(p,Vm,T) measurements of (octane+benzene) at temperatures from (298.15 to 328.15)K and at pressures up to 40MPa (original) (raw)

(p,Vm,T)(p, V_{\mathrm{m}}, T) measurements of (octane + benzene) 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 of the ASCR, v.v.i., 16502 Prague 6, Czech Republic

Received 1 November 2007; received in revised form 19 November 2007; accepted 20 November 2007
Available online 3 January 2008

Abstract

The densities of (octane + benzene) were measured at elevated pressures ( 0.1 to 40 ) MPa at four temperatures over the range (298.15 to 328.15 ) K with a high-pressure apparatus. The high-pressure density data were fitted to the Tait equation and the isothermal compressibilities were calculated with a novel computation procedure with the aid of this equation. The low- and high-pressure values of excess molar volume VmEV_{\mathrm{m}}^{\mathrm{E}} calculated from the density data show that the deviations from ideal behaviour in the system are practically independent of temperature and decreases slightly as the pressure is raised. The VmEV_{\mathrm{m}}^{\mathrm{E}} data were fitted to the fourth-order Redlich-Kister equation, with the maximum likelihood principle being applied for the determination of the adjustable parameters.

© 2007 Elsevier Ltd. All rights reserved.

Keywords: Octane; Benzene; Binary mixture; Density; Isothermal compressibility; Excess volume; High-pressure; Elevated temperature

1. Introduction

Research activities of our laboratory comprise, among others, the systematic measurement of volumetric properties of different groups of organic compounds. Our new project is devoted to the systematic study of liquid systems modelling liquid engine fuels. Up to now, (cyclohexane + alkane) at normal pressure and temperature 298.15 K[1]298.15 \mathrm{~K}[1], (cyclohexane + nonane) at elevated temperatures and pressures [2], and (octane + benzene, or toluene, or 1,3 -xylene, or 1,3,5-trimethylbenzene) at four temperatures and normal pressure [3] were studied.

To our knowledge, there exist no volumetric data for the liquid phase of (octane + benzene) at elevated pressures. Therefore, we have measured densities and calculated isothermal compressibilities and excess volumes of the system. The apparatus based on a high-pressure vibrating-tube densimeter working in a static mode [5] and designed for

[1]measuring the (p,Vm,T)\left(p, V_{\mathrm{m}}, T\right) behaviour of pure liquids and liquid mixtures at elevated temperatures ( 283 to 333 ) K and moderately high pressures to 40 MPa was used for the measurements. The measurements were carried out at the temperatures (298.15,308.15,318.15(298.15,308.15,318.15, and 328.15) K and over the pressure range ( 0.1 to 40 ) MPa .

The densities and excess volumes of the investigated liquids and their mixtures are required, for instance, for relating excess enthalpy and excess Gibbs free energy values. From a practical point of view, the data are useful for the design of mixing, storage, and process equipment. Last but not least, the data reflect interactions between the molecules of the mixtures studied and can serve for testing the theories of the liquid state.

2. Experimental

2.1. Materials

The octane and the benzene used in the experiments were the following products from Fluka: octane, puriss., A.R., g.c. mass fraction purity ⩾0.995\geqslant 0.995; benzene, A.R.,

1. 22{ }_{2}^{2} Corresponding author. Tel.: +420 220370270/296780270; fax: +420 220920661.
   E-mail address: linek@icpf.cas.cz (J. Linek). ↩︎

TABLE 1
Densities ρ\rho and refractive index values nDn_{\mathrm{D}} at T=298.15 KT=298.15 \mathrm{~K} of the pure components, and their comparison with literature; ww is the mass fraction purity as determined by g.l.c

g.c. mass fraction purity ⩾0.997\geqslant 0.997. Both the hydrocarbons were dried and stored over 0.4 nm molecular sieves. In order to check the purity of the substances, their density and refractive index values were determined at T=T= 298.15 K and compared with the literature data [4] with the agreement being, in general, good (table 1). The contents of the substances were also determined by gas chromatography (HP Ser.II. model 5890 chromatograph with capillary column type 1909 1Z-413E and f.i.d., column temperature 413.3 K , helium flow rate 4.2⋅10−4 cm3⋅ s−14.2 \cdot 10^{-4} \mathrm{~cm}^{3} \cdot \mathrm{~s}^{-1} ).

