a test of generalized quasi-lattice theory. calculations of

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July, 1962

A TESTOF GENERALIZED QUASI-LATTICE THEORY

of ThC14 .where the MCl/ThC14 ratio is large, the apparent 13usceptibi;ity of ThCh shows a tendency to increase numerically. This wouid be true if greater numbers of mater molecules were displaced per thorium ion during complex formation, thus releasing the molecules from the deforming influence of the electrostatic field of dissolved ions. As the concentration ratio becomes smaller, the value of “z” in the formula ThCL.xMC: becomes smaller, resulting in fewer water molecules being displaced per thorium ion and a decrease in the apparent susceptibility of ThC14. This view is consistent with the apparent and partial molal volume data.

1301

Conclusion Apparent and partial molal volumes of ThC14 were plotted as a function of ThC14 concentrations in aqueous LiCl, KaC1, and KC1 solutions. Variations in the curves suggest the formation of polynuclear structures, the complexity of which depends upon the concentration ratio of the two dissolved salts. This technique shows promise as a sensitive means of detecting changes in complex structures in solution. It is hoped that densities measured with greater precision mill provide more detailed information regarding such structures.

A TEST OF GENERALIZED QUASI-LATTICE THEORY. CALCULATIONS OF THERMODYNAMIC PROPERTIES OF SOLUTIONS OF ALCOHOLS IN AROMATIC HYDROCARBONS BY J. R. GOATES,R. L. SNOW,AND J. B. OTT Department of Chemistry, Brigham Young University, Pravo, Utah Received Janzaary 8 , I968

Heats and excess free energies of mixing were calculated by means of a generalized quasi-lattice theory for alcohol-hydrocarbon systems and compared with experimental values from the literature. The various lattice parameters of the theory were deduced from the geometry of the molecules. A reasonable and consistent set of energy parameters was obtained from a study of the experimental results of fifteen alcohol-aromatic hydrocarbon systems, The same set of parameters was used to calculate excess free energy data, which were compared with three sets of experimental results. The theory appears to have value in interpreting and, to some extent, predicting thermodynamic properties of solutions.

The use of the generalized quasi-lattice theory described by Barker1,Z to calculate the thermodynamic properties of mixing of solutions appears to have value in interpreting thermodynamic data for systems of associated In a previous paper5 we reported some success in describing the heats of mixing of ethanol with cyclohexane and both methanol and ethanol with benzene through the use of a consistent and reasonable set of energy parameters. Recent1,y an extensive set of heat of mixing measurements on alcohol-hydrocarbon systems has been completed by Mrazek and Van Ness.6 That study includes measurements a t three temperatures on the fifteen binary systems that can be formed from methanol, ethanol, propanol, butanol, and pentanol, each with benzene, toluene, and ethylbenzene. These data, together with the free energy of mixing data of Scatchard and Ticknor,’ Brown and Smith,8 and Kretchmer and WiebeD now make it possible to conduct a rather exacting test of quasi-lattice theory in associated solutions. (1) J. A. Barker, J . Chem. Phgs., 20, 1526 (1952). (2) J. A. Barker, ibid., 21, 1391 (1953). (3) J. A. Barker, I. Brown, and F. Smith, Discussions Faraday Soc., 16, 142 (1953). (4) J. A. Barker and F. Smith, J . Chem. Phys., 22, 375 (1954). ( 5 ) J. R. Goates, R. L. Snow, and M. R. James, J . Phys. Chem., 65, 335 (1961). (6) R. V. ldrazek and E. C. Van Ness, Am. Inst. Chem. Engrs. Paper, 72, 190 (1961). (7) G. Soatchard and L. B. Ticknor, J . Am. Chem. SOC.,74, 3724 (1952). ( 8 ) I. Brow11 and P. Smith, Australian J . Chem., 7, 264 (1954). (9) C. B. Xretchmer and R. Wiebe, J . Am. Chem. Soc.. 71, 1793 (1949).

