ANALYTICAL
BIOCHEMISTRY
79, 406-412 (1977)
Graphical Determination of Acid Dissociation Constants of Substances Contaminated by Strong Mineral Acid or Base ROBERT Department
of
W. GUYNN
Psychiatry, The University of Texas Medical School at Houston, and the University of Texas Health Science Center at Houston, Graduate School of Biomedical Science, Houston, Texas 77030 Received September 3, 1976; accepted December 9, 1976
Nonlogarithmic graphical treatments of acid/base titration data are presented which can identify and compensate for unknown contaminations of a compound by either a strong mineral acid or base. The methods which have been demonstrated allow an accurate determination of an acid dissociation constant of a compound in the presence of up to 50% contamination by strong mineral acid or base.
The determination of the acid dissociation constants (K,) of compounds of biological or pharmaceutical interest is a common research problem, the theoretical and practical advances of which have been reviewed recently (1). Though, mechanically, the titration of an acid with a base is relatively straightforward (2), the determination of the K, from the results is often more complicated. The practical advantage of nonlogarithmic graphical treatments in the handling of titration data has been pointed out (3-5), and several graphical procedures have been suggested (3-l l), including methods useful in the presence of neutral impurities (7-10) and in situations where the product of the titration is insoluble (12,13). However, there seems to have been little attention given to the common problem of titration of a substance contaminated with small but unknown amounts of strong mineral acid or base. The current communication describes nonlogarithmic graphical techniques for the determination of the K, from titration data in such situations. DERIVATION
OF EQUATIONS
The simple case of a titration of a monobasic organic acid contaminated with a strong monobasic mineral acid will serve to illustrate the methods. For derivations, the concentration of the hydrogen ion is indicated by use of square brackets ([H+]). Otherwise, all compounds and ions are expressed in absolute moles rather than concentrations, taking the lead of other investigators (9,10,13). 406 Copyright 8 1977 by Academic Press. Inc. All rights of reproduction in any form reserved.
ISSN MtO3-2697
ACID DISSOCIATION
Definitions used are HA, monobasic acid being titrated, form; A-, monobasic acid being titrated, dissociated form; total monobasic acid being titrated; B+, monovalent cation C-, anion of strong mineral acid contaminant; Y, AT + C-, acid; and K,, the acid dissociation constant. Method
407
CONSTANTS
undissociated AT, HA + A-, of base titrant; total titratable
I
For the situation in which the total titratable acid (Y) is known but neither AT nor C- are known, an exact determination of K, is still readily determinable. During the titration, the system is described by Eqs. [l-3], Eq. [3] fulfilling the requirements of electroneutrality: K, = [H+]A-/HA,
111
AT = HA + A-, and
PI
B+ + H+ = A- + OH- + C-. Algebraic combination becomes Eq. [5]:
of Eq. [l-3]
K, = [H+](B+ + H+ - OH- - C-)/{A,
yields Eq. [4] which,
[31
in turn,
- (B+ + H+ - OH- - C-,},
[4]
and K, = [H+](X
- C-)/( Y - X),
[51
whereX = B+ + H+ - OH-. Equation [5] can be rearranged into Eq. [6], the equation of a straight line:
1 = -(Y - -UN-J+1+ X C-/K,
c-
El
A plot of (Y - X)/[H+] on the ordinate and X on the abscissa will, therefore, yield a straight line with a slope of I/K, and an intercept of C-. If the acid being titrated has been contaminated with a strong mineral base rather than an acid, the slope of the graph will be unchanged, but the intercept will appear as a negative acid contamination. Similarly, equations can be derived for the titration of a monoacidic base contaminated with a strong mineral base (C+). In this situation, a straight line is obtained with a slope of K, and an intercept of C+ by plotting (Y’ - X’)[H+] on the ordinate and X’ on the abscissa, where Y’ = total titratable base, and X’ = B- - H+ + OH-;B- = monovalent anion of acid titrant . Method
II
In the situation where the concentration of the acid to be titrated (AT) can be assayed independently, but the determination is in conflict with end-
408
ROBERT
W. GUYNN
point titration data, or as in the case of polybasic acids, where a comparison with end-point titration data is complicated by the presence of other pK,s, useful information can be obtained from a graphical approximation. Equation [4] can be rearranged into Eq. [7]: 1 = {-(AT
- X)/C-}
+ {[H+](X
- C-)IK,C-}.
