for a nitrate effect. Weak nitrate complexes have been suggested at low Mo(V1) concentrations (8). Rate Constants. The constant k l was evaluated from a least squares analysis of the data under the conditions shown in Table I where Equation 5 holds. The ratio k2/k--1was likewise calculated under the conditions shown in Table I1 where Equation 6 holds. It was not possible to calculate k2 and k-l independently because the concentration of the intermediate was not known. The use of relaxation techniques to evaluate the faster steps could yield additional information. Average values of 22.03 0.42 1-mole-l-sec-l were obfor k 2 / k L Using tained for k l and 15.38 + 1.09 m0le~-1-~ these values for the rate constants, the reaction rates were calculated from the derived rate law [Equation 41 and compared with the experimental values. The results are shown in Figures 1-3, where the solid lines represent the rates calculated from Equation 4 and the rate constants, and the plotted points represent experimental values. The experimental points show an average deviation of about 5 % from the calculated curves.
*
CONCLUSIONS
The results presented here have several important consequences for analytical chemists utilizing 12-MPA procedures for phosphate determinations. The efFect of acid on the reaction is complex, influencing not only the amount of (8) S. P. Vorob'ev, I. P. Davydov, and I. V. S h i h , Zh. Neorg. Kliim., 12 (S), 2142 (1967).
12-MPA obtained ( I ) but also the rate of its formation. Thus, sample acidity must be carefully controlled, and the reaction progress monitored t o ensure that equilibrium has been reached. For those methods utilizing extraction of 12-MPA into organic solvents (9-12) or reduction of 12-MPA t o phosphomolybdenum blue, these problems are avoided because of the shift of the equilibrium. In addition, the kinetic data show a complex dependence on the Mo(V1) concentration and suggest the possibility of a competing reaction at high phosphate concentrations. Users of 12-MPA procedures should be aware of these complications. Based on the above studies, a new procedure for phosphate utilizing rapid initial reaction-rate measurements in the millisecond range has been developed. This new method can avoid complications due t o unfavorable equilibria and interferences. In addition, automatic phosphate determinations in the ppm range can be made accurately in less than 1 second so that the procedure is excellent for routine and continuous analyses. Details of this new procedure will be presented in a subsequent paper. RECEIVEDfor review May 13, 1968. Accepted August 6, 1968. (9) D. F. Boltz and M. G. Mellon, ANAL.CHEM., 20, 749 (1948). (10) T. Hurford and D. F. Boltz, ibid., 40, 379 (1968). (11) C. H. Lueck and D. F. Boltz, ibid., 30, 183 (1958). (12) W. Kirsten, Microc/zimJ., 12, 307 (1967).
Mechanism and Kinetics of Ion Pair Extraction. Rate of Extraction of Dextromethorphanium Ion Takeru Higuchil and Arthur F. Michaelis Department of Pharmacrwtical Analytical Chemistry, Uniaersity of Kansas, Lawrence, Kan., and School of Pharmacy, Unirjersity of Wisconsin, Madison, Wis. Relationships have been derived showing the dependence of the rates of extraction of ionic species from aqueous to organic phases as ion pairs. If the ratedetermining step or steps in the transfer process are assumed to be of intraphase diffusional nature, the classical Whitman two-film theory leads to an equation relating the flux from one layer to the other in terms of concentrations of the cation and anion, diffusivities of the cation and anion in the aqueous phase and that of the ion pair in the organic phase, and the effective thickness of the two diffusion layers. Experimental observations on a dextromethorphanium system were in agreement with the prediction of the theory.
ALTHOUGH THE TENDENCIES of many cations and anions to be extractable as ion-pairs into organic solvents have seen wide usage for separation and analytical purposes, relatively little attention has been paid to the nature of the basic process or processes which determines the rate of extractive transfer of the species involved. from aqueous t o organic phases or vice versa. We ( I , 2 ) among others (3-7) have reported earlier on the equilibrium behavior of these liquid-liquid systems. The 1 Please address all correspondence related to this paper to Professor T. Higuchi, 314 Malott Hall, Department of Chemistry, The University of Kansas, Lawrence, Kan. 66044.
