(p, v, t, x) measurements of the system benzene-i-c8

Fluid Phase Equilibria 209 (2003) 81–94

(P, V, T, x) Measurements of the system benzene+ 1,3,5-trimethylbenzene at temperatures from

298.15 to 328.15 K and at pressures up to 40 MPa

L. Morávková, Z. Wagner, J. Linek∗E. Hála Laboratory of Thermodynamics, Institute of Chemical Process Fundamentals,

Academy of Sciences of the Czech Republic, 165 02 Prague 6, Czech Republic

Received 29 November 2002; accepted 5 March 2003

Abstract

Densities were measured for the liquid benzene and 1,3,5-trimethylbenzene, and for nine of their mixtures at fourtemperatures between 298.15 and 328.15 K and at pressures up to 40 MPa. An apparatus for density measurementsof liquids and liquid mixtures whose main part is a high-pressure vibrating-tube densimeter working in a static modewas used for the measurement. The density data were fitted to the Tait equation and the isothermal compressibilitieswere calculated with the aid of this equation. Excess molar volumes were also calculated from the densities andfitted to the Redlich–Kister equation.© 2003 Elsevier Science B.V. All rights reserved.

Keywords: 1,3,5-Trimethylbenzene; Benzene; Redlich–Kister equation

1. Introduction

Research activities of our laboratory comprise, among others, the systematic measurement of volu-metric properties of different groups of organic compounds. Recently, we have measured densities anddetermined excess volumes at elevated temperatures and moderately high pressures of the alkane+1-chloroalkane mixtures[1–7] with the aim to prepare a database for testing theories of the liquid state(equations of state). Our new project is devoted to the systematic study of liquid systems containingaromatics with respect to their environmental importance.

To our knowledge[8], there exist no volumetric data for the liquid phase of the system benzene+1,3,5-trimethylbenzene (mesitylene) at elevated pressures. Therefore, we have measured densities andcalculated isothermal compressibilities and excess volumes of the system. The apparatus based on a

∗ Corresponding author. Tel.:+420-2-20370270/96780270; fax:+420-2-20920661.E-mail address: [email protected] (J. Linek).

0378-3812/03/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved.doi:10.1016/S0378-3812(03)00079-7

82 L. Moravkova et al. / Fluid Phase Equilibria 209 (2003) 81–94

high-pressure vibrating-tube densimeter working in a static mode[2] and designed for measuring thepVT behaviour of pure liquids and liquid mixtures at elevated temperatures (283–333 K) and moderatelyhigh pressures (40 MPa) was used for the measurements. The measurements were carried out at thetemperatures 298.15, 308.15, 318.15, and 328.15 K and in the pressure range 0.1–40 MPa.

2. Experimental

2.1. Materials

The benzene (Fluka-RdH, A.R., g.c. mass fraction >0.997) and 1,3,5-trimethylbenzene (Fluka, puriss.,g.c. mass fraction 0.99) were used without further purification. Both substances were dried and storedover 0.4 nm molecular sieves. In order to check the purity of the compounds, their densities and refractiveindices were determined atT = 298.15 K and compared with literature values[9–11]. The agreement wasfound, in general, to be good (Table 1). The purity of the chemicals was checked by gas chromatography(HP Series II model 5890 chromatograph with capillary column type 1909 1Z-413E and f.i.d., columntemperature 413.3 K, helium flow rate 4.2 × 10−4 cm3 s−1).

2.2. Apparatus and procedure

A schematic diagram and detailed description of the apparatus used for the measurement was given inour previous work[2]. It consists mainly of the measuring cell DMA 512P, supplied by Anton Paar, Graz,Austria. The temperature of the measuring cell was controlled by a thermostat LAUDA RC 20 CP (Lauda,Koenigshofen, Germany). The thermostat maintained the temperature in the measuring cell under controlwithin ±0.01 K. The pressure was measured with a pressure transducer LPN-N having a voltage output(ECOM, Prague, Czech Republic). The pressure gauge was calibrated with a Ruska pressure calibrationsystem (Ruska Instruments Co., Houston, TX, USA). The accuracy of the pressure measurement is betterthan 0.1 MPa. The pressure in the measuring cell can be set by means of the manual pressure controlleraccurate to 0.01 MPa. The DMA 512P measuring cell is connected to the DMA 58 densimeter which servesas a frequency counter and evaluates the oscillating period from the signals of the measuring cell filled withsample. The samples of measured liquid mixtures prepared by weight in special vessels[3] are moved intothe measuring cell with a liquid chromatography pump LCP 4000.1 (ECOM, Prague, Czech Republic).

The sample densityρ was deduced from the period of vibrationτ of the vibrating-tube densimeter asfollows:

ρ(T, p) = a(T, p)τ2 + b(T, p). (1)

Table 1Densitiesρ and refractive index valuesnD atT = 298.15 K of the pure components, and their comparison with literature

Component ρ (g cm−3) nD w

Experimental Literature Reference Experimental Literature Reference

Benzene 0.87362 0.8737 [9–11] 1.4979 1.49792 [9–11] 0.99961,3,5-Trimethylbenzene 0.86114 0.86111 [9–11] 1.4967 1.49684 [9–11] 0.9927

w is the mass fraction purity as determined by g.l.c.

L. Moravkova et al. / Fluid Phase Equilibria 209 (2003) 81–94 83

The coefficientsa(T, p) andb(T, p) are two characteristic temperature and pressure dependent parametersof the apparatus, which have to be determined by measuring the periodsτ1 andτ2 for two substances ofknown density of theT, p set considered. For calibration (at ambient temperature and pressure), waterand air are usually used as standards. For very accurate measurements, especially at higher temperaturesand pressures, a pair of fluids with accurately determined densities is recommended. The density of asample is then calculated fromEq. (1)with the parameters determined by calibration.

