Fluid Phase Equilibria 303 (2011) 157161

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Fluid Phase Equilibria

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Volum zebenzen ure

Zdenka K

Department of

a r t i c l

Article history:Received 13 SeReceived in reAccepted 13 JaAvailable onlin

Keywords:BenzeneCyclohexane2,2,4-TrimethylpentaneDensityVibrating-tube densimeterBinary systemExcess molar volumeRedlichKister equationPengRobinson equationMixing rulesCombining rul

enecuredthe deed wand ner aue stacesslarity

vents to discern among mixing rules available in literature and those proposed within this paper. Thus,another binary system, i.e. benzene2,2,4-trimethylpentane was investigated in the temperature range293.15323.15K. PengRobinson constants of the components of this system differ in their magnitudeand thus allow to study the effect of different combining rules. It was found that the considered two com-bining rules with slightly different correction constants k12 yielded very similar VEm dependencies on theconcentration.

1. Introdu

The excnamic charand multi-cintroductiomination oaccurate. Exniquemighand exact eVEm from thrules for thand combinVEm for binameasured e[19] playsstructures oelectrostatithese comp

CorresponE-mail add

0378-3812/$ doi:10.1016/j.es 2011 Elsevier B.V. All rights reserved.

ction

ess molar volume belongs to four simple thermody-acteristics of the thermodynamic behavior of binaryomponent mixtures at ambient temperatures. With annof thevibrating-tubedensimetry technique, thedeter-f the excess volume, VEm, is relatively easy and quiteperimental data obtained via this experimental tech-

t thus serve to study the suitabilityof the semi-empiricalxpressions proposed to date, to correlate and predicte equation of state for pure components and mixingeir constants. In the latter case also different mixinging rules have to be applied. Theoretical results onries and ternaries might be tested against accuratelyxperimental VEm data. System benzenecyclohexanea special role among the binaries because of simplef molecules of both the pure uids as well as small

c interactions. From the experimental point of viewounds might be relatively easily prepared and charac-

ding author.resses: tomas.boublik@ujep.cz, boublik@sci.ujep.cz (T. Boublk).

teristic properties (e.g. values of densities or refractive indices attemperatures 293.15 or 298.15K) are well known. In this paperwe measured the benzenecyclohexane system at temperatures293.15, 303.15, 313.15 and 323.15K and atmospheric pressure.To check the absolute precision of the measurement we compareour data obtained within modern technique with values from aclassic method (measured by one of the authors [10]), where den-sity was determined in a SprengelOswald two-arm pycnometer(with calibrated capillaries). The previously published data wereused for comparison [10]. After nding an excellent agreementbetween both the data sets, measured with different techniques,we correlated rstly the present experimental data, employing theRedlichKister expression [11].

Next we developed and applied a simple and versatile pro-cedure/computer program to evaluate VEm on the basis of anequation of state and compared the calculated/predicted val-ues of VEm with the experimental excess volume dependence onthe composition. We considered three cubic equations of state(van der Waals, RedlichKwong and PengRobinson) and mix-ing and combining rules recommended in literature [12]. We alsoconsidered new harmonic mean rule found within our theoret-ical studies. Results and conclusions are given at the end of thepaper.

see front matter 2011 Elsevier B.V. All rights reserved.uid.2011.01.018etric behavior of the binary systems bene2,2,4-trimethyl-pentane at temperat

olsk, Denisa Dvorkov, Jan Mika, Toms BoublkChemistry, J.E. Purkinje University, st nad Labem, Czech Republic

e i n f o

ptember 2010vised form 12 January 2011nuary 2011e 26 January 2011

a b s t r a c t

Densities of the binary system benzat atmospheric pressure were measmolar volumes were calculated fromequation. Present data were comparments; a fair agreement of the oldpresented experimental data of othability of the cubic equations and thconcentration dependence of the exapplied to the present data. Close simim/locate / f lu id

necyclohexane ands 293.15323.15K

yclohexane at several temperatures (293.15323.15K) andusing a vibrating-tube densimeter in a static mode. Excessnsities and correlated using the second-order RedlichKisterith those determined previously by pycnometric measure-ew data sets was found. Also comparison with previouslythors was proved with a good agreement. In order to testndard mixing and combining rules to correlate/predict thevolume, PengRobinson equation of state was successfullyof characteristic parameters of benzene and cyclohexane pre-

