Simplified Spectrophotometric Determination of Acid Dissociation Constants John 0. Frohligerl Department of Occupational Health, Graduate School of Public Health, University of Pittsburgh, Pittsburgh, Pa. 15213
Joseph E. Dziedzicz and Omar W. Steward Department of Chemistry, Duquesne University, Pittsburgh, Pa. 15219 A simplified method for the spectrophotometric determination of acid dissociation constants has been developed. Equations for calculating the acid dissociation constants are presented. The measurements are made on a system at equilibrium containing a weak acid and the sodium salt of a second weak acid. For each system, the total concentration of the two acids and the dissociation constant of one of the acids must be known, and the concentration of one of the anionic species must be determined spectrophotometrically. Acid dissociation constants of the type RR‘R“ MCOOH where R, R‘, R” may be H, CH,, or C6H, and M may be C, Si, or Ge were determined in 45 weight per cent ethanol, 76 weight per cent ethanol, and dimethyl sulfoxide.
ACID DISSOCIATION CONSTANTS in nonaqueous systems have been determined using potentiometric (1-9,conductimetric (8) and spectrophotometric methods (9,lO). Although the potentiometric method usually suffers from the lack of standard buffer solutions, and unknown liquid junction potentials ( I I ) , it has been preferred over the more tedious spectrophotometric procedure (12). The spectrophotometric procedure requires that at least one species, either the anion or the undissociated acid, have an absorption band region which adheres to Beer’s law. After the spectra are obtained, the absorbances of several solutions buffered at different pH are determined. When the activity of the anion equals the activity of the undissociated acid, the pH equals pK,. Usually the activity coefficients are taken to be unity, and concentrations are used instead of activities. In order to measure the pK, of a substance that does not have a pure absorption spectrum, indicators have been used. A small known amount of an indicator with a known pK, is
added to a solution containing known quantities of a weak acid and its salt. The absorbance of the indicator at a known wavelength is measured. The acid dissociation constant is then calculated from the equation, PKHA = pKmn
+ log [HA] - log [A-] - log
01
where ~ K H I is, the dissociation constant of the indicator and the ratio of the absorbance of HIn to In-. In this investigation a simplified approach to the indicator method is presented that permits the determination of dissociation constants of compounds which have either an unstable acid form or an unstable base form. The procedure used in this method does not require that both the acid form and the base form of the compound be available, that a buffer solution be prepared, or that the pH of the solution be determined by an independent method. This method has the added advantage that a spectrophotometric measurement is made at one wavelength on one species and thus does not require an elaborate experimental procedure. As many as 12 separate measurements can be made in 1 hour. The simplified spectrophotometric method utilizes the equilibrium conditions of weak acids and bases. a! is
HA
+ Na+Z-
+ HZ
+ Na+A-
(1)
The concentration relationships involved in an ionic equilibrium of a weak acid with the base form of a second weak acid are,
(3) To whom correspondence should be addressed. Present address, FMC Corp., Princeton, N. J. (1) C. D. Ritchie and P. D. Heffley, J. Amer. Chem. SOC.,87,5402 (1965). (2) E. Grunwald, ibid., 73, 4934 (1951). (3) E. Grunwald and B. J. Berkowitz, ibid., p 4939. (4) J. 0. Frohliger, R. A. Gartska, H. W. Irwin, and 0. W. Steward, ANAL.CHEM., 40, 1408 (1968). (5) C. D. Ritchie and R. E. Uschold, J. Amer. Chem. Soc., 89, 1721 (1967). (6) C. D. Ritchie and G. H. Megerle, ibid., p 1447. (7) Ibid., p 1452. (8) H. 0. Spivey and T. Shedlovsky, J. Phys. Chem., 71, 2171 (1967). (9) I. M. Kolthoff and T. B. Reddy, Inorg. Chem., 1, 189 (1962). (10) B. W. Clare, D. Cook, E. C. F. KO, Y. C. Mac, and A. J. Parker, J . Amer. Chem. SOC.,88, 1911 (1966). (11) L. Meites and H. C. Thomas, “Advanced Analytical Chemistry,’’ McGraw-Hill Book Co., Inc., New York, N. Y . , 1958, p 22. (12) C. E. Meloan and R. W. Kiser, “Problems and Experiments in Instrumental Analysis,” Charles E. Merrill Books, Inc., Columbus, Ohio, 1966, p 9.
[H+l
+ [Na+l
= [A-I
+ [Z-I
(6)
when [A]T and [ZIT are the analytical concentrations of the species present in the system. These equations hold as long as the autodissociation of the solvent is negligible. In the equilibrium system described by Equations 2 through 6, [A]T and [ZIT can be obtained by dissolving a weighed amount of either the acid or base form into a known volume of solvent. Then, if [Z-] can be measured spectrophotometrically and one of the ionization constants is known, the equations can be solved and the other dissociation constant calculated. Since one of the two acids is in the base form and one of the two ionization constants is known, there are four possible combinations of the variables which can be used to solve Equations 2 through 6. The four combinations or cases are given in Table I. In all cases [Z-] is determined spectrophotometrically.
