Role of Solvent Extraction Parameters in Governing the Potential Selectivity of Liquid Membrane Electrodes Stig Back Department of Analytical Pharmaceutical Chemistry, University of Uppsala. Uppsala, Sweden
John Sandblom Department of Physiology and Medical Biophysics, University of Uppsala, Uppsala, Sweden
The relationship between solvent extraction parameters and the potential selectivity of liquid membranes has been examined. An expression for the electrode potential has been derived containing measurable solvent extraction parameters. This expression is used to compare the potential selectivity of a liquid membrane-consisting of tetraalkylammonium salts dissolved in methylene chloride-with the solvent extraction properties of the same system. The potential selectivity constant is related to the extraction constant by a square root dependence which is interpreted in terms of surface diffusion phenomena. The pH-dependence of the electrode potential in the presence of weak acids as well as the role of solvent is also examined. It is concluded that extraction processes determine the potential selectivity of liquid membranes if the extraction constants are sufficiently large and if the solvent favors the counter ions.
The potential selectivity of liquid membrane electrodes is largely dependent on the chemical binding properties of the membrane solubilized extractant, a factor which is usually recognized as the important parameter in the choice of a system for a desired ion selective electrode. These binding properties can be expressed in terms of extraction constants which may then be related to the potential selectivity of the liquid membrane. Such relationships have been examined for a number of systems during the past few years ( 1 - 5 ) . Most often the problem has been approached by assuming that the process which determines the potential response is a straight-forward ion exchange reaction, such as:
A+
+ BX * AX + B+
where X is the ion exchanger and A+ and B+ are exchanging counter ions. A thermodynamic derivation of the boundary potentials based on such an ion exchange equilibrium leads to the Eisenman equation (6):
where n is a constant which takes into account the nonideal behavior of the exchanger. This ion exchange ap-
(1)
(2) (3) (4) (5) (6)
K. Sollner. in "Diffusion Processes," Proceedings of the Thomas Graham Memorial Symposium, University of Strathclyde, Vol. 2 J. Sherwood. A . Chadwick. N. Muir, and F. Swinton, Ed. Gordon and Breach, London. New York, and Paris, 1971, p 121 C. J. Coetzee and H. Freiser,Ana/. Chem., 40, 2071 (1968). t i . James, G . Carmack. and H. Freiser. Anal. Chem.. 44, 853 (1972). M. Whitfield and J. V . Leyendekkers. Ana/. Chem.. 42, 444 (1970). P. R. Danes!. F. Salvemini. G. Scibona. and 8. Scuppa, J. Phys. Chem.. 75, 554 (1971) G. Eisenman. Btophys. J . , 2. Part 2. 259 (1962)
1680
proach has been used to characterize the potential selectivity, expressed in terms of Ki,, of many liquid membrane systems (3, 7, 8), but it neglects the fact that the sites are mobile. A more detailed theory of mobile site membranes which includes different modes of transport-if., ion pairs and free ions in the membrane-was developed by Sandblom, Eisenman, and Walker (9) and has also been tested experimentally (5, 20-12). This theory gives a detailed account of the properties associated with mobile sites, but it does not consider all possible modes of transport or side reactions which might occur in liquid membranes containing solvent extractants. In this paper we have therefore taken a somewhat more general approach in order to explain the properties of certain experimental systems. This approach considers the possible side reactions included in the extraction process. We have chosen to study the potential selectivity of a system which has already been thoroughly characterized with respect to its extraction properties including various forms of side reactions. The primary purpose of the investigation has been to establish a quantitative relationship between the extraction constants defined from Equation 6 and the potential selectivity constants defined from Equation 2. The experimental system consists of the salts of quartemary alkyl ammonium ions which have been extracted from aqueous solutions into methylene chloride. The solvent extraction parameters of this system have been studied and described in a number of papers by Schill and coworkers (13-18). By comparing extraction parameters with the potential response of electrodes containing the corresponding extraction systems, we have attempted to deduce the mechanism of potential select,ivity.
