J. Chem. Thermodynamics 1997, 29, 1223]1236

Benzene–ethanol association. The excessmolar enthalpy and second virial cross-

( ) ( )coefficients for benzene H ethanol g( ) ( )and cyclohexane H ethanol g

C. J. Wormald and C. J. SowdenSchool of Chemistry, Uni ersity of Bristol, Bristol BS8 1TS, U.K.

E � Ž . 4Ž .New measurements of the excess molar enthalpy H for yC H OH q 1 y y C H g andm 2 5 6 6� Ž . 4Ž .yC H OH q 1 y y C H g measured at standard atmospheric pressure over the2 5 6 12temperature range 363.2 K to 433.2 K are reported. These measurements supplement earliermeasurements made over the range 453.5 K to 522.9 K at pressures up to 4.5 MPa. Thenon-ideality of the ethanol vapour is described using a quasi-chemical model in whichonly dimer and tetramer association equilibria are considered. The values of H E formŽ .Ž .ethanol q cyclohexane g were found to agree well with values calculated using the

Ž .Ž . Eassociation model. For ethanol q benzene g the experimental values of H were found tombe approximately 20 per cent smaller than values calculated from the model and this wasattributed to weak association between the unlike molecules. A quasi-chemical model used todescribe the association between the unlike molecules yielded a value of the equilibrium

Ž . y1constant K 298.15 K s 0.28 MPa , and a value for the enthalpy of the ethanol]benzine12. y1association of D H s y14 kJ mol . Second virial cross-coefficients B for ethanol]12 12

cyclohexane and ethanol]benzene have been derived from the H E measurements. Q 1997mAcademic Press Limited

KEYWORDS: excess enthalpy; second virial coefficient; gas mixture; flow calorimeter

1. Introduction

Vapour phase measurements of the excess molar enthalpy H E of a number ofmŽ .Ž .water q hydrocarbon g mixtures made using a flow mixing calorimeter operatingat pressures close to atmospheric have been reported. The values of H E form� Ž . 4Ž . � ŽyH O q 1 y y C H g for n s 1 to n s 8 and for yH O q 1 y2 n 2 nq2 2. 4Ž .Ž1.y C H g could all be fitted using a model in which the cross-term second6 12

virial coefficient B and the cross-term isothermal Joule]Thomson coefficient f12 12were calculated by combining the Stockmayer potential parameters «rk s 233 K,s s 0.312 nm and t* s 1.238 for water with Kihara potential parameters for the

E Ž .hydrocarbon. Unlike the H measurements on water q cyclohexane , similarmŽ .Ž2.measurements on water q benzene could not be fitted using this model. For

this mixture the H E measurements were found to be about 20 per cent smallermthan expected, and this was attributed to a specific association between water andbenzene. This association caused values of B for the water]benzene interaction12

0021]9614r97r111223 q 14 $25.00r0rct970236 Q 1997 Academic Press Limited

C. J. Wormald and C. J. Sowden1224

to be far more negative than expected, and to fit these values it was necessary toincrease the well depth of the water]benzene potential by 35 per cent.Ž1. As theselow pressure H E measurements were made only over the limited range ofmtemperatures from 363.15 K to 393.15 K, additional low pressure H E measurementsmwere made over the temperature range 403.15 K to 453.15 K, which have beenrecently reported.Ž3. The new measurements were analysed using a quasi-chemicalmodel in which the water]benzene interaction was described using an equilibriumconstant K and an enthalpy of association D H derived from the temperature12 12dependence of K . In this model intermolecular potentials were used to calculate12the contribution of the interaction energy arising from dispersion forces. The

Ž . y1values were found to be K 298.15 K s 0.208 MPa and D H s12 12. y1y11.3 kJ mol , and these relate to the specific pairwise interaction between the

water and benzene molecules. For comparison, a similar analysis of the secondŽ . y1virial coefficient of pure water vapour yields K 298.15 K s 0.4085 MPa and11

