Liquid Density of Mixtures of Methyl Nonafluorobutyl Ether (HFE-7100

Article pubs.acs.org/jced

Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Liquid Density of Mixtures of Methyl Nonafluorobutyl Ether (HFE-7100) + n‑Heptane at Pressures up to 80 MPa and Temperatures from 298.15 to 393.15 K Mouna Darkaoui,†,‡ Natalia Muñoz-Rujas,† Fernando Aguilar,† Ahmed El Amarti,‡ Mohamed Dakkach,‡,§ and Eduardo A. Montero*,† †

Departamento de Ingeniería Electromecánica, Escuela Politécnica Superior, Universidad de Burgos, E-09006 Burgos, Spain Laboratoire des matériaux et systèmes interfaciaux, Faculté des Sciences, Université Abdelmalek Essaâdi-Tetouan, 93030 Tetouan, Morocco § Institut Supérieur des Professions Infirmières et Techniques de Santé Tétouan − Annexe Tanger, 93040 Tétouan, Morocco ‡

ABSTRACT: High pressure and high temperature density data for the mixtures methyl nonafluorobutyl ether (HFE-7100) + n-heptane are reported in this work, at pressures from 0.1 to 80 MPa and temperatures from 298.15 to 393.15 K. The uncertainty of experimental measurements is 0.7 kg·m−3, performed by means of a vibrating tube densitometer. The Tait-like equation was used to fit the experimental density data, with low standard deviations. Moreover, the derived properties isobaric thermal expansivity and isothermal compressibility were calculated.

1. INTRODUCTION Hydrofluoroethers (HFEs), a sort of nonflammable and low toxicity fluids,1 are environmentally friendly fluids considered as potential substitutes of fluorocarbons in many applications as solvents, refrigerants, or heat transfer fluids. Such HFEs present near-zero environmental impact, as their ozone depletion potential, low global warming potential, and atmospheric lifetime are quite low.2 The HFE selected in this work is HFE-7100, methyl nonafluorobutyl ether. As pure compound or in mixtures, it can be used as cleaning and rinsing agent, fluorocarbon replacement, lubricant carrier, or low temperature heat transfer fluid. Some of its mixtures with other solvents form azeotropes. More precisely, its mixture with n-heptane presents an azeotrope close to the mole fraction x = 0.888 of HFE-7100, which can replace other solvents as HCFC-225ca/cb and CFC-113 in many applications.3 Concerning the binary mixture methyl nonafluorobutyl ether (HFE-7100) + n-heptane, in this work, we report new pρT experimental data (588 points) at pressures up to 80 MPa and temperatures between 298.15 and 393.15 K. The isobaric thermal expansion and the isothermal compressibility for the same mixture are derived for six mole fractions. No density data were found in the literature for this (HFE-7100) + n-heptane system.

ether or 1,1,1,2,2,3,3,4,4-nonafluoro-4-methoxybutane. Supplied by 3M Company, HFE-7100 has a certified mole fraction purity greater than 0.995. n-Heptane was supplied by Sigma-Aldrich with certified 0.998 mole fraction purity. Previous to its use, n-heptane was stored over type 0.4 molecular sieves to prevent moisture. Careful degassing before use of both fluids was performed. The two fluids were used without any further purification. Data of chemicals is shown in Table 1. 2.2. Measurement Technique. Experimental Procedure. The experimental densities were measured by means of a vibrating tube densitometer, Anton Paar DMA HPM. Density, ρ, was measured at several pressures, p (from 0.1 up to 80 MPa), and temperatures, T (from 298.15 to 393.15 K). The apparatus was described previously.4 The densitometer calibration was performed by the procedures proposed by Comuñas et al.5 and Lagourette et al.6 This procedure needs two reference fluids for calibration, vacuum and water in this case. The density values of water were taken from the Wagner and Pruß7 equation of state. No measurements were performed at 0.1 MPa and over 333.15 K, because of the boiling temperature of water. First, the densitometer was filled with the sample, and when the temperature and pressure desired were reached, the measurements were taken when both thermal and mechanical equilibrium of the system were reached.

2. EXPERIMENTAL SECTION 2.1. Materials. Two inseparable isomers with the same properties are present in HFE-7100, methyl nonafluorobutyl

Received: March 26, 2018 Accepted: May 29, 2018

© XXXX American Chemical Society

A

DOI: 10.1021/acs.jced.8b00245 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Purity and Related Data of Chemicals compound b

HFE 7100 n-heptane

source

formula

molar mass (g·mol−1)

stated puritya (%)

CAS number

3M Company Sigma-Aldrich

C5H3F9O C7H16

250.06 100.21

>99.5c >99.8e

163702-08-7/163702-07-6d 142-82-5

a Determined by gas chromatography (GC). bHFE 7100 = 1,1,1,2,2,3,3,4,4-nonafluoro-4-methoxybutane. cMass fraction purity, %. dBinary mixture of two isomers with mass ratio 0.5. eMole fraction purity, %.

Table 2. Experimental Densities, ρ (g·cm−3), for the Binary Mixture x HFE-7100 + (1 − x) n-Heptane at Various Temperatures T and Pressures pa T (K) x

p (MPa)

298.15

313.15

333.15

353.15

373.15

393.15

0.7706 0.7775 0.7852 0.7922 0.7987 0.8048 0.8105 0.8158 0.8209 0.8256 0.8302 0.8345 0.8387 0.8428 0.8466 0.8539

0.7472 0.7553 0.7644 0.7726 0.7799 0.7867 0.7930 0.7989 0.8044 0.8096 0.8146 0.8193 0.8239 0.8282 0.8325 0.8402

0.7226 0.7325 0.7432 0.7526 0.7610 0.7686 0.7757 0.7822 0.7883 0.7940 0.7995 0.8047 0.8096 0.8143 0.8187 0.8272