THEORY The electrical potential across a membrane is always the result of a distribution and/or transport of electrical charges. In a liquid membrane of low dielectric constant, the number of free ions is very small compared to the number of ion pairs. It is this factor which makes it difficult to state the proper conditions on which to build a theory and which renders most theories of liquid membranes limited in their applications. (7) M . Whitfield and J. V 1.eyendekkers. Anal. Chim Acta. 46, 63 (1969). (8) K. Srinivasan and G. Rechnitz. Anal. Chem.. 41, 1203 (1969). (9) J. Sandblom. G. Eisenman, and J. Walker. J. Phys. Chem., 71, 3862 (1967). (10) J. Walker, G. Eisenman. and J. Sandblom. J . Phys. Chem.. 72, 978 (1968). (11) G. Eisenman.AnaL Chem., 40,310 (1968). (12) J, Sandb1om.J. Phys. Chem.. 73, 257 (1969). (13) G. Schiil. Sv. Kem. Tidskr.. 80. 10 (1968) (14) K . Gustavii and G. Schiil, Acta Pharm. Suecica. 3, 241 (1966) (15) K.Gustavii and G. Schill. Acta Pharm. Suecica. 3, 259 (1966). (16) R. Modin and G. Schill. Acta Pharm. Suecica, 4 , 301 (1967). (17) R. Modin, Acta Pharm. Suecica. 8, 509 (1971). (18) R . Modin and A . Tilly, Acra Pharm. Suecica. 5 , 31 1 (1968).
A N A L Y T I C A L CHEMISTRY, V O L . 45, NO. 9, A U G U S T 1973
In the following, however, we shall limit ourselves to three assumptions which are likely to be fulfilled in most liquid membrane systems used for electrode purposesnamely, 1) chemical equilibrium across the membrane interfaces, 2) the sites (extractant) are completely confined to the membrane (organic)phase, and 3) co-ion exclusion. The first assumption allows us to use the formalism of solvent extraction chemistry and in our treatment we have adopted the notations of Schill (13). The extraction constant defined from equilibrium conditions is given by:
(3) where QX is the concentration of ion pairs in the organic phase and Q, X are the concentrations of the extractant Q and the counter ion X in the aqueous phase. However, an extraction process gives rise not only to ion pairs but to many other reaction products as well. In order to take into account the various types of side reactions in the organic phase, we shall introduce them as different modes of transport of the extractant Q. The total amount of Q which is transported in combination with the counter and is equal to the sum of all the ion X is called products formed in the organic phase as a result of Q reacting with X.
m,
= BQ-forms
~
“QX
Qx
-
)I organic
P ~ ’=
Til(())
d phase solution (”) F,(d) = E l ’ ’
I/
(9)
where (0) and (d) refer to the two sides of the organic phase and where the prime and double prime refer to the adjacent aqueous phases. Introducing the chemical potential p i g of the ion pairs, we get by adding and subtracting the electrochemical potential FQ in Equations 9:
jiI(O) = Cc,,(O)
- &(O>
=
E,’
=
RT In X,’ ,GI(& = p,Q(d)
- &(d)
=
E,’’
=
RT In X,”
+ z,F+‘ + z,F+”
(loa) (lob)
Subtracting Equation 10a from Equation 10b gives an expression for the total membrane potential E = $“ - $’:
RT Q X , ( d ) XI‘ z , E = - In -F QX,(O)
x,”
(11)
where zi is the valence of the counter ions. EQ is the difference in electrochemical potential of the Q ions at the two boundaries and is equal to the sum of the diffusion potential Ediff and the chemical potential difference of the Q ions in the organic phase at the two boundaries. Therefore:
(4)
Some examples of these so-called side reactions which may affect the transport properties of the membrane are a) adduct formation, b) polymerization, and c) dissociation. Each product is transported through the membrane separately, which means that every side reaction gives rise to a particular mode of transport. This permits a direct translation of the transport properties of the membrane in terms of side reactions taking place in the organic phase. The relationship between the total amount of extractant in the organic phase and the concentration of ion pairs is usually expressed in terms of the so called a coefficient defined by Equation 5
Qx =
0
solution (’)
Finally we use assumption number 2 which states that the sites are confined to the membrane phase and unable to flow through the system. According to this assumption and neglecting mobility differences between the complexes, the total concentration of sites CQ must be uniformly distributed in the membrane phase in the stationary state, or:
(13) If we now insert Equations 5, 6, 8, and 13 into Equation 11, we get the desired expression for the electrode poten-
tial: (5)
( Y Q X is either larger than or equal to unity and is equal to unity only when no side reactions take place in the organic phase. Examples of practical measurements of a are found in Refs (13-1 7). The conditional extraction coefficient, E Q ~is ,now given by:
For two ions (i,j) competing for the extractant Q, Equation 6 can be written as:
in close analogy with an ion exchange reaction described by Equation 1. Rearranging Equation 7 gives:
The assumption of chemical equilibrium also allows us to write equilibrium conditions for an ion in terms of its electrochemical potential i i i at the interfaces:
Note that the conditional extraction constants entering the equation are not thermodynamic constants but depend in general on solution conditions. They can be evaluated, however, by calculating the a coefficients corresponding to the particular solution conditions at the two sides of the membrane. In order to evaluate the last term in Equation 14, a knowledge of ion mobilities, dissociation constants, and partition coefficients is needed. In the treatment of Sandblom et al. (9), an explicit evaluation of EQ was made which led to a rather complicated expression. Sandblom and Orme (19) also discussed this term and gave several examples of when it can become important. In the system .to be described, however, the conditions are such that EQ can be neglected. Since the counter ion mobilities in the organic phase are nearly equal, the expression for EQ,Equation 12, reduces to:
(19) J. Sandblom and F. Orme in “Membranes, A Series of Advances, Vol. I, G. Eisenman, Ed.. Marcel Dekker. New York. N . V . . 1972.
