The Modern Student laboratory Determination of the Thermodynamic Dissociation Constant of a Weak Acid by Potentiometric Acid-Base Titration A Three-Hour Laboratory Experiment Jaakko I. Partanen and Merja H. Karki
Laboratow of Phvsical Chemistw, DeDartment of Chemical Technology, Lappeenranta University of Technology, P.O. Box 20, Seymour and Fernando described in this Journal (1) more than a decade ago an interesting laboratory work concerning the determination of the second dissociation constants of o-phthalic acid a t different ionic strengths a t 298.15 K The ionic strengths are adjusted in this work by an inert electrolyte (NaC1) ahd the dissociation constants are determined by potentiometric titrations. According to these workers, each student can perform in a three-hour laboratory period titrations a t six different ionic strengths. The results of these titrations give sufficient experimental data to obtain also the thermodynamical value of the studied dissociation constants. The laboratory work of Seymour et al. (1)has been critically analyzed in our student laboratory. In these analysis, it has been proved to be, afier some improvements, an accurate method for the determination of dissociation cons t a n t s of weak acids. Our suggestions for the improvements and their verifications are illustrated below. Theoretical Considerations
I t is assumed that in the course of the titration of a weak monoprotic acid HA with a solution of a strong base, e.g. NaOH, the pH of the acid solution is measured by a pH meter equipped with a glass electrcde and an appropriate reference electrode. The potential difference (El between these electrodes depends on the activity of the hydrogen ions, a*, according to
perfections in the measuring system do not seriously affect the titration results of this work at the different ionic strengths. From the reading of the calibrated pH meter, en. can be calculated if the activity coefficient of Hi is known. The equations for the ionic activity coefficients are empirical, and the best of those originate from the theory of Debye and Hiickel. It has been observed that the following modification is useful:
where zi is the charge number of ion i and a t 298.15 K is 1.176 (dm3 m ~ l - ' ) ~see , Archer and Wang (2).In eq 2,Bi and Ri are parameters being specific to ion i. For protons, the values of 1.25 and 0.38 for B and R.. res~ectivelv. . .. have proved to be suitable in our calculations. Seymour et al. 1 1 ) used for all ions in this eauation the values of B = 1 and I3 = 0.In eq 2,in addition, i i s the ionic strength of the solution to be titrated. In subsequent considerations, it is assumed that the concentration of the inert electrolyte alone fix the ionic strength. Let us consider, in the same way as Seymour et al. ( I ) , a titration ofhydrogen phthalate ions as an example. In this case, the th~rmod~narnic dissociation constant K. is the equilibrium constant for the equilibrium
E = E' - S log [an+]
where^*- thus refcrs to the phthalateion and so on. Therefore, the following equation can be presented for K,: where y refers to the activity coefficient and c to the concentration and wherec" = 1 mol dm". TheconstantsE'and Scan be determined bvcalibration with two N.B.S. buffers whose pH are known with an accuracy of 0.001 pH units. The pH of the buffer solutions and of the solution to be titrated must be in the pH range of about 3.5-7.5 where the accuracv of the relationshio in eo 1is a t its best. In this range \;e have observed thit, at 268.15 K, the pH values of the N.B.S. buffers of 3.776and 7.413usuallv can be reproduced within 0.003 by a pH meter that has b;ten calibrated with the buffers of 4.008and 6.865a t this temperature. Because of the good results obtained i n this laboratory work, see below, it is probable that the unknown liquid junction potentials and the other imA120
Joumal of Chemical Education
where
At a constant ionic stren@,h. K, and also K, remain constant during a titration a;'th/s ionic strength. Let the initial concentrations of the weak acid sulution and the titrant be CA and ce, respectively, and let the initial volume of the weak acid solution be Vo. V represents the volume of the titrant added. The titration can be done with
Potmtiometric Titrations such a sufficiently strong base solution that during the whole titration V remains much smaller than Vo, see below. With these symbols Seymour et al. ( 1 )presented, as Gran earlier (31,the following equation for the analysis of the titration data:
where the equivalence point V. is given by V. = V&/CB. This equation can be derived by assuming in the relationships of c ~ 2and CHA- that the concentrations of H+and OHare negligible, see eqs 3 and 4 in reference I. In the determination of the Kc values for the different ionic strengths, eq 4 (in this paper) is used so that the quantity c*+V -
P
is presented as a function of V. From the slope of the resulting straight line, the value ofK, is then obtained. To improve this determination we assume in eqs 3 and 4 of reference I that Vis much smaller than Vo and neglect in those only c o ~By . means of these approximations, the following equation is possible to deduce from eq 3 of the present paper:
Table 1. Titration Data for the Calculation of the Dissociation Constant of Hydrogen Phthalale Ion at an lonic Strength of 0.5163 mol dm
0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80
4.705 4.780 4.858 4.939 5.026 5.120 5.225 5.345
14.51 13.57 12.47 11.29 10.01 8.68 7.31 5.91
13.31 12.13 10.93 9.74 8.53 7.32 6.10 4.90
4.696 4.780 4.863 4.947 5.033 5.124 5.221 5.330
4.705 4.780 4.858 4.940 5.027 5.120 5.225 5.345
In the titration, CA = 0.00065co, ce = 0.1 c0and Vo = 155 cm3. # = I mol dm3 'Memod A, see eq 4. b ~ e m o d8, see eq 5. Spredined values. see tea?.
Table 2. The Second Dissociation Constant Kc of Phthalic Acid, Defined in Equation 3, as a Function of the lonic Strength
lo6 &(A)a lo6
I/#
-hC
This equation is used in the same way as eq 4. Only the quantity egVlcois replaced by the quantity fi whose value can be calculated from the titration results for each point. Because the unknown Kc includes in fi, a few iterative steps are required. An initial estimate of Kc can be based on eq 4. Seymour et al. (I)based the determination of K, in eq 3 on the following extrapolation formula: InK,=lnK,+
C
I
~
11 + (l/cO)*
(6)
where C1is a constant. This equation agrees theoretically with their equation for ionic activity coefficients, see above. In our version for the determination of K,, the extrapolation is based on eq 2 with the approximation that for all ions the value of B is 1.00. With this simplification, the following extrapolation formula can be solved from eq 3:
co= I mol dm+ 'Method A, see eq 4. b~ethad8, sew eq 5. 'See eq 7 .
(4) the calibration and the titrations should be performed at the temperature of 298.15 k 0.2 K Results and Discussion
where C2 is a constant. Laboratory Directions
The essentials of the experimental technique have been described adequately in the paper of Seymour et al. ( I ) . We only emphasize the following four things: (1)the careful calibration of the pH meter is very important; (2) this calibration should be checked a few times during the
work; (3) the use of an accurate autamatic buret or a plunger operated micropipette is essential in the titrations (that the appmximation V