2.2. Apparatus and procedure

A schematic diagram and detailed description of the apparatus used for the high-pressure measurement was given in our previous work [5]. 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 control within ±0.01 K\pm 0.01 \mathrm{~K}. The pressure was measured with a pressure transducer LPN-N having a voltage output (ECOM, Praha, Czech Republic). The pressure gauge was calibrated with a Ruska pressure calibration system (Ruska Instruments Co., Houston, TX, USA). The accuracy of the pressure measurement is better than 0.1 MPa . The pressure in the measuring cell can be set by means of the manual pressure controller accurate to 0.01 MPa . The DMA 512P measuring cell is connected to the DMA 58 densimeter which serves as a frequency counter and evaluates the oscillating period from the signals of the measuring cell filled with sample. The samples of measured liquid mixtures prepared by weight in special vessels [6] are moved into the measuring cell with a liquid chromatography pump LCP 4000.1 (Ecom, Praha, Czech Republic).

The sample density ρ\rho was deduced from the period of vibration τ\tau of the vibrating-tube densimeter as follows:
ρ(T,p)=a(T,p)τ2+b(T,p)\rho(T, p)=a(T, p) \tau^{2}+b(T, p).
The coefficients a(T,p)a(T, p) and b(T,p)b(T, p) are two characteristic temperature and pressure dependent parameters of the apparatus, which have to be determined by measuring the periods τ1\tau_{1} and τ2\tau_{2} for two substances of known density of the T,pT, p set considered.

The choice of standards of known density at high pressures and temperatures is rather limited. The manufacturer of the densimeter DMA 512P recommends the following
substances: nitrogen, benzene, pentane, dichloromethane, and water. In our case, the apparatus was calibrated [5] with double-distilled water and heptane. The density data used for the calibration were taken from [7] for water and from [8] for heptane.

The samples for the density measurements were prepared by weight (SCALTEC SBC 21 balance with an accuracy of ±1⋅10−5 g\pm 1 \cdot 10^{-5} \mathrm{~g} ) for the whole mole fraction range and then partially degassed in tightly closed special vessels of negligible vapour space [6] at the maximum measurement temperature for 3 h by means of an ultrasonic thermostatted bath (Bandelin RK 100H, Berlin, Germany) prior to determining their density in order to prevent the formation of bubbles in the densimeter. To estimate the effect of evaporation on the sample composition, the calculations were carried out taking into account the (vapour + liquid) equilibrium of the given system at the conditions applied. The concentration changes are proved to be well below the stated accuracy in composition.

The experimental uncertainty in the mole fraction composition is less than ±5⋅10−5\pm 5 \cdot 10^{-5}, and that in the density is approximately ±1⋅10−4 g⋅ cm−3\pm 1 \cdot 10^{-4} \mathrm{~g} \cdot \mathrm{~cm}^{-3}.

3. Results and discussion

3.1. Densities

The results of the density measurements are given in table 2. Densities of the pure substances and of nine weighed mixtures were measured at 23 pressures over the range 0.1 MPa to nearly 40 MPa . The isothermal densities of pure substances and their mixtures at a given composition were fitted to the Tait equation
(ρ−ρ0)/ρ=Cln⁡{(D+p)/(D+p0)}\left(\rho-\rho_{0}\right) / \rho=C \ln \left\{(D+p) /\left(D+p_{0}\right)\right\},
where CC and DD are adjustable parameters and ρ0\rho_{0} is the density at a reference low pressure p0(p0=0.101325MPap_{0}\left(p_{0}=0.101325 \mathrm{MPa}\right. in this work). The values of ρ0\rho_{0} were those obtained by measuring the liquid samples with a low-pressure DMA 58 densimeter [3] because the high-pressure equipment cannot in principle provide sufficiently accurate data at atmospheric pressure.

