centrations from 0.02-0.14 wt % and all the integrations could be done a t a single gain setting. Thus the factor a t the right in the equation above did not enter. However, when establishing the linear relationship presented in Figure 4, we did have t o use three different gain settings. We have found with A60 and A56160 spectrometers that the use of standards and switching of samples does not introduce any measurable error and allows for any slight or major day-to-day variation of the instrument gain. We have found that our standard N204-NOz samples have exhibited stable proton concentrations for a t least five years. Table I1 gives typical results for oxidizer analyses for both NO and HzO. Each series of analyses with a particular letter were performed on different portions of oxidizer being passed from a large tank into several spacecraft oxidizer storage tanks. The variations observed are typical of the sampling and dispensing errors we have found characteristic from large tanks which are not stirred and not always a t the same temperature when tapped. Results for the H20 content were obtained both by the modified Whitnack-Holford method (2, 7) and the KMR method. Comparison of these HzO analyses shows that the NMR results are about 0.02 wt % lower than the former method.
DISCUSSION The detailed procedure for the N O analysis described here has been in general use in our laboratories for some time. Another procedure for determination of nitric oxide in dinitrogen tetroxide has been described (20). This spectrophotometric method was verified for the concentration range of only 0% to 1.5 wt % nitric oxide. The oxygen titration technique described here has been applied to samples containing 0.5-10 wt YO NO. The spectrometric procedure required a specially designed cell capable of being maintained a t 0 "C. The oxygen titration procedure requires less special equipment and interfaces more smoothly with subsequent analyses usually required from a sample aliquot of liquid nitrogen tetroxide oxidizer. The handling of the samples in the manners we described allows easy preparation of samples for NMR analyses and is also consistent with the transfer of samples t o borosilicate (10) C. M Wright. W. A . Orr. and W. J. Balling, Anal. Chem.. 40, 29 ( 1968).
glass sample bulbs for subsequent total N 2 0 4 assay and nitrosyl chloride determination (7, 9). Our sampling handling procedures do not encounter any difficulties due to hydroscopicity and high volatility because the material is always in a closed system. Also operator exposure to the oxides of nitrogen is not a probIem. Some time ago, a NMR method for measuring H2O in X 0 2 was suggested (3). The procedure described for this determination required t h a t one take a n unknown and add several carefully incremented amounts of H2O to several separate N M R sample tubes which were weighed subsequently. As mentioned above, it is difficult and timeconsuming to do this accurately for increments of water in the 0.1-0.2 wt % range. (Also, the N O formed should be removed.) From spectra of the samples so prepared, the initial amount of H2O present was ascertained (3). This procedure requires much more effort than preparation of one or two sample tubes which do not have to be weighed. We found that the sample preparation procedure and the NMR technique described here, once permanent standards were prepared. is rapid, precise, and convenient for subsequent analyses of other components in nitrogen tetroxide oxidizer (7, 9) In our hands, the time required for a NMR water determination as described here (both sample preparation from product of a n oxygen titration and recording of sample and standard spectra for duplicate samples) can be reduced to about half a n hour. The NMR water results are reproducible to *0.002 wt % in the concentration range 0.01 to 0.2 wt YO water on duplicate samples prepared from the same large sample. We have found t h a t the NMR method gives results about 0.02 wt % lower than the modified Whitnack-Holford method in use in our laboratories (7). The latter procedure requires much more effort to set up and stabilize (more than a day's time). T o accomplish duplicate analyses which require appropriate blanks and standards is much more time-consuming (requires about 5 hours). On multiple analyses of the same sample, this procedure appears to be accurate to about *0.01 wt % in the 0.01 to 0.2 wt % range which is less accurate than the NMR method. Received for review August 28, 1972. Accepted December 27, 1972. Research sponsored by the National Aeronautics and Space Administration under Contract No. NAS 7-100.
Protonation of Weak Bases in Sulfolane as Solvent J.
