ANALYTICAL CHEMISTRY, VOL. 50, NO. 4 , APRIL 1978
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Two-Phase Buffer Systems: Theoretical Considerations Tomislav J. JanjiC” and Emil B. Milosavljevie Chemical Institute, Faculty of Sciences, University of Belgrade, P.O. Box 550, 1 100 1 Belgrade, Yugoslavia
I n this paper, two-phase buffer systems are described. These systems are made of two phases: one is an aqueous (buffered) phase and the other is a less polar water-insoluble phase which serves only as the reservoir for one of the components of an acid-base pair. I t is established that two-phase buffer systems have the following advantages over classical (monophase) systems: (1) With the same acid-base pair, the pH value at which the buffer capacity has its maximum can be varied with variation of experimental conditions; and (2) Acids and bases which are almost insoluble in water can also be used for preparing two-phase buffers. The extraction mechanism of action of such buffers proposed in the present paper has been experimentally confirmed.
So far, numerous monophase buffer systems have been described in the literature. They consist of an acid-base pair dissolved in a single phase, most frequently water. These buffers have their maximum buffer capacity a t p H = pK,, while their region of practical application ( p > 0.19 C,,,) lies within t h e limits p H = pK, f 1 (I). These limitations considerably hinder t h e selection of suitable acid-base pairs, especially since t h e very chemical nature of a buffer is frequently of decisive importance as regards to its applicability in a given case. For t h e above mentioned reasons, synthesis a n d application of acids with suitable pK, values and other properties, as required for their use in the preparation of buffer solutions, is a problem of constant interest. For some time we have been working on a different approach to this problem. We have been studying buffer systems consisting of two phases: a water (buffered) phase, and another, less polar, water insoluble phase, which serves only as t h e reservoir for one of t h e components of the acid-base pair used. In t h e less polar phase, only the charge-free component of t h e acid-base pair will be present in an appreciable concentration, whereas t h e charge-carrying component is retained in t h e more polar, water phase. So far, few papers dealing with acid-base equilibria in two-phase systems, either liquid-liquid (2-4), liquid-resin exchanger ( 5 ) ,or liquid-solid (6-8), have been published. In these papers, buffer capacity of t h e investigated systems has not been considered. Setnikar (9) has studied acid-base equilibria in systems containing t h e insoluble solid base as t h e second phase, and he has derived t h e functional dependence of buffer capacity on t h e fraction titrated for such systems. T h e time needed for equilibration of these heterogenous systems is long, and the buffer curves are essentially different from those obtained for two-phase buffers described in t h e present paper. Komar ( I O ) has theoretically investigated differential titration of two monoprotic acids in an aqueous-organic solvent system, and he has derived t h e equation for calculating t h e buffer capacity a t t h e p H value corresponding to t h e first equivalence point. On the basis of this equation, the possibility of such titrations is considered. As can be seen from the foregoing, two-phase buffer systems proposed in the present paper have not been described in the literature as yet. This paper offers theoretical considerations 0003-2700/78/0350-0597$01 .OO/O
of such buffers and points t o some of their advantages over classical (monophase) buffer systems.