ANALYTICAL CHEMISTRY, VOL. 42, NO. 11, SEPTEMBER 1970
1189
Table I. Cases for the Determination of Acid Dissociation Constants Known dissociation constant KHZ KEA KHZ KEA
Case No. I I1 I11 IV
Acid form HA HA HZ HZ
Base form ZZA-
A-
Table 11. Dissociation Constants Determined by Direct Spectrophotometry Compound 2,6-Dinitrophenol 2,4-Dinitrophenol 2,4-Dinitrophenol
Solvent 45 wt Ethanol-water 76 wt Ethanol-water Dimethyl sulfoxide
PK= 3.97 f 0.04 4.76 iZ 0.02 5.05 iZ 0.02
Case I. The acid dissociation constant of the base form is known and the anion of the base form is measured spectrophotometrically.
(2
- 1)
[H+] = KHZ
[HA]
=
[A],
(7)
- [A-I
(9)
Case 11. The acid dissociation constant of the acid form is known and the anion concentration of the base form is measured spectrophotometrically. The expression for the [H+] is a quadratic.
+ (KHA+ [HZI) [H+l -
[H+12
KHA([A],
- "1)
= 0
[HZI = [ZIT - [z-1
(10)
fied Reagent Grade), 2,6-dinitrophenol (Eastman Grade) dimethylphenylacetic acid (City Chemical Co.), diphenylmethylacetic acid, and triphenylacetic acid (Aldrich Chemical Co.) were crystallized several times from ethanol-water; bromcresol purple (Fisher Scientific Co.) from acetic acid; sodium benzoate (Allied Chemical Corp.) from acetonewater; sodium salicylate (Allied Chemical Corp.) from ethanol. Dimethylphenylsilane-, diphenylmethylsilane-, triphenylsilane-, and triphenylgermanecarboxylic acid were prepared and described previously (13) by a modification of the method of Gilman and coworkers (14,15) and were crystallized several times from benzene-petroleum ether or petroleum ether. Sodium 4-nitrophenoxide, sodium 2,4-diNtrophenoxide, and sodium 2,6-dinitrophenoxide were prepared from the corresponding acid forms and were crystallized several times from distilled water. Solvents. Dimethyl sulfoxide (Fisher Certified Reagent Grade) was distilled under reduced pressure from calcium hydride, bp 55 "C (4.1 mm). The solvents, dimethyl sulfoxide, 95% ethanol (USP Reagent), and distilled water, employed in the determination of the pK, values of the acids, were distilled prior to use. Purified dimethyl sulfoxide was stored in the dark under a nitrogen atmosphere. The 45 wt ethanol-water solvent was prepared by adding 495 ml of water at 25 "C to a 1-liter volumetric flask. This was then diluted to the mark with 95 % ethanol at 25 "C. In a similar ethanol-water solvent was prepared. manner, the 76 wt In this case, 150 ml of water was used. Spectrophotometric Procedures. A known volume of solvent containing a known concentration of the species which shows no absorbance at the wavelength employed was placed in a 10-cm cuvette. The cell was allowed to equilibrate in the temperature controlled cell compartment of the spectrophotometer. An aliquot of the indicator solution was added from a microburet (0.001-ml subdivision), the cell was shaken to mix the solution, and the absorbance was recorded. Additional aliquots were added, and the absorbance was recorded after each addition. In this manner, as many as eight measurements could be obtained. A second analysis was made in every case using different concentrations of the solutions.
z
(11) RESULTS AND DISCUSSION
Case 111. The acid dissociation constant of the acid form is known and the anion concentration of the acid form is measured spectrophotometrically.
The determination of the acid dissociation constant by this method requires that one of the two compounds used have a known acid dissociation constant. Three compounds were chosen as the standards, sodium 2,6-dinitrophenoxide for the 45 wt ethanol-water solvent, sodium 2,4-dinitrophenoxide for the 76 wt Z ethanol-water solvent, and 2,4-dinitrophenol for the dimethyl sulfoxide solvent. The values obtained are shown in Table 11. The application of the spectrophotometric method depends upon the equilibrium conditions of the equation.
z
[HA]
=
[Z-]
- KHZ
(Q [Z-I
1)
Case IV. The acid dissociation constant of the base form is known and the anion concentration of the acid form is measured spectrophotometrically. The expression for the [H+] is again a quadratic equation.
+ (KEA+ [A]T - [Z-I)[H+l - KHA[Z-] = 0
[H+I2
[HA]
=
[ZIT - [z-]
(15) (16)
EXPERIMENTAL
Apparatus. All spectrophotometric measurements were made on a Cary Model 14 Spectrophotometer using 10-cm cells at 25.0 i 0.1 "C. Calculations were carried out on a Control Data G-20 Computer. Reagents. The acids and salts, obtained from commercial sources, were purified as indicated below: benzoic acid, salicylic acid, 4-nitrophenol, 2,4-dinitrophenol (Fisher Certi1190
HA
+ NaZ = NaA + H Z
(19)
If the equilibrium is shifted too far to the right or left, the results will not be valid. The equilibrium conditions are controlled by the acid dissociation constants and the analytical concentration of two species used in the determination. Although it is not possible to accurately determine the necessary equilibrium conditions prior to the measurement, the procedure of adding small increments of the absorbing species from a microburet offsets this disadvantage. This procedure (13) 0. W. Steward, H. W. Irwin, R. A. Gartska, and J. 0. Frohliger, J . Chem. SOC.( A ) , 3119 (1968). (14) A. G. Brook and H. Gilman, J . Amer. Chem. SOC.,77, 2322 (1955).