0.6965 0.7087 0.7215 0.7324 0.7419 0.7505 0.7583 0.7655 0.7722 0.7783 0.7842 0.7897 0.7949 0.7999 0.8051 0.8141

0.9068 0.9162 0.9267 0.9362 0.9448 0.9527 0.9601 0.9671 0.9735 0.9797 0.9855 0.9910 0.9963 1.0015 1.0065 1.0157

0.8763 0.8878 0.9002 0.9111 0.9209 0.9299 0.9382 0.9459 0.9530 0.9598 0.9662 0.9722 0.9779 0.9834 0.9888 0.9986

0.8442 0.8583 0.8733 0.8861 0.8973 0.9074 0.9168 0.9254 0.9332 0.9405 0.9476 0.9541 0.9604 0.9664 0.9720 0.9827

0.8092 0.8272 0.8453 0.8603 0.8733 0.8849 0.8953 0.9049 0.9137 0.9217 0.9294 0.9365 0.9433 0.9497 0.9559 0.9673

1.0388 1.0510 1.0644 1.0764 1.0872 1.0971 1.1063 1.1148 1.1229 1.1303 1.1375 1.1443 1.1508 1.1571 1.1631

1.0009 1.0159 1.0320 1.0459 1.0582 1.0694 1.0796 1.0891 1.0979 1.1062 1.1140 1.1213 1.1284 1.1350 1.1415

0.9608 0.9799 0.9993 1.0159 1.0303 1.0430 1.0548 1.0654 1.0752 1.0844 1.0931 1.1011 1.1088 1.1161 1.1230

0.9170 0.9420 0.9662 0.9858 1.0025 1.0171 1.0302 1.0421 1.0530 1.0629 1.0723 1.0810 1.0893 1.0971 1.1046

ρ (g·cm−3) 0.1509

0.3270

0.5018

0.10 1.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00 60.00 65.00 70.00 80.00 0.10 1.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00 60.00 65.00 70.00 80.00 0.10 1.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00 60.00 65.00 70.00

0.8085 0.8096 0.8149 0.8208 0.8264 0.8316 0.8366 0.8413 0.8457 0.8500 0.8540 0.8580 0.8618 0.8654 0.8690 0.8723 0.8788 0.9553 0.9569 0.9639 0.9719 0.9793 0.9862 0.9926 0.9988 1.0044 1.0099 1.0152 1.0202 1.0250 1.0297 1.0342 1.0385 1.0468 1.0985 1.1004 1.1092 1.1193 1.1285 1.1369 1.1449 1.1524 1.1594 1.1661 1.1725 1.1786 1.1845 1.1901 1.1955 1.2007

0.7918 0.7933 0.7991 0.8057 0.8119 0.8177 0.8231 0.8281 0.8329 0.8374 0.8418 0.8459 0.8500 0.8538 0.8576 0.8612 0.8680 0.9339 0.9359 0.9437 0.9528 0.9609 0.9685 0.9756 0.9821 0.9883 0.9942 0.9998 1.0051 1.0103 1.0151 1.0200 1.0245 1.0332 1.0722 1.0746 1.0846 1.0959 1.1061 1.1155 1.1243 1.1324 1.1400 1.1472 1.1540 1.1605 1.1667 1.1727 1.1785 1.1839 B



Article

Table 2. continued T (K) x

p (MPa)

298.15

313.15

333.15

353.15

373.15

393.15

1.1743

1.1534

1.1360

1.1184

1.1700 1.1850 1.2012 1.2155 1.2283 1.2401 1.2509 1.2609 1.2703 1.2791 1.2874 1.2953 1.3029 1.3101 1.3170 1.3300

1.1250 1.1436 1.1632 1.1801 1.1949 1.2083 1.2205 1.2317 1.2421 1.2519 1.2611 1.2697 1.2779 1.2857 1.2932 1.3071

1.0764 1.1002 1.1242 1.1441 1.1613 1.1765 1.1904 1.2029 1.2144 1.2251 1.2352 1.2446 1.2535 1.2620 1.2700 1.2851

1.0225 1.0544 1.0841 1.1079 1.1279 1.1453 1.1607 1.1747 1.1875 1.1992 1.2101 1.2203 1.2299 1.2390 1.2476 1.2637

1.3046 1.3220 1.3408 1.3573 1.3720 1.3855 1.3979 1.4094 1.4200 1.4301 1.4396 1.4485 1.4571 1.4652 1.4731 1.4878

1.2525 1.2743 1.2972 1.3167 1.3337 1.3491 1.3630 1.3758 1.3877 1.3987 1.4091 1.4189 1.4281 1.4369 1.4454 1.4611

1.1958 1.2242 1.2522 1.2753 1.2951 1.3124 1.3283 1.3426 1.3556 1.3678 1.3793 1.3898 1.3999 1.4095 1.4185 1.4354

1.1325 1.1706 1.2058 1.2334 1.2564 1.2764 1.2940 1.3100 1.3245 1.3378 1.3503 1.3618 1.3727 1.3829 1.3927 1.4108

1.3336 1.3514 1.3707 1.3876 1.4028 1.4166 1.4292 1.4410 1.4519 1.4621 1.4722 1.4810 1.4897 1.4981 1.5061 1.5211

1.2801 1.3025 1.3260 1.3460 1.3635 1.3792 1.3935 1.4066 1.4187 1.4299 1.4406 1.4506 1.4600 1.4690 1.4777 1.4937

1.2218 1.2510 1.2798 1.3036 1.3239 1.3417 1.3578 1.3725 1.3858 1.3983 1.4100 1.4208 1.4311 1.4409 1.4502 1.4674

1.1564 1.1960 1.2321 1.2604 1.2841 1.3045 1.3226 1.3390 1.3538 1.3674 1.3801 1.3919 1.4031 1.4136 1.4235 1.4421