158 Z. Kolsk et al. / Fluid Phase Equilibria 303 (2011) 157161

2. Theory

The excess volume, VEm, similarly as the excess enthalpy, coin-cides with the mixing volume mixV,

VEm = mixV

where Vmsmixture anding mole frPug and Brectly fromand relativesemi-empirthat propos

VEm = xi(1 where parature and prthe molecutures, the epresent timin majority

The cubiand PengRstudy, aimecubicEOSs (too. We starcubic EOS

Z = PVmRT

=

Here the temstants a, bphase or in

Due topossesses vobtained, bsought theoation.

Next, th[13] was co

Z = VmVm b

Parametersconstants, i

a = 0.4275P

The equatioto correlate

Z = VmVm b

where a aholds

a(T) = a(Tc

and the temthrough the

= [1 + (0.

Table 1Values of PengRobinson constants a and b at 298.15K.

Compound a (dm6 MPamol2) b (dm3 mol1)

Benzeneexanerimet

r = T/Valurimerep

EOSs

(3

/u, umn

ltiplyinater, t

ixing

he care usd toure).as fo

xib

case

ki

li

pape

1

ii+

withtion) likegive

erim

emic

zeneexant.%) and 2,2,4-trimethylpentane (Riedel-de Haen., puris. p.a.ACS, Reag. Ph, Eur. 99.5wt.%) were used without furtheration. Their measured densities and refractive indices arered with the literature values [18] in Table 2.= Vms

xiVmi =(x1M1 + x2M2)

x1

M11

x2M22(1)

and Vmi stand for the volume of one mol of the realmolar volumeof component i, and xi is the correspond-

action. With exception of the dilatometer proposed byenson [9], the molar volume has been determined indi-the measured density at the same temperature, t4,molecularmass,Mi, e.g.Vms =

xiMi/t4. The simplest

ical expression used to correlate experimental data ised by Redlich and Kister [11]

xi)[A0 + A1(1 2xi) + A2(1 2xi)2 + ] (2)meters A0, A1, A2, . . . are valid for a single tempera-essure. However, to get more general information onlar interactions of single components and their mix-quations of state (EOS) have been considered. Up toe, different cubic equations of state have been appliedof cases [1].c equations of state (by van der Waals, RedlichKwongobinson) were considered also in this introductoryd in further steps at application of the modern non-suchasBACKandSAFT) topredict themixturebehavior,ted with van der Waals equation as a prototype of thethe compressibility factor of which can be written as

VmVm b

a

RTVm(3)

perature- anddensity independent characteristic con-were adjusted to the uid behavior, e.g. in the liquidthe critical point.the fact that the compressibility factor of liquidsery low values, a pseudo-quadratic equation can bey multiplying the above equation by Vm(Vm b); theretical value of volume results from a few-step iter-

e more realistic EOS, proposed by Redlich and Kwongnsidered, where

a

RT3/2Vm(Vm + b)(4)

of this EOS can be evaluated easily from the critical.e.

