An Alternative Method for the Determination of pK, Carlos Castillo S.. Germania Micolta S.. and Mario Graiales T. Universidad del Valle, Cali, Colombia A. A. 2188
With the advent of relatively inexpensive pH meters, the determination of the titration curve of a weak acid or base has become feasible in fust-year laboraton courses and is included in some laboratory manualsdesigned for first-yearstudents. This experiment, in which the equivalence point of a known acid is found, m i y be extended to the determination of pK. without further experimental work. The value of pK. can he determined fairly accurately using the following procedure.' Consider the simple case of the titration of a weak acid HA with a strong base BOH. After adding u b cm3 of base of concentration Cb to u, cm3 of acid of concentration C., and with a dissociation constant K., the following equations can he written. (We imnlv that the solvent is water. thoueh it need not he, and since we ignore activity coefficients, the constant is "apparent.")
.-
Changes In pH durlng the Tltratlon 0150 cm3 of 0.100 M Acetlc Acld wlth 0.100 M NaOH
Volume NaOH added (crns)
PH
0.0 10.0 25.0 40.0 49.0 50.0
2.88 4.15 4.76 5.36 6.45 8.73
n
PKa
0.987 0.799 0.500 0.200 0.020 1.074 X
4.76 4.75 4.76 4.76 4.76 4.76
lo-'
-
Equilibria K , = [H+][OH-]
(1)
K . = [H+I[A-IIIHAI
(2)
Substituting eqn. (11) into eqn. (10) and solving for ii, yields
and introducing eqns. (I), (3), and (4). we finally obtain
Conservation of species
v&a
+ ub) [B+] = u ~ c ~ / + ( uub) ~
[HA] + LA-] = u.cd(u,
(3)
E=
o.
+ ub
-
UbCb ub
V.
+
Ua
[H+]
+ p+]= [A-] + [OH-]
(5)
The method is based on the concept of the formation function ii, which accounts for the fraction of protons which are still bound to the acid a t any point of the t i t r a t i ~ n . ~ moles of bound H+ - [HA] (6) total moles of acid [HA] + [A-] The concentration in which the acid exists is linked to the pH (the H+ concentration) hy the dissociation constant. From eqn. (2), we get -
n =
[HA] = K.-'[H+]
[A-]
(7)
so that
and solving for K,, we obtain We are now left with the task of finding numerical values for Ti, in order to he able to find K, from eqn. (9) using a pair of Known values, at any point in combined values for Ti and Hf. the titration, are the amount of base added, the total acid concentration C,, and the pH. Let us begin with the electrical neutrality eqn. (5)
+
[H+] [Bf] = [OH-]
+ [A-]
(10)
The [A-] can he expressed in accordance with the definition of ii in eqn. (6)as
5- [H+l [H+]
(13)
U.C.
(4)
Electrical neutrality
+
+ Ub
Numerical values for ii and K, thus can he ohtained, as follows. Select one point on the titration curve. Calculate ii from ean. (9) . (13). . . Eouation . . . can now he solved for K... The table contains representative experimental data used to calculate ii bv ean. (13) and the calculawd values of the DK. by eqn. (9). In our lahoratorv. the ex~erimentis Dart of a sequence in and 0.1 and'standardize-0.1 M N ~ O H which students M HCI and then obtain the titration curve for a wpak acid. The acid may be supplied as a solution of a known acid, such as acetic acid. for which the student determines the concentration and the pK, from the titration curve. Generally, one rough titration curve and two carefully determined titration nwes are obtained during the 4-hrlaboratory period. Despite the approximations made, student results using this method agree well with literature values of pK.. We have found that including the determination of pK, in the experiment enhances student interest in and understanding of acid-base equilibria. Acknowledgment We wish to thank Rodrigo Paredes for helpful discussions. -
-
' A reviewer has pointed out that a less detailed, but similar memod
for pK. determinations was presented oy Ange ic;,R.. 'Synthesis and Technioue in lnorqanic - Chemistry." W. 6. Saunders Co.. New York. 1969, p. 110.
Kolttwff. I. M., and Elving. P. J., "Treatise on Analytical Chemistry." Vol. 1, in "Interscience Encyclopedia." Wiley Interscience, New York, 1959, pp. 440-442 and 552-555. Volume 61
Number 12 December 1984
1067
