Anal. Chem. 1981, 53, 1021-1023
1021
Ion-Selective Electrodes for Determination of Thermodynamic pKValues of Weak Bases Kazuko Tanaka’ and Roger G. Bates” Department of Chemistty, University of Florida, Gainesville, Florida 326 1 1
The determination of thermodynamic dissociation constants for uncharged bases is, in general, more difficult than for weak acids, in view of the solubility of the silver halide of the Ag;AgX electrodes in many basic media. The substitution of a sodium ion selective electrode for the silver halide electrode avoids this difficulty and at the same time enhances the accuracy of the extrapolation to zero ionic strength by eliminating the activity-coefficient term. A convenient method for determining the pK, of protonated bases BH+ by measurements of the emf of cells of the type
p H glass electrodelBH+(rn),B(rn),Na+(rn = 0.01)INa-ISE Is described. The method was tested by determining the dissociation constants of protonated 2-aminopyridine, ammonia, 2-amino-2-methyi-l,3-propanedioi ( “Bis”), n-butylamine, sec-butylamine, and terf-butylamine in water and Bis in 50 mass % methanol. Tris*H+ was chosen as a reference for a determination of relative acidic strengths. The data, which covered the temperature range 15-35 ‘C, agreed well with the constants obtained earlier by more elaborate thermodynamlc methods.
It is well recognized that useful information concerning the relative strengths of weak acids and bases can often be obtained conveniently by pH titrations in a cell with a glass electrode and a suitable reference electrode. Substitution of the hydrogen gas electrode for the glass electrode removes a possible source of uncertainty, but the diffusion potential deprives the results of thermodynamic rigor. Some years ago, however, Roberts (I)and Harned and Ehlers (2) showed how cells without liquid junction could be applied to a determination of equilibrium constants with thermodynamic validity. For the study of acid-base systems HAn+’, An their method utilizes cells with hydrogen electrodes and silver-silver chloride electrodes Pt;H,(g, 1 atm)IHAn+l,An,C1-IAgC1;Ag (A) containing buffer solutions with added chloride. Extensive data for the pK values of weak acids of varied charge types (especially n = -1 and n = -2) over a range of temperature have been obtained with the Harned cell, and from them useful thermodynamic quantities for the dissociation processes have been derived. The method has proved suitable also for the study of some weak bases ( n = 0 and n = +l). Other nitrogen bases, however, form complexes with AgCl of such stability as to greatly reduce the accuracy of the method. In these instances, the Ag;AgBr and Ag;AgI electrodes are sometimes useful, and it was suggested ( 3 , 4 )that sodium amalgam or thallium amalgam electrodes might be suitable. Amalgam electrodes, however, are difficult to use, and accurate results can be obtained only after considerable experience in the techniques involved. Nevertheless, their use On leave 1979-80 from the Institute of Physical and Chemical
Research, Saitama, Japan.
in the study of weak bases (n = 0) offers a distinct advantage over the silver halide electrodes, as a closer examination of the method of calculation reveals.
THE EMF METHOD The pK of an acid-base equilibrium
HA=H++A
(1)
is given in terms of the emf ( E ) and standard emf ( E O ) of cell A by YHAYCI E -Eo HA pK = - log mcl+ log - + log -
k
+
mA
YA
(2)
where k is written for (RTIF) In 10 and the charges of HA, A, and C1 are omitted in the subscripts. The last term, containing the activity coefficients of the participating species, disappears a t zero ionic strength, I. To facilitate the extrapolation of “apparent” values (pK’) of pK to this limit, one usually estimates the magnitude of this term, often by introduction of some form of the Debye-Huckel equation. In this fashion, the plot of pK’ vs. I may be reduced to a straight line for easy extrapolation to I = 0. This procedure is particularly advantageous for the study of uncharged weak acids ( n = -l), of which acetic acid may be considered the prototype. In this case, the last term of eq 2 is small and usually varies linearly with I. Consequently, when the buffer ratio and chloride molality remain constant, E varies only slightly with I. On the contrary, for uncharged weak bases (n = 0), of which NH3 may be considered the prototype, the last term of eq 2 becomes log (YNH,YCI/YNHJ, which is altered considerably in nonlinear fashion as I changes. Some years ago, Roberts pointed out (4) that, in principle, this difficulty could be alleviated by replacing the Ag;AgCl electrode of cell A by an electrode reversible to a univalent cation, such as Na+ or T1+. Nevertheless, it appears that this suggestion has not received the attention it deserves, doubtlesa because of the experimental difficulties attendant on its implementation. In the present work, we have used the sodium ion selective electrode for this purpose and have replaced the hydrogen electrode by the pH glass electrode in an attempt to enhance the simplicity and convenience of the method. The cell can be represented
pH glass electrode(BH+(m),B(m),Na+(m = 0.Ol)INa-ISE (B) where B is written for the uncharged base and the molality of Na+ was kept constant at 0.01 mol kg-’. The expression for pK, thus becomes pK,’
E
pK,
+ b l = E- Eo - log mNa + log ~ B (3) H k
mB
inasmuch as the term log (YBYNJYBH) is now small and varies linearly with I, in the same way as that for cell A when n = -1; b is the slope of the extrapolation line. This advantage is well illustrated in Figure 1,where the change in emf for cells
0003-2700/81/0353-1021$01.25/00 1981 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 53, NO. 7, JUNE 1981
Table I. pK, of Protonated Bases in Water from Cell B Compared with Similar Data from Cell A
tl"C 15 20 25 30 35
2-aminopyridinium A B 6.949 6.841 6.739 6.640 6.543 6
TrisVH' Aa
6.94 6.82 6.73 6.64 6.55
ref, cell A Reference values.