F. C o e t z e e '
and R J. Bertozzi
Department of Chemistry, University of Pittsburgh, Pittsburgh, Pa. 15213
Predominantly anhydrous solutions of perchloric acid in sulfolane were titrated conductimetrically with a variety of mono- and bifunctional weak bases, including water, alcohols, ketones, and amines, and also substances that are themselves important dipolar aprotic solvents, including acetonitrile, nitrobenzene, dimethylformamide, and dimethylsulfoxide. Titration curves of 4 general types were
IPlease address all correspondence to this author. 1064
ANALYTICAL CHEMISTRY, VOL. 45, NO. 7 , JUNE 1973
obtained. Since some water is always present, bases that are stronger proton acceptors than water in sulfolane (S) give separate inflections corresponding to successive protonation by S H + and H 3 0 + . Titrations of this type are useful for the differential determination of anhydrous acid and water. Even bases as weak as acetonitrile and nitrobenzene can be protonated in sulfolane. Homoconjugation of 2,6-dihydroxybenzoic acid was studied in some detail. Uncertainties in a provisional calibration of an acidity scale for sulfolane are discussed.
The dipolar aprotic solvent sulfolane possesses distinct advantages as a medium for acid-base studies. Its proton basicity is much lower than t h a t of water and even acetonitrile,'as shown by its p K a ( S H + ) value of -12.9 (1) as compared to (probably) near -9.5 for acetonitrile (2). Sulfolane is also a very weak BrQnsted acid, with pKa(S) > 31 (3). Consequently, in sulfolane very high acidities and basicities can be reached and very weak bases and acids can undergo proton transfer reactions. It is likely t h a t sulfolane will support a wider range of proton activities than can be reached in any other dipolar aprotic solvent. Another major advantage of sulfolane over solvents such as nitriles and ketones is t h a t it is more resistant to degradation by strong acids and bases. In spite of its low acidity and basicity its dielectric constant (43 a t 30 "C) is sufficiently high to allow straightforward electrochemical measurements. Its main limitation is its high viscosity (0.103 poise a t 30 "C) which reduces the sensitivity of conductimetry and voltammetry and sometimes causes other diffusion-related problems ( 4 ) . Its potentialities for acid-base titrations were clearly demonstrated by Morman and Harlow ( 5 ) who used tetrabutylammonium hydroxide in isopropanol and perchloric acid in dioxane as titrants for a variety of acids and bases and monitored the course of the titrations with a glass electrode. It was subsequently shown t h a t the glass electrode gives Nernstian response in picric acid buffers of constant ionic strength (6). Some measurements also have been made with the hydrogen electrode (6-8). In carboxylic acid buffers, its response parallels t h a t of the glass electrode fairly closely. However, in our view, there still is some question about the response of both electrodes in highly acidic media, as will be discussed below. In solvents such as sulfolane and acetonitrile, which are relatively weak hydrogen bond acceptors and even weaker hydrogen bond donors, acid-base reactions involving anions having a localized charge are complicated by formation of homoconjugate complexes, such as A H . . . A-. Homoconjugation occurs because HA and especially A- can acquire only limited stabilization from their weak hydrogen bonding with the solvent, in contrast to the situation in water. This type of complexation has been studied thoroughly in acetonitrile, particularly by Kolthoff and his coworkers (9), but much less so in sulfolane (6, 10). We report here the results of a more detailed study of the homoconjugation of 2,6-dihydroxybenzoic acid. The concentration dependence of the conductivity of a number of acids (6, 11) and salts (12, 13) in sulfolane has been investigated, but the potentialities of conductimetric titrations have been explored to a limited extent only (6, 24). The main part of this communication is concerned S. K. Hall and E. A . Robinson, Can. J. Chem., 42, 11 13 ( 1964) N. C. Deno and M . J. Wisotsky, J. Amer. Chem. Soc., 85, 1735 (1963). F. G. Bordwell, R. H . Irnes, and E. C. Steiner, ibid., 89, 3905 (1 967). J. F. Coetzee, J. M. Simon, and R. J. Bertozzi, Anal. Chem.. 41, 776 ( 1969) D. H . Morman and G . A . Harlow, ibid., 39, 1869 (1967). J. F. Coetzeeand R. J. Bertozzi, ibid., 43, 961 (1971). P. M D. Ellerand J. A. Caruso,Ana/, Lett., 4, 13 (1971). R. L.henoit and P. Pichet, J. Eiectroanal. Chem., in press. M . K. Chantooni, Jr., and I . M . Kolthoff, J . Amer. Chem. Soc., 92, 7025 (1970) R. L. Benoit. A. L. Beauchamp. and R . Domain, Inorg. Nucl. Chem. Lett.. 7 , 557 (1971). R. L . Benoit, C. Buisson, and G . Choux, Can. J . Chem., 48, 2353 (1970). R. Fernandez-Prini and J . E. Prue, Trans. Faraday Soc., 62, 1257 (1966). M. Della Monica and L. Senatore. J. Phys. Chem., 7 4 , 205 (1970) M . Della Monica, U. Larnanna, and L. Senatore, Inorg. Chim. Acta, 2, 363 (1 968).