The choice of standards of known density at high pressures and temperatures is rather limited. Themanufacturer of the densimeter DMA 512P recommends the following substances: nitrogen, benzene,pentane, dichloromethane and water. In our case, the apparatus was calibrated[2] with bidistilled waterand heptane. The density data used for the calibration were taken from[12] for water and from[13] forheptane.

The samples for the density measurements were prepared by weight (SCALTEC SBC 21 balancewith an accuracy of±1 × 10−5 g) for the whole mole fraction range and then partially degassed intightly closed special vessels of negligible vapour space[3] at the maximum measurement temperaturefor 3 h by means of an ultrasonic thermostatted bath (Bandelin RK 100H, Berlin, Germany) prior todetermining their density in order to prevent the formation of bubbles in the densimeter. To estimate theeffect of evaporation on the sample composition, the calculations were carried out taking into accountthe vapour–liquid equilibrium of the given system at the conditions applied. The concentration changesare proved to be well below the stated accuracy in composition.

The experimental uncertainty in the mole fraction composition is less than±5 × 10−5, and that in thedensity is approximately±1 × 10−4 g cm−3.

3. Results and discussion

3.1. Densities

The results of the density measurements are given inTable 2. Densities of the pure substances and ofnine weighed mixtures were measured at 23 pressures over the range 0.1 to nearly 40 MPa.

The isothermal densities of pure substances and their mixtures at a given composition were fitted tothe Tait equation

ρ − ρ0

ρ= C ln

[D + p

D + p0

], (2)

whereρ0 is the density at a reference pressurep0 (p0 = 0.101325 MPa in this work). The values ofρ0 were those[8] obtained by measuring the liquid samples with a low-pressure DMA 58 densimeterbecause the high-pressure equipment cannot in principle provide sufficiently accurate data at atmosphericpressure. Since the procedure for the parameters determination requires a special approach, it is describeda little more in detail.

Values of parametersC andD were determined by minimisation of the following objective function:

S =n∑

i=1

[ρi,calc − ρi,exp

ρi,exp

]2

, (3)

wheren is the number of data points.


Table 2Experimental values of densityρ and calculated isothermal compressibilityκT for x×benzene+ (1−x)×1,3,5-trimethylbenzeneat pressurep and temperatureT

x p (MPa) T = 298.15 K T = 308.15 K T = 318.15 K T = 328.15 K

ρ

(g cm−3)×104κT

(MPa−1)ρ

(g cm−3)×104κT

(MPa−1)ρ

(g cm−3)×104κT

(MPa−1)ρ

(g cm−3)×104κT

(MPa−1)

0.00000 0.10 0.86104 7.92 0.85292 8.68 0.84472 9.14 0.83640 9.612.13 0.86236 7.80 0.85439 8.51 0.84630 8.97 0.83816 9.444.15 0.86375 7.69 0.85583 8.36 0.84781 8.81 0.83976 9.276.18 0.86511 7.58 0.85728 8.20 0.84931 8.65 0.84134 9.118.21 0.86645 7.47 0.85868 8.06 0.85081 8.50 0.84292 8.95

10.23 0.86778 7.36 0.86010 7.92 0.85226 8.36 0.84443 8.8011.25 0.86845 7.31 0.86078 7.85 0.85299 8.29 0.84520 8.7312.26 0.86912 7.26 0.86146 7.78 0.85369 8.22 0.84597 8.6614.29 0.87040 7.16 0.86278 7.65 0.85511 8.08 0.84744 8.5216.31 0.87166 7.07 0.86412 7.53 0.85652 7.95 0.84892 8.3918.34 0.87292 6.97 0.86545 7.41 0.85791 7.82 0.85038 8.2520.37 0.87415 6.88 0.86673 7.29 0.85924 7.70 0.85179 8.1322.39 0.87536 6.79 0.86802 7.17 0.86060 7.59 0.85317 8.0124.42 0.87655 6.71 0.86926 7.06 0.86195 7.47 0.85456 7.8926.45 0.87774 6.62 0.87050 6.96 0.86322 7.36 0.85592 7.7728.47 0.87889 6.54 0.87171 6.86 0.86449 7.25 0.85725 7.6629.49 0.87947 6.50 0.87229 6.80 0.86510 7.20 0.85791 7.6130.50 0.88007 6.46 0.87292 6.76 0.86574 7.15 0.85856 7.5632.53 0.88120 6.38 0.87410 6.66 0.86699 7.05 0.85988 7.4534.55 0.88231 6.31 0.87528 6.56 0.86823 6.95 0.86113 7.3536.58 0.88342 6.24 0.87643 6.47 0.86939 6.86 0.86238 7.2538.60 0.88452 6.16 0.87757 6.38 0.87059 6.76 0.86363 7.1539.62 0.88503 6.13 0.87812 6.34 0.87117 6.72 0.86423 7.11

0.10849 0.10 0.86088 8.39 0.85217 8.48 0.84393 9.12 0.83554 9.722.13 0.86223 8.24 0.85363 8.35 0.84554 8.97 0.83733 9.554.15 0.86364 8.09 0.85511 8.23 0.84710 8.82 0.83897 9.386.18 0.86507 7.95 0.85656 8.11 0.84864 8.68 0.84057 9.238.21 0.86642 7.81 0.85799 7.99 0.85013 8.54 0.84218 9.08