A N A L Y T I C A L C H E M I S T R Y , V O L . 45, NO. 9 , A U G U S T 1973
1681
It is seen from the table that low extraction constants correspond to slopes which deviate significantly from the theoretical slope. This is probably due to the fact that diffusion of extractant into the aqueous phases will tend to diminish the selectivity. In systems with extraction constants above 4, the slopes are seen to be approximately theoretical and only the hexylammonium ion pairs fulfill this criterion for all the tested ions. Since longer chains will slow down the extraction process, the hexylammonium ion was chosen to be the most suitable extractant for the remainder of the experiments. Selectivity Ratios. A schematic representation of the complete cell in the following experiments is given as follows.
Table I. Potential Slope in mV per Tenfold Change in Concentration in the Range 10-1M-10-3M.a Tetrapentyl Tetrahexyl Tetrabutyl ammonium ammonium ammonium
Chloride slope, log E Q C l
10 rnV -0 46
20 mV 2 18
54 rnV
Perchlorate slope,
45 rnV 58 rnV 50 rnV log E Q C 1 0 4 4 64 a T h e membrane contained 0, 1 M RINCIOl in all of the experiments
I1M NaCl Ag; AgCl equilibrated with m e m b r a n e phase
0.1M TeHexPi
reference
~
Using the additional conditions that the nonextractable co-ions are excluded from the organic phase (assumption 3) and that the dissociation constants in this particular case are equal [see Ref. (13)], we deduce that Q(d) = Q(0). Therefore the logarithmic term in Equation 15 will vanish. The equation for the membrane potential applicable to our system may therefore be written:
It is seen from this equation that the a coefficients enter formally as activity coefficients and therefore incorporate all side reactions-Le., all transport forms.
Defining a potential selectivity coefficient K,, as:
EXPERIMENTAL The system chosen for the experiments consisted of a 0.1M solution of tetraalkylammonium salt in methylene chloride. When used as a membrane between aqueous solutions, this system becomes selective to anions. Methylene chloride has the advantage of being negligibly miscible with water but it evaporates rapidly a t room temperature. The tetraalkylammonium salt in methylene chloride was used as the organic phase in a conventional liquid membrane electrode obtained from Orion Research Inc. (nitrate electrode No. 92-07). The tip of the electrode was immersed in an aqueous solution during the filling procedure to avoid evaporation of organic material from the electrode tip. As internal aqueous solution we used 1M NaCl equilibrated with the organic phase. Electrical contact with the external solution was accomplished with a calomel reference electrode. The potential measurements were made with a Corning pH meter (Model 12) and the values were recorded on a Yokogawa (YEW No 3046) strip chart recorder. The external solutions were vigorously stirred with a magnetic stirrer and were maintained at room temperature.
RESULTS Slope us. Extraction Coefficients. The potential response to different anions was measured for alkylammonium ions of increasing chain length. The results of dilution experiments with an organic phase consisting of 0.1M solutions of tetraalkylammoniumperchlorate are summarized in Table I. In the same table are also indicated the corresponding extraction constants. 1682
ANALYTICAL CHEMISTRY, VOL.