(15) H. Gilman and W. J. Trepka, J. Org. Chem., 25, 2201 (1960).
ANALYTICAL CHEMISTRY, VOL. 42, NO. 11, SEPTEMBER 1970
Table III. pK, Values for Acids in Dimethyl Sulfoxide at 25 "C Using All Four Casesa Acid 2,4-Dinitrophenol Salicylic ~acid Bromcresol purple Bromocresol purple Benzoic acid Acetic acid --
Base
,
Sodium 2,4-dinitrophenoxide Sodium salicylate Sodium benzoate Sodium 4-nitrophenoxide Sodium Cnitrophenoxide
Detns 9 8 13 9 14
Case No. I IV 111 I1 I
10
PK. Found 5.05 f 0.02bpc 6.79 f 0.10 10.08 f 0.10 10.06 f 0.17 9.87 f 0.01 11.41 f 0.02
Lit. 5.2d 6.9~ 10.0dge 11.0, 9.9d 10.40 1 1 . 4 ~11.60
Underlined compounds are compounds for which dissociation constants were determined. pK, value determined by direct spectrophotometry. c Standard deviation. d Ref. (10). e Ref. (9). Ref. (16). 0 Ref. (5).
a I,
Table IV. pK, Values Determined in Various Solvents at 25 "C 45 Wt Ethanol-Water0 No. PKL3 M.p., "C detns Found Lit.d 11 5.61 f 0.016 5.64 f 0.06 34 -35 23 6.41 f 0.08 79.5-80 11 6.05 f 0.01 6.00 f 0.03 177.5-180 11 5.81 f 0.01 5.77 f 0.04 274 -275 56.5-58 16 6.06 f 0.05' 5.96 f 0.10 139 -140 11 5.97 f 0.030 5.66 f 0.05 dec 183 -185 dec 187 -190 dec a Case I: base sodium 2,6-dinitrophenoxide. b Case I: base sodium 2,4-dinitrophenoxide. c Case I: base sodium 4-nitrophenoxide. d Ref. (13). * Standard deviation. 1 Small amount of base-catalyzed decomposition of the acid. 0 Significant base-catalyzed decomposition of the acid. gives a wide concentration variation in the system and the subsequent additions can be adjusted to give absorbance values that yield valid results. The concentration ranges used in the method are usually dilute enough to allow activity effects t o be neglected. N o corrections for activity were made in these measurements. To avoid large differences in the ionization constants of HA and HZ, it is sometimes necessary to utilize compounds with intermediate ionization constants. Table I11 shows how the pK, of 4-nitrophenol was obtained from the known pK, of 2,4-dinitrophenol by the use of several intermediate compounds. All four equilibrium cases were employed since some of the compounds used do not have absorption spectra in the visible region. Table IV shows the results of the determinations of acid ethanol-water solvent on a dissociation constants in 45 wt
x
(16) C. D. Ritchie and R. E. Uschold, J. Amer. Chem. SOC.,90, 2821 (1968).
~
Ethanol-Water6 -76 Wt No. PKG detns Found Lit.d 12 6.57 f 0.028 6.78 f 0.02 19 7.96 f 0.05 6 7.45 f 0.02 7.45 f 0.04 7.15 f 0.09 7.20 f 0.03 12 10 6.70 f 0.03 6.78 f 0.02 7.28 f 0.05 12 10 7.04 f 0.05 7.03 f 0.09 9
6.10 f 0.10
6.23 f 0.04
11
6.27 f 0.03
6.32 f 0.02
Dimethyl sulfoxidec No.
detns
PK~
13 16 24 21
12.39 f 0.128 11.10 f 0.05 10.00 f 0.04 9.29 f 0.07
6
8.43 f 0.06
series of carboxylic acids. The values obtained by this method agree well with the values obtained by a potentiometric method (23). Similar results are found in 76 wt ethanol-water solvent, except that the pK, for acetic acid appears to be lower than the values reported in the literature. These results are shown in Table IV. The method also was applied to the solvent dimethyl sulfoxide. These results are given in Table IV. The siliconsubstituted carboxylic acids were very unstable in this solvent and their dissociation constants could not be determined.
x
RECEIVED for review February 25, 1970. Accepted June 18, 1970. Presented in part at the 154th National Meeting, American Chemical Society, Chicago, Ill,, Sept. 1957. The authors gratefully acknowledge the financial support of the Dow Corning Corporation, Midland, Mich., and a grant from the National Science Foundation for the Cary Model 14 Spectrophotometer.
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