10.23 0.86778 7.68 0.85943 7.88 0.85163 8.41 0.84373 8.9311.25 0.86845 7.61 0.86009 7.82 0.85235 8.35 0.84452 8.8612.26 0.86911 7.55 0.86079 7.77 0.85309 8.29 0.84528 8.7914.29 0.87045 7.42 0.86217 7.66 0.85453 8.16 0.84680 8.6516.31 0.87174 7.30 0.86351 7.55 0.85595 8.04 0.84829 8.5218.34 0.87302 7.19 0.86485 7.45 0.85734 7.93 0.84977 8.3920.37 0.87428 7.08 0.86616 7.36 0.85872 7.82 0.85120 8.2722.39 0.87553 6.97 0.86744 7.26 0.86009 7.71 0.85262 8.1524.42 0.87676 6.86 0.86871 7.17 0.86140 7.60 0.85402 8.0326.45 0.87797 6.76 0.86999 7.08 0.86272 7.50 0.85541 7.9228.47 0.87919 6.66 0.87123 6.99 0.86405 7.40 0.85678 7.8129.49 0.87976 6.61 0.87184 6.94 0.86467 7.35 0.85745 7.7530.50 0.88035 6.57 0.87244 6.90 0.86530 7.30 0.85811 7.7032.53 0.88152 6.47 0.87362 6.82 0.86658 7.21 0.85945 7.6034.55 0.88265 6.38 0.87480 6.74 0.86782 7.12 0.86072 7.50


Table 2 (Continued )

x p (MPa) T = 298.15 K T = 308.15 K T = 318.15 K T = 328.15 K

ρ

(g cm−3)×104κT

(MPa−1)ρ

(g cm−3)×104κT

(MPa−1)ρ

(g cm−3)×104κT

(MPa−1)ρ

(g cm−3)×104κT

(MPa−1)

36.58 0.88379 6.29 0.87597 6.66 0.86903 7.03 0.86199 7.4038.60 0.88490 6.21 0.87712 6.58 0.87024 6.94 0.86325 7.3039.62 0.88547 6.17 0.87769 6.54 0.87086 6.90 0.86389 7.26

0.19391 0.10 0.86068 8.39 0.85189 8.59 0.84350 9.23 0.83501 9.842.13 0.86204 8.24 0.85340 8.45 0.84514 9.07 0.83677 9.674.15 0.86347 8.10 0.85491 8.33 0.84674 8.93 0.83844 9.506.18 0.86489 7.97 0.85636 8.20 0.84829 8.78 0.84008 9.348.21 0.86627 7.84 0.85780 8.08 0.84982 8.65 0.84172 9.18

10.23 0.86765 7.72 0.85920 7.97 0.85131 8.51 0.84330 9.0311.25 0.86834 7.65 0.85992 7.91 0.85206 8.45 0.84408 8.9612.26 0.86901 7.59 0.86061 7.85 0.85281 8.38 0.84486 8.8914.29 0.87036 7.48 0.86200 7.74 0.85427 8.26 0.84640 8.7516.31 0.87166 7.36 0.86337 7.64 0.85570 8.14 0.84792 8.6118.34 0.87294 7.25 0.86470 7.53 0.85711 8.02 0.84941 8.4820.37 0.87422 7.15 0.86603 7.43 0.85851 7.91 0.85087 8.3622.39 0.87550 7.04 0.86734 7.34 0.85989 7.80 0.85231 8.2324.42 0.87674 6.94 0.86863 7.24 0.86126 7.69 0.85374 8.1126.45 0.87796 6.85 0.86992 7.15 0.86258 7.59 0.85514 8.0028.47 0.87917 6.75 0.87119 7.06 0.86389 7.49 0.85653 7.8929.49 0.87977 6.71 0.87180 7.01 0.86455 7.44 0.85721 7.8330.50 0.88036 6.66 0.87240 6.97 0.86520 7.39 0.85788 7.7832.53 0.88156 6.57 0.87362 6.89 0.86648 7.29 0.85922 7.6734.55 0.88270 6.49 0.87482 6.80 0.86772 7.20 0.86051 7.5736.58 0.88385 6.40 0.87599 6.72 0.86894 7.11 0.86179 7.4738.60 0.88498 6.32 0.87717 6.64 0.87016 7.02 0.86305 7.3739.62 0.88552 6.28 0.87774 6.60 0.87078 6.98 0.86369 7.33

0.29799 0.10 0.86067 8.44 0.85197 9.00 0.84340 9.59 0.83488 10.402.13 0.86206 8.30 0.85350 8.84 0.84506 9.41 0.83670 10.204.15 0.86352 8.16 0.85504 8.68 0.84667 9.23 0.83841 10.006.18 0.86495 8.02 0.85654 8.53 0.84825 9.07 0.84008 9.798.21 0.86636 7.89 0.85802 8.38 0.84981 8.90 0.84173 9.59

10.23 0.86774 7.76 0.85947 8.24 0.85134 8.75 0.84335 9.4011.25 0.86840 7.70 0.86018 8.17 0.85209 8.67 0.84415 9.3112.26 0.86911 7.64 0.86089 8.11 0.85284 8.60 0.84494 9.2214.29 0.87046 7.52 0.86231 7.97 0.85433 8.45 0.84652 9.0516.31 0.87178 7.41 0.86369 7.85 0.85579 8.31 0.84805 8.8818.34 0.87309 7.30 0.86507 7.72 0.85723 8.18 0.84955 8.7220.37 0.87439 7.19 0.86641 7.60 0.85864 8.05 0.85105 8.5622.39 0.87563 7.09 0.86774 7.49 0.86002 7.92 0.85252 8.4124.42 0.87689 6.99 0.86905 7.38 0.86140 7.80 0.85396 8.2726.45 0.87813 6.89 0.87035 7.27 0.86275 7.68 0.85539 8.1328.47 0.87934 6.80 0.87164 7.16 0.86409 7.57 0.85680 7.9929.49 0.87995 6.75 0.87226 7.11 0.86474 7.51 0.85748 7.9330.50 0.88055 6.70 0.87287 7.06 0.86540 7.46 0.85818 7.86



x p (MPa) T = 298.15 K T = 308.15 K T = 318.15 K T = 328.15 K

ρ

(g cm−3)×104κT

(MPa−1)ρ

(g cm−3)×104κT

(MPa−1)ρ

(g cm−3)×104κT

(MPa−1)ρ

(g cm−3)×104κT

(MPa−1)