present communication is concerned with a theoretical analysis of the rate process and results of several experimental studies designed to test its predictions. Although our present concern has been largely directed toward the extractive behavior of a protonated amine, dextromethorphanium ion, from water into chloroformic organic phase, the conclusions developed are probably applicable t o other related systems. The particular drug cation was selected for study because its equilibrium behavior has been SO well characterized ( I ) . A tacit assumption appears to have been made by some investigators that the basic transfer mechanism responsible for extraction from the aqueous to the organic phase of these ionic solutes involved preliminary formation of ion pairs in the water phase followed by transport across the interface (7). (1) T. Higuchi, A. Michaelis, T. Tan, and A. Hurwitz, ANAL. CHEM., 39, 974-9 (1967). (2) T. Higuchi and K. Kato, J. Pharm. Sei., 55, 1080-4 (1966). (3) C. W. Ballard, J. Isaacs, and D. G. W. Scott, J . Pharm. Pharmacol., 6, 971 (1954). (4) R. L. Hull and J. A. Biles, J. Pharm. Sci., 53, 869 (1963). ( 5 ) G. J. Divatia and J. A. Biles, 50, 916 (1961). (6) G. Schill, Acta Pharm. Suecia, 2, 13 (1965). (7) T. D. Doyle and J. Levine, ANAL.CHEM.,39, 1282 (1967). VOL. 40, NO. 13, NOVEMBER 1968
1925
DIRECTION OF MASS TRANSFER CASTIRRED ACUEqS
I I I CM+
I'
I
Coi M'A-
I I I
I I I -I obi D- LIOUID
STIRRED ORGANIC
PHASE
N TERFACE
DISTANCE Figure 1. Idealized diagram of a model ion pair transfer system Schematic diagram of ion pair transfer from aqueous to organic phase, through diffusion layer AXa in the former and A X o in the latter In line with this, Freiser et al. have recently shown that for special cases where inorganic cations capable of forming inner coordination compounds are extracted as ion pairs, the rate limiting step may be the formation of the coordination compound in the aqueous phase (8). Other studies of this type of ion pair extraction have been reviewed by Zolotov (9) and all cases confirmed the findings of Freiser et al. Among systems bearing more directly on the behavior of organic cations, Davies has investigated the rate of extraction of several inorganic and quaternary ammonium cations from water t o nitrobenzene (10). It was suggested as a result of these measurements that the rate limiting step was the transport of the ionic solute across the interfacial barrier, the slow process being one of diffusion of water molecules away from the ions in a selective manner at the interface and resolvation by molecules of the organic solvent. Davies' mechanism may not be strictly applicable to this study since these systems were concerned with extraction under conditions whereby only a limited degree of ion pairing occurred even in the organic phase. It is evident that in these interphase transfer processes, the rate limiting step may depend on the degree of agitation produced at and near the phase boundary. If the effective diffusional layers are relatively thick and the intraphase transport rates are slow, the observed overall rate of solute movement from the aqueous to the organic may be independent of the rate of movement across the boundary itself even though the latter may be significantly slow. In the present communication, we have assumed that this was the case and that for the systems considered the extractive process was taken to be rate limited entirely by the diffusional steps. THEORETICAL CONSIDERATIONS
There are a number of mechanisms which can account for the apparent net diffusional movement of ionic components (8) B. E. McClellan and H. Freiser, ANAL.CHEM., 36, 2262 (1964). (9) Yu.A. Zolotov, Dokl. Akad. Nauk SSSR, 162, 577 (1965). (10) J. T. Davies, J. Phys. Coll. Chem., 54, 185 (1950).
1926
ANALYTICAL CHEMISTRY
from a n aqueous phase, across a phase boundary into a n organic layer. Several possibilities exist even if it is assumed that actual movement across the interface is not rate-determining. For the particular systems of present concern where the cation is a n organic ammonium species, we have in effect the overall forward reaction
+
kt
BHH*O+ AH~o- (BH+A-)orgsnio +
It is possible that this may occur essentially through the mechanism
+
fast
BHE~o+ AH,o-
slow
e(BH+A-)E~oe (BH+A-)organic
the ion pair actually forming in the aqueous phase and subsequently diffusing across the boundary. An alternate possibility is that the diffusion of the components occur largely in their respective unionized form,
+
BHH~o+ HzO
A-
+
eB H ~+ O HD+ 4
Baiganic H20 e HAH,o OH-
4
+
H Aorganic HAorganic
+ Barganio e (BH+A-)organio
If the transfer took place largely through this mechanism, it is evident that the rate will depend largely on the concentration only of the anion or only that of the cation and the diffusivity and the acid-base properties of these species. The rate should show a large dependence on pH. The simplest and, in our view, the most reasonable mechanism for the ion-pair transfer process can be developed on a modification of the classical Whitman's two film theory (11, 12). The usual two-film theory is concerned with dif(11) W. G. Whitman, Chem. Met. Eng., 29, 147 (1923). (12) K. F. GordonandT. K. Sherwood, A.Z.Ch.E.J., 1,129(1955).