with exploratory conductimetric titrations of perchloric acid with several classes of weak bases. Although perchloric acid is not completely dissociated in sulfolane (6, 11), while hydrogen hexachloroantimonate is essentially completely dissociated (111, the former acid usually is the better choice for titrations of the type discussed here. One reason is t h a t C104- is chemically more stable than SbClG-. Another reason concerns the sharpness of the inflection obtained a t the equivalence point. The mobility of the solvated proton in sulfolane is not abnormally high, as it is in water and the lower alcohols; it is, in fact, quite similar to t h a t of the majority of protonated bases included in this study. Perchloric acid has the advantage that, while it is sufficiently strong t o protonate even very weak bases, it is less dissociated than the perchlorates of the protonated bases are, so that the titration curves generally exhibit well-defined inflection points. The results obtained allow some conclusions about relative base strengths in sulfolane. EXPERIMENTAL Experimental details were the same as those described earlier (6). Additional chemicals used were all of reagent quality. In view of uncertainties associated with t h e response of t h e hydrogen electrode, additional information on its preparation and conditioning (15) is provided here. Hillebrand-type electrodes were cleaned by immersing them first for 30 seconds in a mixture of 1 volume 16,M nitric acid, 3 volumes 1 2 M hydrochloric acid, and 4 volumes water, and then for 60 seconds in hot 16M nitric acid. After thorough washing, they were made t h e cathode in the electrolysis of 0.1M sulfuric acid for 15 minutes a t an emf of 3 V, and then of 2% by weight chloroplatinic acid in 2 M hydrochloric acid for 1 minute a t a current density of 0.1A c m - 2 . T h e electrodes then were light gray. Finally, the electrolysis of 0.1M sulfuric acid was repeated. Both hydrogen and glass electrodes were stored in water, h u t were immersed in pure sulfolane for 30 minutes just before use.
R E S U L T S AND DISCUSSION Exploratory Conductimetric Study of Reactions of Weak B a s e s with Perchloric Acid. It has been shown conductimetrically (6, 11) t h a t perchloric acid behaves as a relatively strong acid in sulfolane (pKa = 3) and that when a n equimolar amount of water is added, formation of hydronium ion is virtually complete (6). We now have extended such measurements to a variety of weak bases. B. The conductimetric titration curves provide, among other things, information on the proton basicity of B relative to that of sulfolane, S: HC10,
+S
HClO,
+ B S BH'C10,-
SH'C10,-
i . SH'
+
C10,-
BH'
+
C10,-
__
(1)
(2) For all bases studied, the ion pairs BH+C104-, and by analogy probably also SH+C104- ( I I ) , are extensively dissociated into the constituent ions. In all cases, addition of B to a solution of perchloric acid in S resulted in an increase in conductivity, a t least in the early part of the titration (see below), indicating that the proton acceptor power of all bases studied, even those as weak as acetonitrile and nitrobenzene, exceeds t h a t of sulfolane in sulfolane as soluent. Typically, 2 x 10-2M or 5 x 10-2M solutions of perchloric acid were titrated by adding the pure liquid base from a microburet. Since perchloric acid in sulfolane is a ravenous water scavenger (6), some water always was present, so that the end point for reaction 2 always occurred before the equivalence point corresponding to the total concentration of perchloric acid, which is in(15) G . J. Hills and D . J. G . Ives, in "Reference Electrodes." D . J . G. lves and G . J . Janz, E d . , Academic Press, New York. N . Y . , 1961, p p 106, 120.
