW,16/v",.From the slope ( S ) and the initial volume of the aqueous solution, the value of p w , 1 6 can be calculated (eq 14).
(14) Clearly, the advantages of this approach are that there is no need to know the concentration of the solute and there is no need to know the response factor ($); i.e., no standards are needed. This makes the method very attractive and analytically very robust. Equation 13 is valid only when the amount of the solute which partitions into the gas phase is small compared to no.
ANALYTICAL CHEMISTRY, VOL. 65, NO. 10, MAY 15, 1993
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For solutes that have large K, values, this assumption is valid. However, for solutes that have small K, values, partitioning into the gas phase is substantial and cannot be neglected. Similar equations can be derived when the amount of the solute that Dartitions into the gas Dhase is taken into account. Before adding any n-hexade