32.53 0.88172 6.61 0.87411 6.96 0.86671 7.35 0.85954 7.7434.55 0.88287 6.53 0.87533 6.87 0.86798 7.25 0.86087 7.6236.58 0.88404 6.44 0.87652 6.77 0.86922 7.15 0.86217 7.5038.60 0.88516 6.36 0.87771 6.68 0.87046 7.05 0.86346 7.3939.62 0.88575 6.32 0.87829 6.64 0.87108 7.00 0.86411 7.33

0.4346 0.10 0.86111 8.55 0.85231 9.35 0.84337 9.77 0.83457 10.702.13 0.86253 8.41 0.85385 9.17 0.84509 9.59 0.83645 10.404.15 0.86401 8.27 0.85544 8.99 0.84672 9.41 0.83821 10.206.18 0.86549 8.14 0.85697 8.82 0.84834 9.25 0.83992 10.008.21 0.86694 8.01 0.85849 8.65 0.84991 9.08 0.84161 9.80

10.23 0.86833 7.89 0.86001 8.49 0.85150 8.93 0.84327 9.6111.25 0.86902 7.83 0.86072 8.41 0.85225 8.85 0.84408 9.5212.26 0.86973 7.77 0.86145 8.34 0.85302 8.78 0.84490 9.4314.29 0.87112 7.65 0.86291 8.19 0.85453 8.63 0.84651 9.2516.31 0.87245 7.54 0.86432 8.05 0.85603 8.49 0.84808 9.0818.34 0.87377 7.43 0.86574 7.91 0.85750 8.36 0.84962 8.9220.37 0.87509 7.33 0.86710 7.78 0.85894 8.23 0.85115 8.7622.39 0.87637 7.22 0.86847 7.65 0.86038 8.10 0.85265 8.6124.42 0.87769 7.12 0.86979 7.53 0.86177 7.98 0.85413 8.4626.45 0.87892 7.03 0.87113 7.41 0.86316 7.86 0.85559 8.3228.47 0.88017 6.93 0.87242 7.30 0.86452 7.74 0.85703 8.1929.49 0.88077 6.89 0.87305 7.24 0.86521 7.69 0.85774 8.1230.50 0.88139 6.84 0.87368 7.18 0.86587 7.63 0.85845 8.0632.53 0.88258 6.75 0.87497 7.08 0.86721 7.52 0.85984 7.9334.55 0.88378 6.66 0.87622 6.97 0.86850 7.42 0.86120 7.8136.58 0.88495 6.58 0.87745 6.87 0.86977 7.32 0.86253 7.6938.60 0.88612 6.50 0.87865 6.77 0.87104 7.22 0.86385 7.5739.62 0.88669 6.46 0.87922 6.72 0.87166 7.17 0.86451 7.52

0.49717 0.10 0.86123 8.41 0.85227 9.09 0.84339 9.76 0.83460 10.802.13 0.86269 8.28 0.85387 8.94 0.84510 9.59 0.83651 10.604.15 0.86419 8.16 0.85547 8.80 0.84679 9.42 0.83829 10.306.18 0.86566 8.04 0.85702 8.66 0.84841 9.26 0.84001 10.108.21 0.86713 7.93 0.85854 8.53 0.85005 9.11 0.84173 9.92

10.23 0.86854 7.81 0.86007 8.40 0.85162 8.96 0.84340 9.7211.25 0.86925 7.76 0.86081 8.33 0.85239 8.89 0.84423 9.6312.26 0.86994 7.71 0.86155 8.27 0.85318 8.82 0.84505 9.5414.29 0.87134 7.60 0.86301 8.15 0.85471 8.68 0.84668 9.3616.31 0.87270 7.50 0.86444 8.03 0.85623 8.55 0.84827 9.1818.34 0.87404 7.40 0.86584 7.92 0.85771 8.42 0.84982 9.0220.37 0.87537 7.30 0.86725 7.81 0.85919 8.30 0.85137 8.8622.39 0.87666 7.21 0.86862 7.70 0.86063 8.17 0.85290 8.7124.42 0.87796 7.12 0.86998 7.60 0.86206 8.06 0.85439 8.5626.45 0.87924 7.03 0.87130 7.49 0.86345 7.94 0.85586 8.4128.47 0.88049 6.94 0.87263 7.40 0.86482 7.83 0.85732 8.28



x p (MPa) T = 298.15 K T = 308.15 K T = 318.15 K T = 328.15 K

ρ

(g cm−3)×104κT

(MPa−1)ρ

(g cm−3)×104κT

(MPa−1)ρ

(g cm−3)×104κT

(MPa−1)ρ

(g cm−3)×104κT

(MPa−1)

29.49 0.88111 6.90 0.87328 7.35 0.86550 7.78 0.85803 8.2130.50 0.88172 6.85 0.87391 7.30 0.86617 7.73 0.85876 8.1432.53 0.88294 6.77 0.87519 7.21 0.86753 7.62 0.86016 8.0134.55 0.88413 6.69 0.87647 7.12 0.86884 7.52 0.86154 7.8936.58 0.88530 6.61 0.87768 7.03 0.87015 7.42 0.86288 7.7738.60 0.88648 6.54 0.87891 6.94 0.87143 7.33 0.86421 7.6539.62 0.88706 6.50 0.87956 6.90 0.87203 7.28 0.86489 7.59

0.60681 0.10 0.86283 8.99 0.85365 9.89 0.84413 10.10 0.83498 11.102.13 0.86429 8.82 0.85528 9.66 0.84590 9.93 0.83693 10.804.15 0.86581 8.65 0.85691 9.45 0.84762 9.75 0.83875 10.606.18 0.86732 8.49 0.85849 9.24 0.84928 9.57 0.84051 10.408.21 0.86879 8.34 0.86004 9.04 0.85093 9.39 0.84226 10.20