. y1 ŽD H s y18.15 kJ mol . Again these figures apply to the specific hydrogen11.bonding interaction between pairs of water molecules, the contribution from

dispersion forces having been estimated separately.In addition to the low pressure measurements, a parallel series of measurements

using a high temperature high pressure flow-mixing calorimeter have also beenmade. Most of these measurements extend up to temperatures of 698.2 K and topressures in the region of 10 MPa. The mixtures studied include steam with C to1C n-alkanes, cyclohexane and benzene.Ž4. The measurements were analysed using8a cubic equation of stateŽ5. which was constrained to give the correct second virialcoefficients. Again, the values of H E for water]benzene were found to be lessmendothermic than those predicted on the basis of the equations which correctlypredicted the results for water]cyclohexane. The inclusion of association terms in

y1 . y1Ž .the model yielded K 298.15 K s 0.179 MPa and D H s y12.3 kJ mol for12 12the water]benzene interaction.

E Ž .High pressure H measurements for methanol q cyclohexane andmŽ .methanol q benzene at temperatures up to 523.0 K and pressures up to 4 MPahave been reported.Ž6. For the methanol]benzene interaction the quasi-chemical

y1 . y1Ž .model yields K 298.15 K s 0.177 MPa and D H s y14.7 kJ mol . Similar12Ž . Ž .measurements for ethanol q cyclohexane and ethanol q benzene have been

made over the temperature range 453.5 K to 522.9 K and at pressures up to4.5 MPay1, and for the ethanol]benzene interaction the quasi-chemical model

y1 . y1Ž .yields K 298.15 K s 0.219 MPa and D H s y14 kJ mol . Previous12 12experience of taking measurements for steam mixtures showed the importance ofobtaining H E values over as wide a temperature range as possible. As the modelmused for the analysis of the measurements at high pressures and temperatures over450 K is slightly different from that used for the measurements at low pressuresŽ o .p s 0.101325 MPa and at temperatures below 450 K, two slightly differentvalues of D H were obtained from the two data sets. This is also likely to be true12

Ž . Efor measurements on ethanol q benzene for which no low pressure H valuesmhave yet been reported.

E Ž .Ž .We now report new measurements of H for ethanol q cyclohexane g andm

H E and B in benzene]ethanol associationm 12 1225

EŽ o. Ž .Ž .TABLE 1. The excess molar enthalpy H p of 0.5C H OH q 0.5C H g and related quantitiesm 2 5 6 12

E o ET H p dH yf yf yf yB yB yBŽ .m m 11 22 12 11 22 12y1 y1 3 y1 3 y1 3 y1 3 y1 3 y1 3 y1. . . . . . . .K J mol J mol cm mol cm mol cm mol cm mol cm mol cm mol

363.2 182 9 4727 3279 2703 835 999 432368.2 158 3 4369 3163 2564 784 968 419373.2 133 2 4049 3052 2437 737 939 407378.2 118 2 3761 2953 2321 695 912 395383.2 104 2 3502 2857 2215 656 885 383393.2 89 2 3057 2683 2027 588 836 361403.2 76 2 2690 2528 1867 530 791 341413.2 65 2 2385 2388 1727 480 750 322423.2 59 2 2130 2262 1607 437 712 305433.2 54 2 1914 2148 1500 399 677 289473.2 1316 1777 1178 289 558 233483.2 38 5 1212 1702 1117 269 533 221493.2 33 3 1120 1631 1061 250 510 210503.2 30 2 1039 1566 1009 233 488 200513.2 27 1 967 1504 961 218 467 190523.2 25 1 902 1447 918 204 447 180

Ž .Ž . oethanol q benzene g at p made with our low pressure flow-mixing calorimeterover the temperature range 363.2 K to 433.2 K. The results of these experiments

EŽ o.are combined with values of H p derived from high temperature high pressuremmeasurements to obtain further information about the ethanol]benzeneinteraction, and hence about the second virial cross-coefficients.

2. Experimental

The design of the differential flow-mixing calorimeter was as previously described.Ž8.Ž .Analytical reagent-grade ethanol mass fraction: )0.995 was dried by distillation

Žover calcium hydride. Thiophen-free analytical grade benzene mass fraction:.0.995 was dried and distilled before use, as was the analytical grade cyclohexane

Ž .mass fraction: 0.998 .All measurements were made at ambient atmospheric pressure over the

approximate range of mole fractions y s 0.4 to 0.6. Usually, five measurementswere made at each temperature. These were corrected to standard atmospheric

o E Ž .pressure p and values of H y s 0.5 were obtained from plots ofmEŽ . Ž . E Ž o.H y r4 y 1 y y against y. Mean values of H y s 0.5, p s p and them m

uncertainty dH E are listed for temperatures in the range 363.3 K to 433.2 K, inmcolumns 2 and 3 of tables 1 and 2, respectively, and are plotted against temperaturein figures 1 and 2.

