EQUILIBRIA OF BINARY MIXTURES OF HEXANE WITH ALIPHATIC KETONES
404 1
Vapor-Liquid Equilibria of Binary Mixtures of Carbon-14-Labeled Hexane with Aliphatic Ketones'
by Bogdan Magiera and Witold Brostow* Instytut Chemii Fizycznej Polskiej A k a d e m i i N a u k , W a r s a w 42, Poland
(Received February 17, 1971)
Publication costs borne completelu by The Journal of Physical Chemistry
Equilibria of dilute solutions of n-hexane in turn in acetone and methyl ethyl, methyl propyl, and diethyl ketones have been studied. Isotherms and isobars linear with respect to composition were obtained]and thermodynamic consequences of such a behavior discussed. Activity coefficients and excess Plaiick functions of mixing were computed; some methods of obtaining the limiting values of activity coefficientsat infinite dilution have been compared. A version of the quasilattice theory of mixtures, which may be called the model of dilute solutions of molecules of different sizes, was proposed and applied to describe the experimental data.
1. Introduction Thermodynamic behavior of liquid phases containing very small quantities of one of the components is interesting for both fundamental and practical reasons. Consider a homogeneous binary mixture i-j containing very small amounts of component i ; except for local concentration fluctuations which do not affect the averages, each molecule of i may be safely assumed to be surrounded by molecules of j only. From the point of view of the theory, instead of the usual three types of intermolecular interactions only two need to be considered: i-j and j-j. From the point of view of the industrial practice such as separation of components by rectification, information on the system in question enables us to obtain the substance j with a high degree of purity. We have studied isothermal and isobaric vapor-liquid equilibria of dilute solutions of hexane in turn in acetone, methyl ethyl ketone, methyl propyl ketone, and diethyl ketone. The objects of particular attention were the limiting values of activity coefficients of hexane, lim,,,o 11,where 21 denotes the mole fraction of hexane in the liquid phase, obtained by our experimental procedure arid also by other methods.
2. Experimental Section Measurements were made in the vapor-liquid equilibrium still described previously by one of us2*and based on its construction on the Swietoslawski ebulliometer.2b The advantages in the use of such an apparatus have been discussed ~ l s e w h e r e . The ~ ~ ~ manostatic system used in both isobaric and isothermal determinations was the same as described in ref 5 . Pressures were determined in a barometric ebulliometerZbfilled in each case with the respective pure ketone. Temperatures were determined within ?cO.O2"K with Pt resistance thermometers (Heraeus, Hanau, West Germany) with Bundesanstalt (Braunsrhweig, West Germany) cer-
tificates; boiling point differences were measured with Roberteau thermometers, (Prolabo, Paris) within *0.00loK. A dilute hexane solution was taken as one of the components, the respective pure ketone being the other one. The equilibrium determination procedure described in ref 2a was followed. Advantages of the use of internal filling counters for I4C assay have been discussed by Jordan and Lykourezos.6 Before that, in the first determinations of compositions of organic liquid mixtures containing a 14C-labeled component made in this laboratory7 we have found such counters suitable for the purpose at hand; self-quenching mechanisms and properties of internal filling counters have been studied by Frnnke, et aL8 Now, therefore, 14C radioactivity was determined again in internal filling counters, switching however from the Geiger-Muller to proportional range. We have described elsewhereg the details of the 14Cassay technique used in the present work. The reagents used were purified by rectifying each
* To whom
correspondence should be addressed at DBpartment de Chimie, Universitb de MontrBal, Montreal 101, P. Q., Canada.
(1) Based on a dissertation submitted by B. Magiera to the Institute of Physical Chemistry of the Polish Academy of Sciences in partial fulfillment of the requirements for the D.Sci. (in chemistry) degree. (2) ( a ) W. Braostowski, Bull. Acad. Pol. Sei., Ser. Sei. C h i m . , 8 , 291 (1960) ; (b) W, Swietoslawski, "Ebulliometric ,Measurements," Reinhold, New York, N. Y., 1945. (3) W. Swietoslawski, K. Zieborak, and W. Brzostowski, Bull. A c a d . Pol. Sci., Cl. 111,5 , 305 (1957). (4) W. Brzostowski and W. SiTietoslawski, Zh. F i z . Khim., 36, 2090 (1962). ( 5 ) A. Blinowska, W. Brzostowski, and B. Magiera, Bull. A c a d . Pol. Sei., S e r . Sei. Chim., 14,467 (1966). (6) P. Jordan and Ph. A. P. Lykourezos, Int. J . A p p l . Radiat. Isotop., 16, 631 (1965). ( 7 ) W.Brzostowski, B u l l . A c a d . Pol. Sci., Ser. S c i . Chim., 9 , 441 (1961). (8) H . G. Franke, E. Huster, and 0. Kraft, Z . P h y s . , 188, 274 (1965): H . G. Franke, ibid., 188, 339 (1965); H. G. Franke, E. Huster, and K. H . Rohe, ibid.,188, 519 (1965). (9) W.Brzostowski and B. Magiera, a\ukZeonika, 12,781 (1967).