MATHEMATICAL CONSIDERATIONS In deriving the relationships given below, it is assumed that the ionic strength of the solution is equal to zero, since in this case it may be written that: p H = -log CH. Depending on whether t h e acid or base component of t h e acid-base pair is a nonelectrolyte, a distinction must be made between two types of two-phase buffer systems, t h e mathematical treatment of each differing somewhat. Buffer T y p e I (Molecular Acid/Anionic Base). For this type of buffer, t h e following relationship holds:
where K2PP is the apparent acid dissociation constant, CH is t h e concentration of hydronium ions in t h e water phase, Cb is the concentration of t h e anionic base in the water phase, and C Z P P is the apparent concentration of nonprotolyzed acid in the water layer. T h e apparent concentration of a component in the water phase is the concentration that would exist if the total amount of t h a t component, in t h e entire system, were dissolved in t h e water phase alone. From t h e mass balance equation it follows t h a t
where CrotaPP is t h e apparent total concentration of t h e acid-base pair. Substituting in Equation 1 Cto;PP - Cb for C 2 P P and solving for Cb, we obtain
(3) Differentiation, dCb/dCH, of Equation 3 and substitution of dCH with -2.303 CH d p H , gives t h e following relationship for buffer capacity (&b):
(4) Substituting in Equation 1 CtotaPP - CaaPP for Cb and solving t h e resulting equation for CaaPP we get
(5) Multiplying Equation 3 by Equation 5 and dividing the product by CtO;PP we obtain
From Equations 4 and 6, we arrive a t t h e relationship
PHb
=
2.303
CaappCb
GotaPP 1978 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 50, NO. 4 , APRIL 1978
For two-phase buffers containing a molecular acid t h e following relationship applies:
where C, is t h e concentration of nonprotolyzed acid in t h e water phase, V,, and V , are t h e equilibrium volumes of t h e organic and water phase, respectively, and (Kp)ais t h e ratio of the concentration of the molecular acid in the organic phase t o t h a t in t h e water phase (partition coefficient). From Equations 1 a n d 8 it follows t h a t t h e apparent acid dissociation constant (K2PP) and acid dissociation constant, defined as K, = (CHCb)/Ca, are interrelated by the following equation:
s(Kp)a
+1
vw
Taking t h e logarithm of t h e equation obtained, and multiplying it by -1, we get
pKaapp = pKa - p (L(Kp)a
+ 1)
vw
B u f f e r Type I1 (Cationic A c i d / M o l e c u l a r Base). For this type of buffer, t h e following relationship holds:
where C, is t h e concentration of cationic acid in t h e water phase, a n d Chap' is t h e apparent concentration of nonprotolyzed base in t h e water layer. Further mathematical treatment, analogous to t h a t for two-phase buffers of type I, gives t h e following equations:
where (Kp)bis t h e partition coefficient of the molecular base between t h e organic solvent and water. DISCUSSION Equations 4 and 12 are analogous with the corresponding equation for monophase buffer systems which reads:
where C,, is t h e total concentration of the acid-base pair. I t follows that t h e graphic representation of t h e function P H b = f ( p H ) will be also analogous for both monophase and two-phase buffer systems. This plot for two-phase buffer systems has its maximum value, &bmaX = 0.58 Cto?PP (for monophase buffers, j3HbmaX = 0.58 Ctot). Equation 7 shows that for two-phase buffers of type I, maximum buffer capacity will be attained when CaaPP = Cb, because t h e right-hand side of Equation 7 then reaches its maximum possible value. Likewise, from Equation 13, it may be seen that for two-phase buffers of type 11, maximum buffer capacity will be attained when CbaPP= C., Furthermore, from Equations 1 a n d 11, i t is derived t h a t maximum buffer ca-
pacity for two-phase buffers, irrespective of the type to which they belong, will be at:
From t h e acid dissociation constant, phase volumes and partition coefficient of the molecular acid or base, it is possible, by Equation 10 or 14, to calculate t h e apparent acid dissociation constant and thereby also the p H value a t which the buffer capacity will attain a maximum. I t may be seen from Equations 10 and 14 t h a t as t h e volume of the organic phase increases relative to t h a t of t h e water phase, a n d / o r as the partition coefficient increases, the pH value at which the buffer capacity reaches its maximum in buffers of type I shifts to higher p H values, whereas in buffers of type I1 it shifts to lower p H values. Here it should he stressed t h a t t h e very nature of two-phase buffers implies t h a t t h e water phase will be saturated with t h e organic solvent. Therefore, strictly speaking, measurement on a p H meter calibrated with a standard buffer solution in water gives pH(R) values (1 I). T h e mathematical treatment in question as well as the conclusions drawn from it, are completely valid only in the limiting case:
lim pH(R) = pH (concentration o f organic solvent in water)
+
0
For two-phase buffers where the fulfillment of this condition is approached, t h e obtained p H ( R ) values correspond fairly closely to the operationally defined p H values in water. If this is not t h e case, these systems should be considered as two-phase buffers with individual p H ( R ) scales. This, however, does not mean t h a t such two-phase buffers are unusable in practice. T h e mathematical treatment given in this paper is valid only in the simple case when the partition of the molecular component of the acid-base pair is not complicated by secondary reactions. If this is not the case (for example, if appreciable dimerization of the molecular acid occurs in the organic phase), a functional dependence of pm on pH different from the one given by Equations 4 and 1 2 should he expected. A different functional dependence should also be expected if extraction of ion-pairs, containing as one of the constituents anionic base (buffers of type I) or cationic acid (buffers of type 11), occurs in a significant amount. In t h a t case, the assumption t h a t t h e total amount of t h e charge carrying component of the acid-base pair remains in the water phase is not valid. EXPERIMENTAL CONFIRMATIONS As is seen from mathematical considerations of two-phase buffer systems, we have assumed an extraction mechanism of action for such buffers. To prove the validity of the mechanism proposed we prepared a series of two-phase buffers by mixing 40.00 mL of 0.0975M n-caproic acid in l-octanol (the solubility of l-octanol in water is 0.007 mol 70 at 25 O C ( 1 2 ) ) ,(40.00 - A ) mL of water and A mL of a standard sodium hydroxide solution. Prior to determination of the acid and base concentrations in the water phase and the acid concentration in the organic phase, we established that the pH values measured in emulsions of the well stirred two-phase buffers agreed, within the limits of experimental error, with pH values of the separated water layer of the buffer (a Radiometer PHM 62 pH meter with glass-calomel electrode assembly was used for measuring the pH values). The acid and base concentrations in the aqueous phase were determined by potentiometric titrations with standard sodium hydroxide or hydrochloric acid solution. The acid concentrations in the organic phase were determined by taking the water-emulgated aliquots of the organic phase and titrating them with standard sodium hydroxide solution. On the basis of good accordance between the analytically found concentration of anionic base and the concentration of sodium hydroxide solution added to achieve partial neutralization of the acid, it may be concluded that extraction of ion pairs containing
ANALYTICAL CHEMISTRY, VOL. 50, NO. 4 , APRIL 1978
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1 r
*-*.-.-+-, e
aP
9
Figure 1. Buffer capacity as a function of the pH value of the solution for a two-phase buffer made up of 20.00 mL of 0.1000 M n-caproic acid in I-octanol and 20.00 mL of water. Values determined experimentally are denoted by circles. Values calculated by Equation 4, using the mean pKaaPP value (6.90)from Table I, are represented by
the unbroken line. The pH value corresponding to the maximurn buffer capacity of the monophase buffer in water is indicated by an arrow. All data are valid for I = 0 and t = 25 f 0.1 OC the n-caproic anion does not occur in a significant amount. The results obtained are summarized in Table I, from which it can be seen that there is high agreement between the measured p H values and those calculated from the acid and base concentrations found in the water layer. In order that the value of pK;PP (which corresponds to the pH value at the maximum buffer capacity of the two-phase buffer) may be calculated from the results of the determinations presented above (Table I), it is necessary to know the equilibrium volumes of the phases. They can be calculated by the following equation:
&tot - V N a O H M N a O H
where 6 is the increase in the organic phase volume, or the decrease in the water phase volume relative to the initial volumes of the phases, Tois the amount of acid in the organic phase aliquot, V," is the volume of the titrated organic phase aliquot, T , is the amount of acid in the water layer aliquot, Vwtis the volume of the titrated water aliquot, V,' and V,' are the initial volumes of the organic and water phase, respectively, Qmt is the total amount of acid, VNaoH is the volume, and MyaoH is the molarity of the sodium hydroxide solution used for the preparation of the two-phase buffer (all the amounts are in moles, all the volumes are in liters). In the given experiments, no appreciable change in the total volume of the two phases has been observed, which represents the condition of applicability of Equation 17 for the calculation of the equilibrium phase volumes. The dependence of buffer capacity on the p H value of the two-phase buffer investigated was determined by an analysis of the corresponding titration curve with the necessary corrections made for the salt effect and for the change in solution volume during titration. The time needed for establishing equilibrium in vigorously stirred two-phase buffers is short, and p H values could be measured almost immediately after the addition of a strong acid or base to the buffer. The results of the experimental determination of the functional dependence of aHbon pH are presented in Figure 1. From Figure 1, it may be seen that the values of the function i j H b = f(pH) determined experimentally are in good agreement with those calculated theoretically by Equation 4. It may also be noticed that there is very high agreement between the experimentally determined pH value corresponding to the maximum value of 3 ~ , (pH 6.89) and the pKaappvalues calculated by Equation 10 (see Table I). Finally, from Figure 1. it may be seen that the point
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ANALYTICAL CHEMISTRY, VOL. 50, NO. 4, APRIL 1978
Table 11. Most Important Characteristics of Some Two-Phase Buffersa
Acid (base) used
PK, (Ref.)
Buffer type
pH value corresponding to oHbrnax for two-phase buffer, pKaaPP
Shift in pH units, pKaaPP-- pKa
Benzoic p-Nitrophenol n-Hexylamine A'J-Diethylaniline
4.20 (15) 1 6.12 1.92 7.15 ( 1 6 ) I 9.13 1.98 10.64 ( 1 7 ) I1 5.55 --2.09 6.61 (18) I1 3.52 -3.09 (at 22 "C) a The systems investigated were prepared by mixing 20.00 m L of 0.1000 M solution of t h e molecular acid (base) in 1-octanol and 20.00 m L of water. The systems were titrated with a standard sodium hydroxide (hydrochloric acid) solution. If n o t otherwise stated, all data are valid for Z = 0 and t = 25 "C.
_______
of maximum buffer capacity of the two-phase buffer under consideration has shifted by about 2 p H units with respect to a corresponding monophase buffer in water, since the thermodynamic pK, value for n-caproic acid at 25 "C is 4.88 (13). In Table 11, the most important characteristics of some other two-phase buffer systems of type I and I1 are presented. In ail investigated tivo-phase buffer systems with 1-octanolas the organic phase, the functional dependence P H b = f(pH) agrees well with the equations derived in this paper. It may be concluded from the foregoing that the experimental evidence completely confirms the validity of the conclusions to which we arrived on the basis of our mathematical considerations of such simple systems. In the course of our investigations of two-phase buffers of type I, we encountered cases when the functional dependence of &b on p H did not agree with Equation 4. This was the case with twephase buffer systems containing n-caproic acid and the solvent pair toluene/water or cyclohexane/water. In both of these systems, buffer curves &b = f(pH) were higher (&bmaX > 0.58 C,WP) and asymmetrical (the right-hand side sloping more steeply than the left-hand side of the curve). Mathematically it can be proved that such buffer curves should be expected in cases of appreciable dimerization of the molecular acid in the organic phase.