E( o)3. Values of H p from high pressure measurementsm

The high pressure H E measurements reported previously Ž7. extend over themtemperature range 453.5 K to 522.9 K and for pressures up to 4.5 MPa. These

C. J. Wormald and C. J. Sowden1226

EŽ o. Ž .Ž .TABLE 2. The excess molar enthalpy H p of 0.5C H OH q 0.5C H g and related quantitiesm 2 5 6 6

E o ET H p dH yf yf yf yB yB yBŽ .m m 11 22 12 11 22 12y1 y1 3 y1 3 y1 3 y1 3 y1 3 y1 3 y1. . . . . . . .K J mol J mol cm mol cm mol cm mol cm mol cm mol cm mol

363.2 155 4 4725 3119 2987 834 916 562368.2 118 3 4367 3000 2826 783 886 542373.2 101 2 4047 2890 2679 736 859 523378.2 95 2 3759 2787 2546 694 832 505383.2 76 2 3500 2690 2423 655 807 488393.2 61 2 3055 2515 2206 587 760 457403.2 49 2 2688 2360 2021 529 717 428413.2 44 2 2383 2222 1861 479 678 403423.2 37 2 2128 2098 1723 436 643 379433.2 34 2 1912 1986 1602 399 610 357473.2 22 3 1314 1627 1240 289 499 286483.2 20 2 1210 1555 1170 268 476 271493.2 18 1 1118 1488 1108 250 455 258503.2 17 1 1037 1426 1051 233 435 245513.2 16 1 965 1367 999 218 415 233523.2 15 1 901 1313 951 204 397 221

measurements were made using a single mixing calorimeter rather than adifferential arrangement, but at high pressures the speed of flow through thecalorimeter is much less than at low pressures and the Joule]Thomson effect inthe calorimeter is consequently negligible. Using this calorimeter it is difficult tomake accurate measurements at pressures much below 0.5 MPa because H E

mdiminishes as the pressure is reduced, and because the error due to temperaturefluctuations in the fluidized alumina bath surrounding the calorimeter increases ininverse proportion to the pressure. The best way to extrapolate the high pressure

Ž E .excess enthalpies to standard atmospheric pressure is to plot graphs of H rpmagainst p. The measurements at pressures up to 2 MPa and at temperatures from473.2 K to 523.2 K reported previously Ž7. are plotted this way in figure 3. Values of

E Ž o .H p s p , y s 0.5 obtained by graphical extrapolation to p s 0.101 MPa aremlisted in tables 1 and 2 and plotted in figures 1 and 2.

4. Association modelE Ž .Ž . Ž .Ž .The H measurements on water q cyclohexane g and water q benzene gm

reported previously Ž2. were analysed using pair potentials for the pure componentsand for water interacting with hydrocarbon. This could be done for these watermixtures only because an extensive database of H E measurements made on 12mmixtures of gases which do not associate with steam was available, and thisinformation made it possible to obtain parameters of the Stockmayer potential forwater interacting with normal fluids.Ž1. A similar database for ethanol mixtures isnot available, and Stockmayer potential parameters for ethanol interacting withhydrocarbon are not known. Furthermore, the extent of association in ethanolvapour is greater than that for steam, and to describe the non-ideality at

H E and B in benzene]ethanol associationm 12 1227

EŽ o. oFIGURE 1. The excess molar enthalpy H p at standard atmospheric pressure p formŽ .Ž .0.5C H OH q 0.5C H g . `, measurements made with the low pressure differential flow mixing2 5 6 12

EŽ o. ocalorimeter, table 1. ^, values of H p obtained by extrapolating to p s p measurements mademusing a single stage mixing calorimeter operating at high temperatures and pressures. The extrapolation

Ž .is shown in figure 3 a . The curve through the points was calculated from the association model withj s 0.94 as described in the text.

temperatures around 373 K it is necessary to take account to the fourth virialcoefficient as well as the second. For these reasons we shall analyse the H E

mmeasurements using a quasi-chemical model, which describes the properties ofethanol in terms of association equilibria, and which can be extended by theaddition of further terms which describe the specific interaction between ethanoland benzene.