The Journal of Physical Chemistry, Vol. 76, N o . 16,1971
BOGDAN MAGIERAAND WITOLDBROSTOW
4042 twice through a laboratory column. 14C-labeledhexane from Orlando Research Inc., in 5-mCi samples with specific acitivity 1.6 mCi/mmol, was diluted with a large excess of the inactive liquid. Refractive indices were measured with an Abbe-type refractometer, Carl Zeiss, Jena, East Germany; normal boiling points and ebulIiometric degrees of purity were determined by the standard Swietoslawski procedure2b on a differential ebulliometer. The physicochemical characteristics of the reagents are given in Table I. To siniplify the description, in the following text the substances will be designated by numbers given in the same table.
Table I : Properties of Reagents Ebulliometrio
degree of NO.
Substance
BP, " K
nzoD
purity"
1 2 3
%-Hexane Acetone Methyl ethyl ketone Methyl propyl ketone Diethyl ketone
341.90 329.35 352.71
1.3750 1.3588 1.3786
IV IV V
375 51
1.3905
IV
374.85
1.3926
IV
4 5 a
I
f
COIJ
As defined in ref 2b.
X,
Figure 1. Isothermal vapor-liquid equilibria for 1-2 mixtures: 0 , liquid points; x, vapor points.
3. Concentrational Relationships For 1-2 mixtures four isotherms have been studied at 308.15, 318.15, 323.15, and 328.15"K. The results obtained are shown in Figure 1. The vapor phase is richer in the less volatile component, as at higher concentrations an azeotrope is formed-cf. Schafer arid Rall.l0 In the concentration ranges of the measurements linear behavior is observed, so that the total vapor pressure at given T i s
P
==
Pj,
+ bxl
Compo-
Pjj,'
nents
T , "K
Torr
b , Torr
YllZl
1-2
308.15 318.15 323 15 328.15 323.15 333 15 343,15 328.15 343.15 363.15 328. 15 343.15 363.15
348 2 511.1 612.7 729.8 226.8 389.8 554.6 142.3 257.2 517.1 144.8 261.8 626.2
1180 1554 1765 2028 940 1225 1540 660 950 1650 616 975 1648
4.31 3.94 3.80 3.63 4.42 4.05 3.71 5.19
I
I
1-3
I
(1)
Index j denotes here the component other than hexane. Generally, in this paper quantities without indices refer to a mixture, with a single index to a component in the mixture, and with a double index t o a pure component. For the remaining pairs of components studied, Le., 1-3, 1-4, and 1-5, linear behavior was also found for all isotherms. The respective experimental values of constants P,, and b in eq 1 for a11 systems and temperatures are listed in Table 11. As the linear behavior is observed for both liquid and vapor curves, along each isotherm we have the ratio yl/xr constant within the experimental error, with yl denoting mole fraction of hexane in the vapor phase; the respective values of these ratios are listed in the same table. For each of the systems me have determined one isobar at a pressure close to atmospheric. The results are shown in Figure 2. For our dilute solutions linT h e Journal of Physical Chemistry, Vol. 7 6 , -Yo. 26, 1972
Table 11: Constants in Eq 1
1-4
1-5
a
We use 1Torr
=
4.70 4.12 5.11 4.66 4.08
0.00013332 J om-*.
ear concentration behavior is observed here too, so that at any P = constant we have yl/xl = constant and
T ( z ) = T,,
+
b'xl
(2)
Parameters of this equation are listed in Table 111. Consider now some consequences of eq 1. The relevant thermodynamic formula is PyJ'i'
= Piixifi
(3)
(10) K1. Schiifer and W , Rall, Be?. Bunsenges. Phys. Chem., 62, 1090 (1958).
4043
EQUILIBRIA OF BINARY MIXTURES OF HEXANE WITH ALIPHATIC KETONES
so that the first right-hand-side term is for our solutions concentration independent. Further b2(
-$) -- _y1 -_x1_- _b _
(7)
The last part of equality 7 follows, when one notices that according to the definition ( 5 ) for 1-j mixtures b( - Y E / R ) / b a= In (fi/fj); the Gibbs-Duhem equation gives for our case b In fj/bzl = - (zl/zt)( bIn P/bq), so that b2(- Y E / R ) / h 1 2= zj-l(b In P/bzl). The last relation is used in conjunction with eq 1. Zelvenskii and his collaborators in a series of studiesll - 14 using I4C- and a5S-labeledcompounds found the relative volatility /3
concentration independent, Using (3) and neglecting again variations of fl’ and f,’ with composition of dilute solutions, we find that the condition /3ij(z) = constant leads to 1
0
(OR4
@08
I
q0/2
-c
Xf
Figure 2. Isobaric vapor-liquid equilibria: 0 , liquid points; X, vapor points.