10.23 0.87025 8.19 0.86158 8.85 0.85254 9.23 0.84397 9.9511.25 0.87096 8.12 0.86233 8.76 0.85334 9.15 0.84481 9.8512.26 0.87169 8.05 0.86310 8.67 0.85414 9.07 0.84566 9.7514.29 0.87310 7.91 0.86458 8.49 0.85570 8.91 0.84732 9.5616.31 0.87449 7.78 0.86603 8.33 0.85724 8.76 0.84894 9.3818.34 0.87584 7.65 0.86748 8.17 0.85876 8.62 0.85054 9.2120.37 0.87718 7.53 0.86891 8.01 0.86026 8.48 0.85211 9.0422.39 0.87854 7.41 0.87030 7.87 0.86172 8.35 0.85367 8.8824.42 0.87984 7.30 0.87168 7.72 0.86319 8.22 0.85520 8.7226.45 0.88114 7.19 0.87306 7.59 0.86460 8.09 0.85670 8.5828.47 0.88241 7.08 0.87438 7.46 0.86601 7.97 0.85818 8.4329.49 0.88304 7.02 0.87504 7.39 0.86671 7.91 0.85892 8.3630.50 0.88368 6.97 0.87570 7.33 0.86741 7.85 0.85965 8.2932.53 0.88492 6.87 0.87702 7.21 0.86877 7.74 0.86109 8.1634.55 0.88611 6.77 0.87828 7.09 0.87010 7.63 0.86249 8.0336.58 0.88735 6.68 0.87953 6.97 0.87142 7.52 0.86386 7.9038.60 0.88853 6.58 0.88078 6.86 0.87273 7.41 0.86522 7.7839.62 0.88911 6.54 0.88141 6.81 0.87337 7.36 0.86590 7.72

0.70885 0.10 0.86437 9.08 0.85492 9.95 0.84536 10.60 0.83600 11.702.13 0.86585 8.91 0.85654 9.74 0.84718 10.40 0.83798 11.404.15 0.86743 8.75 0.85819 9.53 0.84892 10.10 0.83983 11.106.18 0.86895 8.59 0.85983 9.33 0.85062 9.93 0.84164 10.808.21 0.87046 8.44 0.86143 9.14 0.85230 9.72 0.84344 10.60

10.23 0.87194 8.29 0.86299 8.96 0.85394 9.52 0.84517 10.3011.25 0.87268 8.22 0.86375 8.87 0.85476 9.43 0.84605 10.2012.26 0.87341 8.15 0.86453 8.78 0.85556 9.33 0.84690 10.1014.29 0.87483 8.02 0.86605 8.61 0.85716 9.15 0.84859 9.8616.31 0.87626 7.89 0.86755 8.45 0.85874 8.97 0.85027 9.6418.34 0.87766 7.76 0.86899 8.30 0.86028 8.80 0.85191 9.4420.37 0.87903 7.64 0.87044 8.15 0.86180 8.64 0.85348 9.2422.39 0.88037 7.52 0.87187 8.00 0.86331 8.49 0.85508 9.0524.42 0.88170 7.40 0.87328 7.87 0.86479 8.34 0.85666 8.87



x p (MPa) T = 298.15 K T = 308.15 K T = 318.15 K T = 328.15 K

ρ

(g cm−3)×104κT

(MPa−1)ρ

(g cm−3)×104κT

(MPa−1)ρ

(g cm−3)×104κT

(MPa−1)ρ

(g cm−3)×104κT

(MPa−1)

26.45 0.88302 7.29 0.87467 7.73 0.86622 8.19 0.85815 8.7028.47 0.88435 7.19 0.87601 7.60 0.86766 8.05 0.85969 8.5329.49 0.88495 7.13 0.87670 7.54 0.86838 7.98 0.86044 8.4530.50 0.88559 7.08 0.87736 7.48 0.86909 7.92 0.86118 8.3732.53 0.88687 6.98 0.87871 7.36 0.87046 7.79 0.86267 8.2234.55 0.88809 6.88 0.87999 7.24 0.87183 7.66 0.86408 8.0736.58 0.88932 6.79 0.88128 7.13 0.87316 7.54 0.86550 7.9238.60 0.89052 6.69 0.88257 7.02 0.87450 7.42 0.86687 7.7939.62 0.89113 6.65 0.88323 6.97 0.87515 7.37 0.86757 7.72

0.79512 0.10 0.86629 9.35 0.85647 10.10 0.84664 10.70 0.83688 11.702.13 0.86783 9.17 0.85814 9.84 0.84848 10.50 0.83890 11.404.15 0.86942 9.00 0.85982 9.64 0.85026 10.30 0.84079 11.106.18 0.87101 8.83 0.86148 9.44 0.85198 10.10 0.84263 10.908.21 0.87256 8.67 0.86310 9.25 0.85371 9.86 0.84446 10.60

10.23 0.87410 8.52 0.86470 9.07 0.85538 9.66 0.84623 10.4011.25 0.87484 8.45 0.86548 8.98 0.85622 9.57 0.84711 10.3012.26 0.87559 8.37 0.86627 8.90 0.85704 9.47 0.84800 10.2014.29 0.87707 8.23 0.86781 8.73 0.85867 9.29 0.84972 9.9716.31 0.87851 8.09 0.86934 8.57 0.86027 9.12 0.85142 9.7718.34 0.87994 7.96 0.87082 8.42 0.86185 8.96 0.85308 9.5720.37 0.88137 7.83 0.87230 8.27 0.86340 8.80 0.85471 9.3922.39 0.88274 7.71 0.87376 8.13 0.86493 8.64 0.85634 9.2124.42 0.88414 7.59 0.87518 7.99 0.86645 8.49 0.85792 9.0426.45 0.88547 7.48 0.87659 7.86 0.86792 8.35 0.85948 8.8728.47 0.88682 7.36 0.87797 7.73 0.86938 8.21 0.86102 8.7129.49 0.88748 7.31 0.87866 7.67 0.87011 8.14 0.86178 8.6330.50 0.88814 7.26 0.87934 7.61 0.87084 8.08 0.86255 8.5632.53 0.88940 7.15 0.88071 7.49 0.87225 7.95 0.86405 8.4134.55 0.89067 7.05 0.88202 7.37 0.87363 7.82 0.86550 8.2736.58 0.89195 6.95 0.88333 7.26 0.87500 7.70 0.86693 8.1338.60 0.89319 6.85 0.88462 7.15 0.87636 7.59 0.86834 8.0039.62 0.89382 6.81 0.88527 7.10 0.87702 7.53 0.86904 7.93