171
If C- were known, a plot of [H+](X - C-) on the ordinate and (AT - X) on the abscissa would yield a straight line with a slope of K, and an intercept on the abscissa of -C. Since C- is unknown, however, one can plot [H+]X on the ordinate and (AT - X) on the abscissa to obtain a graph from which the following interpretations can be made: (i) If a straight line is obtained which passes through the origin, the slope of the line will be K,, and the acid can be judged to uncontaminated. (ii) If a straight line is obtained which does not pass through the origin, the slope of the line will be K,, and the acid can be judged to be uncontaminated but misassayed. (iii) In the presence of acid contamination, an upward concave curve will be produced which will approach linearity as it approaches the abscissa with a slope approximating K, and an intercept on the abscissa approximating -C-. The approximate value of C- can be used to replot the data, but with [H+](X - CL) on the ordinate instead of [H+]X. This replotting will straighten the curve, yielding closer approximations of both K, and C-. The process can be repeated if necessary to refine the value further. If the curve cannot be converted into a straight line by successive approximation of C-, either one of the terms making up X is in error (either the concentration of the base or the pH measurements) or there is a contaminating organic acid with a pKa close to the one being studied. (iv) In the presence of base contamination of the acid, the curve will be concave downward and will extrapolate to the other side of the origin as a negative acid contamination . The corresponding plot for the titration of a monoacidic base contaminated with a strong mineral base is [H+](BT - X’) on the ordinate and X’ on the abscissa, where X’ = B- - H+ + OH-(BT = total monacidic base being titrated; B- = monovalent anion of acid titrant). The slope of the graph will approximate K,, and the intercept on the abscissa will approximate C+. Using the estimate of C+, the data can be regraphed, plotting [H+](Br - X’ + C+) on the ordinate and X’ on the abscissa, to straighten the curve and obtain better estimates of C+ and K,. Method
III
In the case in which neither AT nor Y is known with any accuracy, since AT is a constant, a plot of [H+]X on the ordinate and -X on the abscissa for the titration of the monobasic acid will yield the same graph as Method II, except that the curve will be displaced along the abscissa. The intercept on
ACID
DISSOCIATION
CONSTANTS
409
the abscissa will be -A, - C-. From the shape of the curve, the presence and type of contamination can be determined. A qualitative estimate of the degree of contamination can also be made from the severity of the deviation of the graph from linearity. Based on this information, successive guesses of a value for C- can be made in a plot of [H+](X - C-) (ordinate) and -X (abscissa) to obtain a straight line, allowing determination of both K, and AT. METHODS To illustrate the use of the graphical procedures, 0.1 N acetic acid, with and without contamination by strong mineral acid or base, was titrated with 0.1 N carbonate-free standardized NaOH. All reagents were analytical grade, the solutions being prepared immediately before use in degassed distilled water (2). The titrations were performed in a vessel equilibrated to 25°C in a constant-temperature water bath. A Sargent Welch Model NX pH meter with Corning glass electrode 476050 was used. The glass electrode utilized was calibrated versus Sargent Welch buffers which had been verified on a Radiometer Copenhagen PHM 71MK2 pH meter and G2971G2 microelectrode standardized with Radiometer precision buffers. The acetic acid was assayed by both an end-point titration and an enzymatic procedure (14). Determination of the slope and intercepts of the graphs was by linear regression analysis. The data is presented as the mean t SEM. RESULTS AND DISCUSSION At 25”C, the titration of the uncontaminated acetic acid produced a pK, value of 4.77 ? 