ρ (g·cm−3) 0.6767

0.8515

0.8884

80.00 0.10 1.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00 60.00 65.00 70.00 80.00 0.10 1.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00 60.00 65.00 70.00 80.00 0.10 1.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00 60.00 65.00 70.00 80.00

1.2107 1.2407 1.2432 1.2537 1.2657 1.2767 1.2867 1.2961 1.3049 1.3132 1.3210 1.3285 1.3356 1.3424 1.3490 1.3552 1.3612 1.3727 1.3857 1.3886 1.4007 1.4145 1.4270 1.4384 1.4492 1.4591 1.4685 1.4774 1.4858 1.4938 1.5015 1.5089 1.5159 1.5227 1.5356 1.4170 1.4200 1.4324 1.4465 1.4593 1.4710 1.4820 1.4922 1.5018 1.5109 1.5194 1.5277 1.5355 1.5431 1.5503 1.5571 1.5703

1.1944 1.2097 1.2126 1.2247 1.2383 1.2506 1.2618 1.2721 1.2817 1.2906 1.2991 1.3071 1.3147 1.3220 1.3288 1.3356 1.3420 1.3540 1.3500 1.3534 1.3675 1.3832 1.3972 1.4100 1.4218 1.4327 1.4429 1.4525 1.4616 1.4702 1.4784 1.4862 1.4938 1.5010 1.5145 1.3804 1.3839 1.3983 1.4144 1.4287 1.4419 1.4540 1.4651 1.4755 1.4853 1.4946 1.5034 1.5118 1.5198 1.5276 1.5349 1.5488

Estimated expanded uncertainties (k = 2): temperature, U(T) = 0.03 K; pressure, U(p) = 0.04 MPa; mole fraction, U(x) = 5 × 10−4; density, U(ρ) = 0.7 kg·m−3.

a

The estimated expanded uncertainty of the temperature measured with a Pt 100 calibrated probe was 0.03 K, while the same for the pressure measured with a pressure transducer WIKA CPH 6000 was 0.04 MPa. The sensors of temperature and

pressure were calibrated before and after the measurements. The measuring cell of the DMA HPM is coupled to the Anton Paar mPDS 2000 V3 evaluation unit, in charge of measuring the oscillation period from the vibrating cell. Considering the C


Article

. dStandard Deviation,

uncertainties of the pressure, the temperature, the period of oscillation for water and vacuum, and the water density, the estimated expanded density uncertainty (k = 2) is 0.7 kg·m−3, following the EA-4/02 document.8 The pure fluids were degassed by means of an ultrasonic bath PSelecta, model Ultrason-H. A Mettler Toledo balance model MS2045 was used to prepare, by weighing, the binary mixtures inside sealed glass vials, in order to prevent evaporation. The balance shows a resolution of 10−4 g and an estimated expanded uncertainty of 0.0001 g. For mole fraction, the estimated expanded uncertainty is 5 × 10−4. As a result, the uncertainty for the excess molar volume is 0.004 cm3·mol−1.

N

ρ ( T , p) =

ρ0 (T )

(

)

(1)

ρ0 (T ) = A 0 + A1T + A 2 T 2 + A3T 3

(2)

B(T ) = B0 + B1T + B2 T 2

(3)

1 − C ln

B(T ) + p B(T ) + 0.1 MPa

where

The values of the parameters Ai, Bi, and C were calculated by simultaneous correlation of the experimental densities reported in Table 2 versus pressure and temperature. Then, Table 3 presents the Tait-correlation results obtained with this equation for the binary mixtures of x HFE-7100 + (1 − x) n-heptane. Table 3 shows that the values of all of the deviation parameters are lower than the experimental uncertainty, which means a good correlation of data. Moreover, Figure 1 describes how the measured and calculated densities with eq 1 evolve as a function of temperature at (a) p = 1 MPa and (b) p = 80 MPa, at each composition. The nonlinearity of density versus temperature, particularly at low pressures, is observed, as a large temperature range is taken into account. This nonlinear behavior of density decrease when temperature increases justifies the use of eq 1. The evolution of density with the pressure at T = 298.15 and 373.15 K is described in Figure 1c and d. It is observed that, at constant temperature, the shape of the curves is concave. This density increase with respect to pressure increase means the existence of a negative second order derivative, as the logarithmic Tait-type equation reflects.

N−m

∑iN= 1(ρiexp − ρicalc )2

; N is the number of experimental data; m is the number of parameters (eight parameters).

3. RESULTS AND DISCUSSION 3.1. Density. The measured densities of the binary mixtures x HFE-7100 + (1 − x) n-heptane (molar compositions, x = 0.1509, 0.32705, 0.5018, 0.6767, 0.8515, and 0.8884) along the 6 temperatures (interval 298.15−393.15 K) and 17 pressures (interval 0.1−80 MPa) are reported in Table 2. Because of the HFE-7100 boiling point (T = 332.85 K), density measurements at p = 0.1 MPa were limited to T = 313.15 K for the binary systems. Many of the binary mixtures would be under the vapor phase at temperatures higher than 333.15 K. 3.2. Tait Representation. The Tait equation is considered to be a good equation to correlate density values over wide temperature and pressure ranges, and is widely used by many experimental authors to fit the high pressure and high temperature density data of pure compounds and mixtures. Its main advantage is that the Tait equation gets very good results for the fitting (and interpolation) not only of density data but also for the derived properties like the isothermal compressibility and the isobaric expansion. The Tait equation has been used by the authors in previous works,4,9−11 and is as follows:

σ=

∑iN= 1(ρiexp − ρicalc )2

⎞ c ⎟. Root Mean Square Deviation, RMSD = ⎠ ρiexp

ρiexp − ρicalc

⎛ . bMaximum Deviation, MD = Max⎜100 ⎝ ρ exp − ρ calc 100 N ∑i = 1 i ρ exp i N i

Absolute Average Deviation, AAD = a

0.8884

2.8190868 −9.8568099 × 10−3 2.6828760 × 10−5 −3.1997706 × 10−8 278.28565 −1.1922810 1.2819731 × 10−3 0.084652033 0.01 0.05 2.02 × 10−4 1.93 × 10−4

0.8515

2.7429573 −9.5261630 × 10−3 2.5898484 × 10−5 −3.0907732 × 10−8 276.90505 −1.1824933 1.2669848 × 10−3 0.084932581 0.01 0.04 1.88 × 10−4 1.81 × 10−4

0.6767

2.4009752 −7.9462266 × 10−3 2.1007685 × 10−5 −2.4839936 × 10−8 279.13830 −1.1801976 1.2531003 × 10−3 0.085767166 0.01 0.05 1.60 × 10−4 1.53 × 10−4

0.5018

1.8722558 −4.7265121 × 10−3 1.1376019 × 10−5 −1.4175371 × 10−8 282.66504 −1.1717314 1.2197299 × 10−3 0.086546179 0.02 0.06 2.91 × 10−4 2.79 × 10−4

0.3270 0.1509

1.2208013 −2.1489663 × 10−3 4.1834636 × 10−6 −5.4099497 × 10−9 310.64326 −1.2385241 1.2565622 × 10−3 0.087082459 0.01 0.05 1.24 × 10−4 1.19 × 10−4

parameter

A0 (g cm−3) A1 (g cm−3 K−1) A2 (g cm−3 K−2) A3 (g cm−3 K−3) B0 (MPa) B1 (MPa K−1) B2 (MPa K−2) C AADa (%) MDb (%) σc (g·cm−3) RMSDd (g·cm−3)

1.6365832 −4.2554646 × 10−3 1.0273016 × 10−5 −1.2284774 × 10−8 279.67487 −1.1171961 1.1192069 × 10−3 0.086791814 0.01 0.04 1.35 × 10−4 1.41 × 10−4

x

Table 3. Obtained Parameters and Deviations for Density Correlation by Using eqs 1−3 for x HFE-7100 + (1 − x) n-Heptane


D



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Figure 1. Experimental values of densities, ρ, for different mole fractions of x HFE-7100 + (1 − x) n-Heptane vs (a) the temperature, T, at 1 MPa, (b) the temperature, T, at 80 MPa, (c) the pressure, p, at 298.15 K, and (d) the pressure, p, at 373.15 K: ○, x = 0.1509; △, x = 0.3270; □, x = 0.5018; ●, x = 0.6767; ▲, x = 0.8515; ■, x = 0.8884; , Tait equation (eq 1).

3.3. Excess Molar Volumes. The following equation was used to calculate the excess molar volumes VE n

VE =

⎡

∑ xiMi⎢⎣( 1 ρ ) − i=1

( 1 ρ )⎤⎥⎦ i

of the approximation of the molecules when the pressure increases, which leads to a volume reduction. Figure 2c shows excess volumes at different pressures and at T = 298 K, while Figure 2d shows the same pressures but at T = 393.15 K. The highest values of VE are shown at 393.15 K, corresponding to the spacing between the molecules, resulting in an increment on volume values. The packing effect of the molecules is boosted by the pressure increase, leading to a decrease of excess molar volumes. The fitting of VE to a Redlich−Kister equation

(4)

where xi is the mole fraction of component i in the mixture while Mi is its molar mass; n is the number of components; and ρ and ρi are the measured densities of the mixture and pure component i, respectively. The densities of pure HFE-7100 and pure n-heptane were reported in our previous works (refs 11 and 4, respectively) and used for the present VE calculations. The excess molar volumes calculated with eq 4 present a positive values for all mole fractions within the range of measured temperatures and pressures. The positive behavior corresponds to the volume expansion along the mixing process: different molecules, with different size, which approximate when mixing. The presence of an oxygen atom in the ether molecule of HFE7100 makes it slightly polar, while the hydrocarbon molecule is nonpolar. This statement means that weak interactions between the molecules will take place in the mixture, which is related to the high values of excess volumes observed. Figure 2 represents the experimental excess volumes for the binary mixture HFE7100 + heptane versus the mole composition, at several temperatures for a fixed pressure (Figure 2a and b) and at several pressures at a given temperature (Figure 2c and d). Figure 2a refers to pressure P = 1 MPa, whereas Figure 2b refers to the maximum pressure measured, P = 80 MPa. When comparing both graphs, it can be seen that, the higher the pressure is, the lower the values of excess volume are. It is a result

V E = x(1 − x)∑ zi(2x − 1)i − 1

(5)

i

is shown also in Figure 2. There, x is the mole fraction of HFE7100 and zi are the parameters of the Redlich−Kister equation. The values of the parameters, zi, and the deviations were obtained at several pressures for temperatures T = 298.15 and 393.15 K and at several temperatures for pressures at p = 1 and 80 MPa, and are shown in Table 4. 3.4. The Derived Thermodynamic Properties. The properties of thermal compressibility and isobaric expansivity, which can be derived from the densities, give more valuable information than the density itself on the volumetric properties dependence with respect to temperature and pressure. The effect of pressure on density is given by the isothermal compressibility, κT, following the equation ⎛ 1 ⎞⎛ ∂ρ ⎞ κT = ⎜ ⎟⎜ ⎟ = ⎝ ρ ⎠⎝ ∂p ⎠ T

C

(1 − C ln(

B(T ) + p B(T ) + 0.1 MPa

))(B(T) + p) (6)