We previously Ž10. made use of the quasi-chemical model in the form developedby GinellŽ11. who gave expressions for the second, third, and fourth virial coefficientsB, C, and D in terms of equilibrium constants K , K , and K for the association2 3 4of molecules into clusters of 2, 3, and 4 molecules, respectively. Ginell’s equationsdiffer from the earlier equations of Woolley Ž12. in that they include terms whichare a crude estimate of the hard sphere second, third, and fourth virial coefficients.We found, as others have done,Ž13,14. that the non-ideality of ethanol could be fittedadequately by considering the formation of dimers and tetramers only, and the

C. J. Wormald and C. J. Sowden1228

EŽ o. oFIGURE 2. The excess molar enthalpy H p at standard atmospheric pressure p formŽ .Ž .0.5C H OH q 0.5C H g . `, measurements made with the low pressure differential flow mixing2 5 6 6

EŽ o. ocalorimeter, table 2. ^, values of H p obtained by extrapolating to p s p measurements mademusing a single stage mixing calorimeter operating at high temperatures and pressures. The extrapolation

Ž .is shown in figure 3 b . The broken curve shown in the figure was calculated from the association modelŽ .Ž .with j s 0.94 which fits the measurements on 0.5C H OH q 0.5C H g shown in figure 1 to within2 5 6 12

the uncertainty on the measurements. The continuous curve was calculated by including additionalterms to describe the specific association between ethanol and benzene for which the interaction energy

. y1was found to be D H s y14 kJ mol .12

inclusion of a trimer term was not necessary. This procedure uses K as a ‘‘catch4all’’ term which approximates trimer, tetramer, and higher n-mer formation withadequate accuracy. With K set to zero the first three virial coefficients are:3

B s B y K RT 1Ž .h 2

22 2. .C s B y 21r16 B K RT q 4 K RT 2Ž . Ž . Ž .h h 2 2

2 33 2 2 3. . . .D s B y 13r8 B K RT q 89r16 B K RT y 20 K q 3 K RT .Ž . Ž . Ž . Ž .Ž .h h 2 h 2 2 4

3Ž .

Here, B is the second virial coefficient of a homomorph approximating theh

H E and B in benzene]ethanol associationm 12 1229

E Ž . Ž .Ž . Ž .FIGURE 3. Measurements of H p for 0.5C H OH q 0.5C H g , figure 3 a , andm 2 5 6 12Ž .Ž . Ž . E0.5C H OH q 0.5C H g , figure 3 b , plotted in the form H rp against p to facilitate extrapolation2 5 6 6 mto p s po. The experimental values were reported in reference 7, and the extrapolated values are listedin tables 1 and 2.

non-specific forces between the ethanol molecules. Differentiation of B, C, and Dwith respect to temperature gives:

f s B y T d BrdT , 4Ž . Ž .0

c s C y Tr2 dCrdT , 5Ž . Ž . Ž .and

L s D y Tr3 d DrdT . 6Ž . Ž . Ž .

Ž .Differentiation of equation 1 yields:

f s f q K D H . 7Ž .0 h 2 2

Here, D H is the enthalpy of formation of the dimer which is a negative quantity,2and f is the zero pressure isothermal Joule]Thomson coefficient. Differentiation0

Ž .of equation 2 yields:

y1 2. .c s B f y 21r32 f y D H B RT K RT y 4 D H K RT , 8Ž . Ž . Ž .� 4h h h 2 h 2 2 2

C. J. Wormald and C. J. Sowden1230

Ž .and differentiation of equation 3 yields:

y12 2. . .L s B f y 1r48 52 B f y 26 D H B RT K RTŽ . Ž . Ž .� 4h h h h 2 h 2

y1 2. . .q 1r48 89 f y 178 D H B RT K RTŽ . Ž . Ž .� 4h 2 h 2

22.q 20 K D H q K D H RT . 9Ž . Ž .Ž .2 2 4 4

For a fluid at low densities the residual molar enthalpy H R is given by:m

H R s RT frV q crV q LrV q ??? , 10� 4Ž . Ž . Ž . Ž .m m m m

and for a binary mixture of components 1 and 2 the excess molar enthalpy H E ismgiven by