R2T5/2cc

b = 0.08664RTcPc

(5)

n of Peng and Robinson [14] is the most often used EOSand predict VEm [1]. It reads

a

Vm(Vm + b) + b(Vm b) (6)

nd b are two characteristic constants, for which it

), a(Tc) = 0.45724R2T2c

Pcb = 0.07780RTc

Pc(7)

peraturedependenceof theattractive termisexpressedrelation

37464 + 1.54226 0.269922)(1 T0.5r )]2

(8)

Cycloh2,2,4-T

Here Tfactor.2,2,4-t

As aWaalstioned

Z = 1 +

+

T r = kTk and Dby mudenomHowev

2.1. M

In tEOSs a(relatea mixt

as =

where

bs =

In thee.g.

aij = (1

bij =(1

In this

2aij

=a

foundinterac(1 kijrules is

3. Exp

3.1. Ch

Bencycloh99.9wReag.puriccompa2.8797 0.075223.3239 0.06791

hylpentane 5.3510 0.13701

Tc is the reduced temperature and Pitzers accentrices of constants a and b for benzene, cyclohexane andthylpentane at 298.15K are listed in Table 1.resentant of the family of modern augmented van der the EOS by Chen and Kreglewski [15] might be men-

2)y + (32 3 + 1)y2 2y3(1 y)3

nDmn

(1T r

)m( V0Vm

)n(9)

/k is the potential well, divided by Boltzmann constantconstants of the polynom; yb/Vm. It is obvious thating numerator and denominator of the rst term by V,or possesses the form (Vm b)(1 y)2,whereb =VmV0.his equation is not used in the following sections.

and combining rules

se of mixtures the characteristic parameters of the usedually determined from the linear and quadratic rulesthe exact expression for the second virial coefcient ofFor constant a thus holds true

xixjaij (10)

r b

i or bs =

xixjbij (11)

of quadratic expression, a combining rule is considered,

j)[aiiajj]1/2 (12)

j)(bii + bjj)2

or bij =(b1/3

ii+ b1/3

jj)3

8(13)

r we considered for aij also the harmonic mean

1ajj

(14)

in the quantum mechanical study of intermoleculars of simple molecules [16], eventually multiplied byin (12). (A review of EOSs and mixing and combiningn e.g. in Refs. [12,17].)

ental

als

(Fluka Analytical, puris. p.a. ACS; purity 99.5wt.%),e (SigmaAldrich, CHROMOSOLV, Plus, for HPLC, purity

Z. Kolsk et al. / Fluid Phase Equilibria 303 (2011) 157161 159

Table 2Physical constants of pure compounds.

Substance Constant Found Ref. [18]

Benzene 204 (g cm3) 0.87898 0.8790

n20D

1.5010 1.5010

Cyclohexane 204 (g cm3) 0.77854 0.7783

n20D

1.4263 1.42623

2,2,4-Trimethypentane 254 (g cm3) 0.68776 0.68774

n20D

1.39145 1.39145

3.2. Apparatus and procedure

Refractive indices of pure compoundsweremeasuredbyRefrac-tometerr RM40, Mettler Toledo.

Vibrating tube densimetr (DMA 4500) supplied by Anton Paar,Graz, Austria was used for density determination of pure u-ids and binary systems. The apparatus yields the direct densityvalues within density range 03g cm3, reproducibility of the den-sity measurement 1.105 g cm3 and accuracy 5.105 g cm3. Thetemperature range of the apparatus was 273.15363.15K, repro-ducibility of temperature was 0.01K and its accuracy 0.03K. Timeof measurement was 30 s for the sample of volume cca 1 cm5.Apparatusatmospherimeasuremeand pressudards; also twater by Athe densityToledobalamass maximThe experimless than 5

ResultsbenzenecyIn this gumeasuremethe presentgives evidemethod.

From thlated, see [1second ordof the benze

Fig. 1. Compavs. x1, at 293.1at 283.15 and

Fig. 2. Correlaat 293.15K, froof state.