0.01 (Fig. l), in very good agreement with the value of 4.76 derived from electromotive force measurements under similar conditions (25°C; ionic strength, 0.01-o. 18 M) (15). Ionic strength effects can be ignored in the current titrations since, under the conditions chosen, the observed pK, is sensitive only to the third decimal place to variations in ionic strength up to 0.18 M (15). In most situations, however, it is understood that the ionic strength may need to be kept constant throughout the titration or activity coefficient corrections may need to be made (1,2). Titrations of acetic acid solutions containing approximately 10% contamination by either HCI or NaOH were carried out, the results being analyzed by either Method I or II. When Method I was used, straight lines parallel to the graph of the uncontaminated acid were obtained (Fig. 1). Values for the pK, of 4.78 + 0.01 (correlation coefficient = 0.9996) and 4.77 5 0.01 (correlation coefficient = 0.9998) were obtained for the acidand base-contaminated solutions, respectively. When Method II was used, upward and downward concave curves were obtained in the presence of acid and base contaminations, respectively (Fig. 2). In the case of acid
410
ROBERT W. GUYNN
FIG. 1. Titration data plotted by Method I. The graphs represent titrations of 0.100 N acetic acid with 0.100 N NaOH at 25°C. Included is the titration of the pure acid (0 0) and this same acid contaminated with approximately 10% strong mineral acid (x x) or base n ). The NaOH titrant was added in fixed aliquots, and each curve represents the (m average ofat least three titrations. Y = Total titratable acid;X = B+ + H+ - OH-(where B+ is the cation of the base titrant). Square brackets indicate concentration; otherwise, all compounds or ions are expressed in absolute moles rather than concentration.
contamination, the straight line portion of the graph approached the abscissa, giving an approximate pK, of 4.70. A single replotting of the data, using the estimate of C- defined by the extrapolation to the abscissa, straightened the line (correlation coefficient = 0.9998) and yielded value of 4.77 -+ 0.01 for the pK,. Likewise, the original estimate of the pK, from the graph of the base-contaminated solution (4.83) was easily refined. A single correction again produced a straight line (correlation
AC,- X x lo-’
FIG. 2. Titration data plotted by Method II. The conditions and symbols are the same as those of Fig. 1. AC, = total acetic acid as assayed enzymaticalt y ( 14)) rather than by end-point titration.
ACID DISSOCIATION
CONSTANTS
411
coefficient = 0.9999) with an estimate of 4.77 _t 0.01 for the pK,. The same value was obtained in the case of a 50% contamination of the acetic solution by base, although three corrections (based on successively better estimates of C-) were required to straighten the graph (correlation coefficient of final estimate = 0.9998). It is apparent that Method II could be used primarily to determine the purity of a substance, since the graph can distinguish among neutral, acid, or base contaminations. Since Method I always produces straight lines with a slope of l/K,, the amount of contamination which the system can tolerate is limited only by the technical aspects of the titration itself. Method II, on the other hand, seems to have a practical limit near 50% contamination by either acid or base, at least in the systems which have been tested, However, if Method II predicts the presence of a very large contamination, it would be possible to partially neutralize the contamination and repeat the titrations in order to use Method II effectively. Method III has not been specifically illustrated, since the form of the graphs is identical to that of Method II, except that the curves are displaced to the left. Unless a straight line is obtained initially, the usefulness of Method III depends upon how quickly guesses of the value of C- can be refined to straighten the line. In most practical cases, a computer program designed to find the value of C- which produces a correlation coefficient closest to 1 .Ofor the linear regression of the experimental points (-X on the abscissa,X - C- on the ordinate) would be very useful, potentially allowing the determination of the pK, of an acid of unknown concentration, contaminated with unknown amounts of mineral acid or base. Though the titration of a monobasic acid has been used to illustrate the methods, the graphical procedures can be used readily with polybasic acids, provided there is not a significant overlap of pK,s [i.e., provided the difference between the pK,s is greater than rt.7 (2)3. For example, the methods have been successfully applied, recently, to the titration of salts of phosphoric acid and phosphorylcholine under physiological conditions (16). ACKNOWLEDGMENT This work was supported by Grant No. AU-631 from the Robert A. Welch Foundation, Bank of the Southwest Building, Houston, Texas 77002.