The picrate ion was now used as the counter ion in the organic phase, having the highest affinity for the exchanger of all the tested ions. This ensured a minimum loss of exchanger to the aqueous phases. Using this cell as liquid membrane electrode, the selectivity of a series of anions was measured. The results are shown in Figure 1. The electrode potential is plotted as a function of the ion concentration in solution. The solid lines represent theoretical slopes drawn through the points a t 10-2M concentration. The range in which the electrode responds with a theoretical slope is seen to extend approximately from 10-1 to lO-3M and the points a t 10-2M were therefore used in calculating the selectivities. Approximating the activity coefficients with unity a t 10-2M, the vertical distance between two lines represents a potential which, according to Equation 16, is given by:
In K , ,
=
FE,,/RT
(18)
the calculated values of K,, can be compared with the corresponding extraction constants. Using the chloride ion as a reference in calculating the potential selectivity constants, the values of log Kxcl can be related to the extraction constants. In Figure 2, the values of log Kxcl are . that the extraction conplotted against log E Q ~Note stants refer to tetrabutylammonium salts but since the ratios of extraction constants are independent of chain ~ tetrahexylammolength (Is),the values of log E Q for nium salts are the same as those for tetrabutylammonium salts except for an additive constant. It is clearly seen from the figure that the potential selectivity increases with the extraction constant as predicted by the theory, Equation 18. The best fit to the data, however, is a straight line with a slope, approximately equal to Ih. This means that, empirically, the potential selectivity constant K,, and the ratio of extraction constants are related by the following power law: (19) A comparison between Equations 17 and 19 would then indicate that increasing extraction coefficients are accompanied by decreasing a coefficients. This has not been
45, NO. 9, A U G U S T 1973
Ag ; AgCl
TeHexPi 11 NaX 11 reference electrode I 1M NaCl I( 0.1MCHZC,2
mV
t
/
*
r N o r i d y r n i d e
t +5 t
I
0
salicylate
log
EQX
(TEA1
Figure 2. Log Kxcl for membranes containing tetrahexylammonium picrate are plotted vs. log EQX for tetrabutylammonium salts. The values of Kxcl are calculated from the curves in Figures 1 and 4 organic phase
Figure 1. The potential plotted vs. log C for a series of anions. T h e solid lines are theoretical slopes drawn through the points confirmed by extraction experiments but some of the lesser extracted substances such as hydroxyl ions and phenol have large a coefficients (18). Another explanation which seems more reasonable, however, can be found in the nature of the surfaces. In liquid membranes as opposed to solid membranes, the diffusion coefficients in the two phases have equal orders of magnitude and this affects the ion exchange processes at the boundaries. The situation is shown in Figure 3. There will always be stagnant layers adjacent to the interfaces, in which an interdiffusion of species takes place. This will bring about an alteration of the ion distribution of exchanging ions across the boundaries so that the actual distribution will no longer represent that of an equilibrium situation. We can incorporate this effect into our theoretical formalism by a correction of the a coefficients. Considering that an a coefficient is defined as the ratio between and QX [see Equation 51, and that in the biionic case Q T is equal to Cg, the effective a coefficient entering Equation 16 is obtained by calculating the ratio between CQand QX. Referring to Figure 3 the ratio between C g and QX is obtained from the following four equations
Qx+ QX Pi
-
+-X
=
CQ CY
=
(20) (21)
(22)
Equations 20 and 21 state that the total concentration of species in the two phases is uniform in each surface layer (no transport of sites and co-ions across the boundaries).
