Determination of Ionization Constants of Monobasic Acids in Ethanol-Water Solvents by Direct Potentiometry J. 0. Frohliger and R. A. Gartska Departments of Occupational Health and Chemistry, University of Pittsburgh, Pittsburgh, Pa.
15213
H. W. Irwin and 0. W. Steward Department of Chemistry, Duquesne Unioersity, Pittsburgh, Pa,
A direct potentiometric method for the determination of ionization constants for monobasic acids has been developed. The method does not require the standardization of the indicator or reference electrodes since an absolute potential measurement is not necessary. Measurements are carried out in a cell without a liquid junction. The absence of the liquid junction potential and standardization requirement allows the method to be applied to solvents other than water. The ionization constants of acetic acid in water, 45% ethanol-water and 76% ethanol-water were determined and compared to values obtained by conductometric methods. The PKS values for dimethylphenylacetic acid, diphenylmethylacetic acid and triphenylacetic acid were determined in ethanol-water solvents.
THEUSUAL POTENTIOMETRIC METHOD for the determination of ionization constants of weak acids is to measure the pH of a solution of the acid at its half equivalent point. This method requires that the indicator electrode be standardized. If a cell with a liquid junction is used, then the assumption is made that the difference between the liquid junction potential of the standardizing buffer and the system being measured is small enough to be neglected. The determinations of pK, values in aqueous media can be done quite well. Standard buffers accurate to one thousandth of a pH unit are available. Since many weak acids are not soluble in water, the problem of making meaningful potential measurements in solvents other than water arises. Although Bates, Paabo, and Robinson ( I ) have developed standard buffers for some methanol-water solvent systems, it is impossible to have a buffer system for all possible solvent compositions. In order to utilize potentiometric methods for pKa determinations in mixed solvents, a method that does not require standardization of the electrodes and the use of liquid junction is necessary. A method for the potentiometric determination of acid dissociation constants in a system without liquid junction has been reported by Grunwald (2). The rate of change of pH as a function of neutralization near the equivalent point was measured using a glass-silver, silver chloride electrode system. The method was used to measure acid dissociation constants in ethanol-water mixtures (3). In this investigation a more straightforward potentiometric method is proposed. The potential ( E ) of the cell glass electrode/HCl/AgCl, Ag at 25 "C can be expressed in the following manner (1) R. G. Bates, M. Paabo, and R. A. Robinson,J . Phys. Chem., 67, 1833 (1963). ( 2 ) E. Grunwald, J . Am. Chem. SOC.,73,4934 (1951). (3) E. Grunwald and B. J. Berkowitz, J. Am. Chem. SOC., 73, 4939 (1951).
1408
ANALYTICAL CHEMISTRY
15219 EI = k
- E'Ag,
Agci
-k 0.118 log
4-
,0.059 log [H+]I
+ 0.059 log [Cl-]
(1)
where El is the observed cell potential, k is the asymmetry constant of the glass electrode, E ' A ~AgCl ~ is the standard potential of a silver-silver chloride electrode and y is the mean ion activity coefficient. When a weak acid, HA, is added to the cell in such a way as to hold the ionic strength and the hydrochloric acid concentration constant, a new potential, E2 can be expressed Ez = k
- E ' A ~A, ~ C I+ 0.118 log yk
+ 0.059 log [H+]z + 0.059 log [Cl-]
(2)
Under the conditions stated the difference in the potentials of the two cells AEis A E = 0.059 log [H+]z - 0.059 log [H+]i
(3)
Since only hydrochloric acid was present in the original cell [H+I1= [CI-1. Solving Equation 3 for zI"[ [HfIz = [Cl-]
10AE/59.'6
(4)
The concentration of the anion [A-] of the weak acid is equal to the difference between [H+]zand [H+Iland can be expressed in terms of A E and [Cl-] thus [A-]
=
C1-
(10AE/59.16
- 1)
(5)
The concentration of the undissociated weak acid is then the difference between the analytical concentration of the weak acid and the concentration of the anion. All of the terms necessary to solve for K ' , the concentration ionization constant can be obtained if the chloride ion concentrations, and the weak acid concentration are known and A E is measured under conditions such that the ionic strength and the chloride ion concentration does not change. Method for Determining AE. To meet the requirement for determining AE, the following method is employed. A sufficiently large known volume of ethanol-water solvent is prepared. The ionic strength is adjusted by dissolving an inert electrolyte in the solvent. Hydrochloric acid is added to give a known concentration of strong acid. This gives a solvent of known ionic strength and acid concentration. The weak acid is then dissolved in a known quantity of this stock solvent, The potential difference between these two solutions should be a measure of the hydrogen ion concentration due to the weak acid. The measurements are made in the following manner. The electrodes are placed in a known quantity of solvent without the weak acid and the potential is measured. Known quantities of the weak acid solution are added from a buret. Since both solutions contain identical concentrations of inert electrolytes and hydrochloric acid, the change in volumes on addition does not alter the composition of the system except for the weak
acid concentration. In this manner a series of potential changes from a given acid can be measured. The difference between the starting potential and the potential after each addition is AE. EXPERIMENTAL
Apparatus.