ANALYTICAL CHEMISTRY, VOL. 45, NO. 7, JUNE 1973
1065
2 OOk
g 1.10 u
Volume o f (-Propanol Added. pl
Figure 1. Conductimetric titration of 20 ml of 0.020M HCIO4 with 1-propanol. "Total stoichiometric point" (TSP) = 30 pl: end point occurs earlier owing to presence of water (see text)
.
TSP 5
10
15
20 25 30 35 Volume of P y r r o l e A d d e d , pl
40
45
50
Figure 4. Conductimetric titration of 10 mi of 0.020M HSbCl6 with pyrrole
9
x.2 IO
0
Volume o f Diaxone Added, p i
Figure 2. Conductimetric titration of 20 ml of 0.020M HCiO4 with 1,4-dioxane 2.20
r
10
20
40 50 60 70 80 ' 90 130 V o l u m e o f I,3-Oiorninopropone Added.pl
30
110
120
Figure 5. Conductimetric titration ot 20 ml of 0.050M HCiO4 with 1,3-diaminopropane.
v
P 1.20 -
s
TSP
0
TSP
tions of this type, the second end point coincides exactly with the TSP. From the practical point of view, titrations of this type are useful for the differential determination of an anhydrous acid (provided it is not very weak) and water, the latter as hydronium ion. Finally, in Figures 3 and 4, the types of titration curves given by pyrrole with perchloric acid and with hydrogen hexachloroantimonate are compared. Since the latter acid is essentially completely dissociated and the solution used was virtually anhydrous, the only important reaction was SH'
+ B=BH'
+S
(4) with the result t h a t the titration curve has the simple shape and less-than-ideal inflection shown. Type 111. Piperazine (diethylenediamine) and 1,3-diaminopropane gave the more complex type of titration curve presented in Figure 5 . Our assignment of the reactions responsible for the different branches of the curve is as follows: a b : 2HC10, bc: 2H30'
+ B-BZH'B-BH' + B-B
+
CH'B-BH'
+ 2C104+ 2H20
(5)
(6)
c d : H'B-BH' B-BS2B-BH' (7) Again, the differential determination of anhydrous acid and water, the latter as hydronium ion, can be accomplished by titrations of this type. Type IV. Acetonitrile and nitrobenzene produced the drawn-out type of titration curve given in Figure 6. Here the proton transfer reaction no longer is complete, but it nevertheless is noteworthy that the proton acceutor power of these two bases, which are important dipolar aprotic solvents, exceeds t h a t of sulfolane, a t least in sulfolane as solvent. In sulfuric acid as solvent, nitrobenzene and sulfolane show little difference in proton basicity, as indicated by p K a ( S H + ) values of -12.4 and -12.9, respectively ( I ) . The behavior of acetonitrile should be contrasted with that of acetic acid, which is a Type I base. Perchloric acid 1066
ANALYTICAL CHEMISTRY, VOL. 45, NO. 7, JUNE 1973
2.45
Table I. Comparison of Glass and Hydrogen Electrode Potentials in Solutions of Various Acids Acid, HA
HSbClsb
CHA
0.021 0.051 0.21 0.05 to 0.2 0.010
HC1Odd
2,6-Dihydroxybenzoic acid 0.010M Bu~NA 2-Hydroxyben0.010 zoic acid 0.010M B u ~ N A
EGO
- EH
EHQ
EG
7ac 31OC
212 121
29 0 431 51 5 569 to 590e -383
61 to a4e -1052
ca. 510
-653
-1340
687
...