Table 111: Constants in Eq 2 Components
1-2
1-3 1-4 1-F)
P,Torr
Tjj,
728.5 728.6 724.5 717.8
OK
328.10 351.40 373.85 373.04
b‘, OK
-80.7 -75.6 -98.5 -100.1
2/1/21
3.62 3.44 3.84 3,85
fl- ( x ) fJ
=
-b In
_ -Y E R
=
x1 l n f l
+ z, In f J
wherr R is the gas constant. We have
-
bx i
dx i
The variant I1 for the component for which leads t’o
bX i XI. Introduce now the excess Planck function of mixing Y E , related to the more frequently used excess Gibbs function of mixing GE by Y E = -GE/T, so that
Yi
Xi
-
(4)
Le., f1 along the isotherm varies linearly with
(9)
Generally, (9) could be realized in the following cases: (1) f i = f, = 1; (11) one of the activity coefficients is different from unity, but both are concentration independent; (111) bjl/bz, and bff,/dx, are both #O, with the same concentration dependence o f f for both components. Case I is trivial as that of ideal solutions; case I11 violates the Duhem-Afargules equation; the only case of interest is thus 11. A further consequence of (9) under the same condition is
b 111 P ji’ is the activity coefficient of ith component in the vapor phase; numcrical values show that for our dilute solutions variations of f i ’ with concentrakion may be neglected. We thus have
constant
=
In
fi
# 1
fi
and hence
);-
bZ(
bXi2
=o
(5) (11) Ya. D. Zelvenskii and V. A . Shalygin, Z h . Fiz. K h i m . , 31, 1501 (1957). (12) Ya. D. Zelvenskii, V. A . Shalygin, and Yu. V. Golubkov, K h i m . Prom., 6,347 (1962); Ya. D. Zelvenskii and V. A. Shalygin, ibid., 6, 424 (1962). (13) Ya. D. Zelvenskii, A. A . Titov, and V. A. Shalygin, K h i m . Tekhnol. T o p l i ~Masel, (4), 5 (1962); Ya. D. Zelvenskii, A . ii.Titov, and V. A. Shalygin, K h i m . Telchnol. T o p l . Masel, (3) 1 (1964).
The Journal of Physical Chemistry, Vol. 7K, .Vo. 26, 1971
4044
BOGDAN MAGIERA AND WITOLD BROSTOW
Thus, considering the two types of experimental behavior, namely, y , / ~=~ constant and plJ = constant in terms of the derivatives of the excess Planck function with composition, Le., comparing (6) with (11) and (7) with (12) we find differences in thermodynamic characteristics. It should be emphasized, however, that the differences at the level of Y Eitself are by no means pronounced. This is related to the fact that in the concentration ranges considered by us the differences between &, and yl/zl are small. For z1 = 0.00001 and y;/z, = 3, PI, - yl/xl = 0.002 while for yl/xl = 5 the difference is 0.004. At z = 0.01000 the respectivc values of the difference are 0.060 and 4.210. One might expect similar behavior, i.e., independence of either /3 or yL/zi of composition in dilute solutions containing other components provided of course that they are zeotropic. I n mixtures of benzene and hexane, studied previously, using 14C-labcled at the atmospheric pressure the azeotrope is formed with mole fraction of benzene z = 0.00213; in this case the variation of y , / ~ with , concentration is quite pronounced.
