G. M. danini and 5 . E. Martire
1644
Measurenient arid Interpretation of Activity Coefficients for Aromatic Solutes at Infinite Dilution in n-Octadecane and n-Hexadecyl Halide Solvents (2. M. Janini and D, E. Martire” ilepartment o f Chemistry. Georgetown University. Washington. D. C. 20007
(Received January 21. 1974)
lDub/icationcosts assisted by the Nationai Science Foundation
Activity coefficients in the range 30-60” are obtained by gas-liquid chromatography for n-heptane (N) and eleven homonuclear aromatic solutes (Z) at infinite dilution in n-octadecane (R) and three n-hexatlecyl halide solvents (U): chloride, bromide, and iodide. From these data interaction parameter differences .Ax (= X R Z - X Y Z - X R N X Y N ) are determined and are related to molecular energetic paramelers through a first-order perturbation treatment. Comparison with experiment verifies Ihe predicted (a) linear relation between A x and E Z Z (pairwise potential energy well depth per segment) in a given solvent ‘Y,(b) linear relation between Ax and t y y for a given solute Z, and (c) temperature dependence of A x . The nature of these aromatic-haloalkane interactions is discussed and it is concluded that they are predominantly electrostatic in nature.
+
Introduction Elution gas-liquid chromatography (glc) is a rapid and accurate technique for determining infinite dilution solute activity coefficients ( y z m ) in high molecular weight solvents.1,2 In recent years glc has provided much of the necessary excess free energy data for testing current theories of nonelectrlolytic solutions of molecules of different size .2-ao This paper represents a further contribution to the study of moleculaa interactions between unlike molecules in binary mixtures through glc. 7 2 ” values are reported for n-heptane (the reference solute) and eleven aromatic solutes in four solvents: the reference solvent n-octadecane, n-hexadecyli chloride, n-hexadecyl bromide, and n-hexadecyl iodide. The results are interpreted by utilizing a corresponding si,ates approach for mixtures of molecules of different sizef0 in conjunction with a first-order perturbation treatment of the energetic terms.? Theoretical Recently, R refined version of Rrigogine’sll corresponding states theory of chain molecule mixtures was successfully employed in the prediction of the excess properties of n-alkane mixtures.l0 In its most general form, the resulting expression for yzm is given bysJo
In y2*
= In y z c t In Y~~
where Vh is the hard-core volume of component k (1 = solvent, 2 = solute). The sum of the energetic and structural terms is usually referred to as the interaction parameter x, L e . iIn y2s =
xe + xs
=
x
Combining eq 1-3 and dropping the superscript have
VZ In y z = In --
vi
+
1--
v2 Vl
A further useful simplification, from the points of view of both experimental accuracy (see later) and treatment of the energetic terms (see below), is to introduce a nonpolar reference solute (N) belonging to the same homologous series as R (e.g., n-hexane) which is skudied along with the solute of interest (Z) in solvents R and Y. Then, from eq 5
+ In y2’
(1) where the superscripts c, e, and s refer to, respectively, the combinatorial, energetic, and structural contributions to In y z m . The combinatorial part js given by
In y*e
Thus, if it is one’s intention to examine the energetics of solute-solvent interactions in a given system, account must be taken of the structural (or “free volume9’8,9J2) contribution xs. Unfortunately, a quantitative evaluation of xs requires quite accurate values for the temperature dependence of the solute and solvent d e n ~ i t i e s , ~ Jin~J~ formation which may not be available. One way of circumventing this problem is to also study the solute of interest in a “reference” solvent (R) which is closely related and similar in size, shape, and structure to the solvent of interest (Y), so that the thermal expansion coefficients of R and Y are approximately equal and, hence, x p r_. xR5.8’9’12’13 For example, if Y is di-n-octyl ether, R might be n-heptadecane. Then, from eq 4
) + x e + xs
The Journal of Physica! Chemistry, Voi, 78. No. 16. 1974
(31 m,
we
(4)
X R Z ~- XYZ‘ X R N ~-+ Xwe (6) where x i “ is the energetic contribution to the interaction parameter of solute j in solvent i. Finally, if Vz = VN and/or V , = VR, eq 6 yields
where Axe x R ~ xyze - X R N ~+ x y ~ e Again, . it is assumed in eq 7 that Axs = 0, by vjrtue of a proper choice for the re€erence solvent. To relate Axe to molecular energetic parameters, we take7 ,IO,I4
Activity Coefficients for Aromatic Solutes at Infinite Dilution
1645
TABLE I: Hard-Cbre Volumes (Vk)and Molecular Energetic Parameters (&) for Solutes and Solvents
TABLE 11: Comparison of Experimental Activity Coefficients (rz")
_ I _ _ _
T,O
Solvents
Vk,cm3 mol-1
6k
System
n-Octaducane iR) 1-Chlorohexadecane 1-Bromohexadecane 1-Iodohcxadecane n-Heptane (N) Benzene To1u en e Ethylbermem o-Xylene m-Xylene p-Xylaene n-Propylbenzene Isopropy (benzene Mesitylene Chlorobenzene Bromobcnzene
377.1 349.7 354.5 366.6 152.2 93.75 113.7 132.7 131.4 133 . 0 133.7 153 . 0 152.4 151.7 111.3 116.5
0.0316 0,1546 0.1718 0.1952 0.0000 0.2233 0.2085 0.1957 0.2263 0,1957 0.1917 0.1789 0.1680 0.1818 0,2974 0.3587