EFFECT OF DILUTION ON pH,VALUES OF TWO-PHASE BUFFERS In addition to the factors cited in the literature which induce a change in p H value with dilution of monophase buffers (14), t h e following factors a r e of significance in two-phase buffer systems: (1) Shift of Distribution Equilibrium. On a twofold dilution of t h e water layer of a two-phase buffer t h e concentration of t h e ionic component of t h e acid-base pair reduces to nearly one half of t h e original value, whereas t h e concentration of t h e molecular component, in the cases where
decreases only negligibly. This brings about a change in p H value of t h e water layer of about 0.3 p H unit, t h e shift in buffers of type I being to lower pH values and in those of type I1 to higher ones. (2) Decrease in Equilibrium Volume of Organic Phase Due to Dissolution of Organic Solvent in Water. T h i s factor induces a change in t h e p H value of t h e water layer in t h e same direction as a shift in t h e distribution equilibrium does. In the case of organic solvent with a very low solubility in water and if V,/ V , ratio is not too low, it seems t h a t t h e effect of this factor on p H value, after a twofold dilution of t h e water layer of two-phase buffer, is considerably smaller t h a n t h a t of factor 1. It follows t h a t two-phase buffers are very sensitive to dilution of the aqueous phase only. On dilution of both phases such t h a t their ratio remains unchanged, it may be expected for factors 1 and 2 to have no effect. This is confirmed by
_-
Table III. Effect of Dilution on p H Values of Two-Phase Buffers" pH value ___-___
Total acid neutralized, 7%
25 50
75
of the buffer
6.34 6.85 7.35
of the buffer after 15.00 m L of the of water buffer after and 15.00 15.00 m L mL of 1of water octanol were addedb were added 6.00
6.52 7.02
6.31 6.82 7.33
a The systems investigated were prepared by mixing 15.00 m L of 0.1041 M n-caproic acid in 1-octanol, (15.00 - B ) mL of water and B mL of a standard sodium The difference behydroxide solution, t = 25 F 0.1 C. tween the initial and equilibrium phase volumes is less than 3.5%.
experimental investigation of the effect of dilution on p H values in such buffers (Table 111).
CONCLUSION I t may be concluded that for two-phase buffer systems, the pH value a t which t h e buffer capacity has its maximum can be varied by changing t h e ratio of the phase volumes as well as by choosing a n appropriate organic phase. Investigations of new two-phase buffer systems a n d their applicability in analytical chemistry are in progress.
LITERATURE CITED R. G. Bates, "Determination of pH; Theory and Practice", 2nd ed., Wiley-Interscience, New York, N.Y., 1973, p 128. J. A . Christensen, Acta Cbem. Scand., 16, 2363 (1962). D. Ratajewics and Z. Ratajewics, Chem. Anal. (Warsaw), 16, 1299 (1971). D. Dyrssen, Sven. Kem. Tidskr., 64, 213 (1952). F. F. Cantwell and D. J. Pietrzyk, Anal. Cbem., 46, 344 (1974). C. F. Hiskey and F. F. Cantwell. J . Pbarm. Sci., 57, 2105 (1968). D. Ratajewics and Z. Ratajewics, Cbem. Anal. (Warsaw), 16,913 (1971). A . E. Mans and G. J. Vervelde, Recl. Trav. Cblm. Pays-Bas, 71, 977 (1952). 1. Setnikar, J . Pbarm. Sci., 5 5 , 1190 (1966). N. P. Komar, Zavw'. Lab., 34, 513 (1968). D. D. Perrin and B. Dempsey, "Buffers for pH and Metal Ion Control", Chapman and Hall, London, 1974, p 79. G. L. Dorough, H. B. Glass, T. L. Gresham, G. B. Malone. and E. E. Reid, J . Am. Chem. Soc., 63. 3100 (1941). J. F. J. Dippy, J . Chem. SOC., 1222 (1938). R. G. Bates, Anal. Chem.. 26, 871 (1954). F G. Brockman and M. Kilpatric, J . Am. Chem. SOC..56, 1483 (1934). R. A . Robinson and A . J. Biggs, Trans. faraday SOC.,51, 901 (1955). C. W . Hoerr, M. R. McCorkle and A. W. Ralston, J . Am. Cbem. SOC., 65, 328 (1943). H. F. Hall and M. R. Sprinkle, J . A m . Cbem. Soc., 54, 3469 (1932).
R F X ~ ~ I Vfor E I review I May 17, 1977. Accepted December 12, 1977. T h i s work was presented in p a r t a t t h e 20th Annual Meeting of the Serbian Chemical Society, Belgrade, January 17, 1977. T h e authors are grateful to t h e Serbian Republic Research F u n d for financial support.