4. Activities From (3), writing out the necessar) terms explicitly In
j'i
=
In
P yi
-PiiXi
B Vo
=
Tc 0.430 - O.S8G--- - 0.694 X T
Index c refers to the critical state and m is a characteristic paranictcr, equal to 5 for hexane; we have computed m ( T ) for the remaining components from the experimental valups of B,, for acetonelz2methyl ethyl ket0ne,~3and methyl propyl l r ~ t o n e ;for ~ ~diethyl ketone we havc assumed the same m ( T ) as for its isomer. I t is still common to apply the Lewis and Randall rule, Le., to ncglect the term involving the mixed virial coefficient Bij. Errors resulting from such an assumption are known for hexane-chloroform mixtures from an earlier paper.24 We have obtained B,, from the same formula (15) assuming
T,,? = (To,,5",,,)0*5
(16)
v,,, = o.125(v,~,"a+ vc,,1'a)3
(17)
?%J
+
For solutions studied we have calculated activity coefficients of components and excess Planck functions of mixtures using Tables I1 and 111, eq 1, 2, 13, and 5. Further terms omitted in (13) are negligible. Vapor pressures of components P I , were computed according to the formulas given in ref 16 for 1, in ref 10 for 2, and in ref 17 for 3 and 4. Given a number of vapor pressure equations of hexane we h a w thus decided to rely 011 the critical compilation of Tatevslrii, et aZ.;16 as for acetone, we have chosen the formula of Schafer and Rall,lo as it is their data that we subsequently use for some comparisons. For diethyl ketone we have not found any equation in the literature. TKOseries of vapor pressure data, reported in ref 18 and 19, differ distinctly from one another (except giving the same normal boiling point). We have therefore performed measurements of our own, found them to agree with the Dreisbach and Shrader and described both sets by log Pjj(Torr)
of corresponding statesz0with the numerical coefficients from ref 21, viz.
=
7.03583 -
1313.9 (14) 214.52 t("C)
+
Incidentally, the temperature dependence of vapor pressure is the same for the two isomers, i.e., methyl propyl ketone and diethyl ketone. 3Iolar volumes of liquids V , , were computed from the density expansions, and second virial coefficients B,, from a generalized principle T h e Journal of Physical Chemistry, Vol. 76, S o . 26>1971
=
0.5(m,,
+ mu)
(1%
The last of the combining rules has been recommcnded by Cruickshank, et aLZ5 The results of calculations for hexane are shown in Figure 3. Qualitatively, as expected, deviations from ideality decrease with dccreasing polarity of ketone, Le., with substitution of one ketone solvent by another with a larger aliphatic part of the molecule. We notice that the values for the two isomers studied a t a given temperature are relatively close to one another. Adcquatc quanlitive description does not appear feasible at the present stage of the liquid-state theory. Consider now in some detail values of limxl--10In fi, confining ourselves for a while to isotherms of 1-2 mixtures. First, by extrapolating the data shown in (14) A. A. Efremov and Ya. D. Zelvenskii, Z h . Prikl. Khim.(Leningrad), 38, 2313 (1965). (15) R . Brzostowski, Bull. Acad. PoZ. Sci., Ser. Sei. Chim., 9, 471 (1961). (16) V , hI. Tat#evskii, Ed., "Fiailtokhimicheskie svoistva individualnykh uglevodorodov," Gostoptekhizdat, Moscow, 1960. (17) T. E. ,Jordan, "Vapour Pressure of Organic Compounds," Interscience, NeivYork, N . Y., 1954. (18) D . R. Stull, I n d . E n g . Chem., 39,514 (1947). (19) M. Dreisbach and K . Shrader, ibid., 41, 2879 (1949). (20) E. A. Guggenheim and C. J. Wormald, J . Chem. P h y s . , 42, 3775 (1965). (21) 11.L. RIcGlashan and D. J. B. Potter, Proc. R o y . Soc., Ser. A , 267,478 (1962). (22) J. S. R o d i n s o n , T r a n s . Faraday Soc., 45,974 (1949). (23) J. K. Kickerson, K . A. Kobe, and J. J. McKetta, J . P h y s . Chem., 65, 1037 (1961). (24) W ,Brzostowski and L. Verhoye, Rocz. Chem., 42, 507 (1968). (25) A. J. B. Cruickshank, M . L. Windsor, and C. I,. Young, T r a n s . Faraday Soc., 62,2341 (1966).
EQUILIBRIA OF BINARYMIXTURESOF HEXANEWITH ALIPHATICKETONES
'
4045
Using the data for both dilute and concentratcd benzene-hexane mixtures, l5 calculations were made27 which show the hazard involved in concentration extrapolation. Ideality in the Raoult sense cannot be assumed for dilute solutions either, as Edwards and Encina28have found for hexane-isooctane solutions with the mole fraction of isooctane 2 0.00118. Vernier and his colleagues29have obtained values of limzz,o f i for a number of systems by gas-liquid chromatography; when possible, they compared their results with those extrapolated from vapor-liquid equilibria of concentrated solutions; in some cases the differences were striking. It seems now, therefore, a safe conclusion that extrapolation from concentrated solutions should be avoided. When not, the behavior of dilute solutions but the limiting values alone are needed, then the chromatographic method is an alternative to such a method as used in the present work. We conclude this section with comments on the Ellis and Jonah30 method of obtaining lim,,,ofi. Rearranging eq 13 and introducing for the isothermal case the parameter
f+Z