H E s H R y y H R y y H R , 11Ž .m m 1 1 2 m

Ž .where the first term on the right-hand side refers to the mixture. Equation 11 canbe written:

H E s frV q crV 2 q LrV 3Ž .� 4Ž . Ž .m m m m

y y f rV q c rV 2 q L rV 3Ž .� 4Ž . Ž .1 11 m , 1 111 m , 1 1111 m , 1

y y f rV q c rV 2 q L rV 3 . 12Ž . Ž .� 4Ž . Ž .2 22 m , 2 222 m , 2 2222 m , 2

Ž .In equation 12 f, c , and L refer to the mixture and are given by the equations:

f s y2f q 2 y y f q y2f , 13Ž . Ž .1 11 1 2 12 2 22

c s y3c q 3 y2 y c q 3 y y2c q y3c , 14Ž .Ž . Ž .1 111 1 2 112 1 2 122 2 222

L s y4L q 4 y3 y L q 6 y2 y2L q 4 y y3L q y4L . 15Ž .Ž . Ž . Ž .1 1111 1 2 1112 1 2 1122 1 2 1222 2 2222

The molar volume V of the mixture at the experimental pressure p is calculatedmby iterative solution of the equation:

p s RTrV 1 q BrV q CrV 2 q DrV 3 . 16Ž . Ž .Ž .m m m m

The mixture virial coefficients B, C, and D were calculated from equations ofŽ . Ž .similar form to equations 13 to 15 . The molar volumes V and V of them , 1 m , 2

pure components at pressure p were calculated in a similar fashion.Ž . Ž .It is not possible to calculate all the terms in equations 14 and 15 , nor is it

necessary to do so. The focus of interest is the term f , and hence B , in12 12Ž .equation 14 . As pair potentials for ethanol interacting with hydrocarbon are not

available the corresponding states correlation of Pitzer and Curl,Ž15. or that ofTsonopoulos,Ž16. can be used. A corresponding states correlation will adequatelyrepresent B and f for benzene or cyclohexane, and can be used to calculate22 22similar properties for the chosen homomorph. To develop the quasi-chemical

H E and B in benzene]ethanol associationm 12 1231

model for ethanol the non-specific forces between two ethanol molecules wereestimated by assuming them to be the same as the forces between two fluoroethanemolecules. This choice of homomorph follows from the use of fluoromethane as ahomomorph for methanol, and it is useful to recall the reasons for this choice. Themolar masses of methanol and fluoromethane are the same, and the polarizabilities

. y25 3 . y1a and dipole moments m are similar. For methanol a s 32.5 10 cm mol. y25 3 . y1and m s 1.70 D, and for fluoromethane a s 35.0 10 cm mol and m s

1.85 D. The molar masses of ethanol and fluoroethane are the same. For ethanol. y25 3 . y1a s 52.1 10 cm mol and m s 1.7 D, and for fluoroethane a s

. y12 3 . y145.7 10 cm mol and m s 2.0 D. The closeness of these electrical propertiessuggests that the non-ideality of the fluoroalkane should approximate the non-specific forces of the corresponding alcohol fairly well, though clearly thedipole]dipole interaction energy will be a little stronger for the homomorph thanfor ethanol. As this energy diminishes with increase of temperature, fluoroethanewill be a better model for ethanol at high temperatures.

In its interaction with cyclohexane, ethanol forms no hydrogen bond. In ourmodel this interaction is represented by the interaction between cyclohexane andfluoroethane, and the appropriate cross-terms B and f were calculated using12 12the following combining rules in which subscript h refers to the homomorph:

1r2T s j T T , 17Ž . Ž .ch 2 ch c 2

1r3 1r3V s V y V r8, 18Ž . Ž . Ž .� 4ch 2 ch c 2

v s v q v r2, 19Ž . Ž .h 2 h 2

and

p s Z RT rV , 20Ž .ch 2 ch 2 ch 2 ch 2

where

Z s 0.291 y 0.08v . 21Ž .ch 2 h 2

Ž . Ž17.Equation 21 is due to Pitzer. The interaction parameter j was calculated fromthe formula:Ž18.