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Figure 2. Experimental values of excess molar volumes for the mixtures x HFE-7100 + (1 − x) n-heptane as a function of the mole fraction at different temperatures (a) at 1 MPa and (b) at 80 MPa, where ○, 298.15 K; △, 313.15 K; □, 333.15 K; ●, 353.15 K; ▲, 373.15 K; ■, 393.15 K, and (c) at T = 298.15 K and (d) at T = 393.15 K, where ○, 0.1 MPa; ◇, 1 MPa; △, 10 MPa; □, 30 MPa; ●, 50 MPa; ■, 80 MPa; , Redlich−Kister’s equation.5

Table 4. Values of Parameters zi of eq 5 and the Corresponding Standard Deviation, σ, for Binary Mixtures of x HFE-7100 + (1 − x) n-Heptane at 298.15 and 393.15 K for Different Pressures and at 1.00 and 80.00 MPa for All of the Temperatures Measured z1 p (MPa) 0.10 1.00 10.00 25.00 50.00 80.00 p (MPa) 1.00 10.00 25.00 50.00 80.00 T (K) 298.15 313.15 333.15 353.15 373.15 393.15 T (K) 298.15 313.15

13.6531 13.5717 12.3497 10.9146 9.3177 7.9410 22.0773 17.8865 13.7766 10.1961 8.0240 13.5645 14.5448 16.0440 18.0405 19.9538 22.0696 7.9341 8.3869

z2

z3

(T = 298.15 K) 2.6676 2.6168 2.6023 2.3862 2.4604 2.5522 (T = 393.15 K) 6.5482 2.8825 2.7141 3.0159 1.0275 3.8700 0.1038 4.2554 −0.0452 3.8428 (p = 1.00 MPa) 1.0734 2.7332 1.5342 2.4724 2.0923 2.2859 2.9258 2.1629 4.4097 2.5883 6.4883 3.0057 (p = 80.00 MPa) 0.0671 2.6646 0.1346 2.3800 1.3030 1.1299 0.8139 0.4683 0.1987 0.1217

Table 4. continued z1 T (K)

σ (VE) (cm3·mol−1) 0.01 0.01 0.01 0.01 0.01 0.01

z2

z3

σ (VE) (cm3·mol−1)

(p = 80.00 MPa)

333.15

8.5959

−0.0298

2.3867

0.04

353.15

9.0956

−0.0432

2.0358

0.02

373.15

8.5427

0.1724

3.3067

0.06

393.15

8.0165

−0.1038

3.9634

0.08

In a similar way, by deriving density with respect to temperature at constant pressure, we could obtain the isobaric thermal expansivity: ⎛ 1 ⎞⎛ ∂ρ ⎞ αp = −⎜ ⎟⎜ ⎟ ⎝ ρ ⎠⎝ ∂T ⎠ p

0.05 0.07 0.07 0.08 0.08

(7)

Nevertheless, the form of functions B(T) and ρ0(T) influences the estimated isobaric thermal expansivity, as cited by refs 12 and 13. Moreover, ref 14 points out that the values reported for the isobaric thermal expansivity could vary not only due to differences in density values but also due to the fitting equation used. This temperature influence can be considered more properly deriving the isobaric thermal expansivity from the isobaric densities. Thus, at each pressure, we suppose that ρp(T) = a0 + a1T + a2T2 and then (∂ρ/∂T)p = a1 + 2a2T, and we get a set (a0, a1, a2) for each pressure. As a result, by integrating the differentiated density and also the estimated densities ρp(T) into αp = −(1/ρ(∂ρ/∂Τ)p, under

0.01 0.01 0.02 0.01 0.01 0.05 0.01 0.01 F



Article

Table 5. Isothermal Compressibility 104κT for x HFE-7100 + (1 − x) n-Heptane as a Function of Pressure p and at Different Temperatures Ta T (K) x

p (MPa)

298.15

313.15

0.3270

0.5018

0.10 1.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00 60.00 65.00 70.00 80.00 0.10 1.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00 60.00 65.00 70.00 80.00 0.10 1.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00 60.00 65.00 70.00 80.00

16.4 16.1 15.1 14.0 13.1 12.3 11.5 10.9 10.3 9.8 9.4 9.0 8.6 8.2 7.9 7.6 7.1 18.8 18.5 17.1 15.7 14.6 13.6 12.7 11.9 11.3 10.7 10.1 9.6 9.2 8.8 8.5 8.1 7.5 20.7 20.3 18.7 17.0 15.7 14.5 13.5 12.7 11.9 11.2 10.6 10.1 9.6 9.2 8.8 8.5 7.8

353.15

T (K) 373.15

x

393.15

p (MPa)

298.15

−1

κT·10 (MPa ) 18.9 18.6 22.7 17.2 20.7 15.8 18.7 14.6 17.1 13.6 15.7 12.7 14.6 12.0 13.6 11.3 12.7 10.7 12.0 10.2 11.3 9.7 10.7 9.3 10.2 8.9 9.7 8.5 9.3 8.2 8.9 7.6 8.2 21.9 21.4 26.6 19.7 23.9 17.9 21.3 16.4 19.2 15.1 17.5 14.0 16.1 13.1 14.9 12.3 13.9 11.6 13.0 11.0 12.3 10.4 11.6 9.9 11.0 9.5 10.4 9.1 9.9 8.7 9.5 8.0 8.7 24.4 23.9 30.3 21.7 26.9 19.5 23.6 17.7 21.1 16.3 19.0 15.0 17.4 14.0 16.0 13.1 14.9 12.3 13.9 11.6 13.0 11.0 12.2 10.4 11.6 9.9 11.0 9.5 10.4 9.1 9.9 8.4 9.1 4