REFERENCES 1. Cookson, R. F. (1974) C/rem. Rev. 74, 5-28. 2. Albert, A., and Serjeant, M. R. (1962) Ionization Wiley, New York. 3. Joseph, N. R. (1958) Science 128, 1207. 4. Druckrey, H. (1959) Science 129, 1492. 5. Joseph, N. R. (1959) Science 129, 1493. 6. Hofstee, B. H. J. (1960) Science 131, 39.
Contants of Acids and Bases, John
412 7. 8. 9. 10. 11.
ROBERT W. GUYNN
Benet, L. Z., and Goyan, J. E. (1965) J. Pharm. Sci. Benet, L. Z., and Goyan, J. E. (1965) J. Pharm. Sci. Leeson, L. J., and Brown, M. (1%6)J. Pharm. Sci. Benet, L. Z., and Goyan, J. E. (1967) J. Pharm. Sci. Phan-Tan-Luu, R., Surzur, J.-M., Metzger, J., Aune, Sot.
12. 13. 14. 15. 16.
Chim. Setnikar, I.
Fr.
3274-3277. J. Pharm.
54,983-987. 54, 1179- 1182. 55, 431-433. 56,665~680.
J.-P., and Dupuy, C. (1967) Bull
(1966) Sci. 1190-1195. Levy, R. H., and Rowland, M. (1971)J. Pharm. Sci. 60, 1155-1159. Guynn, R. W., and Veech, R. L. (1974) Anal. Biochem. 61,6-15. Hamed, H. S., and Ehlers, R. W. (1932) J. Amer. Chem. Sot. 54, 1350-1356. Guynn, R. W. (1976)J. Biol. Chem. 251,7162-7167.
BIOCHEMISTRY
79, 406-412 (1977)
Graphical Determination of Acid Dissociation Constants of Substances Contaminated by Strong Mineral Acid or Base ROBERT Department
of
W. GUYNN
Psychiatry, The University of Texas Medical School at Houston, and the University of Texas Health Science Center at Houston, Graduate School of Biomedical Science, Houston, Texas 77030 Received September 3, 1976; accepted December 9, 1976
Nonlogarithmic graphical treatments of acid/base titration data are presented which can identify and compensate for unknown contaminations of a compound by either a strong mineral acid or base. The methods which have been demonstrated allow an accurate determination of an acid dissociation constant of a compound in the presence of up to 50% contamination by strong mineral acid or base.
The determination of the acid dissociation constants (K,) of compounds of biological or pharmaceutical interest is a common research problem, the theoretical and practical advances of which have been reviewed recently (1). Though, mechanically, the titration of an acid with a base is relatively straightforward (2), the determination of the K, from the results is often more complicated. The practical advantage of nonlogarithmic graphical treatments in the handling of titration data has been pointed out (3-5), and several graphical procedures have been suggested (3-l l), including methods useful in the presence of neutral impurities (7-10) and in situations where the product of the titration is insoluble (12,13). However, there seems to have been little attention given to the common problem of titration of a substance contaminated with small but unknown amounts of strong mineral acid or base. The current communication describes nonlogarithmic graphical techniques for the determination of the K, from titration data in such situations. DERIVATION
OF EQUATIONS
The simple case of a titration of a monobasic organic acid contaminated with a strong monobasic mineral acid will serve to illustrate the methods. For derivations, the concentration of the hydrogen ion is indicated by use of square brackets ([H+]). Otherwise, all compounds and ions are expressed in absolute moles rather than concentrations, taking the lead of other investigators (9,10,13). 406 Copyright 8 1977 by Academic Press. Inc. All rights of reproduction in any form reserved.