1r2 y1 1r2 y1j s 2 V V V I I I q I . 22Ž . Ž . Ž . Ž . Ž .� 4ch c 2 h 2 h 2 h 2

This formula was used previously for water]alkane interactions.Ž19. Here, I is theionisation energy.

At temperatures around 373 K the contribution to the enthalpy of mixing arisingŽ . Ž .from equations 14 and 15 is about 5 per cent, and at temperatures around 473 K

it is about 1 per cent. We therefore made some simplifications, the first of whichŽ .was to set all terms in equation 14 to zero, and the second was to set all terms

Ž .except the first in equation 15 to zero. This term is related to K and D H ,4 4parameters which characterize tetramer formation in ethanol, and it is by far the

Ž .biggest of the five terms in equation 15 . In analysing similar measurements on

C. J. Wormald and C. J. Sowden1232

Ž . Ž20.steam q hydrocarbon mixtures these same approximations were made andfound to be adequate. These simplifications have no consequences for equationsŽ . Ž .1 to 3 , which were used as written.

( ) E5. Analysis of the ethanol H cyclohexane H measurementsm

Ž21. E Ž .Ž .Measurements of H for ethanol q nitrogen g over the temperature rangem333.9 K to 412.5 K at pressures up to 0.095 MPa were analysed in terms of theabove association model and values of the second virial coefficient of ethanol wereobtained. These values were found to be consistent with isothermal Joule]Thomsoncoefficients measured by Francis et al.Ž22. and the pressure derivative of theisobaric heat capacity obtained from heat capacity measurements.Ž13,14. Attemperatures above 373 K the values of B derived from the H E measurementsm

Ž .were found to be in good agreement with values obtained from p, V, T studies.Below T s 373 K, it is evident that most of the second virial coefficients obtained

Ž .using p, V, T techniques are wrong, probably because of large adsorption errors.Ž . EThe model for the analysis of the ethanol q nitrogen H measurements, whichm

Ž .used fluoroethane as a homomorph for ethanol, yielded K 298.15 K s2y1 . y10.824 MPa and D H s y19.8 kJ mol for dimer formation, and2

y1 . y1Ž .K 298.15 K s 1206 MPa and D H s y93.7 kJ mol for tetramer formation.4 4Measurements of the isothermal Joule]Thomson coefficient of benzene and

cyclohexane have been made by Francis et al.Ž23. and Wormald et al.Ž24. usingthrottling calorimeters of quite different design. The measurements are in goodagreement with each other, and are consistent with the best measurements of the

Ž .second virial coefficient made using p, V, T techniques. While the measurementscan be fitted with the corresponding states correlation of McGlashan and Potter Ž25.

this correlation is of little use in the present application, as any correspondingstates correlation used must also fit the second virial coefficient of fluoroethane.We therefore turned to the correlation of Pitzer and CurlŽ15. and its modified formsuggested by Tsonopoulos.Ž16. Since these correlations were developed much morework on the non-ideality of benzene and cyclohexane vapours has been done, andit is now clear that many of the virial coefficient measurements on which thecorrelations were based are in error. At temperatures below 400 K the Tsonopouloscorrelation gives values of B, and more importantly f, which are too negative. Thecorrelation of Pitzer and Curl is better and using the acentric factor v s 0.212 anadequate, though not perfect, fit with values of f for benzene is obtained. Forcyclohexane v s 0.213, but this choice gives values of f which are about 5 percent too negative, and to fit the measurements of f it is necessary to use v s 0.17.