... 669
+
1 6 5 r
'
IO
1
I
,
40 50' 60 Volume of Acetonitrile Added. pI
20
30
+
8
I
70
80
Figure 6. Conductimetric titration of 20 rnl of 0.050M HClO4 with acetonitrile
in acetic acid has been used extensively as a titrant for solutions of bases in acetonitrile as solvent. It is likely t h a t in solutions titrated in this way the proton will be solvated by acetic acid rather than by acetonitrile, even though acetonitrile typically will be present in large excess. Consequently, caution should be exercised in interpreting results obtained in such media. On the Response of Hydrogen and Glass Electrodes. We have reported (6) a provisional calibration of a n acidity scale for sulfolane. The calibration was based on hydrogen electrode measurements in solutions of perchloric acid prepared in situ by adding between 0.990 and 0.999 mole of silver perchlorate to 1.000 mole of hydrogen chloride in sulfolane. The standard (reduction) potential of the hydrogen electrode was +0.075 V us. AgRE. Recently, Benoit and Pichet (8) reported a value 0.18 V less positive than ours, also based on hydrogen electrode measurements in perchloric acid solutions, but using perchloric acid prepared by distillation. At this time we can only speculate on possible reasons for the large discrepancy. First, it appears t h a t the most obvious source of error, water uptake by the perchloric acid solutions, has been allowed for adequately in both sets of measurements. However, the presence of another, even less basic, impurity in one or both sets of measurements cannot be ruled out. Second, our perchloric acid solutions contained some silver ion, in concentrations of the order of 0.1% of those of perchloric acid (and also ca. lO-I3M AgC12-). In spite of the very low solubility product constant of silver chloride, the reaction of silver ion with hydrogen chloride is not ideally complete because of the very weak dissociation of the latter (see below). It is well known t h a t in aqueous solutions of noble metal salts, the hydrogen electrode acquires false potentials that are too positive (1.5). The possibility must be considered that in our measurements deposition of trace amounts of silver metal, while not apparent, nevertheless resulted in false potentials. However, the following experiment provided evidence to the contrary. A hydrogen electrode was equilibrated with a 0.3M perchloric acid solution. After bubbling hydrogen for another hour, the electrode was withdrawn, cleaned with aqua regia, replatinized and reconditioned, and was then reinserted into the same solution. It acquired the same potential as before, A third uncertainty is associated with the magnitude of liquid junction potentials (6, 8). Benoit and Pichet (8) employed 0.1M Et4NI or Bu4NC104 as salt bridge. Most of our measurements were carried out with a fiber-tip AgRE which had been shown to introduce no measurable contamination by silver ion; hence, a salt bridge usually was omitted. Although we found no signifi-
In mV YS. AqRE. All values are reduction Dotentials. *Water content ca. 10 mole %. C For complications, see text. Water content typically 40 to 60 and 20 to 50 mole % in measurements with hydrogen and glass electrodes, respectively. e Values listed are standard potentials, caiculated by allowing for water content (6). Q
cant change in potential when a O.1M solution of tetraethylammonium perchlorate was inserted between the AgRE and 0.2M perchloric acid, there remains some question about the relative magnitude of the liquid junction potentials in our measurements and in those of Benoit and Pichet, and this problem certainly should be studied further. Finally, as reported before (Si, an unsuccessful attempt was made to calibrate the hydrogen electrode in solutions of hydrogen hexachloroantimonate, even though arsenic compounds are known to poison the hydrogen electrode in aqueous solution, and similar problems conceivably could arise with antimony