Theparameof benzene

ons a

ults

sitiee2,, 313volured1. TKismetres 2rison0.67excevantencenc

of thall c

orrel thed, wecyclohexane from three cubic equations of state, i.e. vanals, RedlichKwong and PengRobinson. The rst EOS withommended parameters yielded rather insufcient values ofsities (volumes) of the pure uids and was withdrawn fromther considerations. Application of the remaining two EOSsicted in Fig. 2 for temperature T=293.15K. Because fromwo equations that of PengRobinson yielded better predic-values of the pure uid volumes and also VEm we dealt in theing part only with the PengRobinson EOS. Its parameters,ted for temperature T=298.15K are given in Table 1. Forworks with an automatic pressure compensation toc pressure and with a viscosity correction for the wholent range. For its calibration (at ambient temperaturere), the redistilled water and air were used as stan-he standard sample (liquiddensity standard Ultrapurenton Paar) was used for calibration. The samples formeasurements were prepared by weighing [by MettlernceXS205DU/Mwitha scale interval either 1.105 g (forum of 81g), or 1.104 g (for mass maximum of 210g)].ental uncertainty in composition (the mole fraction) is.105.of the density measurement for the binary systemclohexane are given in Table 3 and illustrated in Fig. 1.re we presented also the old data from pycnometricnt [10] at 283.15 and 333.15K. The agreement withsmoothed data at 293.15 and 323.15K is excellent andnce in favor of the accuracy of the modern densimetric

ese density data the excess molar volumes were calcu-9] from relation (1). The data were also tted by the

er RedlichKister type equation, see (2). Similarly, VEmne2,2,4-trimethylpentane are summarized in Table 4.

deviati

4. Res

Denbenzen303.15excesscompain Fig.Redlichof paraperatucompain [10]of theThe addependdependdenceonly smof kij-cgenerathis enbenzender Wathe recthe denour furis depthese ttion ofremaincalcularison of experimental data of benzenecyclohexane, VEm (cm3 mol1)

5 and 323.15K (dashed and full lines) with the pycnometric results333.15K ( and ).

other tempand the accane =0.20of the corrpresented iof the presmall valueobvious.tion of VEm experimental data (cm3 mol1) of benzenecyclohexane,

m RedlichKwong (dashed) and PengRobinson (full line) equations

tersA0A2 of thebenzenecyclohexane systemand that2,2,4-trimethylpentane, A0 A2 and their standardre summarized in Table 5. for individual temperatures.

s of the binary systems benzenecyclohexane and2,4-trimethylpentane at temperatures T=293.15,.15 and 323.15K were measured. From these data theme dependence on concentration was calculated andwith the older data [10]. This comparison is shownhe present experimental data were correlated by theter (RK) equation. From the temperature dependenceer A0 we found the values of VEm at x1 =0.5 and at tem-83.15 and 333.15K VEm = 0.657 and 0.691 cm3 mol1 inwith RK values calculated from fragmentary results

6 and 0.723 cm3 mol1. Next, we present a predictionss volumes by means of the cubic equations of state.age of their application to predict (correlate) the VEme on the composition is twofold: (i) the temperaturee of VEm on xi is mainly due to the temperature depen-e constants (dependence of as on Tr) of the used EOS;hanges of as is caused by the temperature dependencections, (ii) the PV expressions might be used in thermodynamic description of the mixture behavior. Toe dealt with the correlation of the measured data oferatures the a-constant can be calculated from Eq. (8)entric parameter; for benzene =0.2183, for cyclohex-81 and =0.3030 for 2,2,4-trimethylpentane. Resultselation for temperatures T=293.15 and 323.15K aren Fig. 3. A fair agreement (with =0.025 cm3 mol1)dicted VEm and found experimental data for quites of kij =0.0670.051 at T=293.15 and 323.15K are

160 Z. Kolsk et al. / Fluid Phase Equilibria 303 (2011) 157161

Table 3Density, T (g cm3), and excess molar volume, VEm (cm

3 mol1), calculated from Eq. (1) for binary system benzenecyclohexane at temperatures 293.15323.15K.