ISSN MtO3-2697
ACID DISSOCIATION
Definitions used are HA, monobasic acid being titrated, form; A-, monobasic acid being titrated, dissociated form; total monobasic acid being titrated; B+, monovalent cation C-, anion of strong mineral acid contaminant; Y, AT + C-, acid; and K,, the acid dissociation constant. Method
407
CONSTANTS
undissociated AT, HA + A-, of base titrant; total titratable
I
For the situation in which the total titratable acid (Y) is known but neither AT nor C- are known, an exact determination of K, is still readily determinable. During the titration, the system is described by Eqs. [l-3], Eq. [3] fulfilling the requirements of electroneutrality: K, = [H+]A-/HA,
111
AT = HA + A-, and
PI
B+ + H+ = A- + OH- + C-. Algebraic combination becomes Eq. [5]:
of Eq. [l-3]
K, = [H+](B+ + H+ - OH- - C-)/{A,
yields Eq. [4] which,
[31
in turn,
- (B+ + H+ - OH- - C-,},
[4]
and K, = [H+](X
- C-)/( Y - X),
[51
whereX = B+ + H+ - OH-. Equation [5] can be rearranged into Eq. [6], the equation of a straight line:
1 = -(Y - -UN-J+1+ X C-/K,
c-
El
A plot of (Y - X)/[H+] on the ordinate and X on the abscissa will, therefore, yield a straight line with a slope of I/K, and an intercept of C-. If the acid being titrated has been contaminated with a strong mineral base rather than an acid, the slope of the graph will be unchanged, but the intercept will appear as a negative acid contamination. Similarly, equations can be derived for the titration of a monoacidic base contaminated with a strong mineral base (C+). In this situation, a straight line is obtained with a slope of K, and an intercept of C+ by plotting (Y’ - X’)[H+] on the ordinate and X’ on the abscissa, where Y’ = total titratable base, and X’ = B- - H+ + OH-;B- = monovalent anion of acid titrant . Method
II
In the situation where the concentration of the acid to be titrated (AT) can be assayed independently, but the determination is in conflict with end-
408
ROBERT
W. GUYNN
point titration data, or as in the case of polybasic acids, where a comparison with end-point titration data is complicated by the presence of other pK,s, useful information can be obtained from a graphical approximation. Equation [4] can be rearranged into Eq. [7]: 1 = {-(AT
- X)/C-}
+ {[H+](X
- C-)IK,C-}.
171
If C- were known, a plot of [H+](X - C-) on the ordinate and (AT - X) on the abscissa would yield a straight line with a slope of K, and an intercept on the abscissa of -C. Since C- is unknown, however, one can plot [H+]X on the ordinate and (AT - X) on the abscissa to obtain a graph from which the following interpretations can be made: (i) If a straight line is obtained which passes through the origin, the slope of the line will be K,, and the acid can be judged to uncontaminated. (ii) If a straight line is obtained which does not pass through the origin, the slope of the line will be K,, and the acid can be judged to be uncontaminated but misassayed. (iii) In the presence of acid contamination, an upward concave curve will be produced which will approach linearity as it approaches the abscissa with a slope approximating K, and an intercept on the abscissa approximating -C-. The approximate value of C- can be used to replot the data, but with [H+](X - CL) on the ordinate instead of [H+]X. This replotting will straighten the curve, yielding closer approximations of both K, and C-. The process can be repeated if necessary to refine the value further. If the curve cannot be converted into a straight line by successive approximation of C-, either one of the terms making up X is in error (either the concentration of the base or the pH measurements) or there is a contaminating organic acid with a pKa close to the one being studied. (iv) In the presence of base contamination of the acid, the curve will be concave downward and will extrapolate to the other side of the origin as a negative acid contamination . The corresponding plot for the titration of a monoacidic base contaminated with a strong mineral base is [H+](BT - X’) on the ordinate and X’ on the abscissa, where X’ = B- - H+ + OH-(BT = total monacidic base being titrated; B- = monovalent anion of acid titrant). The slope of the graph will approximate K,, and the intercept on the abscissa will approximate C+. Using the estimate of C+, the data can be regraphed, plotting [H+](Br - X’ + C+) on the ordinate and X’ on the abscissa, to straighten the curve and obtain better estimates of C+ and K,. Method