compounds. Potentials were much more positive than those expected on the basis of the calibration in perchloric acid. In addition, a marked change occurred in the appearance of the electrode from gray to almost white. In view of the uncertainties associated with the behavior of the hydrogen electrode, measurements also were made with the glass electrode in solutions of perchloric acid and of hydrogen hexachloroantimonate. In Table I three kinds of comparisons are presented: the response of the glass electrode in perchloric acid us. t h a t in hydrogen hexachloroantimonate, the response of the glass electrode in perchloric acid us. t h a t of the hydrogen electrode, and the response of the glass electrode in two buffer solutions us. that of the hydrogen electrode. It is evident that the apparent response of the glass electrode in hydrogen hexachloroantimonate solutions is not Nernstian, but it is uncertain whether the deviation is caused by dehydration of the gel layer (S), by changes in the liquid junction potential (B), or by some other factor. In view of these uncertainties, the fact t h a t in perchloric acid solutions the apparent response of the glass electrode approximated Nernstian behavior may be fortuitous. We are left with the conclusion t h a t while in carboxylic acid buffers of constant ionic strength, both the hydrogen and the glass electrode give Nernstian response (6), there remains some question about the response of both electrodes in highly acidic solutions (However, also see Ref. 8). Homoconjugation of 2,6-Dihydroxybenzoic Acid. 'The homoconjugation of 2,6-dihydroxybenzoic acid (HA) was studied in some detail by measuring glass electrode potentials in a series of buffer solutions of constant ionic strength prepared by adding varying volumes of a solution containing 0.745M HA and 1.00 X 10-2M Bu4NA to a 1.00 x 10-2M Bu4NA solution. The glass electrode generally required between 30 and 60 minutes to reach equilibrium, after which its potential remained stable to within f l mV. However, on repeating the same measurements ANALYTICAL CHEMISTRY, VOL. 45, NO. 7, JUNE 1973
1067
Table 11. Distribution of Major Solute Species in Buffer Solutions Consisting of 2,6-Dihydroxybenzoic Acid and Its Tetrabutylammonium Salt Experimental valuesa
Calculated valuesb ~~
Ca, M
8.94 k 2.38 x 5.03 x 7.38 x 1.00 x 2.50 X 5.00 X 7.50 X 1.00 x 2.13 X
1 0 - ~ 10-3 10-3 10-3 10-2 10 -2
lo-* lo-* lo-' 10-1
-Ec,mV
[HA1
467 435 404 39 1 375c 31 8 251 218 199 132
2 . 7 ' ~1b-4 7.8 x 10-4 1.7 x 10-3 2.7 x 10-3 3.9 x 10-3 1.3 X l o - ' 3.4 x 10-2 5.8 X 8.2 X l o - ' 1.9 x l o - '
9.4-x 8.4 x 6.9 x 5.8 x 4.7 x 1.6 x 4.4 x 1.8 x 9.7 x 2.0 x
x 10-2M. Concentrations of solute species calculated by assuming Krl = 240 and Kf2 = 50. Calculated values Of the glass electrode potential are normalized (arbitrarily) with respect to the experimental value in the buffer solution for which Ca = C s ; note that for this buffer [HA] # [A-1, and paH = pKa 0.1 4- log 1, = pKa, so that a Cs kept constant at 1.00
+
with the same electrode at intervals of a few months, corresponding equilibrium potentials differed by as much as rtl0 mV, which might have been caused by changes in the asymmetry potential; similar observations have been made by Benoit and Pichet (8). Experimental results are presented in Table 11, which also contains calculated values of the concentrations of different solute species present and hence of the potential. The experimental data are consistent with the formation of two homoconjugate complexes, AHA- and (AH)2A-. Assuming that, as in acetonitrile as solvent (9), ion association of tetrabutylammonium ion with (AH)2A- and AHA- and even with A- is insignificant, the mole balance expressions for the analytical concentrations of acid (C,) and salt (C,) are
Ca
= [HA]
+ [AHA-] + B[(AH),A-]
( 8)
and
c,
= [A-]
+
[AHA-]
+ [(AH),A-]
= 1.00 X lo-'
(9)
