Identification of Weak Acids and Bases by Titration with Primary Standards A Modern Version of an Old Analytical Chemistry Experiment Robert 0. Thompson Oberlin College. Oberlin. OH 44074 The most widelv used laboratow exercise for a first course in analytical chemistry is the aqueous acid-base titration. In a typical experiment, the reaction is monitored with a pH electrodelmeter, the equivalence point is determined by m a ~ h i c ameans, l and the only objective is to determine the ambunt of sample titrated. o f seven quantitative analysis textbooks published since 1981 (1-7) five include acid-base experiments that are exclusively quantitative in nature. This overriding emphasis on the equivalence point is unfortunate information garnered from oth. ~ hecausimu&h ~ - ~ ~ ~ ~ can - he " er parts of the titration curve. A qualitative experiment, one in which important physical constants (acid dissociation constants, K., and molecular weight, MW) are extracted from the data and the s a m ~ l eis identified, is more educational because it maintains the emphasis on accurate volumetric work while bringing to practice the concepts of acidbase equilibria, activity coefficients, and thermodynamic constants. The best and most modern way of determining MW and K, values is nonlinear least-squares analysis. This microcomputer-based method uses any of the points from the titration curve, is not based on extrapolation as are the Gran methods (8,9), can yield K, values for polyequivalent compounds, and provides estimates of the confidence intervals for the derived Dhvsical constants. Furthermore, accurate data analysis does bat necessitate large breaks i n t h e titrationcurve. and. thus. weak~rimarvstandardacids and bases can he usdd astitrants. ~ e c a u s ei f this and because laborious graphical analysis is omitted, a considerable savings in materials and time can he realized. The mathematicalmodel that forms the foundation of the data analysis was derived from primary equilibrium relationships and accurately predicts titration curves for any acidbase--weak or strong, mono- or polyequivalent--titrated with a monoequivalent acidbase, which can also be weak or strong. T h e central equation is given below ~
~
~~~~~~
~
~
Activity coefficients for the first and last points in the data set must he determined by the user and passed on to the computer program. The activity coefficients for the other points are linearly interpolated. Described below is a four-hour experiment in which students are aiven a weak acid or hase and asked to determine its identit;:by titration with primary standard grade rridhydroxvmerhsl)aminomethane ('l'ris~ or sulfamic acid. The sample may he an uncharged acid or base or a derived sodium or potassium salt and may have one or two equivalents. A ntmlinear regression program is used toralrulat&the hest fit of the titration data, and the resulting K. and M W values allow a positive identification of the sample to he made. Experlmenlal Equipment Experimental conditions matched those found in our teaching Laboratory as much as possible. Pipets and volumetric flasks were of Class A manufacture and used without further calibration. The buret was calibrated by measurement of the amount of deionized water (DW)delivered. The pH was monitored with a Ross eombination electrode (Orion) attached to a Beckman pH131 meter. The nonlinear regression program, NLLSQ 1.4 from CET Research Group, Lid., was run on an Apple IIe computer. The program is written in Basic and is unprotected so that the model equations can be added and other changes can he made. Reagents Titrant and sample solutions were of low concentration to keep the ionic strength low and were prepared in an identical manner. Pure solids, ACS reagent grade or better, were dried and then dissolved in freshly boiled DW to make approximatelyfour millimolar solutions. Procedure for the Titrations First, determine whether the sample is an acid or a base by measuring the pH of a 1%solution in DW. Next, prepare the appropriate titranGTris or sulfamic acid-as described above. Titrate 5 mL of sample using phenol red to signal the endpoint. If the endooint volume is less than 7 mL. use a 20-mL samole in the oH of sample titration described below; if mor; than 7 mL, put 1 O ' m ~ and 10 mL of hailed DW in the titration beaker. Table 1.
The terms are defined in Table 1.The term a, is a summation of acid alpha values,
An alpha value is the ratio of the concentration of a particular species to the total amount of the compound. For example, the alpha expression for NH3 is [NH3]l([NH3j [NH4+])and is equal to Q1l(Q1 [H+]). The equilibrmm quotients, Qi, are calculated in terms of equilibrium constants and activity coefficients:
+
g, = Kf,@(C~-i)J
+
(3)
a,
AB
Definitionof Svmbols Used in the Model Equations
Summallon of a pna va ues tor the sample T 1 tor oas c I tmnls. - 1 for ~ C I O I Ct lrant~ Charge on parent acid (e.9..+l tor NU3) Charge on sample compound (eg.,0 for N H d Activity coefficient for singly charged ion Acid dissociation constant of sample Acid dissociation constant of the titrant: equals 10-2qA8)if the titrant is a strong acidlbase Molarity of titrant Moles of sampie Number of equivalents in parent acid (e.g.,1 for NH.) Equilibrium quotients tor acid dissociation of sample Initial volume of sample in titration beaker Volume of titrant Alpha value for species that has iacid equivalents Volume 65 Number 2
February 1988
179
Calibrate the pH electrodeJmeter hetween pH 4 and 7 or I and 10 depending on the initial pH of the sample solution. Perform the titration hv addine l-mL increments of titrant while the DH is within the Ealibratid range and 3-mL increments at all other times. Determination of the Sample Type
Measure the melting point of the sample. If the sample does not melt below 250 'C, it is most likely a salt. To distinguish between mono- and diequivalent samples plot the titration data. If the titration curve has only a single break, measure the difference in pH between the % and 31d equivalence points. A differenceof about 0.95 indicates one equivalent, while a difference of one or greater is evidence of two equivalents (10). Initial Estimates
From the titration curve estimate the moles of sample and the acid dissociation constants. If a diequivalentsample shows only one break calculate the apparent K, from the half-equivalence point, and use this value as initial estimates for both dissociation constants. Knowing the sample type and the approximate moles of sample, calculate the concentrations of all species present at the first and last points in the data set. Then calculate the ionic strength values and the singly charged ion activity coefficients from the Davies equation (11). Data Analysis
Enter into the computer only the data that falls in the calibration range of the pH electrodeJmeter. Run the nonlinear regression proeram. first enterine the rewired information and initial estimates A mod fit is indicated hv, a rootand then waitine,. f& eonve;eenee. ,. mean-squhrcdrvistim rHbl5D1 that is comparable to the expected erwr in the vcdume readings. The magnitudes of the residudls of rhe fit, Y(ealculated) - Y(experimental), should also have a random srrangement. ~
~
~
~~~~
~
-~
~~
~
~
Discussion Comoounds re~resentinefour samole . twes-unchareed ". diprot; acid, acihic salt, &sic salt, and uncharged moioequivalent base-were titrated with Tris or sulfamic acid. The results are shown in Table 2. The data sets fit very well as indicated hv low RMSD values (0.043-0.083) and random arrangemeotsif and - residuals. The errors in the molecular weight averaged less than 0.3%. while the errors in the pK, values were higher, ranging from 0.5 to 7%. Nevertheless, these are very good results when one considers that an inexnensive n H ele&rode/meter was used. the temoerature was hot conkolled, and the ionic strength was assumed to varv linearlv with titrant volume. Data from oolveauivalent spe"cies seem to fit better than data from monoequivalent ones, most likely because there are more parameters to he
+
&
"
.