It is evident that the calculated density is not sensitive to the value of parameter DD. The sensitivity is given by
(∂/∂D){(ρ−ρ0)/ρ}=C(p0−p)/{(D+p)(D+p0)}(\partial / \partial D)\left\{\left(\rho-\rho_{0}\right) / \rho\right\}=C\left(p_{0}-p\right) /\left\{(D+p)\left(D+p_{0}\right)\right\}.
At p→p0p \rightarrow p_{0}, the value of density approaches ρ0\rho_{0} for arbitrary values of parameters CC and DD. The sensitivity becomes

TABLE 2
Experimental values of density ρ\rho, difference of calculated and experimental density Δρ\Delta \rho and calculated isothermal compressibility κT\kappa_{T} for {x\{\mathrm{x} octane +(1−x)+(1-x) benzene }\} at pressure pp and temperature TT

TABLE 2 (continued)

(continued on next page)

TABLE 2 (continued)

TABLE 2 (continued)

Overall standard deviation in ρ\rho is 0.00018 g⋅ cm−30.00018 \mathrm{~g} \cdot \mathrm{~cm}^{-3} and in κT=1.3⋅10−6MPa−1\kappa_{T}=1.3 \cdot 10^{-6} \mathrm{MPa}^{-1}. The constants of equations (5) to (8): a1=0.937716,b1=−0.000800,a2=1.192974,b2=−0.001070,A90=2.10108a_{1}=0.937716, b_{1}=-0.000800, a_{2}=1.192974, b_{2}=-0.001070, A_{90}=2.10108, A01=0.002642,A10=−0.75436,A11=0.00034,A20=0.187913,A21=−0.0000244,A30=0.203579,A31=−0.00083,C0=−0.07289,Cs=−0.02904,CT=0.000848,Css=−0.04118A_{01}=0.002642, A_{10}=-0.75436, A_{11}=0.00034, A_{20}=0.187913, A_{21}=-0.0000244, A_{30}=0.203579, A_{31}=-0.00083, C_{0}=-0.07289, C_{s}=-0.02904, C_{T}=0.000848, C_{s s}=-0.04118, CsT=0.000212,CTT=−0.00000114,D0=139.405,Ds=−112.794,DT=0.086542,Dss=−15.0274,DsT=0.344095,DTT=−0.00095C_{s T}=0.000212, C_{T T}=-0.00000114, D_{0}=139.405, D_{s}=-112.794, D_{T}=0.086542, D_{s s}=-15.0274, D_{s T}=0.344095, D_{T T}=-0.00095.

larger at higher pressures but it still remains low. Our previous study [2] revealed that D>Pmax⁡D>P_{\max }. The value of DD obtained by optimization thus compensates for measurement errors rather than reflecting a property with rational physical meaning.

3.2. Isothermal compressibility

Isothermal compressibility κT\kappa_{T} can be calculated from equation

κT=−(1/V)(∂V/∂p)T,s={1/[1−Cln⁡((D+p)/(D+p0))]}[C/(D+p)]\begin{aligned} \kappa_{T} & =-(1 / V)(\partial V / \partial p)_{T, s} \\ & =\left\{1 /[1-C \ln \left((D+p) /\left(D+p_{0}\right)\right)]\right\}[C /(D+p)] \end{aligned}

Self-compensation of the DD parameter therefore vanishes. Even if the agreement between experimental and calculated densities is good, the values of isothermal compressibility may be obtained with high systematic error. If the CC and DD parameters are determined separately for each temperature and composition, the pressure dependence curves may cross. Therefore, the computational procedure developed and fully described by us [2] was applied. The following system of equations is solved:

C=c0+crx+cTT+cxsx2+csTxT+cTTT2D=d0+drx+dTT+dxsx2+dsTxT+dTTT2V0E=x(1−x){∑i=0p(A0,i+AT,iT)(2x−1)i}ρ0,i=a0,i+aT,iT,i=1,2\begin{aligned} & C=c_{0}+c_{r} x+c_{T} T+c_{x s} x^{2}+c_{s T} x T+c_{T T} T^{2} \\ & D=d_{0}+d_{r} x+d_{T} T+d_{x s} x^{2}+d_{s T} x T+d_{T T} T^{2} \\ & V_{0}^{\mathrm{E}}=x(1-x)\left\{\sum_{i=0}^{p}\left(A_{0, i}+A_{T, i} T\right)(2 x-1)^{i}\right\} \\ & \rho_{0, i}=a_{0, i}+a_{T, i} T, \quad i=1,2 \end{aligned}

The values of experimental density, difference of calculated and experimental density, and calculated isothermal compressibility are given in table 2. The dependence of isothermal compressibility on pressure and composition is illustrated in figure 1 for the temperature of 298.15 K .

FIGURE 1. Isothermal compressibility κT\kappa_{T} plotted against pressure pp and mole fraction of octane for {x\{x octane +(1−x)+(1-x) benzene }\} at T=298.15 KT=298.15 \mathrm{~K}.