Quasi-lattice Theory Lattice Parameters.-The theory described by Barker112is based on a quasi-lattice model that has been generalized by recognizing different types of contact sites on a molecule. For example, an alcohol is considered to have three types of siteshydrocarbon type (designated as type I), hydroxyl hydrogen (H), and oxygen (0)type sites. Toluene and ethylbenzene are considered to have two types, an aromatic hydrocarbon type (S) on the benzene ring, and an aliphatic type (S’) on the alkyl substituents. Benzene is treated as having only the S type site. The theory requires a knowledge of the number and type of sites on each molecule and the energies for all possible interactions of these sites. The number of sites present on the alcohol molecules was cqlculated on the assumption that each carbon and each oxygen atom occupied one position in a fourfold coordinated lattice. Some of the four nearest neighbors of each carbon or oxygen atom are atoms within the same molecule. The remainder, the number of those sites available for contact with another molecule, are designated by the letter &, with a superscript A for alcohol and B for the other component of the solution. Subscripts to Q (H, 0, I, S, and s’)refer to the type of site. Table I gives the values of the Q’s used in this study. The number of contact sites for both the alcohols and aromatic compounds was deduced directly from the structural formulas of the compounds. Energy Parameters.-For the system containing

in the bcnzcric ring infliienccs t hc>t.lcct roil density of the ring, and \\ill, therclforc, nffcct the 13-S and 0-S (and to sorw extent even the I-S) iiiteractions, &I" 00" Qr" QsB 06,J' a new set of values for the cnergics associatcd with CHIOH 1 2 3 .. thcsr intcraetions I\ as ncedvd for the toluene and CZH~OH 1 2 5 .. .. nib. Sinre the alkyl substituents CIHTOH 1 2 I .. .. increase the rlrctron density of the ring, and the CdHsOH 1 2 !I .. .. rffect of thc (>tliylgroup is greater than that of t h e C,Hl,OII 1 P 11 .. .. rnvt hyl, on(>11ould c q w t from n consideixt ion of CoHb .. .. , . 12 .. purely cwuloniltic*forccxs t h:it in going from h i z ( ~ i i ( ~ CBHOCIl8 .. .. .. I1 3 to ioliicnr to et hyll)rnxcw~s y s t m ~ s ,[ . ~ - d should COI I:,C21Is .. .. .. 11 5 d(w('as(x anti [ 0- slioiild irirrcasv. The valiies of t hrse paraniotcrs that prodiicctl t h r lwst f i t of I)enzcne :ind :iii alcohol four type. of sitos are thc c~xpcrirnont:ildata did, in f w t , follow the preprcmit , rosiiliirig in t h follor\iiig ~ ten intcmc*tions: t l i c s t cd (.hung.. H-11, 1 1 4 , 1-[-I, I€+, (I- four ~ IInI t I I ip the c'sc(w t1ic.rniodyiiarnic properties of t h s c that arc t)ctivec~nlike sites is z ~ r otjy de- Iiavc hccn given by Barker',? in terms of a function finition. siliw I is drfiiied as t h~ onwgy c~haiigc~ designated by X . E'or the tolucw and ethylof the cliiasi-c.iicliiiicn1 prowss I , (i-i) I/* (jrj) 1)etlxenesystems the X' functions arc' d~fincdby the = (i-j). with i :tiid j rcprcwiiting aiiy of the f i i ~ s(1t of five qii:uhti(#ccyiiat ions TAIHX I

NUlfBlCH ANT) T Y P E OF CONTACT SITES

I .