III
In the case in which neither AT nor Y is known with any accuracy, since AT is a constant, a plot of [H+]X on the ordinate and -X on the abscissa for the titration of the monobasic acid will yield the same graph as Method II, except that the curve will be displaced along the abscissa. The intercept on
ACID
DISSOCIATION
CONSTANTS
409
the abscissa will be -A, - C-. From the shape of the curve, the presence and type of contamination can be determined. A qualitative estimate of the degree of contamination can also be made from the severity of the deviation of the graph from linearity. Based on this information, successive guesses of a value for C- can be made in a plot of [H+](X - C-) (ordinate) and -X (abscissa) to obtain a straight line, allowing determination of both K, and AT. METHODS To illustrate the use of the graphical procedures, 0.1 N acetic acid, with and without contamination by strong mineral acid or base, was titrated with 0.1 N carbonate-free standardized NaOH. All reagents were analytical grade, the solutions being prepared immediately before use in degassed distilled water (2). The titrations were performed in a vessel equilibrated to 25°C in a constant-temperature water bath. A Sargent Welch Model NX pH meter with Corning glass electrode 476050 was used. The glass electrode utilized was calibrated versus Sargent Welch buffers which had been verified on a Radiometer Copenhagen PHM 71MK2 pH meter and G2971G2 microelectrode standardized with Radiometer precision buffers. The acetic acid was assayed by both an end-point titration and an enzymatic procedure (14). Determination of the slope and intercepts of the graphs was by linear regression analysis. The data is presented as the mean t SEM. RESULTS AND DISCUSSION At 25”C, the titration of the uncontaminated acetic acid produced a pK, value of 4.77 ? 0.01 (Fig. l), in very good agreement with the value of 4.76 derived from electromotive force measurements under similar conditions (25°C; ionic strength, 0.01-o. 18 M) (15). Ionic strength effects can be ignored in the current titrations since, under the conditions chosen, the observed pK, is sensitive only to the third decimal place to variations in ionic strength up to 0.18 M (15). In most situations, however, it is understood that the ionic strength may need to be kept constant throughout the titration or activity coefficient corrections may need to be made (1,2). Titrations of acetic acid solutions containing approximately 10% contamination by either HCI or NaOH were carried out, the results being analyzed by either Method I or II. When Method I was used, straight lines parallel to the graph of the uncontaminated acid were obtained (Fig. 1). Values for the pK, of 4.78 + 0.01 (correlation coefficient = 0.9996) and 4.77 5 0.01 (correlation coefficient = 0.9998) were obtained for the acidand base-contaminated solutions, respectively. When Method II was used, upward and downward concave curves were obtained in the presence of acid and base contaminations, respectively (Fig. 2). In the case of acid
410
ROBERT W. GUYNN
FIG. 1. Titration data plotted by Method I. The graphs represent titrations of 0.100 N acetic acid with 0.100 N NaOH at 25°C. Included is the titration of the pure acid (0 0) and this same acid contaminated with approximately 10% strong mineral acid (x x) or base n ). The NaOH titrant was added in fixed aliquots, and each curve represents the (m average ofat least three titrations. Y = Total titratable acid;X = B+ + H+ - OH-(where B+ is the cation of the base titrant). Square brackets indicate concentration; otherwise, all compounds or ions are expressed in absolute moles rather than concentration.
contamination, the straight line portion of the graph approached the abscissa, giving an approximate pK, of 4.70. A single replotting of the data, using the estimate of C- defined by the extrapolation to the abscissa, straightened the line (correlation coefficient = 0.9998) and yielded value of 4.77 -+ 0.01 for the pK,. Likewise, the original estimate of the pK, from the graph of the base-contaminated solution (4.83) was easily refined. A single correction again produced a straight line (correlation
AC,- X x lo-’
FIG. 2. Titration data plotted by Method II. The conditions and symbols are the same as those of Fig. 1. AC, = total acetic acid as assayed enzymaticalt y ( 14)) rather than by end-point titration.
