Eugene E. Schrier State University of New York Binghomton, New York 13901
I
Intermolecular Association
I
by Vapor Pressure Osmometry
I
A physical chemistry experiment
The study of molecular association in solution has provided important thermodynamic information relating to hydrogen bond formation and other noncovalent interactions. The data derived from these investigations, while of interest in themselves, have found additional application in discussions of the stability of the secondary and tertiary structure of proteins and other biologically important macromolecules ( I $ ) . A previous experiment (3) described an examination of the concentration dependence of the molar polarization of two compounds containing the amide group. The compounds investigated were 2-oxohexamethyleneimine (caprolactam), I, and N-methylacetamide (NMA), 11,in benzene solution: 0 H
L A\
/
cH,
c H L N - Ic n ,
The molar polarization, P*M,of each of the solutes in benzene exhibited contrasting trends with increasing solute concentration. The value of P2Nfor NMA increased with increasing solute concentration while this quantity showed the opposite behavior for caprolactam. These trends were interpreted (3) by assuming that an extended series of multimers is formed with NMA while only monomers and dimers exist in benzene solutions of caprolactam. The diierent modes of association are considered to arise from the diierent stereochemical configurations of the amide group in the two compounds. The interpretation of the molar polarization curves in accordance with the hypothesis of association in these systems has been discussed (3). The experiment to he described deals with a further examination of association in these systems. Measurement of the effective concentration of all molecules in various solutions containing amide1 and lactam are made using vapor pressure osmometry. Equilibrium constants for association are calculated from the data utilizing two models. One model supposes the existence of a monomer and a single associated species. The other assumes that an extended series of multimers is formed with each stepwise association, A , A SA , + ,, characterized by the same equilibrium constant. Use of each scheme in turn with the data for the amide and the lactam allows the student to choose the model which
+
1 N-n-butylaoetamide was substituted for N-methyl acetamide for reasons mentioned below.
176
/
lournal of Chemical Educafion
yields the most self-consistent set of equilibrium constants. The results lend support to the proposal of different modes of association in amide and lactam solutions. Vapor Pressure Osmometry
The principles and practice of vapor pressure osmometry have been reviewed previously (4, 5) and the capabilities of the commercial instruments have been discussed (6). Therefore, only a brief discussion of the method will be given here. The diagram given in Figure 1 illustrates the principle. A matched pair of thermistors is located in an isotherma1 chamber which is saturated with solvent vapor. A 75;E;'g; drop of puresolvent @Em is placed on one of o t h e thermistor I -2t;iEm;b~ heads while the ! other bead holds a I , drop of solution. I Since the vapor I ! pressure (and the chemical potential) Figure 1. A rchernotic diogram of a vapor of the solvent in the pre$lure osmometer. drop of solution is lower than that of the pure solvent, solvent vapor will condense on the solution drop a t a greater rate than on the drop of pure solvent. A steady differential rate of condensation is soon established. Since condensation releases heat to the surroundings, the solution drop is warmed relative to the solvent drop. This differential heating is reflected in a steady temperature difference between the drops. I t has been established empirically (4) that this temperature difference is a colligative property. Studies of association in solution may therefore be carried out using this method. The equations used to calculate equilibrium constants from the experimental data are developed in the following section. Theory of the Calculation of Association Consknts
The quantity obtained from vapor pressure osmometry is the effective concentration of all species in solution. Each particle is counted as one unit whether it is monomer, dimer, or higher multimer. Using the mole fraction concentration scale, the effective mole fraction may be written as
equilibria are occurring simultaneously in the system: 2A1 A,, 3A1 e A,, . . . ., pA, a A, (13) The equilibrium constants for this case may be denoted asfollows:
*
where q indicates the stoichiometry of the largest complex. The stoichiometric mole fraction, X., is defined in terms of the actual concentration of solute which is mixed with the solvent to prepare the solution. We may then write X.
= 21
+ 2 2 ~+ 3zs + . .. + qz.
(3)
where the x's again are mole fractions of the various species. In this case, we may write by analogy to eqn. (8) X. = z, 2K12 (21)' 3 K e ( z 2 + . . . qKl,(u)* (15) and, similar to eqn. (9) X. = a K d z d ' K I ~ z I ) ' . .. KdzJ' (16) A set of equilibrium constants which are related to the Kl,'s may be written as
+
+
The experimental values of X , and X , are the quantities which are utilized to obtain equilibrium constants for association. The calculation of equilibrium constants using these data requires the postulation of a model for the possible stoichiometry of the complexes formed. In addition, an assumption which is necessary for any treatment is that differences between X , and X, must be considered to arise solely from molecular association. Any other effects leading to nonideal behavior are assumed to be of lesser importance. With this assumption in mind, we consider the following models. In Model I, the monomer and one other polymeric species of degree of association q are assumed to be in equilibrium in the system. We write the equilibrium constant for the reaction
+
+
+
+ +
-.
K,= K,, = A,;K,, = (XI) 21.2,'
"
-.
Z4 (17) za.z,, K (q-ll(d = 2 ~ 1 . 2 1
Using the equilibrium constants of eqn. (17), eqn. (15) may be written as X.
=
n
+ 2K~121'+ ~
.. . +
K U ~ Z I qK