0.89947 0.10 0.86961 9.73 0.85913 10.10 0.84893 11.00 0.83856 11.702.13 0.87118 9.53 0.86086 9.93 0.85082 10.70 0.84062 11.404.15 0.87283 9.33 0.86258 9.74 0.85265 10.50 0.84256 11.206.18 0.87445 9.15 0.86427 9.55 0.85443 10.30 0.84445 10.908.21 0.87603 8.97 0.86591 9.37 0.85618 10.10 0.84633 10.70

10.23 0.87761 8.79 0.86755 9.20 0.85793 9.88 0.84817 10.5011.25 0.87836 8.71 0.86837 9.12 0.85878 9.78 0.84908 10.4012.26 0.87912 8.63 0.86916 9.03 0.85963 9.69 0.84998 10.3014.29 0.88064 8.47 0.87074 8.87 0.86130 9.51 0.85176 10.1016.31 0.88215 8.31 0.87229 8.72 0.86296 9.33 0.85349 9.9318.34 0.88361 8.17 0.87383 8.57 0.86457 9.16 0.85520 9.7520.37 0.88505 8.02 0.87533 8.43 0.86615 9.00 0.85686 9.58



x p (MPa) T = 298.15 K T = 308.15 K T = 318.15 K T = 328.15 K

ρ

(g cm−3)×104κT

(MPa−1)ρ

(g cm−3)×104κT

(MPa−1)ρ

(g cm−3)×104κT

(MPa−1)ρ

(g cm−3)×104κT

(MPa−1)

22.39 0.88646 7.89 0.87682 8.29 0.86773 8.84 0.85854 9.4124.42 0.88790 7.75 0.87829 8.16 0.86927 8.69 0.86015 9.2526.45 0.88927 7.63 0.87973 8.03 0.87079 8.54 0.86177 9.1028.47 0.89065 7.50 0.88116 7.90 0.87230 8.40 0.86335 8.9529.49 0.89134 7.44 0.88187 7.84 0.87306 8.33 0.86413 8.8830.50 0.89201 7.38 0.88255 7.78 0.87382 8.27 0.86492 8.8132.53 0.89334 7.27 0.88395 7.66 0.87523 8.13 0.86644 8.6734.55 0.89465 7.16 0.88528 7.55 0.87667 8.01 0.86793 8.5336.58 0.89594 7.05 0.88663 7.44 0.87806 7.88 0.86939 8.4138.60 0.89720 6.94 0.88794 7.33 0.87943 7.77 0.87083 8.2839.62 0.89785 6.89 0.88861 7.28 0.88011 7.71 0.87154 8.22

1.00000 0.10 0.87356 9.41 0.86290 10.40 0.85209 11.00 0.84128 11.802.13 0.87516 9.25 0.86466 10.20 0.85399 10.80 0.84333 11.604.15 0.87681 9.09 0.86642 9.97 0.85583 10.60 0.84532 11.406.18 0.87844 8.94 0.86815 9.77 0.85765 10.30 0.84729 11.108.21 0.88004 8.79 0.86984 9.58 0.85946 10.10 0.84921 10.90

10.23 0.88161 8.65 0.87152 9.39 0.86122 9.96 0.85110 10.7011.25 0.88240 8.58 0.87235 9.30 0.86208 9.87 0.85203 10.6012.26 0.88319 8.51 0.87317 9.21 0.86296 9.78 0.85295 10.5014.29 0.88472 8.38 0.87477 9.04 0.86465 9.60 0.85477 10.3016.31 0.88619 8.25 0.87635 8.87 0.86633 9.43 0.85654 10.1018.34 0.88767 8.13 0.87794 8.72 0.86800 9.27 0.85830 9.9420.37 0.88913 8.01 0.87946 8.56 0.86960 9.12 0.86001 9.7622.39 0.89055 7.89 0.88099 8.42 0.87119 8.97 0.86173 9.6024.42 0.89197 7.78 0.88246 8.27 0.87276 8.82 0.86337 9.4426.45 0.89337 7.67 0.88394 8.14 0.87432 8.68 0.86503 9.2828.47 0.89476 7.56 0.88539 8.00 0.87584 8.54 0.86664 9.1329.49 0.89543 7.51 0.88611 7.94 0.87659 8.48 0.86742 9.0630.50 0.89611 7.46 0.88683 7.88 0.87735 8.41 0.86823 8.9932.53 0.89744 7.36 0.88822 7.75 0.87884 8.28 0.86979 8.8534.55 0.89876 7.26 0.88962 7.63 0.88029 8.16 0.87130 8.7136.58 0.90007 7.16 0.89099 7.52 0.88171 8.04 0.87283 8.5838.60 0.90135 7.07 0.89232 7.41 0.88313 7.92 0.87432 8.4539.62 0.90200 7.03 0.89297 7.35 0.88384 7.87 0.87502 8.39

It was found that parametersC andD are correlated and the objective function has a great many localminima. The global minimum was therefore determined by non-deterministic minimisation algorithmES2 developed by Tvrdık and Krivý [14]. The algorithm requires a few parameters, which must beproperly set. In this work, the size of the pool is 10 nodes. The new pool in each iteration step inheritsfive nodes with the lowest value of the objective function. The probability at which the node with anincrease of the objective function is accepted was set to 0.05. The initial pool contained 10 randomlygenerated nodes uniformly distributed in the square satisfying 0.01 < C < 20 and 0.1 < D < 250.