0.1509

333.15

313.15

28.2 25.2 22.3 20.1 18.2 16.7 15.4 14.4 13.4 12.6 11.9 11.3 10.7 10.2 9.7 8.9

35.7 31.1 26.9 23.7 21.2 19.2 17.5 16.2 15.0 14.0 13.2 12.4 11.7 11.1 10.6 9.7

46.2 38.8 32.4 27.9 24.5 21.9 19.9 18.2 16.7 15.5 14.5 13.6 12.8 12.1 11.5 10.4

33.9 29.7 25.7 22.8 20.5 18.6 17.0 15.7 14.6 13.7 12.8 12.1 11.5 10.9 10.4 9.5

44.4 37.5 31.5 27.2 24.0 21.5 19.5 17.8 16.4 15.3 14.3 13.4 12.6 11.9 11.3 10.3

60.4 48.4 38.9 32.6 28.2 24.8 22.2 20.1 18.4 17.0 15.8 14.8 13.9 13.1 12.4 11.2

39.5 33.9 28.9 25.2 22.4 20.2 18.4 16.9 15.6 14.6 13.6 12.8 12.1 11.5 10.9 9.9

53.5 43.7 35.8 30.4 26.4 23.4 21.1 19.2 17.6 16.3 15.2 14.2 13.3 12.6 11.9 10.8

75.6 57.6 44.7 36.7 31.2 27.2 24.2 21.7 19.8 18.2 16.8 15.7 14.7 13.8 13.0 11.7

0.8515

0.8884

0.10 1.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00 60.00 65.00 70.00 80.00 0.10 1.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00 60.00 65.00 70.00 80.00 0.10 1.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00 60.00 65.00 70.00 80.00

22.1 21.7 19.8 18.0 16.4 15.2 14.1 13.1 12.3 11.6 11.0 10.4 9.9 9.5 9.0 8.7 8.0 22.9 22.4 20.5 18.5 16.8 15.5 14.3 13.4 12.5 11.8 11.1 10.5 10.0 9.5 9.1 8.7 8.0 23.0 22.5 20.5 18.5 16.8 15.5 14.3 13.4 12.5 11.8 11.1 10.5 10.0 9.5 9.1 8.7 8.0

353.15

373.15

393.15

43.9 37.0 31.1 26.8 23.7 21.2 19.2 17.6 16.2 15.1 14.1 13.2 12.4 11.8 11.2 10.1

60.6 48.3 38.8 32.5 28.0 24.7 22.1 20.0 18.3 16.9 15.7 14.6 13.7 12.9 12.2 11.0

88.0 64.4 48.7 39.3 33.1 28.6 25.3 22.7 20.6 18.8 17.4 16.2 15.1 14.2 13.4 12.0

46.6 38.9 32.3 27.7 24.3 21.7 19.6 17.9 16.5 15.3 14.3 13.4 12.6 11.9 11.3 10.2

65.4 51.2 40.5 33.7 28.9 25.3 22.6 20.4 18.6 17.1 15.9 14.8 13.9 13.1 12.4 11.1

96.9 69.0 51.1 40.8 34.1 29.4 25.9 23.1 20.9 19.2 17.7 16.4 15.3 14.4 13.5 12.1

46.9 39.1 32.5 27.8 24.4 21.7 19.6 17.9 16.5 15.3 14.3 13.4 12.6 11.9 11.3 10.2

66.1 51.6 40.7 33.8 28.9 25.4 22.6 20.4 18.6 17.1 15.9 14.8 13.9 13.1 12.3 11.1

98.3 69.6 51.4 41.0 34.2 29.5 25.9 23.2 21.0 19.2 17.7 16.4 15.3 14.4 13.5 12.1

−1

κT·10 (MPa ) 26.4 25.7 33.0 23.2 29.0 20.7 25.2 18.7 22.3 17.1 20.0 15.7 18.2 14.5 16.7 13.6 15.4 12.7 14.4 12.0 13.4 11.3 12.6 10.7 11.9 10.2 11.3 9.7 10.7 9.3 10.2 8.5 9.3 27.4 26.7 34.7 24.0 30.2 21.3 26.1 19.2 23.0 17.4 20.6 16.0 18.6 14.8 17.0 13.8 15.7 12.9 14.6 12.1 13.6 11.4 12.8 10.8 12.0 10.3 11.4 9.8 10.8 9.4 10.3 8.6 9.4 27.5 26.8 34.9 24.1 30.3 21.3 26.2 19.2 23.0 17.5 20.6 16.0 18.6 14.8 17.0 13.8 15.7 12.9 14.6 12.1 13.6 11.4 12.8 10.8 12.0 10.3 11.4 9.8 10.8 9.4 10.3 8.6 9.4 4

0.6767

333.15

a Estimated expanded uncertainty (k = 2): temperature, U(T) = 0.03 K; pressure, U(P) = 0.04 MPa; mole fraction, U(x) = 5 × 10−4; isothermal compressibility, U(κT) = 0.001κT.

different T, p conditions, the isobaric thermal expansivity is then obtained: αp = −

a1 + 2a 2T a0 + a1T + a 2T 2

Following the stated procedures, the isobaric thermal expansivity, αp, and the isothermal compressibility, κT, were calculated and reported in Tables 5 and 6, respectively. The increase of temperature leads to an increase of κT and αp. On the other hand, the increase of pressure leads to the decrease of κT

(8) G



Article

Table 6. Isobaric Thermal Expansion Coefficient 104αp for x HFE-7100 + (1 − x) n-Heptane as a Function of Pressure p and at Different Temperatures Ta T (K) x

p (MPa)

298.15

313.15

0.3270

0.5018

0.10 1.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00 60.00 65.00 70.00 80.00 0.10 1.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00 60.00 65.00 70.00 80.00 0.10 1.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00 60.00 65.00 70.00 80.00

13.5 13.3 13.0 12.4 12.0 11.5 11.1 10.8 10.4 10.1 9.9 9.6 9.4 9.1 9.0 8.8 8.5 14.3 14.4 13.8 13.2 12.7 12.2 11.8 11.4 10.9 10.7 10.4 10.1 9.9 9.7 9.5 9.3 9.0 15.0 15.2 14.7 14.0 13.4 12.8 12.4 11.9 11.5 11.2 10.9 10.6 10.3 10.1 9.8 9.6 9.3