All potential measurements were made at
25.0 =t 0.1 “C on a Beckman Research Model pH meter. The cell consisted of a glass electrode (Beckman 41263) and
a silver-silver chloride electrode. The silver-silver chloride electrode was prepared by electroplating silver from a cyanide free potassium dicyanoargentate solution onto a platinum inlay electrode (Beckman 39273) ( 4 ) . The silver chloride was deposited on the electrode by anodizing the silver electrode in an acidic solution of potassium chloride (5).
Reagents. Glacial acetic acid (Fisher Scientific Co.) was used without further purification. Dimethylphenylacetic acid (City Chemical Co.), diphenylmethylacetic acid and triphenylacetic acid (Aldrich Chemical Co. )were recrystallized from ethanol-water. All were analyzed by titration with standard sodium hydroxide to a phenolphthalein end point. All of the acids were better than 99.8% pure except acetic acid which gave an assay of 98.81%. The impurity in the acetic acid was assumed to be water. Solvent Composition. The solvent composition on a weight percent basis was found by determining the specific gravity of the solvent mixtures with a picnometer. The weight per cent was obtained from specific gravity tables for ethanolwater mixtures (6).
RESULTS AND DISCUSSION The relationship of AE to the hydrogen ion contributed by the weak acid is dependent upon the concentration of hydrochloric acid, the total concentration of weak acid and the accuracy to which the potential can be measured. The concentration of hydrochloric acid must be sufficient to prevent the proton from the solvent from contributing to the potential. In the case of water, a concentration of 10-5F HCl is sufficient to prevent the self-dissociation of the solvent from interfering. The hydrochloric acid must be a strong acid in the solvent. This can be determined by measuring the potential of a series of hydrochloric acid solution in the solvent. A ten-fold change in hydrochloric acid should give a 118 mV change in potential. Table I shows (4) A. S.Brown, J. Am. Chem. SOC.,56,646 (1934). ( 5 ) J. 0. Frohliger and R. T. Pflaurn, Tuluntu, 9,755 (1962). (6) “Handbook of Chemistry and Physics,” 36th ed., Chemical Rubber Publishing Co., Cleveland, Ohio, 1954, pp. 1932-1938.
Table I. Response of Electrodes to Hydrochloric Acid in Solvent Systems at 25 “C Pot entia1 Potential change, Concn range change, rnV rnV Solvent 8.79 X to -79.2 to 55.0 119 Water 76% EtOH 4 5 z EtOH
1 . 0 3 x 10-3 5.81 X to 6.72 x 10-4 5.26 X to 6.89 X l W 4
-6.6 to 119.4
118
-63.8 to 69.9
119
that hydrochloric acid is completely dissociated in the solvent systems used, In the case of water, hydrochloric acid concentrations below about 1 X 10-4Fdid not give results that corresponded to Equation 1. This is due to the contribution of chloride ion from the silver chloride surface of the electrode, For this reason, a concentration of 1 X 10-4F hydrochloride acid was chosen as the lower limit. The total concentration of weak acid is dependent upon its solubility and degree of dissociation. An arbitrary choice of a solubility of 1 x 10-2Fwas chosen. Of the compounds used in this investigation, only acetic acid was soluble to that extent in water. The dimethylphenylacetic acid and diphenylmethylacetic acid were soluble to that extent in 45 % ethanol but the triphenylacetic acid required 76 ethanol to be soluble to 1 X 10-2F. The Beckman Research Model pH meter can be read to the nearest 0.001 mV and is accurate to 0.05 mV. With these figures as guidelines, if a 1 x 10-2F solution of a weak acid containing a 1 x 1 O - T hydrochloric acid would give a 1.00 mV change. The K, of the acid would be about 4 X It is necessary that the concentration of the hydrochloric acid be kept at a very low concentration in order that the contribution of hydrogen ion from the weak acid be sufficient to give a measurable potential change. An error of one millivolt will give a four percent error in the hydrogen ion concentration (7). From this preliminary investigation, acid dissociation constants on the order of 5 X lo-* can be measured. Ionization Contents of Acetic Acid in Water. The validity of Equations 1 through 5 was tested by measuring the ionization constant of acetic acid in water. The results of a typical experiment are tabulated in Table 11. The observed potential (7) M. Stern, H. Shwachman, T. Light, and A. deBethune, ANAL. CHEM., 30, 1506 (1958).
Table 11. Representative Determination of Acetic Acid in Water by Differential Potentiometry at 25 ‘Ca VOl.