-

+

sis iiitcrartions, four ( H - 0 , 11-3, 0-S, and I-S) \ v ( w singlcd o i i t as thc nimt significant, either bec:uisc the cw'rgy of iiitcrnction was expec*tcd to tw rrlatively high (11-0, 11-3, :ml O S ) or the nunit)er of siich ititcwctions of that type is large> (143). 'Fhe riiergy trrms for the remaining two (14-1 and 0-1) I\ e r set ~ equal to zcro. Since both I4 niid 0 sites niight be expected to be prcfercntially involvcd in the moro enrrgcltic interactions (13-0, II-S, : ~ n dOM),the contributions of 11-1 :ind 0-1 \\ere espc>cstccl, and arc in fact fOlllld, to he srnall. ].'or the byst rms coniaining toliicric and cthylbenz(w, o w ndditional typc of contact site (S' for th(1 aliphut ic part of the solvent molecule) and, therefore, five addii ionnl types of interactions (11-S', 0-S', I-S', S-S', and S ' 4 ' ) had to be considered. Siircc the intoraction S-S' is similar to that of 1-43, i.e., each is an aliphatic-aromatic hydrocarbon intcraciion, the valiic of I'S-S. \\-as assigned thr same valiic as I-1-s. Thr othw foiir, considcrcd to \w less significant parameters, were wt rqiial i o zcro. l ' l l - s t , t - ~ ) - saiid , ~ ('1-s. would be c.spcbctrd t o he similar to ('11-1, t'o-I, and ('1-1, which were assigned a value of zero in t hc 1)cnzenc systems. t y s t - s f is zcro by definition. Values for I'o-M, I-H-s, T'o-s;, and C-1. that apply to thc benzene systems had been determined in a previoiis The s:iini' values, with small changes in were used for the hcnzcnc systrms of this stiidy. C-O-H had beeti fisd froin a study of the rclat ivcly simple system ethanol-c~yc*lohesane, for which only two energy parameters are Lry t o gi1.c t h ( b rorrcd shape t o t h c ing- composit ion (wrvcs of hrnzenc nith mcth:inol and rthanol, and I'I-s had t y n f i x t d at a v:ilur that gn\-c the correct difftwncc i n hright he! u ccm t lie Incthanol- h n z c n c and ethanoll)rnzcnc sybtcms. In the prrsent stiidy, the value of ( ' 1 - 5 \+:is adillst ccl indcpcndcntly for t m a h systcm t o give the correct hciqht, to each curve at 0.4 molt. fraction :dcohol, \\ hich is n t w the miisiniunl heat of misirig v:ililo for thew hystcms. Inasmiit-li :IS t h c prcscncci of an alkyl siibst,itucnt

SII[Sl,

+

+ &f + XS?". + + s,,-t ,I + .Ys?o-q -c + + SI + $So?lr-,I

,Yo[~YIi?,,-c

S l l S t i

.Yql'\lr?lI

I

9

I

[ experimental data with several combinations of energy values. To fit more than one system and yet maintain consistency among the constants used limits very appreciably the number of ways of producing a

satisfactory fit. Calculation of free energies as well as heats places a further strain on the freedom of choice of energy values. It is interesting to not#e that the set of constants UH-o = -3200, C T ~ - s = -545, UO-S = -300, UI-s = 82, and Us-S' = -45, which are not reasonable because of the discrepancy in the last two values, nevertheless produces a fairly good fit of the heat of mixing data of ethanol-toluene and ethanol-ethylbenzene. When these values of the energy parameters are used to calculate the free energy, however, very poor results are obtained. Temperature Effect.-In order to test the extent to which the energy parameters are temperature dependent, aHXM values were calculated at X A = 0.4 from the 25' data of Table I1 for temperatures of 35 and 45'. The experimental AH,M data increase with an increase in temperature. The theoretical calculations, made on the assumption that the energy parameters are independent of temperature, account for 4045% of this increase. The remainder can be accounted for by assuming a 2-3Oj, change in the U's for each 10' change in temperature. Since AFXEis quite insensitive %tosecond-order changes in AHXM,the temperature dependence of the energy parameters is of much less significance in the calculation of AFXEthan it is for AHXM. Conclusions.-It appears from this study of 15 systems that the generalized quasi-lattice model is useful for interpreting, and to some extent predicting a priori, thermodynamic data of mixing in alcohol-hydrocarbon systems. By assigning values to the lattice parameters that are based solely on the geometry of the molecules and making only rough estimates of reasonable values of the energy parameters, one can get qualitative information about the height and shape of the thermodynamic propertycomposition curves. By having access to a set of parameters such as those in Table 11,one can make semi-quantitative ( f10%) estimates. Acknowledgment.-The authors gratefully acknowledge the support given this project by the National Science Foundation.