The best fit of the experimental values of the potential was obtained with the following values for the formation constants of the two complexes:
Kfl = [AHA-]/[HA][A-] = 240 = [(AH)zA-]/[HA][AHA-] = 50
(11) Calculated values of the potential were obtained from calculated values of [HA] and [A-l, assuming t h a t the response of the glass electrode is Nernstian, as it has been shown to be in picric acid buffers of constant ionic strength (6). Calculated values of the potential agree with experimental values to within A6 mV over the entire range covered, which amounts to 335 mV or 5.6 p H units. All evidence so far is consistent with Nernstian response of the glass electrode in buffer solutions of intermediate acidity. Dissociation Constants of Bransted Acids. In view of the uncertainty in the calibration of a n acidity scale, as discussed above, it would be especially desirable to determine some acid dissociation constants in a manner which is independent of the calibration. This was done in the case of hydrogen chloride. Solutions of anhydrous hydrogen chloride were titrated potentiometrically with anhydrous silver perchlorate in sulfolane ( S ) , using a silver indicator electrode. The equilibrium constant of the reaction is related to the dissociation constant of hydrogen chloride (Ka) and the solubility product constant of silver chloride ( K s o )as follows: 1068
6 . i x 10-4 1.6 x 10-3 2.8 x 10-3 3.7 x 10-3 4.4 x 10-3 5.0 x 10-3 3.6 x 10-3 2.5 x 10-3 1.9 x 10-3 9.3 x 10-4
io-3
10-3 10-3 10-3 10-3 10-3 10-4 10-4 10-5 10-5
l(AHjzA-1
-Ec,mV
x io-6 x 10-5 x 10-4 5.0 x 10-4 8.7 x 10-4
46 2 43 2 405 39 0 375 31 5 25 7 21 9 194 131
8.3 6.2 2.4
3.4 x 10-3 6.0 x 10-3 7.3 x 10-3 8.0 x 10-3 9.0 x 10-3
allowance for (AH),A; formation changes the pKa value given in ref. 6 by -0.1 unit. C Potentla1 differs by 8 rnV from that given in Table I. The same electrode was used. but the two sets of measurem'ents were made one year apart: for comments see text.
Table I II. Comparison of Provisional Dissociation Constants of Br6nsted Acids in Sulfolane (SL) and Acetonitrile (AN) Acid
PKa(SL1'
HC104 HCI
Picric acid 2,6-Dihydroxybenzoic acid
3.0b * 14.5 17.4
PKa(AN1 c
PKa(SL1
- pKa(AN1' ...
8.gd 11.0e
5.6 6.4
Pyridinium+
18.8 18.8
12.6e 12.3d
6.2 6.5
2-Hydroxybenzoic acid
23.6f
16.7e
6.9
'Based on the provisional calibration of an acidity scale described in ref. 6. except for HClO4 and HCI. The calibration by Benoit and Pichet (8) leads to values that are 3 units smaller. independent of calibration of acidity scale; see text. Essentially completely dissociated. From compilation given in ref. 77. e Ref. 78. (also refer to eariier papers) 'Assuming that ( A H ) P A - formation is roughly comparable to that of 2.6dihydroxybenzoic acid.
HC1
+
Ag'
+S
s AgCl(s)
+ SH+
(12)
(10)
and
Kfz
[AHA-]
[A-I
ANALYTICAL CHEMISTRY, VOL. 45, NO. 7, JUNE 1973
where Kso = 3 X l O - l 9 (16). Values of a A g , - , were calculated a t various points on the titration curve by assuming that the silver electrode exhibits Nernstian response (as it does in many solvents) and t h a t the activity coefficient of silver ion in the test solution and also in the reference electrode is adequately represented by the Debye-Huckel equation with a = 5 A. Corresponding values of a S H , + , were computed from the dissociation constant of perchloric acid, 1.1 X 10-3, making allowance for the presence of water as described before (61, so that
The concentration of water present as hydronium ion (C,) was determined by the indirect conductimetric procedure described before (6). Since typical values of aAg( + , were of the order of 10-4, values of a c l , - ] were of the order of (16) R. L Benoit, A L Beauchamp, and M Deneux, J Phys C h e m , 73, 3268 (1969). (17) J. F. Coetzee, in "Progress in Physical Organic Chemistry," A. Streitwieser, Jr., and R. W. Taft, Ed., Interscience, New York, N.Y., Vol. 4, 1967. (18) i . M . Kolthoff. M . K. Chantooni, Jr., and S. Bhowmik, J. Amer. Chem. SOC.,90, 23 (1968).
