Ames Laboratory Technical Reports Ames Laboratory 2-1964 Calculation of acid dissociation constants Wayne Woodson Dunning Iowa State University Don S. Martin Iowa State University Follow this and additional works at: http://lib.dr.iastate.edu/ameslab_isreports Part of the Chemistry Commons Recommended Citation Dunning, Wayne Woodson and Martin, Don S., "Calculation of acid dissociation constants" (1964). Ames Laboratory Technical Reports. 55. http://lib.dr.iastate.edu/ameslab_isreports/55 This Report is brought to you for free and open access by the Ames Laboratory at Iowa State University Digital Repository. It has been accepted for inclusion in Ames Laboratory Technical Reports by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Calculation of acid dissociation constants Abstract A computational method has been developed for the determination of dissociation constants of acids (and bases). The method is applicable to mono or polybasic acids and, in certain cases, to mixtures of acids. A least- squares treatment is employed, and no simplifying assumptions are made in any of the equations or factors involved. All the available data are utilized, and provision is made for including or calculating activity coefficients. Utilization of the method requires a medium to large size digital computer. Disciplines Chemistry This report is available at Iowa State University Digital Repository: http://lib.dr.iastate.edu/ameslab_isreports/55 IS-822 IOWA STATE UNIVERSITY CALCULATION OF ACID DISSOCIATION CONSTANTS by Wayne Woodson Dunning and DonS. Martin RESEARCH AND DEVELOPMENT REPORT U.S.A.E.C. IS-822 Chemistry (UC -4) TID 4500 April 1, 1964 UNITED STATES ATOMIC ENERGY COMMISSION Research and Development Report CALCULATION OF ACID DISSOCIATION CONSTANTS by Wayne Woodson Dunning and DonS. Martin February, 1964 Ames Laboratory at Iowa State University of Science and Technology F. H. Spedding, Director Contract W -7405 eng-82 ii LS-822 This report is distributed according to the category Chemistry (UC -4) as listed in TID-4500, April 1, 1964. Legal Notice This report was prepared as an account of Government sponsored work. Neither the United States, nor the Commission, nor any person acting on behalf of the Commission: A. Makes any warranty or representation, expressed or implied, with respect to the accuracy, completeness, or usefulness of the information contained in this report, or that the use of any information, apparatus, method, or process disclosed in this report may not infringe privately owned rights; or B. Assumes any liabilities with respect to the use of, or for damages resulting from the use of any information, apparatus, method, or process disclosed in this report. As used in the above, "person acting on behalf of the Commission" includes any employee or contractor of the Commission, or employee of such contractor, to the extent that such employee or contractor of the Commission, or employee of such contractor prepares, dissemi­ nates, or provides access to, any information pursuant to his employ­ ment or contract with the Commission, or his employment with such contractor. Printed in USA. Price $ 1. 7 5 Available from the Office of Technical Services U. S. Department of Commerce Washington 25, D. C. iii IS -822 TABLE OF CONTENTS Page ABSTRACT • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • v I. INTRODUCTION ...................................... .. 1 A. Experimental Background ••••••••••••••••••••••••••••• 1 B. Computational Methods .............................. 7 II. EXPERIMENTAL 11 A. Materials .......................................... 11 B. Equipment ..• 11 III. MATHEMATICAL THEORY 12 A. Titration of a Single Acid 12 B. Mixture of Two Acids . 15 C. Modified Titrations . 18 D. Calculation of Titration Curves 19 E. Calculation of Acid Concentrations 20 F. Determination of Errors 20 IV. CALCULATIONS 22 A. Calculation of the Dissociation Constants for a Single Acid ........................... 22 B. Calculation of the Dissociation Constants for a Two Acid Mixture •••••••• 25 c. Calculation of Intermediate Quantities •••••• .......... 27 D. Options and Considerations • • • • • • • • • • • • • • • • • • • • • • • • • • • 28 v. RESULTS . ............................................ 30 A. Resolution of Successive Constants • • • • • • • • • • • • • • • • • • • • 30 iv Page B. Resolution of Mixtures . ............................ 38 c. Consistency .••••.•••• 39 D. Improper Calculations . ............................ 40 E. Experimental Titrations ••••••••••••••••••••••••••••• 41 VI. DISCUSSION ••••• . .................................... 43 VII. SUMMARY .............................•............... 