x1 293 VEm,293 303 VEm,303 313 V

Em,313 323 V

Em,323

0.0000 0.77854 0.0000 0.76913 0.0000 0.75960 0.0000 0.74994 0.00000.1000 0.78499 0.2648 0.77547 0.2720 00.1805 0.79071 0.4273 0.78114 0.4332 00.2347 0.79492 0.5015 0.78530 0.5078 00.3029 0.80047 0.5755 0.79079 0.5815 00.3801 0.80710 0.6369 0.79733 0.6444 00.4453 0.81309 0.6597 0.80325 0.6667 00.5223 0.82056 0.6608 0.81063 0.6674 00.5814 0.82662 0.6411 0.81662 0.6467 00.6563 0.83472 0.5923 0.82462 0.5970 00.7135 0.84121 0.5395 0.83103 0.5434 00.7654 0.84744 0.4704 0.83718 0.4736 00.8191 0.85416 0.3836 0.84382 0.3853 00.8771 0.86175 0.2762 0.85131 0.2771 00.9161 0.86703 0.1969 0.85652 0.1973 01.0000 0.87898 0.0000 0.86830 0.0000 0

Table 4Density, T (g cm3), and excess molar volume, VEm (cm

3 mol1), calculated from Eq. (1) for binary system

x1 293 VEm,293 303 VEm,303

0.0000 0.69188 0.0000 0.68364 0.0000 00.1248 0.70406 0.2569 0.69566 0.2629 00.1642 0.70826 0.3258 0.69980 0.3316 00.3682 0.73374 0.5266 0.72494 0.5367 00.4538 0.74653 0.5546 0.73757 0.5637 00.5020 0.75434 0.5629 0.74527 0.5736 00.5388 0.76070 0.5572 0.75154 0.5689 00.6023 0.77244 0.5362 0.76315 0.5438 00.6896 0.79037 0.4858 0.78086 0.4908 00.9443 0.85913 0.1490 0.84873 0.1488 01.0000 0.87898 0.0000 0.86830 0.0000 0

Table 5Parameters of RedlichKister Eq. (2) (in cm3 mol1) for binary systems benzenecyclohexane (BC293.15323.15K.

Parameter T

293.15 STD 303.15 STD

A0 (BCH) 2.657 0.008 2.682 0.009A1 (BCH) 0.184 0.015 0.206 0.017A2 (BCH) 0.164 0.034 0.173 0.039A0 (BTMP) 2,233 0.013 2,273 0.013A1 (BTMP) 0.048 0.041 0.021 0.042A2 (BTMP) 0,377 0.080 0,349 0.082

Fig. 3. Correlation of VEm experimental data (cm3 mol1) of benzenecyclohexane

at 293.15 and 323.15K by PengRobinson equation of state. and experimentaldata at 293.15 and 323.15K.

Originalmonic meaaij in (12). Hhexane arenegligibly, ion the couobserved.

In ordmeasuredtrimethylpePengRobindiffer subst(12) and (1the latter sdence for thpredicted cFig. 4. A fairrule (14) avalues of VmHowever, wcorrection w.76587 0.2745 0.75614 0.2776

.77146 0.4394 0.76167 0.4440

.77557 0.5149 0.76573 0.5207

.78100 0.5886 0.77110 0.5949

.78747 0.6511 0.77750 0.6575

.79332 0.6735 0.78327 0.6817

.80062 0.6730 0.79048 0.6817

.80653 0.6530 0.79634 0.6590

.81444 0.6020 0.80414 0.6095

.82077 0.5480 0.81041 0.5530

.82683 0.4792 0.81641 0.4821

.83339 0.3898 0.82289 0.3918

.84079 0.2801 0.83019 0.2823

.84595 0.1978 0.83528 0.2000

.85757 0.0000 0.84676 0.0000

benzene2,2,4-trimethylpentane at temperatures 293.15323.15K.