3.2.1. Excess molar volumes

The values of VmEV_{\mathrm{m}}^{\mathrm{E}} were calculated from the mixtures densities, ρ\rho, and the densities, ρi\rho_{i}, and molar masses, MiM_{i}, of pure components i(i=1,2)i(i=1,2) using the relation
VmE={xM1+(1−x)M2}/ρ−{xM1/ρ1+(1−x)M2/ρ2}V_{\mathrm{m}}^{\mathrm{E}}=\left\{x M_{1}+(1-x) M_{2}\right\} / \rho-\left\{x M_{1} / \rho_{1}+(1-x) M_{2} / \rho_{2}\right\},
where subscript 1 refers to octane and 2 to benzene and xx stands for the mole fraction of octane.

TABLE 3
Excess molar volume VmE/(cm3⋅ mol−1)V_{\mathrm{m}}^{\mathrm{E}} /\left(\mathrm{cm}^{3} \cdot \mathrm{~mol}^{-1}\right) for {x\{x octane +(1−x)+(1-x) benzene }\} at temperature TT and pressure pp

TABLE 4
Coefficients AiA_{i} of the Redlich-Kister equation (equation (10)) and standard deviations σ(VmE)\sigma\left(V_{\mathrm{m}}^{\mathrm{E}}\right) determined by the maximum likelihood principle for {x\{x octane +(1−x)+(1-x) benzene }\} at temperature TT and pressure pp

The experimental uncertainty in the VmEV_{\mathrm{m}}^{\mathrm{E}} is estimated to be about ±1⋅10−2 cm3⋅ mol−1\pm 1 \cdot 10^{-2} \mathrm{~cm}^{3} \cdot \mathrm{~mol}^{-1}, which is about five times worse compared to measurements at T=298.15 KT=298.15 \mathrm{~K} and atmospheric pressure. The measurements at high pressures naturally worsen the uncertainty owing to hysteresis of the densimeter vibrating tube and error in the pressure mea-

FIGURE 2. Excess molar volumes VmEV_{\mathrm{m}}^{\mathrm{E}} plotted against mole fraction of octane for {x\{x octane +(1−x)+(1-x) benzene }\} at T=298.15 KT=298.15 \mathrm{~K}. Pressures: □\square, 2.13 MPa , experimental points, -.- calculated from equation (10); ◯\bigcirc, 11.25 MPa , experimental points, ⋯⋯\cdots \cdots calculated from equation (10); △\triangle, 20.37 MPa , experimental points, -.-. calculated from equation (10); ◯\bigcirc, 29.50 MPa , - - experimental points, calculated from equation (10); ∇\nabla 38.60 MPa , experimental points, ---- calculated from equation (10).
surement. The values of excess volumes VmEV_{\mathrm{m}}^{\mathrm{E}} at five chosen pressures equal approximately to (2,11,20,29(2,11,20,29, and 38$)$ MPa are given in table 3.

The VmEV_{\mathrm{m}}^{\mathrm{E}} data were fitted to the Redlich-Kister equation VmE/(cm3⋅ mol−1)=x(1−x){∑n=02An(1−2x)n}V_{\mathrm{m}}^{\mathrm{E}} /\left(\mathrm{cm}^{3} \cdot \mathrm{~mol}^{-1}\right)=x(1-x)\left\{\sum_{n=0}^{2} A_{n}(1-2 x)^{n}\right\}.

The coefficients AnA_{n} and standard deviations σ(VmE)\sigma\left(V_{\mathrm{m}}^{\mathrm{E}}\right) of the fit are summarized in table 4 . The number of parameters AnA_{n} was predetermined by the statistical FF-test.

The illustration of the pressure dependence of VmEV_{\mathrm{m}}^{\mathrm{E}} is given in figure 2 for the temperature of 298.15 K . It is obvious from the data in table 3 and from the figure that the VmEV_{\mathrm{m}}^{\mathrm{E}} curves are shifted in a regular way with increasing pressure, vizv i z. decrease with increasing pressure for the same composition. The temperature dependence of VmEV_{\mathrm{m}}^{\mathrm{E}} is negligible (and follows the temperature dependence of VmEV_{\mathrm{m}}^{\mathrm{E}} at atmospheric pressure [3]).

Acknowledgements

The authors acknowledge the partial support from the Grant Agency of the Czech Republic. The work has been carried out under Grant No. 104/06/0656.

References

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JCT 07-351