HAC addedb 0.885 X 10-2M 0.00 1 .oo 2.00 5.00 10.00 20.00 40.00
E -
rnV
AE rnV 0
-34.7 -29.2 5.5 -25.8 8.9 -20.1 14.6 -16.1 18.6 -11.5 23.2 -8.4 26.3 c[HCl] = 2.02 X lO-’M, [NaNOt] = 2.00 X 10-lM. * Original volume of solution = 25 rnl. Calculated using the extended Debye-Huckel Law.
[H+] x lo4
[Ac-] X lo6
Eq 4
Eq 5
[HAC]X lo4
...
...
2.50 2.86 3.57 4.17 4.99 5.63
4.83 8.37 15.5 21.5 29.6 36.0
...
3.30 6.46 14.9 26.0 40.8 57.0
K X lo6 ...
...
3.66 3.71 3.71 3.45 3.62 3.56
1.80 1.82 1.82 1.70 1.78 1.75
K2
~~
VOL. 40, NO. 10, AUGUST 1968
1409
5.01
I
I
I
0.1
0.2
0.3
4
I 0.4
I
I
0.5
0.6
I
Figure 1. Ionization constants of acetic acid in water as a function of ionic strength was affected by stirring the solution after each addition and required a few minutes to reach a stable value. Potential readings were taken at one minute intervals for the first five minutes after stirring. It was found that the reading taken at the three, four, and five minute intervals were within 0.5 mV of each other. All potentials used in this investigation were the three minute values. Since all measurements were made at constant ionic strength, the change in potential is a measure of the concentration of the hydrogen ion. Figure 1 gives the data of the concentration dissociation constant of acetic acid in water as a function of ionic strength. The upper straight line is the variation of pK as a function of the square root of the ionic strength using the Debye-Huckel limiting law while the curved line is arrived at using the extended Debye-Huckel equation (8): I-
The values which were obtained in this investigation follow the extended Debye-Huckel equation. The results are shown in Table 111. If the ionic strength is 0.01M or less, then the limiting law can be used to calculate pKa. Acetic Acid in Ethanol-Water Systems. The pKa of acetic acid in ethanol-water systems have been studied potentio(8) H. A. Laitinen, “Chemical Analysis,” McGraw-Hill, New York, 1960, p. 11.
10
20
30
40
Diphenylmethylacetic acid Dimethylphenylacetic acid Triphenylacetic acid
45 45 45 76 45 76 45 76 76
ANALYTICAL CHEMISTRY
10 10 10 5 25 4 10 4 4
0.01 0.05 0.005 0.0005 0.01 0.01 0.01 0.01 0.01
50
60
Weight Percent Ethanol
70
80
Figure 2. Ionization constants of acetic acid in ethanol-water mixtures o = Values of E. Grunwald and B. J. Berkowitz. J. Am. Chem. SOC.. A = =
73,4939 (1951) Values of H. 0. Spivey and T. Shedlovsky, J. Phys. Chem., 71, 2171 (1967)
Values obtained by differential potentiometry
Table 111. Ionization Constant of Acetic Acid in Water at 25 “C KQ x 105 3.66 3.64 3.36 3.62 3.76 3.54 3.44 3.53 3.37 3.26 2.59 2.47 2.52 2.09
Kab X 1Oj 1,78 1.78 1.66 1.78 1.84 1.74 1.98 2.03 1.94 1.88 1.71 1.63 2.10 1.70 Av 1.82
P
0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.1 0.1 0.1 0.05 0.05 0.01 0.01
PKG 4.75 4.75 4.78 4.75 4.74 4.76 4.70 4.69 4.71 4.73 4.77 4.79 4.68 4.77 4.74
a Each value represents at least five measurements on a given solution. b Calculated from the Extended Debye-Huckel Law.
Table IV. Ionization Constants in Ethanol-Water Solvents at 25 “C Number of measure2 EtOH ments P K K,
Acid Acetic acid
1410
4.5
3.98 X 5.29 x 3.35 x 1.99 x 2.70 X 1.39 x 1.60 X 7.80 X 4.32 x
10-6 10-6 10-7 10-8 10-7 lo-*
10-7
2.51 x 1.98 X 2.44 x 1.66 x 1.70 x 6.27 x 1.10 x 3.52 X 1.95 x
2 Std dev
10-6 12 10-8
10-7
10-6 lo-* 10-7
6 7 8 6 3 8
PK= 5.60 5.70 5.61 6.78 5.77 7.20 6.00 7.45 6.70
metrically by Grunwald and Berkowitz (3) and more recently by Spivey and Shedlovsky using an electrolytic conductance method (9). The two methods give good agreement over a wide range of ethanol-water mixtures. The pK, of acetic acid in 45% ethanol-water and 76% ethanol-water mixtures were determined using the differential potentiometric method. These results are shown in Table IV. The results at 45z EtOH agree with the results of both Grunwald and Berkowitz and Spivey and Shedlovsky while the results in 76% EtOH agree with the values of Spivey and Shedlovsky. The comparison is shown in Figure 2. The
agreement of the values obtained by the differential potentiometric technique and the conductiometric technique indicates that the method is applicable in ethanol-water mixtures. The acid dissociation constant of diphenylmethylacetic acid, dimethylphenylacetic acid and triphenylacetic acid were then determined in 76 ethanol-water. The diphenylmethylacetic acid and the dimethylphenylacetic acid were determined in 45z ethanol-water as well. The triphenylacetic acid was not soluble to 10-2M in less than 76 ethanol-water and thus could not be measured by the differential potentiometric procedure. The results are given in Table IV.