313 VEm,313 323 VEm,323

.67530 0.0000 0.66684 0.0000

.68716 0.2652 0.67853 0.2727

.69124 0.3385 0.68255 0.3486

.71605 0.5471 0.70704 0.5593.72851 0.5755 0.71933 0.5896

.73612 0.5836 0.72685 0.5961

.74233 0.5753 0.73296 0.5910

.75377 0.5531 0.74428 0.5636

.77125 0.4994 0.76154 0.5081

.83826 0.1500 0.82770 0.1519

.85757 0.0000 0.84676 0.0000

H) and benzene2,2,4-trimethylpentane (BTMP) at temperatures

313.15 STD 323.15 STD

2.708 0.009 2.739 0.0090.216 0.017 0.225 0.0170.186 0.039 0.174 0.0402,313 0.013 2,366 0.013

0.012 0.042 0.012 0.0430,338 0.083 0,336 0.085

ly, we intended to study the effect of the use of har-n (hm) (14) instead of geometric mean (gm) for constantowever, values of aii-parameters of benzene and cyclo-so closed, that the resulting values of aij differed only.e. ahm =3.086 in comparison with agm =3.093; no effectrse of the theoretical dependence of VEm vs. xi was

er to study different combining rules weanother binary system, i.e. system benzene2,2,4-ntane (formerly considered e.g. in Refs. [1924]).son characteristic constants of its pure componentsantially and thus allow to discern between relations4). To this end we plotted experimental data of VEm (ofystem at 293.15K) together with calculated depen-e combining rule (12) with k12 =0.0 and compared theourse of VEm (dashed line) with experimental data inagreement was found. Next, we considered combining

nd k12 =0.0, and got a curve with signicantly higherE than experimental ones for the single concentrations.

hen we multiplied calculated value of a12 by theith k12 =0.05, we obtained practically indistinguish-

Z. Kolsk et al. / Fluid Phase Equilibria 303 (2011) 157161 161

Fig. 4. Correltrimethylpentdata; dashed lmonic mean.

able depen0.016 cm3 mgenerally afor the lattefor temperaature T=32combiningof k12 (for tk12hm =0.0

5. Conclus

In thisthe excess vT 293.15,tems benzeExperimenthighest temcate a fairequation; fwe found v333.15K toRK values 0estimates otechniques

The useempirical Rexcess voludependenceused in diffthe consideof state.

As the use of the harmonic combining rule is concerned, nodenitive conclusion can be drawn because of the negative signof the correction parameter kij.

List of symbolsAi constants of RedlichKister equationsa,b constants of semi-empirical equationsa constant of PengRobinson equation (dm6 MPamol2)b constant of PengRobinson equation (dm3 mol1)Dmn constants of a polynomM molecular massP pressure (Pa)

crgatecrrevomexmpaconodestac

wled

s wornce o

nces

Inglesilibr.Wang. Beg,300OswaundhWangWangWang. Pugoubl kation of VEm experimental data (cm3 mol1) of benzene2,2,4-

ane at 293.15 by PengRobinson equation of state. experimentaline, calculated employing the geometric mean; full line, from har-

dence (see full line in Fig. 4). In both the cases wasol1. However, because positive values of k12 are

ssumed to be the correct ones, we can conclude thatr binary system the usual combining rule is preferableture T=293.15K. [For the highest measured temper-3.15K a fair agreement can be obtained for both therules, however, in both the cases with negative valueshe geometric mean k12gm =0.009 in comparison with57).]

ion

contribution we measured densities and calculatedolume dependence on concentration at temperatures303.15, 313.15 and 323.15K for the binary sys-necyclohexane and benzene2,2,4-trimethylpentane.al results of VEm for the former system at the lowest andperatures were compared with the older data and indi-mutual agreement. These data were correlated by RK