10-15, with the result t h a t the influence of HC12- (20) and AgC12- (16) formation was insignificant in these calculations. The mean pKa value obtained for hydrogen chloride is 14.5 f 0.1, but in view of the indirect method of calculation, its uncertainty must be considerably larger than fO.l unit. In Table I11 dissociation constants of several Brfinsted acids in sulfolane are compared with those in acetonitrile. For those dissociation constants t h a t are based on calibration of an acidity scale, our provisional calibration gives pKa(SL) - pKa(AN) 6 to 7 units, while t h a t of Benoit and Pichet (8) gives 3 to 4 units, which is close to the estimated difference in p K a ( S H + ) values of the two solvents. Unfortunately, these comparisons can only be inexact at present, for a t least two major reasons. First, it is not known how the (somewhat uncertain) difference in pKa(SH+) values measured in sulfuric acid is related to the relative basicities of the two bulk solvents. Second, in comparing the position of the equilibrium
-
HA(so1vated)
+ S z=SH+(solvated) + A-(solvated)
(15) in two solvents, it is necessary to consider not only the relative proton basicities of the two solvents, but also their relative abilities to stabilize the species HA, SH+ and A - . For the two ions SH+ and A - , such a comparison would require extrathermodynamic assumptions which introduce uncertainties of generally unknown magnitude.
ACKNOWLEDGMENT We thank R. L. Benoit and P. Pichet for information prior to the paper's publication. We also acknowledge the help of J. Bykowski, E. Devitt, and J. Meyn in carrying out some of the conductimetric titrations. Received for review October 18, 1972. Accepted December 20, 1972. We thank the Kational Science Foundation for financial support under Grant GP-16342.
Single-Ion Activity of Fluoride in Mixed Alkali Halide Solutions John Bagg' and G. A. Rechnitz Department of Chemistry, State University of New Y o r k . Buffalo, N. Y . 14274
The activity coefficients of F - in mixtures of trace concentrations of NaF, and KF in NaCI, KCI, KBr, and K I , at concentrations up to 4 molal have been measured in a cell with a F--selective electrode. The single-ion activities of F- in NaF-NaCI mixtures up to 1 molal, and KF-KX mixtures up to 4 molal, were, within experimental error, equal to the values in pure N a F or KF of the same ionic strength. The values in pure fluoride solutions were assigned using the convention based upon hydration theory as proposed by Robinson, Duer, and Bates. The experimental and theoretical difficulties in assigning single-ion activities in mixed solutions are relevant to the determination of selectivity parameters for ion-selective electrodes. In the light of the results reported in this paper, a procedure is described which maintains a simple ion-activity convention and absorbs the uncertainty in activity coefficients in the selectivity parameter.
The primary advantage of an ion-selective electrode is its ability to measure the activity of one particular ion in the presence of several others. T o make full use of this ability in analytical applications, it is necessary to devise a single-ion activity convention for mixed solutions in order to convert activities into concentrations. Although there has been considerable research into the measurement of mean molal activity coefficients in mixed electrolytes ( I ) , there has been little corresponding work for single-ion activities ( 2 ) . 'On study leave from the Department of Industrial Science. University of Melbourne, Parkvilie, Victoria 3052, Australia H. S. Harned and R. A. Robinson, "Multicomponent Electrolyte Solutions, International Encyclopedia of Physicai Chemistry and Chemical Physics," Topic 15, Voi. 2, Pergamon Press, Elmsford, N.Y., 1968. J. V. Leyendekkers, Anal. Chem., 43, 1835 (1971).
I t is desirable to choose a cell for the estimation of single-ion activities in which a minimum of assumptions is required in calculations derived from the measured emf. Several workers have used combinations of two electrodes in order to remove junction potentials (2-4); in particular, Leyendekkers ( 2 ) has used a F--selective electrode in combination with a liquid-membrane C1- -electrode to determine the trace activity of F - in NaF-XaC1 and NaFKC1 mixed solutions. Another type of cell, consisting of a double-junction reference electrode and a n ion-selective electrode was applied recently to single electrolyte solutions (5) and offers some advantages for determination of trace activities. Consider the following solution chain for a binary electrolyte mixture, NY-MX, with ml