(9) H. 0. Spivey and T. Shedlovsky, J . Phys. Chem. 71, 2171 (1967).
RECEIVED for review April 5, 1969. Accepted May 29, 1969.
z
A Study of Operational Amplifier Potentiostats Employing Positive Feedback for ;R Compensation 1. Theoretical Analysis of Stability and Bandpass Characteristics Eric R. Brown' and Donald E. Smith2 Department of Chemistry, Northwestern Unicersity, Ecanston, Ill.
60201
Glenn L. Booman Idaho Nuclear Corporation, P. 0. Box 1845, Idaho Falls, Idaho
The stability and bandpass characteristics have been investigated theoretically for an operational amplifier potentiostat which utilizes positive feed back for compensation of iR drop in three-electrode cell configurations. Major sources of instability are identified and a reasonably efficient stabilization procedure is elucidated which greatly suppresses previously noted stability mar in degradation associated with the use of the positive Veedback loop. The calculations indicate that a substantial improvement over previously noted performance with 100% iR compensation can be realized through the use of high performance operational amplifiers and appropriate stabilization techniques.
To EFFECT COMPENSATION of ohmic potential loss (iR drop) in electrochemical relaxation techniques, a number of workers have considered the addition of a positive feedback loop to conventional potentiostats for three-electrode cell configurations (1-11). Most of these studies have employed potentiostats constructed from operational amplifiers (1-7). Ideally, the positive feedback loop permits addition of a signal equal to the iR drop to the potentiostat input voltage. Although noteworthy success was realized in most cases, it was noted by some workers that degradation of the potentiostat stability margin accompanied the use of the positive feedback loop (3, 5, 6, IO, 11). Maintenance of a safe stability margin was achieved, at the cost of notable reduction in bandwidth, by operating with something less than the ideal of 100% iR compensation (5, 7) and/or by utilizing damping capacitors in the feedback of the control amplifier (6). The damping Present address, Research Laboratories, Eastman Kodak Co., Rochester, N. Y . 14650. To whom correspondence should be addressed.
83401
capacitor approach enabled realization of 100% iR compensation with low and moderate frequencies (6). Although the crudeness of this stabilization method was acknowledged, together with the possibility that a more sophisticated approach might avoid the attendant severe loss of bandpass (6), no attempt at improvement has been reported to our knowledge. To realize faster potentiostat response while maintaining a safe stability margin with 100% iR compensation, it appeared essential to obtain more detailed insight into the factors controlling stability and bandpass through an appropriate theoretical analysis of the potentiostat-cell response characteristics. Results of such a study are given below for a potentiostat in the current-follower mode ( 2 ) which employs positive-feedback iR compensation. The stability-bandpass calculations are modeled after the treatment of Booman and Holbrook ( I , 2), which explicitly accounted for positive feedback sufficient to negate effects of i R drop in the load resistor
(1) G. L. Booman and W. B. Holbrook, ANAL.CHEM., 35, 1793 (1963). (2) G. L. Booman and W. B. Holbrook, ibid., 37, 795 (1965). (3) J. W. Hayes and C. N. Reilley, ibid., 37, 1322 (1965). (4) D. Pouli, J. R. Huff, and J. C. Pearson, ibid., 38, 382 (1966). (5) G . Lauer and R. A. Osteryoung, ibid., 38, 1106 (1966). (6) E. R. Brown, T. G. McCord, D. E. Smith, and D. D. DeFord, ibid., 38, 1119 (1966). (7) R. R. Schroeder, Ph.D. Thesis, University of Wisconsin, Madison, Wis., 1967. (8) J. W. Hayes and H. H. Bauer, J . Electroanal. Chem., 3, 336 (1962). (9) M. E. Peover and J. S. Powell, J . PoIarog. SOC.,12, 64 (1966). (10) H. Gerischer and K. E. Staubach, Z . Elektrochemie, 61, 789 (1957). (11) P. Valenta and J. Vogel, Chem. Listy, 54, 1279 (1960). VOL. 40, NO. 10, AUGUST 1968
141 1