fusional transport of a neutral solute across two hypothetical film layers in contact with each other at the interface, the ratedetermining step or steps being the diffusional movements in the immediate neighborhood of the interface and within the two contacting layers. The ion-pair process would be expected t o differ largely from this situation in that in the aqueous phase we are concerned with simultaneous transport of two species, cations and anions. Consider a model system as diagrammed in Figure 1 consisting of a stirred aqueous layer and a stirred organic layer with ions being extracted from the former t o the latter, ion pair formation occurring at the interfacial barrier. Following Whitman as confirmed by Gordon and Sherwood (12), assume that the solute species in the immediate interphasal zone are effectively in equilibrium across the interface and that the rate limiting steps involve diffusional movement effectively across a film thickness AX, in the aqueous layer and AXo in the lipoidal layer both directly adjacent to the interface. On this basis, the overall rate of passage of the ionic species in either direction can be readily derived. The following symbols are used :
K,,
= extraction constant as defined before
- _Pi_
and
- Cildc __ AXo
[C
Pi =
dp
By substituting Equation 4 into Equation 2, we obtain
where
Solving for Ci we have 2Ca
=
-[Ada
- Cdc + W ] dc
= concentration
of cation in bulk aqueous
phase and aqueous interface, respectively A and A i
*
[(Ada
-2+
0)’ +
4%] dc
’”
(6)
Since it is evident that Ci must be positive, only the positive second term need be considered. An excellent approximation for C, can be obtained for cases where A is substantially greater than C or the converse. For C > A Q=-
A Xu
[
Cdc
“+ I w
These equations should describe the rates of forward movement (from aqueous t o organic) if these processes are purely diffusionally controlled as we had assumed in their development. In systems where essentially all of the cation (or the anion) is initially as the ion pair in the organic phase, P cannot be taken to be zero and the diffusional movement will be in the opposite direction. For the reverse flowing system, it can be shown readily that for the case where the anion concentration in the aqueous layer is relatively large and the initial cation concentration in the aqueous layer is essentially zero, the flux of ion pair species from the organic phase would be
e=--
W
AXo (Ada
PdP
- Cdc + W>
the negative sign indicating flow in the opposite direction. w >> AdAthis reduces to
If
And if we consider only the forward rate where P is effectively zero [C
- Cildc -- Pidp _ AXa
AX0
(3)
a completely logical relationship; the indicated rate determining step being in the organic phase. VOL. 40, NO. 13, NOVEMBER 1968
1927
STIRRER SAMPLING TUBE U W R PHASE
e
WATER OUT
WATER ACKET
I
'
4:
J
INERT R P S T l C COVERED MAGNETIC STIRRING BAR
I
LOWER STIRRER (MAGNET)
8
a
ri/
Figure 2. Diagram of extraction cell used in determination of extraction rates
2
ForAdA >> w
This suggests that for this system the rate determining step is the diffusional movement of the released cation from the interface into the aqueous phase. EXPERIMENTAL
With the exception of the procedures used for the determination of the rate of extraction, the experimental equipment, reagents, and procedures have been previously described ( I ) . Essentially all rate studies were carried out with dextromethorphan as the test substance. Procedure for Determination of Rate of Extraction. A schematic diagram of the extraction cell used in these experiments is shown in Figure 2. Each phase was smoothly stirred, separately and in opposite directions, using two DC driven universal motors which powered an overhead stirring bar and a lower magnetic stirring bar. The relative stirring rates were so adjusted as to provide an essentially quiescent interface. Incoming line voltage was passed through a large constant voltage transformer. Frequent determinations of the stirring speeds during the course of all runs showed them to be constant within =t2%. Temperature was maintained by circulating water from a constant temperature bath through the water jacket of the cell. Temperatures within the cell were held constant within 1 0 . 1 degree. The rates of solute transfer were determined in the following manner: aqueous buffer solutions and the organic phase were first mutually saturated with respect to each other and 100 ml of each were placed in the cell. While thermal equilibrium was being reached the stirring speeds of the motors were adjusted to a selected value, nearly all of the runs being carried out at 40 rpm. At the beginning of each run, a definite volume of a solution of the substance to be studied was added by syringe to the appropriate phase after withdrawal of an identical amount of that phase with another syringe. Samples of the other phase were withdrawn by syringe at time of intervals such that at least two half-lives were observed in most cases. At the same time an equal volume of the nonsampled phase was withdrawn in order to maintain a constant volume ratio between the two phases. Infinity values were obtained by withdrawing 5.0-ml samples of each phase after sampling was completed and shaking them in a separatory funnel while immersed in a water bath at the same temperature as the extraction cell until equilibrium was obtained. 1928