Fig. 1. Isothermal compressibilityκT for x × benzene+ (1− x) × 1,3,5-trimethylbenzene atT = 328.15 K: (�) x = 0.00000;(�) x = 0.19391; (�) x = 0.43460; (�) x = 0.60681; (+) x = 0.79512; (�) x = 1.00000.

It was verified by repeated calculations that these settings guarantee that the global minimum is alwaysreached.

The optimised parametersC andD of the Tait equation along with the standard deviations in densityare given inTable 3. It is evident that the equation fits accurately the densities over the entire pressurerange.

3.2. Isothermal compressibilities

The isothermal compressibilityκT was calculated from the equation

κT = − 1

V

(∂V

∂p

)T,x

= ρ

ρ0

[C

D + p

], (4)

whereV is the molar volume. The values ofκT are given inTable 2and illustrated inFig. 1 for the tem-perature of 328.15 K. They increase monotonously with increasing temperature in the given temperaturerange.

3.3. Excess molar volumes

The values ofV Em were calculated from the mixtures densities,ρ, and the densities,ρi, and molar

masses,Mi, of pure componentsi (i = 1 and 2) using the relation

V Em = xM1 + (1 − x)M2

ρ− xM1

ρ1− (1 − x)M2

ρ2, (5)


Table 3CoefficientsC andD of the Tait equation (Eq. (2)) for x × benzene+ (1 − x) × 1,3,5-trimethylbenzene at temperatureT andstandard deviationsσ of the fit

T (K) x ×102C D (MPa) ×105σ (g cm−3)

298.15 0.00000 9.5221 120.0914 60.10849 8.2920 98.6747 30.19391 8.8510 105.4166 20.29799 8.8956 105.2774 30.43460 9.2837 108.4189 40.49717 10.0000 118.7828 160.60681 8.5149 94.5882 30.70885 8.7916 96.7004 20.79512 8.8552 94.6388 20.89947 8.3949 86.1419 61.00000 9.7066 103.0082 4

308.15 0.00000 8.3866 96.5685 10.10849 10.0000 117.7840 90.19391 10.0000 116.3515 90.29799 8.9436 99.2341 30.43460 8.4952 90.7228 20.49717 10.0000 109.9046 110.60681 7.8103 78.8602 70.70885 8.2662 82.9404 50.79512 8.5491 84.9284 30.89947 9.1055 89.7098 11.00000 8.8456 84.9233 2

318.15 0.00000 8.9658 98.0183 30.10849 9.9213 108.7366 70.19391 10.0000 108.2913 90.29799 9.1390 95.2044 30.43460 9.4516 96.6350 40.49717 10.0000 102.3909 90.60681 9.4595 93.2957 40.70885 8.5289 80.2462 30.79512 8.9025 82.8579 20.89947 9.1216 83.0771 21.00000 9.6791 87.9827 3

328.15 0.00000 9.5747 99.5464 70.10849 10.0000 102.8135 100.19391 10.0000 101.5355 130.29799 8.7059 83.2743 20.43460 8.9848 84.2059 30.49717 9.0401 83.7152 30.60681 8.9727 80.9032 20.70885 8.0470 68.5701 90.79512 8.7001 74.3007 30.89947 9.7211 83.3075 61.00000 10.0000 84.3040 7


Fig. 2. Excess molar volumesV Em for x × benzene+ (1−x) × 1,3,5-trimethylbenzene atT = 328.15 K. Pressures: (�) 2.13 MPa,

experimental points, (– - - –) calculated fromEq. (6); (�) 11.25 MPa, experimental points, (—) calculated fromEq. (6); (�)20.37 MPa, experimental points, (- - -) calculated fromEq. (6); (�) 29.50 MPa, experimental points, (– – –) calculated fromEq. (6); (×) 38.60 MPa, experimental points, (– - –) calculated fromEq. (6).

where subscript 1 refers to benzene and subscript 2 to 1,3,5-trimethylbenzene andx stands for the molefraction of benzene.

The experimental uncertainty in theV Em is estimated to be about±1 × 10−2 cm3 mol−1, which is

about five times worse compared to measurements atT = 298.15 K and atmospheric pressure. Themeasurements at high pressures naturally worsen the uncertainty owing to hysteresis of the densimetervibrating-tube and error in the pressure measurement. The values of excess volumesV E

m at five chosenpressures equal approximately to 2, 11, 20, 29, and 38 MPa are given inTable 4.

TheV Em data were fitted to the Redlich–Kister equation

V Em = x(1 − x)

[2∑

n=0

An(1 − 2x)n

]. (6)

The coefficientsAn and standard deviationsσ(V Em) of the fit are summarised inTable 5. The number of

parametersAn was predetermined by the statisticalF-test.The illustration of the pressure dependence ofV E

m is given inFig. 2 for the temperature of 328.15 K.From the analogous figures for all the temperatures follows that theV E

m curves are shifted in a regular waywith increasing temperature and pressure. The decrease inV E

m values with increasing temperature followsthe temperature dependence ofV E

m at atmospheric pressure[8]. The pressure dependence at constanttemperature is also regular. TheV E

m values are apparently decreasing with increasing pressure for thesame composition. The positions of maxima on the curves are only slightly shifted with pressure.