353.15

T (K) 373.15

x

393.15

p (MPa)

298.15

−1

αp·10 (K ) 14.4 14.0 15.0 13.5 14.2 12.8 13.2 12.2 12.5 11.7 11.9 11.2 11.4 10.8 10.9 10.4 10.5 10.1 10.1 9.8 9.8 9.6 9.5 9.3 9.2 9.1 9.0 8.9 8.8 8.7 8.5 8.4 8.2 15.9 15.3 16.6 14.4 15.4 13.6 14.2 12.9 13.3 12.4 12.6 11.9 12.0 11.4 11.5 11.0 11.0 10.6 10.6 10.3 10.2 10.0 9.9 9.8 9.6 9.6 9.4 9.4 9.1 9.1 8.9 8.8 8.5 17.3 16.3 17.9 15.4 16.4 14.5 15.0 13.6 14.0 13.0 13.1 12.4 12.4 11.9 11.8 11.4 11.3 11.1 10.9 10.7 10.5 10.4 10.1 10.1 9.8 9.9 9.5 9.6 9.3 9.4 9.0 9.0 8.6 4

0.1509

333.15

313.15

16.1 14.9 13.7 12.8 12.1 11.5 11.0 10.5 10.1 9.8 9.4 9.1 8.9 8.7 8.4 8.0

17.3 15.7 14.2 13.2 12.3 11.6 11.0 10.5 10.1 9.7 9.3 9.0 8.8 8.5 8.2 7.7

18.6 16.6 14.8 13.5 12.5 11.7 11.1 10.5 10.0 9.6 9.3 8.9 8.7 8.4 8.0 7.5

18.0 16.4 14.9 13.8 12.9 12.1 11.5 11.0 10.5 10.1 9.8 9.5 9.1 8.9 8.6 8.2

19.6 17.4 15.5 14.2 13.1 12.3 11.6 11.0 10.5 10.0 9.6 9.3 8.9 8.6 8.4 7.9

21.3 18.6 16.3 14.7 13.4 12.4 11.6 11.0 10.4 9.9 9.5 9.0 8.7 8.4 8.1 7.6

19.6 17.5 15.7 14.3 13.3 12.5 11.8 11.2 10.7 10.3 9.9 9.5 9.2 8.9 8.7 8.2

21.5 18.7 16.4 14.7 13.5 12.5 11.7 11.0 10.5 10.0 9.6 9.2 8.8 8.5 8.3 7.8

23.7 20.0 17.1 15.1 13.7 12.6 11.7 10.9 10.2 9.7 9.2 8.8 8.5 8.1 7.8 7.3

0.8515

0.8884

0.10 1.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00 60.00 65.00 70.00 80.00 0.10 1.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00 60.00 65.00 70.00 80.00 0.10 1.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 50.00 55.00 60.00 65.00 70.00 80.00

15.5 15.7 15.1 14.4 13.7 13.1 12.6 12.1 11.7 11.3 11.0 10.7 10.4 10.1 9.9 9.7 9.3 15.9 15.7 15.4 14.7 13.9 13.3 12.8 12.2 11.8 11.4 11.1 10.7 10.5 10.2 10.0 9.7 9.4 15.9 15.7 15.4 14.7 14.0 13.3 12.8 12.3 11.9 11.5 11.1 10.8 10.5 10.3 10.0 9.8 9.4

353.15

373.15

393.15

21.1 18.6 16.5 15.1 14.0 13.1 12.4 11.7 11.2 10.7 10.3 10.0 9.6 9.3 9.1 8.6

23.4 20.0 17.4 15.6 14.3 13.3 12.4 11.7 11.1 10.6 10.2 9.8 9.4 9.1 8.8 8.3

26.1 21.7 18.4 16.2 14.7 13.5 12.5 11.7 11.0 10.5 10.0 9.5 9.2 8.8 8.5 8.0

22.0 19.3 17.0 15.5 14.3 13.4 12.7 12.0 11.5 11.0 10.6 10.2 9.9 9.6 9.3 8.8

24.9 21.0 18.0 16.2 14.8 13.7 12.8 12.1 11.5 11.0 10.5 10.1 9.8 9.4 9.1 8.6

28.1 22.8 19.1 16.9 15.2 14.0 13.0 12.2 11.5 10.9 10.4 10.0 9.6 9.3 9.0 8.4

22.2 19.4 17.1 15.6 14.4 13.5 12.7 12.1 11.5 11.1 10.7 10.3 9.9 9.6 9.4 8.9

25.1 21.1 18.1 16.2 14.8 13.8 12.9 12.2 11.5 11.0 10.6 10.2 9.8 9.5 9.2 8.7

28.4 23.1 19.2 16.9 15.3 14.1 13.1 12.2 11.6 11.0 10.5 10.1 9.6 9.3 9.0 8.4

−1

αp·10 (K ) 18.2 17.0 18.9 16.0 17.2 14.9 15.7 14.1 14.5 13.3 13.6 12.7 12.9 12.2 12.3 11.7 11.7 11.3 11.2 10.9 10.8 10.6 10.5 10.3 10.1 10.0 9.8 9.8 9.6 9.5 9.3 9.1 8.9 18.9 17.2 19.5 16.3 17.7 15.3 16.1 14.3 14.9 13.6 13.9 12.9 13.2 12.4 12.5 11.9 11.9 11.4 11.5 11.1 11.0 10.7 10.6 10.4 10.3 10.1 10.0 9.9 9.7 9.6 9.5 9.2 9.0 19.0 17.3 19.6 16.4 17.8 15.3 16.2 14.4 15.0 13.6 14.0 13.0 13.2 12.4 12.6 11.9 12.0 11.5 11.5 11.1 11.1 10.7 10.7 10.5 10.4 10.2 10.1 9.9 9.8 9.7 9.5 9.3 9.1 4

