Simultaneous Equilibria in the Benzoic Acid-Benzene-Water System
Herbert R. Ellison
Wheaton College Norton, Massachusetts 02766
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A distribution experiment
The study of simultaneous equilibria is often a very difficult task for students. Calculations involving systems of polybasic acids, weak acids, or complexing agents with precipitates are usually understood only after much labor on the parts of both the student and his instructor. The laboratory determination of equilibrium constants in these systems is likewise a challenging problem and unfortunately in many cases rigorous calculations can only be made with the aid of a high speed computer. For the begiuning student, however, it is usually desirable that he be able to perform the necessary calculations without the need for such devices. One of the experiments that has frequently been used in physical chemistry laboratories to illustrate simultaneous equilibria is the distribution of an acid between aqueous and nouaqueous phases. In order to ease the computational burden this experiment is often simplified by assuming that the acid exists entirely as the dimer in the nonaqueous phase, an assumption that is not always justified. In this experiment the distribution of benzoic acid between benzene and water is studied. In water benzoic acid dissociates into hydrogen and benzoate ions while in benzene it forms a dimer. Students are able to obtain values for both the distribution coefficient and the equilibrium constant for the dimerieation by employing simple acid-base titrations and a graphical procedure for evaluation of the data. Theoretical
The system consisting of benzoic acid (HBz), benzene
124 / Journol o f Chemical Education
(B), and water (W) can be characterized by three equilibria.
= HBz(bensene)
Distribution: HBz(wster)
Aqueous phase: HBz e H+ + BzBenzene phase: 2 HBz
= (HBZ)~
I n these equations K D is the Nernst distribution coefficient, K, is the acid dissociation constant, and K , is the monomer-dimer equilibrium constant. [HBzIa and [ ( H B Z ) ~are ] ~the equilibrium molar concentrations of benzoic acid monomer and dimer in benzene, respectively, and [HBzIw is the equilibrium molar concentration of benzoic acid in water. The total concentrations of benzoic acid in water and benzene, Cw and CB,respectively, obtained by titratiou of the appropriate phase with base, are given by
where a is the degree of dissociation of benzoic acid, and CB = [HBzIB 2 [(HBzMB 65 Noting that [HBzIw = Cw(l - w) and using eqns. (1) and (3) allows eqn. (5) to be rearranged to
+
Student Results fE. LaCaval at 25'C
Soh. no.
ml NaOHc CJIr laver
Cn X 10%hl
ml NaOHs HPOlaver
1 Cw X lo3-M
CB/C~
a>
-a X 10'
Cn/Cw(1 - a )
[NaOH] = 0.01539 N . mole-' and eqn. (7). *Used K. = 6.30 X
Equation (6) predicts that a plot of CB/Cw(l - or) versus Cw(1 - a) will be linear with a slope. of 2KD2Kx and an intercept of K p The value of a used in eqn. (6) is obtained from t,he known value of K., i.e.
Experimental .\ .