Table 4Excess molar volumeV E

m in (cm3 mol−1) for x × benzene+ (1 − x) × 1,3,5-trimethylbenzene at temperatureT and pressurep

T (K) x p (MPa)

2.13 11.25 20.37 29.50 38.60

298.15 0.00000 0.000 0.000 0.000 0.000 0.0000.10849 0.165 0.153 0.143 0.128 0.1230.19391 0.305 0.292 0.282 0.264 0.2540.29799 0.439 0.430 0.415 0.405 0.4020.43460 0.553 0.541 0.529 0.517 0.5080.49717 0.615 0.601 0.590 0.577 0.5710.60681 0.559 0.548 0.540 0.526 0.5180.70885 0.517 0.503 0.493 0.485 0.4800.79512 0.420 0.401 0.385 0.369 0.3590.89947 0.225 0.209 0.194 0.178 0.1671.00000 0.000 0.000 0.000 0.000 0.000

308.15 0.00000 0.000 0.000 0.000 0.000 0.0000.10849 0.238 0.237 0.229 0.220 0.2270.19391 0.362 0.363 0.357 0.343 0.3440.29799 0.454 0.445 0.435 0.421 0.4180.43460 0.547 0.531 0.517 0.505 0.4970.49717 0.610 0.594 0.580 0.566 0.5580.60681 0.543 0.533 0.517 0.507 0.5000.70885 0.504 0.492 0.480 0.469 0.4600.79512 0.419 0.409 0.398 0.389 0.3820.89947 0.253 0.247 0.240 0.231 0.2271.00000 0.000 0.000 0.000 0.000 0.000

318.15 0.00000 0.000 0.000 0.000 0.000 0.0000.10849 0.212 0.206 0.200 0.195 0.1920.19391 0.342 0.330 0.322 0.312 0.3110.29799 0.433 0.421 0.411 0.404 0.3970.43460 0.534 0.522 0.512 0.500 0.4920.49717 0.579 0.561 0.545 0.535 0.5240.60681 0.557 0.540 0.527 0.514 0.5060.70885 0.479 0.465 0.455 0.444 0.4380.79512 0.398 0.384 0.374 0.363 0.3570.89947 0.231 0.217 0.210 0.197 0.1951.00000 0.000 0.000 0.000 0.000 0.000

328.15 0.00000 0.000 0.000 0.000 0.000 0.0000.10849 0.199 0.190 0.189 0.180 0.1790.19391 0.333 0.320 0.312 0.299 0.3020.29799 0.394 0.379 0.371 0.359 0.3540.43460 0.497 0.481 0.471 0.457 0.4510.49717 0.519 0.504 0.493 0.479 0.4720.60681 0.513 0.501 0.490 0.476 0.4690.70885 0.429 0.418 0.411 0.397 0.3930.79512 0.364 0.357 0.349 0.339 0.3340.89947 0.228 0.221 0.217 0.207 0.2061.00000 0.000 0.000 0.000 0.000 0.000


Table 5CoefficientAi of the Redlich–Kister equation (Eq. (6)) and standard deviationsσ(V E

m) determined by the maximum likelihoodprinciple forx × benzene+ (1 − x) × 1,3,5-trimethylbenzene at temperatureT and pressurep

T/K p/MPa A0/(cm3 mol−1) A1/(cm3 mol−1) A2/(cm3 mol−1) ×102σV Em /(cm3 mol−1)

298.15 2.13 2.3579 −0.4837 −0.3549 1.5811.25 2.3141 −0.4576 −0.5047 1.4620.37 2.2759 −0.4534 −0.6354 1.4429.50 2.2345 −0.4567 −0.7946 1.5738.60 2.2117 −0.4451 −0.8826 1.71

308.15 2.13 2.2868 −0.2337 0.4187 2.0311.25 2.2276 −0.2013 0.4824 1.9420.37 2.1728 −0.1935 0.4660 1.9529.50 2.1232 −0.2051 0.4024 1.8638.60 2.0898 −0.1636 0.4513 1.91

318.15 2.13 2.2426 −0.2573 0.1324 1.3511.25 2.1822 −0.2357 0.0720 1.2120.37 2.1344 −0.2309 0.0560 1.0529.50 2.0917 −0.2066 −0.0103 1.0738.60 2.0551 −0.2015 0.0181 1.00

328.15 2.13 2.0347 −0.1997 0.2978 1.7011.25 1.9775 −0.2273 0.2727 1.6920.37 1.9349 −0.2196 0.2799 1.6029.50 1.8821 −0.2233 0.2210 1.5138.60 1.8533 −0.2062 0.2610 1.61

Acknowledgements

The authors would like to acknowledge the partial support of the Grant Agency of the Czech Republic.The work has been carried out under grant no. 203/02/1098.

References

[1] E. Kovács, K. Aim, J. Linek Jr., J. Chem. Thermodyn. 33 (2001) 33–45.[2] L. Morávková, K. Aim, J. Linek, J. Chem. Thermodyn. 34 (2002) 1377–1386.[3] L. Morávková, J. Linek, J. Chem. Thermodyn. 34 (2002) 1387–1395.[4] L. Morávková, J. Linek, J. Chem. Thermodyn. 34 (2002) 1397–1405.[5] L. Morávková, J. Linek, J. Chem. Thermodyn. 34 (2002) 1407–1415.[6] L. Morávková, J. Linek, J. Chem. Thermodyn. 35 (2003) 113–121.[7] L. Morávková, J. Linek, J. Chem. Thermodyn., in press.[8] L. Morávková, J. Linek, J. Chem. Thermodyn., in press.[9] A. Riddick, W.B. Bunger, T.K. Sakano, Physical Properties and Methods of Purification, vol. II, Organic Solvents, Wiley,

New York, 1986.[10] R.R. Dreisbach, Physical Properties of Chemical Compounds, vol. 1, American Chemical Society, Washington, 1955.[11] J. Timmermans, Physico-Chemical Constants of Pure Organic Compounds, vol. 1, 1950, vol. 2, 1965, Elsevier, Amsterdam.[12] E. Schmidt, U. Grigull, Properties of Water and Steam in SI-Units. Springer-Verlag, Berlin, 1982.[13] R. Malhotra, L.A. Woolf, J. Chem. Thermodyn. 23 (1991) 49–57.[14] J. Tvrdık, I. Krivý, A genetic type algorithm for optimization, in: Proceedings of MENDEL’96, 2nd International Conference

on Genetic Algorithms, Brno, VUT 1996, pp. 176–180.

(p, v, t, x) measurements of the system benzene-i-c8

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