PcRTTcTrVVmVEmxiyZ

Ackno

Thiof Scie

Refere

[1] M.Equ

[2] H.J.[3] S.A

289[4] S.L.[5] N. S[6] H.J.[7] H.J.[8] H.J.[9] H.D

[10] T. Brom the temperature dependence of its parameter A0alues of VEm at x1 =0.5 and at temperatures 283.15 andbeVEm = 0.657 and0.691 cm3 mol1 in comparisonwith.676 and 0.723 cm3 mol1. Taking into account the errorf the old pycnometric- and the modern experimentala fair agreement was found.of the newer equations of state instead of the semi-edlichKister expression for the correlation of theme brings with itself an inclusion of the temperatureof VEm. Values of terms PV

Em might be thus correctly

erent thermodynamic expressions. The best results forred binaries were obtained by PengRobinson equation

[11] O. Redlich[12] B. Giner,

(2007) 14[13] O. Redlich[14] D. Peng, D[15] S.S. Chen[16] J. Fiser, T.[17] J.V. Senge

Fluids an[18] J. Timmer

I. and II, E[19] L. Morvk[20] S.E. Wood[21] R. Malho[22] E. Lieberm[23] R. Battino[24] H. Houskitical pressure (Pa)s constant (J K1 mol1)mperature (K)itical temperature (K)duced temperaturelume (m3)olar volume (m3 mol1)cess (molar) volume (cm3 mol1)olar fractioncking fractionmpressibility factorn-sphericity factornsity (kgm3, g cm3)andard deviation in VEm (cm

3 mol1)centric factor

gement

k was carried out within the Grant Agency of Academyf Czech Republic project no. IAA 400720710.

ias, M.M. Pineiro, G. Marino, B. Orge, M. Dobinguez, J. Tojo, Fluid Phase154 (1999) 123138., J.C. Sun, X.X. Zhou, J. Chem. Thermodyn. 30 (1998) 14011410.N.M. Tukur, D.K. Al-Habri, E. Hamad, Fluid Phase Equilibr. 94 (1994).l, M.M. Maisuria, R.L. Gardas, J. Mol. Liq. 109 (2004) 155166.aram, L. Palaniappan, Indian J. Phys. 79 (2005) 11731178., J.C. Sun, J. Solut. Chem. 34 (2005) 375385., J.C. Sun, J. Solut. Chem. 35 (2006) 133511335., Y.H. Wu, J. Solut. Chem. 34 (2005) 10671080., G.C. Benson, Can. J. Chem. 46 (1968) 287291., Collect. Czech. Chem. Commun. 28 (1963) 17711779., A.T. Kister, Ind. Eng. Chem. 40 (1948) 34514345.

C. Lafuente, A. Villares, M. Haro, M.C. Lopez, J. Chem. Thermodyn. 398157., J.N.S. Kwong, Chem. Rev. 44 (1949) 233244..B. Robinson, Ind. Eng. Chem. Fundam. 15 (1976) 5964.

, A. Kreglewski, Ber. Bunsen Ges. Phys. Chem. 81 (1977) 10481052.Boubl k, R. Polk, Collect. Czech. Chem. Commun. 69 (2004) 177188.rs, R.F. Kayser, C.J. Peters, H.J. White Jr. (Eds.), Equations of State ford Fluid Mixtures. Part I and II, Elsevier, Amsterdam, 2000.mans, Physico-Chemical Constants of Pure Organic. Compounds Vol.lsevier, New York, 1950 and 1965.ov, J. Linek, J. Chem. Thermodyn. 35 (2003) 11391149.s, O. Sandus, J. Phys. Chem. 60 (1956) 801803.

tra, L.A. Woolf, J. Chem. Thermodyn. 14 (1993) 11531172.ann, Monatsh. Chem. 108 (1977) 505515., Chem. Rev. 71 (1971) 5.ov, Thesis PF UJEP, st n. L., in press.

Volumetric behavior of the binary systems benzene-cyclohexane and benzene-2,2,4-trimethyl-pentane at temperatures 293.15-323.15KIntroductionTheoryMixing and combining rules

ExperimentalChemicalsApparatus and procedure

ResultsConclusionAcknowledgementReferences