8.362 8.214 8.075 7.934 7.803 7
Bis-H' A 9.105 8.951 8.801 8.659 8.519 8
ammonium A B
B 9.10 8.95 8.79 8.66 8.52
9.245 9
9.25
n-butylammonium Ab B 10.812 10.640 10.471 10
10.93 10.79 10.65 10.48 10.30
ammonium sec-but~lB 10.90 10.73 10.58 10.41 10.24
tert-butylammonium A B 11.048 10.862 10,685 10.511 10.341 11
11.05 10.86 10.68 10.48 10.32
Data from concentration cells with hydrogen electrodes, silver chloride electrodes not used.
CELL A
Eleclrode
AE,mV
IONIC STRENGTH
Flgure 1. Change of emf of cells A and B with ionic strength. In each case the solution contains 1:l buffers of Tris.H+ and Tris In 0.01 m NaCI.
A (upper curve) and B (lower curve), both containing a Tris buffer with added NaCl ( m = 0.01), is plotted as a function of I. (Tris(hydroxymethy1)aminomethane is the common name for Tris.) A limitation on the use of eq 3 is imposed by the combination of p H glass electrode with the Na-ISE, for the value of E" is not known and may even vary over relatively short periods of time. Furthermore, the Nernst slope 12 may not apply with sufficient exactitude when wide ranges of pH are involved. For these reasons, the most effective use of cell B and eq 3 is for the determination of differences of pK, between an unknown base and a reference base of comparable strength. When mNs is constant a t 0.01 mol kg-I and the buffer ratio is always unity, subject only to small corrections for solvolysis (4)
where R designates the reference base. The difference of emf, E - ER,is obtained from the intercepts of E and E R a t I = 0. In the present study, Tris was chosen as the reference base, and the usefulness of this convenient and rapid method was demonstrated by comparing the dissociation constants of several other protonated bases with data obtained by accepted thermodynamic procedures. Acceptable agreement was found in aqueous solutions in the temperature range 15-35 "C, and for one base also in 50 mass % methanol.
EXPERIMENTAL SECTION Tris, Tris hydrochloride, and Bis (2-amino-2-methyl-l,3propanediol) were obtained from Sigma Chemical Co, St. Louis,
MO. Bis was recrystallized twice from methanol and dried under vacuum at 40 "C (5). Ammonia, ammonium chloride, and the butylamines were of reagent grade; 2-aminopyridine was crystaJlizedfrom benzene and dried under vacuum (6). Reagent-grade NaCl was recrystallized and HCl was distilled twice. Buffer solutions were prepared either by weighing the base and salt or from the base and a standardized solution of HC1; a weighed amount of NaCl was added. In general, five buffer solutions consisting of equal molalities of base and base hydrochloride in a solution of NaCl, molality 0.01 mol kg-', were studied. In a typical experiment, a stock solution containing 0.05 m B and 0.05 m B.HC1 in 0.01 m NaCl was diluted with 0.01 rn NaCl to prepare the other four mixtures studied. General-purpose pH glass electrodes were used. The sodium glass electrodes were obtained from Orion Research (Cambridge, MA), Corning Glass Works (Corning, NY), and Radelkis Electrochemical Instruments Co. (Budapest, Hungary). Measurements of the potential differences between pH electrodes and Na-ISE were made with a Corning Model 130 pH meter in one of two ways, either directly with the aid of a high-impedance differential amplifier constructed by the electronics shop of the Chemistry Department or indirectly via a saturated calomel reference electrode inserted in the solutions. The temperature of the cell was controlled by circulating water, and stirring was provided. The potentials were reproducible to a few tenths of a millivolt.