ANALYTICAL CHEMISTRY
0
20
40
60
80
100
TIME (MIN.) Figure 3. A typical experimentally observed rate plot for the extraction of dextromethorphan hydrobromide from aqueous to organic phases observed spectrophotometrically, T = 25 "C Concentrations: 5 X 10-4M dextromethorphan, 0.10M NaBr, 0.10M phosphate buffer. Organic phase = 100% CHCL,, stirring rate = 40 rpm Other than those designed to determine pH dependence all runs were carried out with the aqueous phase at pH = 3.00 with 0.10M phosphate buffer. No pH change was observed during or after any run. Potassium sulfate was added to maintain constant ionic strength. The experimental plots were prepared by plotting the logarithm of the absorbance of the infinity sample minus that of the sample as a function of time. Linear plots were obtained over the observed time interval and the observed rate constants were calculated from the slopes. It was necessary to correct the observed values for the reverse process when the latter became appreciable. The forward rate constant, k ) , was taken as the rate constant for the extraction from water to organic phases and the reverse rate constant k,, for the extraction from organic to aqueous phases. Since the distribution ratio, D , is equal to the ratio of the forward to the reverse extraction rate constant, k ) may be expressed as a function of the observed rate of constant and the distribution ratio : kobs
+
k , = ____ 1 1ID Similarly when the reverse extraction was observed :
It is evident that kf,for example, is related to Q,the diffusional flux per unit area by k ) = FQ/C where F is the geometric factor corresponding to the surface area volume ratio (approximately 0.2 cm-l in the present case) and C, the concentration of the extracted species in the aqueous phase.
STIRRING RATE ( R P M )
~
0
Figure 4. Effect of stirring rate on forward extraction rate constant for extraction of dextromethorphan from aqueous to organic phases, T = 25 "C
0.50
1.00
Figure 5. Effect of bromide ion concentration on k, for extraction of dextromethorphan hydrobromide from aqueous to organic phases, T = 25 "C, p =1.09
Concentrations: 5 X 10-4M dextromethorphan, 0.01M NaBr, 0.10M phosphate buffer. Organic phase = 100% CHCL3
Concentrations: 5 X 10-4M dextromethorphan, 0.10M phosphate buffer, K2S04 to maintain ionic strength. Organic phase = 100% CHCL3. Stirring rate = 40 rpm
RESULTS AND DISCUSSIONS
Rate of Extraction and Stirring Rate. Although the experimental setup employed in these studies was relatively unsophisticated, the equipment and the procedure employed gave remarkably consistent and readily reproducible data. Figure 3 shows a typical first order plot obtained from these kinetic measurements. In general the slopes of these lines, corresponding to kobs,were reproducible to roughly 5% for repetitive runs. Usually systems were so selected that the k , term in kobs = kf
+ k,
could be neglected. Where this could not be done, the forward rate constants were corrected by using distribution values. In Figure 4 is shown the observed dependence of k , on the stirring rate. These experimental observations were made using pure chloroform as the organic phase and an aqueous phase having the following concentrations: 5.0 x 10-4M dextromethorphan phosphate, 0.10Msodium bromide, and 0.10M phosphate buffer. The pH of the aqueous phase was 2.10 and the temperature 25.0 "C. Attempts to obtain values of k for stirring speeds greater than 50 RPM led to less reproducible results, the behavior probably being due to disturbances caused by vortex formation at these speeds. The rate constant was essentially independent of dextromethorto 5 X 10-4M. phan concentration from 1 X The linear and direct correlation of the extraction rate with stirring (which would be expected to be inversely related to the effective thicknesses of the diffusional film layers) provides a strong support for the film theory. It is evident that markedly higher rates of stirring which may reduce the effective thickness of the layer by one or two orders of magnitude may lead to interface controlled process but such conditions appear to be difficult to attain in practice. Dependence of Extraction Rate on Anion Concentration and Nature. Distribution ratios of dextromethorphan and other high molecular weight ammonium species between chloroform and water are highly dependent on the concentration and the nature of the anions present (1-7). The rate of forward extraction does not, however, appear to be influenced by these factors. In Figure 5 the experimentally observed forward rate constant for dextromethorphan is shown plotted
against the bromide concentration in the aqueous phase, the data indicating relatively small dependence over 20-fold change in the concentration of the anion. In Table I are listed the observed rate constants for the extraction of dextromethorphan in presence of several anions along with their mobilities. It is evident that the several values of k f are approximately constant although the ionic mobilities vary by as much as 50%. These findings are in agreement with Equation 9. Since in these systems w