47 VIII. LITERATURE CITED. • . • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 48 IX. APPENDIX A .•• . ..................................... 50 X. APPENDIX B ••• 53 v IS-822 CALCULATION OF ACID DISSOCIATION CONSTANTS):< Wayne Woodson Dunning and DonS. Martin ABSTRACT A computational method has been developed for the determination of dissociation constants of acids (and bases). The method is applicable to mono or polybasic acids and, in certain cases, to mixtures of acids. A least-squares treatment is employed, and no simplifying assumptions are made in any of the equations or factors involved. All the available data are utilized, and provision is made for including or calculating activity coefficients. Utilization of the method requires a medium to large size digital computer. The resolution of successive dissociation constants of small ratio has been shown to present no difficulties attributable to such ratios; ratios as small as three were resolved as readily as those much larger. The accuracy attainable depends entirely upon the accuracy of the titra­ tion data. Tests have shown that titrations accurate to better than one part in five thousand may still produce two percent errors in the result­ ing constants. Consistent or random titration errors are likely to cause considerable variations in the dissociation constants. Experimental work must be performed with the greatest care if constants of even two significant figures are desired. Ordinary pH titrations may give uncer­ tainties in even the first figure. Mixtures of acids proved to be no more difficult to resolve than sin­ gle acids, within certain severe limits. If there is a considerable sep­ aration in constants, and the data are extremely accurate, useful results may be obtained. In most cases, overlap of constants and/ or experi­ mental errors will prevent successful resolution. Many previous methods of calculating dissociation constants have treated polybasic acids as mixtures of monabasic acids. It has been shown that if the ratio of successive constants is one hundred or more, no appreciable error results. With the present method, however, such assumptions are completely unnecessary. Examination of the literature, together with experimental results obtained in this work, indicates that many "accepted" values are either very inaccurate, or at least given to more significant figures than justi­ fied. ~:~ This report is based on a Ph. D. thesis submitted by Wayne Woodson Dunning, Febraury, 1964, to Iowa State University, Ames, Iowa. 1 I. INTRODUCTION The determination of the dissociation constants of acids1 -- though sometimes considered to be a very straight­ forward procedure -- entails in practice numerous experimental and theoretical difficulties. The variety of experimental methods that have been used, the corrections applied to the data, the numerous manners in which data for identical pro­ cedures have been treated, and the considerable disagreement in values of the dissociation constants obtained are all in- dicative of the difficulties. The research reported in this work was undertaken primarily for the purpose of developing computational methods that would furnish the best possible values of dissociation constants from the data of any of several different experimental procedures. ,. A. Experimental Background Among the many experimental procedures used in the past, one of the most common was the measurement of the conductance of an aqueous solution of the acid. This method was used primarily on monobasic acids, since polybasic acids presented great mathematical difficulties. As late as 1959, Dippy £! !!• (1) expressed the opinion that there was still no wholly satis­ factory method of calculating th~ second and higher thermo- :' ·.... · .... , ' 1Although this work deals specifically with acids, the treatment of bases is quite analogous, and the necessary modi­ fications to the theoretical equations and the computer pro­ gram are included. 2 dynamic dissociation constants of polybasic acids from con­ ductivity data. Conductance methods are now considered ob­ solete by some authorities (2). Another common procedure, and one which still sees ex­ tensive use, is that of optical measurement. This may be either colorimetric or spectrophotometric. The colorimetric method enables one to obta.in a pH titration curve while avoid­ ing some of the problems arising in standard electrometric de­ terminations. However, standards of known dissociation con- stant are necessary for calibration of the indicators, and thi~ can give rise to other difficulties. Spectrophotometric meth­ ods are quite useful in many cases, though extensive computa­ tions, similar in principle to those employed in this work, are often required. 1'- . Among the