w
aqueous phase
Figure 3. The membrane boundary between organic and aqueous phases with adjacent surface layers. The concentration profiles and the concentrations at different points are indicated in the figure Equation 22 describes the equilibrium condition a t the boundary. Equation 23 expresses the continuity of flow of picrate across the boundary. However, the permeability of the is not necessarily a picrate ions in the aqueous phase, Pay, constant but depends in general on the solution conditions, and on surface potentials. Combining Equations 20-23 and setting = CQ and X z CX we get the following expression for the desired ratio:
We see that if Po,, is much less than Paq,as it would be in a solid membrane, the ratio approaches unity. If, on the other hand, the two permeabilities are approximately is much larger than E Q ~the , ratio beequal and if E= comes inversely proportional to d%. This limit satisfies Equation 19. The relationship expressed by Equation 19 implies that the electrode potential is subject to a partial loss of the selectivity inherent in the solvent extraction process. This has some practical consequences for the functioning of an electrode-namely, with respect to interfering ions. The usefulness of an ion selective electrode depends on the degree of interference of other ions and we have shown that the degree of interference (the inverse of selectivity) is larger in a potential measurement than in a solvent extraction measurement. Titration of Acids. Several of the anions included in Figure 2 are salts of weak acids. It was therefore of inter-
ANALYTICAL CHEMISTRY, VOL. 45, NO. 9, A U G U S T 1973 * 1683
n
series of organic acids and the electrode is seen to function as an ideal indicator for several of the anions where the points fall on theoretical slopes. In two cases, however, namely those of nitrophenol and phenol, the curves are seen to deviate from ideal behavior. This could possibly be due to adduct formation in the organic phase between acid and alkylammonium salt and which could make the 01 coefficients pH-dependent (17). In the case of phenol, however, the surface effect may again account for the observed departure from the expected behavior since phenol has a high pK value. At a low pH the picrate ions are the dominant ions in the surface layers and the potential is independent of phenol concentration. At higher pH values the phenolate ions begin to have an effect and the titration curve rises more steeply than the theoretical slope. The electrode can therefore be used as a very sensitive indicator for phenol titration if this effect is utilized. Role of Solvent. As organic phase in a liquid membrane electrode selective to anions, methylene chloride has the advantage of being a hydrogen bonding (protic) solvent which therefore favors anions. It will consequently contribute to the exclusion of co-ions from the membrane, in this case the cations in solution. For discussion of the role of solvent, see Ref. (19). In order to examine the importance of the solvent, the electrode properties of methyl isobutyl ketone (MIBK) was tested. This is an equally good solvent for ion pair extraction with alkylammonium ions but its oxygens will tend to favor cations rather than anions. The experiments described with methylene chloride were therefore repeated with MIBK as a solvent. As expected, the potential selectivity as well as the potential slopes practically disappeared in this case. It is concluded from these experiments that a suitable solvent is important for the proper functioning of a liquid membrane electrode as well as a highly extractable and selective ligand.
Ag ; AgCl
+zoo \
+150
+loo
L
PK
I 1.\hydroxy
b-
benzoic a{id
+ 50
\
\
\
0 pK
- 50
\
be
>-,
Figure 4. The membrane potential vs. pH for a series of weak organic acids
est to examine the pH-dependence of the electrode potential measured in these acids. A 10-2M solution of the acid was equilibrated with a 10-1M solution of the corresponding tetrahexylammonium salt dissolved in methylene chloride. An equilibrium distribution of tetrahexylammonium ions between organic and aqueous phases was thereby accomplished. The electrode was immersed in the acid and the potential was measured as the acid was titrated by adding sodium hydroxide. Figure 4 shows the titration curves for a
Received for review December 4, 1972. Accepted February 12, 1973.
Ionic Hydration and Single Ionic Activities in Mixtures of Two Electrolytes with a Common Hydrated Cation and One Hydrated Anion R. A. Robinson and Roger G. Bates Department of Chemistry, University of Florida, Gainesville, Fla. 32607 A convention described in earlier contributions makes it possible to derive the activities of the individual ionic species in solutions of unassociated electrolytes and in mixtures of two uni-univalent electrolytes with a common unhydrated ion. With the aid of a thermodynamic treatment of mixtures of electrolytes, it has now been shown that this convention can also be applied to mixtures of two electrolytes with a common hydrated cation, one hydrated anion, and one unhydrated anion. The method is illustrated by deriving the single activity coefficients of potassium, fluoride, and chloride ions in mixtures of potassium fluoride and potassium chloride at a total ionic strength of 3 mol kg-'. 1684
In earlier papers (1, Z), an approach to the establishment of internally consistent numerical scales for the activities of the single ionic species to which ion-selective electrodes respond has been suggested. This method is based on the concept of individual ionic hydration numbers which account fully for the specific differences in ionic activity coefficients apparent in concentrated electrolyte solutions. Hydration numbers for electrolytes are derived from the Stokes-Robinson hydration model ( 3 ) ; (1) R . G Bates, 8. R . Staples, and R . A. Robinson, Anal. Chem., 42, 867 (1970). (2) R. A. Robinson, W. C. Duer, and R G. Bates, Anal. Chem., 43, 1862 (1971). 7 0 , 1870 (3) R . H. Stokes and R . A. Robinson, J. Amer. Chem. SOC., (1948).
ANALYTICAL C H E M I S T R Y , VOL. 45, NO. 9, AUGUST 1973
