ACTIVITY COEFFICIENTS AND MOLECULAR STRUCTURE Hydrocarbon Solutes in Fixed Solvent Environments C. H . DEAL, E. L. DERR, AND Shell Development Co., Emeryville, Calif.
This article shows that three solvent-characterizing parameters a r e sufficient i o describe accurately the distribution coefficients for a large variety of hydrocarbons between two fixed solvent ervironments.
The generality of the d e -
scription arises from :simple rules which interrelate hydrocarbon structure to hydrocarbon-solvent interaction in such fixed environments.
These rules, taken individually or in
combination, a r e very useful in considering separations of complicated hydrocarbon mixtures.
M. N. PAPADOPOULOS
This complication can be avoided by dealing with any suitable solvent environment as a reference state-that is, by dealing with the ratios of solute activity coefficients in one fixed environment to that in a second fixed environment. T h e present paper uses this approach. It treats the ratios of activity coefficients of hydrocarbons in polar solvents of interest to those in normal heptane or, simply, it correlates on the basis of limiting distribution ratios (ko’s). Thus, k0, the limiting distribution ratio a t infinite dilution, is equal to yc in a polar solvent divided by yo in n-heptane. By virtue of the use of a well known nonpolar solvent as a reference phase, the present correlation implicitly furnishes a basis for correlations and estimates of limiting activity coefficients, as well as the k0’s themselves. limiting Distribution Ratios for Hydrocarbon Solutes
N THE FIRST ARTICLE
of the present series, Pierotti, Deal, and
I Derr ( 2 ) have given attention to the use of molecular structure as a basis for making quantitative estimates of activities in mixtures of nonelectrolytes. They have dealt with the changes of limiting (infinite dilution) activity coefficients as solute and solvent inolecular structures are systematically changed, as for instance within homologous series. With these systematic studies they have, in essence, indicated that structural changes are important and in what way these may be quantitatively evaluated and accounted for in making quantitative or semiquantitative estimates for a wide range of cases. This work has also led to a simple physical picture of mixtures such that, in certain respects, individual interactions of the structural groupings of a solute molecule with those of a n environment can be considered separately. T h e present report extends the PLerotti correlations in the restricted area of hydrocarbon solutes in fixed solvent environments so that a n even broader ranqe of estimates can be made from a few experimental data. limiting Distribution Coefficients
T h e Pierotti correlations deal directly with the limiting activity coefficients (,yo) referred to the pure liquid solute as standard reference state-that is, with net differences between interactions of solute groups with the standard state environment made u p of like molecules and the solvent environment made up of generally unlike molecules. As a result, the relation between activity coefficients in a given family of solutes is somewhat complicated by a change from one solute to another in the standard state environment, even though the solvent environment in question remains fixed.
For a fixed solvent system, k0 values for a large number of hydrocarbon solutes can be estimated from as few as three data which characterize the important properties of the solvent system and a generalized pattern of solute behavior. Analytically, the pattern of behavior can be described by the following relation between k0 and the number of groups in the respective solute structures: log kg = AK
+ ABD (n. + 127 nn -
nn.5
9
-
7
fi nn.n
11 no,o -
12 11 -
+ -
:: -
)
n,,,~
Here, AK, AB,, and AB, are the same solvent system characteristic parameters defined by Pierotti, Deal, and Derr ( 2 ) ) and n,: n,, nu, nn,a, n,,%, no,^, no,l, and no,2 are the numbers of carbon atoms in the solute structure of the following types: paraffinic, total naphthenic, total aromatic, naphthenic alpha to aromatic rings, naphthenic common to two rings, olefinic with two hydrogens, olefinic with a single hydrogen, and olefinic with no hydrogens, respectively. T h e basis of the above relation lies in the following observations for a range of solvent systems: Rule 1. Plots of log kO values of the members of methylene homologous series are linear in methylene carbon number with a slope which depends only on the solvent pair. Rule 2. Plots of log kO values of the cyclic aromatic family (benzene, naphthalene, and so on) are linear in the number of aromatic carbon atoms with a slope which depends only on the solvents. VOL.
1
NO. 1
FEBRUARY 1962
17
Rule 3. Plots of log h-0 values of the naphthene and naphtheno-aromatic families are linear in naphthenic and aromatic number, provided the carbon atoms common to two naphthenic rings or in the a-position to an aromatic ring are counted as aromatic, with a rate of change with naphthenic carbon groups which depends only on the solvent pair. Rule 4. Plots for the naphthenes and aromatics cited above have a common value in the limit of zero carbon number. Rule 5 . In the limit of zero carbon number, the n-paraffin plot and cyclic plots mentioned above have a common point. Rule 6. The log ko for cyclohexane is the same as that of a 3.5-carbon numbered paraffin. Rule 7. The log k@values for olefins are less than those of the corresponding carbon numbered paraffin by 1/5.5 of the difference in log kO values of cyclohexane and benzene for each group:
R
I
= C H
0.15/5.5 of this difference for each =CH2 group, and 1.25/5.5 of this difference for each group:
="