Table 2. Comparison of Llterature and Experimental Values for Molecular Weiaht and OK. Sample
Literature Values' MW p&
Succinic acid
118.1
Potassium hydrogen tanrate
188.2
Tris Scdiurn acetate
121.1 136.1
4.207 5.636 3.036 4 366 .. 8.075 4.757
Experimental Values MW P& 118.3 189.0 121.6 136.0
4.201 5.631 3.034 4.867 .. 8.106 4.729
'Manell, A. E.; Smith. R. M. ~itislSmblll~Constants:Plenum: New Yoh. 1882;Voi. 5.
180
Journal of Chemical Education
fitted. Identification of the samples from among those compounds listed in our textbook ( 6 )was perfect. Accurate results require accurate information about the titration. This information includes the molarity and acid dissociation constant of the titrant and the initial volume of sample in the titration beaker. all of whirh should be known at the start of the titration. The sample woe and answers to the questions-number of equivale&s in-parent compound, charge on parent acid, and charge on sample species-must also be determined correctly. For example, if succinic acid were thought to be a monoprotic acid, the RMSD would he 1.25 and the pK value would he 4.78. The large RMSD signals that one or more of the initial values is incorrect. Finally, the nonlinear regression is significantly affected by the activity coefficients calculated by the user. If the ionic streneth were estimated a t onlv one-half the correct value for the succinic acid ritration, the pK, values would be 4.197 and 5.606, in error by an averaae of 4.5%.This cornnares with an error of only 1.3%when theactivity coefficients-are calculated correctly. The laboratory exercise described above has several advantages over similar experiments. First, savings in time and reagent use is The data analysis can he done in about one-half hour, much less than the several hours it takes students to calculate and plot the first derivatives of the data and to calculate the pK. values by hand. Since primary standard titrants are used, preparation and standardization of NaOH or HCI are no longer required, also saving time and saving several grams of primary standard acid or hase per student. Only about 0.5 g of titrant compound and sample are needed per student in this experiment. Second, polyequivalent samples can he used, and this makes the detective work much more interesting for students. Almost any pure, solid acidhase can he used, hut best results are ohtained when the pK, values are within the calibrated p H range. Samples with far-removed pK. values may show a poor fit or even nonconvergence. Another advantage is that the results are as accurate or better than those obtained by graphical means, and error estimates are provided. Finallv. this exoeriment eives students more exoerience with computers a i d providks the opportunity to introduce the t o ~ i of c nonlinear rearession analvsis, which might otherwise he omitted from tKe chemistrycurrirulum. ~ i u dent satisfaction with this new version of an old analytical method has been very high. Acknowledgment The author would like t o thank Signe Holmbeck, Peter Jacob, Hidong Kim, David McGarvey, and Krisanto Pranata for testing and reviewing this experiment. Llterature Cited 1986. ed.: PrentiecHdk Eqle. woad Cliffa, NJ, 1986. Hdris D. C. Quantitative Chemical Analysis; W.H.Freemar: San Francism. 1982.
1. Chriatim, G. D. Anolyfieol Chemistry; Wiley: New York, 2. Day, R. A.: Undwood. A. L. Quontitotivs Anolysb. 5th
3. 4. Kennedy. J. H.Anolyrirol Chemistry Plinciples; Harmurt Brace Jovanovieh: New York, 1984. 5. Manahan, S. E. W n t i l o t i u e Chemical Anolyab; BmoWCole: Monterey, CA, 1986. 6. Ramette, R. W. Chemical Equilibrium and Analy~ir;Addiaon-Wesley: Reading, MA,
."". UOL.
7. Skoog, 0. A,; West, D. M. Anrrlyfirol Chomblry: An Intmducfion, 4thed.; Ssuoders:
New Yark.
1886.
8. Gmn.G.Amly8t 1952.77.661. 9. Gran, G. Act. Chem. Scondimvico 1950.4.553. lo. Ramene, R. W. Chemical Equilibrium and Anolyris; Addison-Wesley Reading, MA. , on.."" ,a? ."".,w""*-"". 11. Davies. C. W, Ion Aaaociotion; Butteworth: London, 1961: p 41.
