In the Laboratory
Determination of the Equilibrium Constants of a Weak W Acid: An Experiment for Analytical or Physical Chemistry R. A. Bonham Department of Biological, Chemical, and Physical Science, Illinois Institute of Technology, 3101 South Dearborn St., Chicago, IL 60616
A simple experiment, utilizing readily available equipment and chemicals, is described. It allows students to explore the concepts of chemical equilibria, nonideal behavior of aqueous solutions, least squares with adjustment of nonlinear model parameters, and errors. The relationship between the pH of a solution of known initial concentration and volume of a weak acid as it is titrated by known volumes of a monohydroxy strong base is developed rigorously assuming ideal behavior. A distinctive feature of this work is a method that avoids dealing with the problems presented by equations with multiple roots. The volume of base added is calculated in terms of a known value of the pH and the equilibrium constants. The algebraic effort involved is nearly the same as the alternative of deriving a master equation for solving for the hydrogen ion concentration or activity and results in a more efficient computational algorithm. This approach offers two advantages over the use of computer software to solve directly for the hydrogen ion concentration. First, it avoids a potentially lengthy iterative procedure encountered when the polynomial exceeds third order in the hydrogen ion concentration; and second, it provides a means of obtaining results with a hand calculator that can prove useful in checking computer code. The approach is limited to weak solutions to avoid W
Supplementary materials for this article are available on JCE Online at http://jchemed.chem.wisc.edu/Journal/Issues/1998/ May/abs631.html .
dealing with molalities and to insure that the Debye–Hückel limiting law is applicable. The nonlinear least squares algorithm Nonlinear Fit, found in the computational mathematics library Mathematica, is utilized to fit the measured volume of added base to the calculated value as a function of the measured pH subject to variation of all the equilibrium constants as parameters (including Kw). The experiment emphasizes both data collection and data analysis aspects of the problem. Data for the titration of phosphorous acid, H3PO3, by NaOH are used to illustrate the approach. Fits of the data without corrections for the ionic strength and with corrections for two forms of the Debye–Hückel limiting law were carried out. Equilibrium constants obtained by this method should correspond to their thermodynamic values. The correspondence was checked by carrying out the titration in two different concentration ranges and extrapolating the practical values of the equilibrium constants to zero ionic strength. The results obtained are compared to literature values and suggestions for further experimentation are made along with a discussion of errors. Supplementary Material The complete description of this experiment and supplementar y materials are available on JCE Online at http://jchemed.chem.wisc.edu/Journal/Issues/1998/May/ abs631.html.
JChemEd.chem.wisc.edu • Vol. 75 No. 5 May 1998 • Journal of Chemical Education
631