n-C7-n-Cl8 Benzene-n-Cla
a
I
2 E i j - E 11 . . - E J. J.
35 30 40 50
0.903b 1.001 0.961 0.930
0.896 1.001 0.966 0.927
Ref
3 4 4 4
*
Data listed in microfilm edition. Interpolated value.
from Eastman Kodak. Or) had a stated purity in excess of 99.5% and was not purified further. HG and HB were purified by vacuum distillation, while traces of iodine were removed from HI by drying in a vacuum oven at 60" for 10 hr. High-temperature glc analysis of OD and the three purified solvents indicated purities in excess of 99.5%. The nonpolar reference solute (N) n-heptane and the eleven homonuclear aromatic solutes chosen for this study (see Table I) were used without further purification (solute purity is not an important consideration in these glc studies). The method of column preparation and analysis, the glc apparatus used, and the procedure followed for obtaining specific retention volumes ( Vg0)are described elsewhere.2 V80's were measured for the 48 binary systems a t 30, 40, 50, and 60" (see the microfilm edition for values). The uncertainty in Vg0is estimated to be about 0.5%.2
where U , is the configurational internal energy of Tu' and d,j is given by
dij
This studyU Bristol group
C
(9)
EN,
where the E'S refer to pairwise potential energy well depths p e r segment (or p e r u n i t hard core uolume).lOJ1 Combining eq 7-9, one obtains
and all the 6's are small compared to unity.
Results and Data Reduction Infinite dilution activity coefficients ( 7 2 ) for the twelve solutes in each of the four solvents were calculated at 30, 40. 50, and 60" from the Vgo data using the usual procedure and equations2 (see the microfilm edition for values). The uncertainty in In y ~is, estimated to be *0.007.2 Some of our results are compared with available literature value^^,^ in Table 11, where the excellent agreement (k0.004 in In 7 2 , on the average) is evident. Vgo values were also determined a t 45" by interpolation of the linear Vg0 I J S . reciprocal temperature plots, and are listed in Table III along with the corresponding 7 2 values. Hard-core volumes (Vk) were found through Kreglewski's procedure15 of determining molar volumes at T = 0 . 6 T c , where Tc is the critical temperature. The necessary densitiesT6 and critical temperatures17 were obtained from available compilations. For the haloalkane solvents the contribution of the halogen group to b'k was determined by applying Kreglewski's method to the lower molecular weight homologs for which the necessary data are available.16,17 The contributions of methylene and methyl groups to V, are known.1° The V, values are listed in Table I. The total interaction parameter ;y was calculated through eq 4 for each binary system a t 30, 40, 50, 60 (values listed in the microfilm edition), and 45" (see Table 111). From these, the Ai( values ( X R Z - X Y Z - X R N x Y ~were ) determined €or the aroniatic (Z)-alkyl halide (Y) systems at each temperature and are listed for 45" in Table IV. Alternatively, Ax could have been directly computed through eq 6 (or, with minimal error, eq 71, where it is assumed that A x = Axe, i.e., that Axs = 0. Note that, since2
Experimental Section The solvents n-hexadecyl chloride (HC) and n-hexadecy1 bromide (HB) were obtained from Humphrey Chemical Co., as was the reference solvent (R) n-octadecane (OD). The solvient n-hexadecyl iodide (HI) was obtained
where
Since N is chosen to belong to the same homologous series as R (and, thus, i s closely related to Y), the usual geometric mean comhining rule will be assumed for ~ R Nand t y ~ i e.
cij =
( E ~ ~ E ~ ~ ) *(with ' ~
j = N)
(11)
However, since Z might be chemically dissimilar to R and Y, allowance should be made for possible deviations from eq 11.Hence, we take E , ~=
E i ( ~ i l ~ j 3 ) 1 / 2 (with j
E
'7)
(12)
where j-, i s close to ulnity. Combining eq 10-12, expanding ( t , , / ~ " ) ~ ' ~and ( E ~ , / E N N ) and ~ ' ~ keeping first-order terms only,: we obtaiii
where KR E ( ~ R R / E N N ) t)\r
(EYy/