E ŽThe above parameters now allow us to calculate H for ethanol qm.Ž .cyclohexane g . The value of the interaction parameter calculated from equation

Ž . E22 is j s 0.98, and using this value the above model gives values of H whichmagree with the measurements at temperatures below 450 K to within 2 per cent, butwhich are 5 per cent less than the values obtained from the high pressure hightemperature measurements. The calculated value of j depends on the propertiesassumed for the homomorph. Although the ionisation energy of fluoroethane

H E and B in benzene]ethanol associationm 12 1233

Ž . Ž .I s 12.6 eV is greater than that I s 10.6 eV for ethanol this makes littledifference to the value of j , as it is the ratio of the critical volumes which has thebiggest effect. Because there is no way of knowing what the critical volume ofethanol might be in the absence of hydrogen bonding, we treated j as an

EŽ o.adjustable parameter and found that the choice j s 0.94 gives values of H pmwhich agree with the experiment over the full temperature range to within theuncertainty on the measurements. The continuous curve shown in figure 1 wascalculated using j s 0.94. As can be seen from this figure the curve is an excellentfit with the measurements made using the low pressure differential flow mixing

EŽ o.calorimeter at temperatures up to 433.2 K, and to the values of H p derivedmfrom the high pressure measurements in the temperature range 473.2 K to 523.2 K.

( ) E6. Analysis of the ethanol H benzene H measurementsm

The first step was to make adjustments to the association model similar to thoseŽ . Ž .made for ethanol q cyclohexane . Equation 22 gives j s 0.98, the same as for

Ž .ethanol q cyclohexane , and so the same adjusted parameter j s 0.94 isŽ .appropriate to ethanol q benzene . Putting the critical parameters for benzene,

EŽ o.together with v s 0.212, into the above equations yields values of H p whichmare shown as the broken curve in figure 2. The calculated values are approximately

. y120 J mol greater than the experimental values, and this suggests that theendothermic mixing process is offset by an exothermic ethanol]benzene interaction.To describe this interaction the terms for B and f were modified to include12 12new parameters K and D H such that12 12

B s B y RTK r2, 23Ž . Ž .12 h 2 12

and

f s f q K D H r2. 24Ž . Ž .12 h 2 12 12

These equations were used previously Ž26. to fit measurements on mixtures ofgases which strongly associate. B and f were calculated from the Pitzerh 2 h 2CurlŽ15. correlation by combining parameters for fluoroethane and benzene and

EŽ o.using j s 0.94 as described above. The H p measurements shown in figure 2mŽ .are fitted to within experimental error by the parameters K 298.15 K s12

y1 . y10.28 MPa and D H s y14 kJ mol . Our previous analysis of high temperature12E Ž .Ž .high pressure H measurements on ethanol q benzene g was made using am

cubic equation of state with added association terms,Ž7. and this yielded. y1Ž .K 298.15 K s 0.2197 MPa and D H s y14 kJ mol . These parameters are12 12

almost the same, but as the cubic equation generates different values for thenon-ideality of the homomorph it would be surprising if the values obtained wereany closer than they are. Our new values, obtained from measurements over amuch wider temperature range and derived from the virial equation rather than acubic equation, are to be preferred.

Second virial cross-coefficients obtained from the analysis are not sensitive to

C. J. Wormald and C. J. Sowden1234

EŽ o. Žthe choice of homomorph. At T s 373 K the calculated value of H p for 0.5m. y1 . y1.cyclohexane q 0.5 fluoroethane is 32 J mol , and at T s 523 K it is 13 J mol .

EŽ o. Ž .The experimental values of H p for cyclohexane q ethanol at thesem. y1 . y1temperatures are 150 J mol and 23 J mol , respectively, and the difference

between the two sets of figures is the contribution to H E from hydrogen bonding.mAt T s 373 K more than 80 per cent of the B term arises from the specific forces12between the unlike molecules. Changing the choice of homomorph does not greatlyaffect the values of B for the simple reason that if a smaller molecule is chosen12the values of K and D H will compensate by being larger so that the sum of the12 12non-specific and specific contributions will remain about the same.

Second virial cross coefficients for cyclohexane]ethanol and benzene]ethanolderived from the parameters used in the above analysis are listed in tables 1 and 2.To facilitate comparison with other work the second virial coefficients B and B11 22and isothermal Joule]Thomson coefficients f of ethanol and f of benzene or11 22cyclohexane, and the cross coefficients f are also listed.12

Of particular interest is the comparison of the values of K and D H for the12 12benzene]ethanol interaction with those of the benzene]methanol andbenzene]water interactions. In a parallel publicationŽ27. we report similar