RESULTS AND DISCUSSION In view of the unavoidable changes in the standard emf of cell B with time, it was necessary to repeat the measurements with the reference buffer (Tris.H+, Tris) concurrently with the measurements of each new buffer system. Instead of the absolute values of E and ER, it is only their difference in the limit of I = 0 that is significant, as eq 4 shows. Figure 2, a plot of the data for the determination of the pK of protonated 2-aminopyridine (2-AmPy), is typical of the results. It is evident that the emf changes only slightly with ionic strength. The intercept from the data of Tris at 25 "C is 0.0612 V, whereas that for 2-AmPy is -0.0181 V, from which the pK of 2-AmPy.H+ was found to be 1.341 unit lower than that (8.075 (7))for Tris.H+, or 6.734. As Table I indicates, this value agrees well with the pK obtained by extensive measurements of cell A with palladium-hydrogen electrodes (6). In the same way, pKa values for Bis, ammonia, and the three isomeric butylamines were determined in aqueous solution. In most instances, the data were obtained at five temperatures from 15 to 35 "C. Below 15 "C,the potentials were slow to reach equilibrium, whereas above 35 "C increasing instability was noted. The results are compared with accepted data for the respective pK values in Table I. The agreement is quite satisfactory, departures usually amounting to less than 0.01 unit. The applicability of this method for determining pK values of protonated bases in mixed solvents was examined by a determination of the pK of Bis-H+ in 50 mass % methanol, also in the range 15-35 "C. The pK, of the reference base (Tris) was determined earlier with the hydrogen electrode in
ANALYTICAL CHEMISTRY, VOL. 53, NO. 7, JUNE 1981
007
%
-
s
=
e
15'C
A 0 065
-
006
-
P
0055 0 05
W
W
W
t *c
w
-0 0151 A
e
35oc
I
-
n
A
-0.02
I -0 03
25OC
TR IS
m
-0025
0
"
25OC
*I
I
2-AmPy
t
-
. ?
u
0 02
0
0 04
35oc
4
0 06
Figure 2. Emf of cell B as a function of ionic strength (I)at 15, 25, and 35 OC: (A) Tris buffers; (B) 2-aminopyridlne buffers.
Table 11. p K , of Protonated Bis( 2-Amino-2-methyl-1,3-propanediol) in 50 Mass % Methanol
a
Bis- H
tl"C
Tris.H+ cell A a
cell A b
cell B
15 20 25 30 35
8.113 7.962 7.818 7.681 7.550
8.730 8.570 8.416 8.268 8.125
8.74 8.58 8.42 8.27 8.16
Reference values ( 1 2 ) .
+
Data from ref 5.
cell A (12). For values for the pKa of Bis for comparison with those furnished by the new method, a study of Bis.H+ in 50% methanol was also undertaken with cell A. The results are reported elsewhere (5). As Table I1 shows, good agreement
1023
was found at the four lowest temperatures; at 35 "C, however, the departure amounts to 0.035 unit. It may be concluded from this study that thermodynamic pK values for weak bases can be obtained simply and conveniently from measurements of the emf of cells with a pH glass electrode and a sodium ion selective electrode. Inasmuch as the extrapolation plots of Figure 2 are straight lines, two measurements with the reference buffer and two the "unknown" buffer should suffice for an accuracy of 0.03 unit or better in pKa. Suggested compositions for these solutions are (1)BH+ (0.04 m), B(0.04 m), Na+ (0.01 m) and (2) BH+ (0.02 m), B(0.02 m),Na+(O.Ol m). The values of E and ER in the limit of I = 0 (eq 4) are then simply given by 2.5E2 1.5E1. When the pKa exceeds 10 at 25 O C , small corrections to the buffer ratio for basic dissociation may have to be made. Usually a rough calculation using a preliminary value of pKa is sufficient. Unfortunately, most standard instrumentation is inadequate for the direct measurement of the emf of cells with resistances as high as that of cell B. In the absence of a suitable electrometer, one must obtain the desired potential differences by combining values for each electrode, measured individually against a reliable reference electrode, for example the SCE,of low resistance.
LITERATURE CITED (1) Roberts, E. J. J . Am. Chem. SOC. 1930, 52, 3877-3881. (2) Harned, H. S.; Ehiers, R. W. J. Am. Chem. SOC. 1932, 54, 1350. (3) Harned, H. S.; Owen, 8. B. J. Am. Chem. SOC. 1930, 52, 5091-5 102. (4) Roberts, E. J. J . Am. Chem. SOC.1934, 56, 878-879. (5) Bates, R. G.; Tanaka, K. J. Solution Chem., in press. (6) Yoshio, M.; Bates, R. G. submitted for publication in J . Chem. Eng. Data. (7) Bates, R. 0.; Hetzer, H. B. J. Phys. Chem. 1961, 65, 887-871. (8) Hetzer, H. B.; Bates, R. G. J . Phys. Chem. 1962, 66, 308-311. (9) Bates, R. G.; Pinching, G. D. J . Res. Natl. Bur. Stand. 1949, 42, 419-430. (10) Cox, M. C.; Everett, D. H.; Landsman, D. A.; Munn, R. J. J . Chem. SOC. B 1968, 1373-1379. (11) Hetzer, H. 8.; Robinson, R. A.; Bates, R. G. J. Phys. Chem. 1962, 66, 2698-2698. (12) Woodhead, M.; Paabo, M.; Robinson, R. A,; Bates, R. 0.J. Res. NaH. Bur. Stand. Sect. A 1965, 69A, 263-270.
RECEIVED for review December 1,1980. Accepted March 16, 1981. This work was supported in part by the National Science Foundation under Grant INT78 11287.