ACID DISSOCIATION
CONSTANTS
411
coefficient = 0.9999) with an estimate of 4.77 _t 0.01 for the pK,. The same value was obtained in the case of a 50% contamination of the acetic solution by base, although three corrections (based on successively better estimates of C-) were required to straighten the graph (correlation coefficient of final estimate = 0.9998). It is apparent that Method II could be used primarily to determine the purity of a substance, since the graph can distinguish among neutral, acid, or base contaminations. Since Method I always produces straight lines with a slope of l/K,, the amount of contamination which the system can tolerate is limited only by the technical aspects of the titration itself. Method II, on the other hand, seems to have a practical limit near 50% contamination by either acid or base, at least in the systems which have been tested, However, if Method II predicts the presence of a very large contamination, it would be possible to partially neutralize the contamination and repeat the titrations in order to use Method II effectively. Method III has not been specifically illustrated, since the form of the graphs is identical to that of Method II, except that the curves are displaced to the left. Unless a straight line is obtained initially, the usefulness of Method III depends upon how quickly guesses of the value of C- can be refined to straighten the line. In most practical cases, a computer program designed to find the value of C- which produces a correlation coefficient closest to 1 .Ofor the linear regression of the experimental points (-X on the abscissa,X - C- on the ordinate) would be very useful, potentially allowing the determination of the pK, of an acid of unknown concentration, contaminated with unknown amounts of mineral acid or base. Though the titration of a monobasic acid has been used to illustrate the methods, the graphical procedures can be used readily with polybasic acids, provided there is not a significant overlap of pK,s [i.e., provided the difference between the pK,s is greater than rt.7 (2)3. For example, the methods have been successfully applied, recently, to the titration of salts of phosphoric acid and phosphorylcholine under physiological conditions (16). ACKNOWLEDGMENT This work was supported by Grant No. AU-631 from the Robert A. Welch Foundation, Bank of the Southwest Building, Houston, Texas 77002.
REFERENCES 1. Cookson, R. F. (1974) C/rem. Rev. 74, 5-28. 2. Albert, A., and Serjeant, M. R. (1962) Ionization Wiley, New York. 3. Joseph, N. R. (1958) Science 128, 1207. 4. Druckrey, H. (1959) Science 129, 1492. 5. Joseph, N. R. (1959) Science 129, 1493. 6. Hofstee, B. H. J. (1960) Science 131, 39.
Contants of Acids and Bases, John
412 7. 8. 9. 10. 11.
ROBERT W. GUYNN
Benet, L. Z., and Goyan, J. E. (1965) J. Pharm. Sci. Benet, L. Z., and Goyan, J. E. (1965) J. Pharm. Sci. Leeson, L. J., and Brown, M. (1%6)J. Pharm. Sci. Benet, L. Z., and Goyan, J. E. (1967) J. Pharm. Sci. Phan-Tan-Luu, R., Surzur, J.-M., Metzger, J., Aune, Sot.
12. 13. 14. 15. 16.
Chim. Setnikar, I.
Fr.
3274-3277. J. Pharm.
54,983-987. 54, 1179- 1182. 55, 431-433. 56,665~680.
J.-P., and Dupuy, C. (1967) Bull
(1966) Sci. 1190-1195. Levy, R. H., and Rowland, M. (1971)J. Pharm. Sci. 60, 1155-1159. Guynn, R. W., and Veech, R. L. (1974) Anal. Biochem. 61,6-15. Hamed, H. S., and Ehlers, R. W. (1932) J. Amer. Chem. Sot. 54, 1350-1356. Guynn, R. W. (1976)J. Biol. Chem. 251,7162-7167.