Ž . Ž .measurements on methanol q cyclohexane and methanol q benzene . Thesewere analysed the same way, using fluormethane as a homomorph for methanol.The specific methanol]benzene interaction association energy was found tobe similar to that for ethanol]benzene and is much the same as the valuefor water]benzene reported previously.Ž4. For water]benzene K s 0.21 MPay1

12. y1 y1Ž .and D H s y 12 " 1.5 kJ mol . For methanol]benzene K s 0.22 MPa and12 12

. y1 y1Ž .D H s y 13 " 2 kJ mol . For ethanol]benzene K s 0.28 MPa and12 12. y1Ž . Ž .D H s y 14 " 2 kJ mol . The uncertainties on the values of K 298.15 K are12 12

about 5 per cent. It is possible that these energies may bear comparison withinformation obtained from low temperature molecular beam experiments designedto study the formation of van der Waals complexes. For example, lines in the

Ž .Ž .microwave spectrum of jet-cooled water q benzene g show that water forms avan der Waals complex with benzene in which the water molecule freely rotatesabove the plane of the ring with both hydrogen atoms pointing towards the ring.Ž28.

The binding energy of the complex has been calculated and found to be. y1y15.8 kJ mol . Structures of similar complexes formed between methanol and

benzene have deduced, and binding energies calculated.Ž29. Comparison of thecalculated binding energy for the water]benzene with that obtained from theassociation model is to some extent justifiable only because Stockmayer potentialparameters for water in its interaction with a non-polar fluid have been obtainedŽ1.

and there is no need to fall back on the homomorph approach. To usefluoromethane and fluoroethane as homomorphs which hopefully provide areasonable approximation to the non-specific forces for methanol and ethanol ismuch less satisfactory. Both homomorphs probably overestimate the non-specificforces with the consequence that the values of D H obtained for the12methanol]benzene and ethanol]benzene interactions are likely to be too small.

The uncertainties on the values of D H arising from the choice of fluoromethane12

H E and B in benzene]ethanol associationm 12 1235

and fluoroethane as homomorphs can be considerably reduced by approaching theproblem another way. This is based firstly on the fact that the measurements on

Ž8. E . y1Ž .benzene q cyclohexane vapour show that H is less than 1 J mol , andmsecondly on the fact that values of B for water]benzene and water]cyclohexane12calculated using the Stockmayer potential with parameters appropriate towater]non-polar fluid interaction, are quite close together. For example,Ž2. attemperatures around 363 K the calculated value of B for water]benzene is12

3 . y1 3 . y1y120 cm mol and for water]cyclohexane it is y130 cm mol . The freshapproach to the analysis is to assume that the difference between the values of B12for ethanol]benzene and ethanol]cyclohexane listed in tables 1 and 2 is entirelydue to the specific ethanol]benzene interaction. From table 1 we see that at

3 . y1Ž .temperature T s 363 K, B ethanol q cyclohexane s y432 cm mol , and at1 123 . y1T s 523 K, B s y180 cm mol . From table 2 we see that T s 363 K2 12 1

3 . y1Ž .B ethanol]benzene s y562 cm mol , and at T s 523 K B s y22112 2 123 . y1 3 . y1Ž . Ž . Ž .cm mol . At T the difference dB s y432 y y562 s 130 cm mol ,1 12 1

3 . y1Ž . Ž . Ž .and at T the difference dB s y180 y y221 s 42 cm mol . The quasi-2 12 2Ž . y1chemical formula dB s RTK r2 gives K s 0.0861 MPa at T s 363 K and12 12 12

K s 0.0188 MPay1 at T s 523 K. Finally, D H is obtained from:12 12

ln dH r dH s y D H rR Ty1 y Ty1 . 25� 4Ž . Ž . Ž . Ž .Ž .12 12 12 2 12 1

. y1Ž .Equation 25 gives D H s y14.98 kJ mol for the ethanol]benzene interaction.12Ž .Ž . Ž27.A similar analysis of the methanol q benzene g measurements yields

y1 . y1D H s y13.02 kJ mol for the methanol]benzene interaction, and analysis of12Ž3. . y1Ž .Ž .water q benzene g measurements yields D H s y12.05 kJ mol . These12

values are close to those obtained above using the homomorph approach, and gosome way to justifying the choice of fluoroethane for this purpose.

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( )Recei ed 23 January 1997; in final form 26 March 1997

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