0.6767

333.15

a Estimated expanded uncertainty (k = 2): temperature, U(T) = 0.03 K; pressure, U(P) = 0.04 MPa; mole fraction, U(x) = 5 × 10−4; isobaric expansion, U(αp) = 0.003αp.

and αp. The estimated uncertainty for the isothermal compressibility is 1%, while the isobaric thermal expansivity reaches 3%, following ref 8. Similar values are reported, when using the same calculations, in other high-pressure density studies.4,15,16

4. CONCLUSIONS This work reports experimental densities for the binary mixture methyl nonafluorobutyl ether (HFE-7100) + n-heptane in the compressed liquid state. The pressure range from 0.1 to 80 MPa H



Article

(7) Wagner, W.; Pruß, A. The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. J. Phys. Chem. Ref. Data 2002, 31, 387−535. (8) Expression of the Uncertainty of Measurement in Calibration, European Cooperation for Accreditation, EA-4/02, 1999. (9) Dakkach, M.; Aguilar, F.; Alaoui, F. E. M.; Montero, E. A. Liquid density of oxygenated additive 2,4-dimethyl-3-oxapentane at pressures up to 140 MPa and temperatures from (293.15 to 393.29) K. J. Chem. Thermodyn. 2015, 80, 135−141. (10) Dakkach, M.; Aguilar, F.; Alaoui, F. E. M.; Montero, E. A. Liquid density of oxygenated additives to biofuels: 2-Butanol at pressures up to 140 MPa and temperatures from (293.15 to 393.27). J. Chem. Thermodyn. 2015, 89, 278−285. (11) Muñoz-Rujas, N.; Aguilar, F.; Bazile, J. P.; Montero, E. A. Liquid density of mixtures Methyl nonafluorobutyl ether (HFE-7100) + 2propanol at pressures up to 140 MPa and temperatures from 298.15 to 393.15 K. Fluid Phase Equilib. 2016, 429, 281−292. (12) Cerdeiriña, C. A.; Tovar, C. A.; González-Salgado, D.; Carballo, E.; Romaní, L. Isobaric thermal expansivity and thermophysical characterization of liquids and liquid mixtures. Phys. Chem. Chem. Phys. 2001, 3, 5230−5236. (13) Troncoso, J.; Bessières, D.; Cerdeiriña, C. A.; Carballo, E.; Romaní, L. Automated measuring device of (p, ρ, T) data. Application to the 1-hexanol + n-hexane system. Fluid Phase Equilib. 2003, 208, 141− 154. (14) Jacquemin, J.; Husson, P.; Mayer, V.; Cibulka, I. High-pressure volumetric properties of imidazolium-based ionic liquids: effect of the anion. J. Chem. Eng. Data 2007, 52, 2204−2211. (15) Miyake, Y.; Baylaucq, A.; Plantier, F.; Bessieres, D.; Ushiki, H.; Boned, C. High-pressure (up to 140 MPa) density and derivative properties of some (pentyl-, hexyl-, and heptyl-) amines between (293.15 and 353.15) K. J. Chem. Thermodyn. 2008, 40, 836−845. (16) Watson, G.; Lafitte, T.; Zéberg-Mikkelsen, C. K.; Baylaucq, A.; Bessières, D.; Boned, C. Volumetric and derivative properties under pressure for the system 1-propanol + toluene: A discussion of PC-SAFT and SAFT-VR. Fluid Phase Equilib. 2006, 247, 121−134.

and the temperature range from 298.15 to 393.15 K were taken to perform the measurements. No literature reference was found on the volumetric properties for the same binary system at high pressure. When correlating the experimental densities versus a Tait-type equation, a good agreement was found, showing AAD lower than 0.02%, which allows interpolation with the cited equation. Excess molar volumes and the properties isothermal compressibility and isobaric expansivity were also derived from density calculations.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +34947258916. Fax: +34947258910. E-mail: [email protected]. ORCID

Eduardo A. Montero: 0000-0001-9948-3767 Funding

M. Darkaoui acknowledges financial support for this research from the Centre National pour la Recherche Scientifique et Technique CNRST, Morocco (Pre-Doctoral Grants 2017). Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This paper is part of the Doctoral Thesis of M. Darkaoui. The research was performed along an M. Darkaoui research stay at the University of Burgos, Spain, November 2017− March 2018.

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LIST OF SYMBOLS AAD, absolute average deviation; ai, coefficients of isobaric thermal expansivity correlation; Ai, Bi, C, coefficients of density correlation; bias, average deviation; calc, calculated; exp, experimental; i, constituent identification; lit, literature; MD, maximum deviation; NP, number of experimental data points which are in our p, T ranges; p, pressure; p0, reference pressure; RMSD, root mean square deviation; T, temperature; VE, excess molar volume

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GREEK LETTERS σ, standard deviation; αp, isobaric thermal expansivity; ρ, density; ρ 0 , density at a reference pressure p 0 ; κ T , isothermal compressibility

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REFERENCES

(1) Tsai, W. T. Environmental risk assessment of hydrofluoroethers (HFEs). J. Hazard. Mater. 2005, 119, 69−78. (2) 3MTM NovecTM Engineered Fluids. https://www.3m.com/3M/ en_US/company-us/all-3m-products/?N= 5002385+8711017+8717595+8734647+3294857497&rt=r3 (last accessed March 15, 2018). (3) Durkee, J. B., II. Cleaning with Solvents: Science and Technology; Elsevier: Oxford, U.K., 2014. (4) Alaoui, F. E. M.; Montero, E. A.; Qiu, G.; Aguilar, F.; Wu, J. Liquid density of biofuel mixtures: 1-Heptanol + heptane system at pressures up to 140 MPa and temperatures from 298.15 to 393.15 K. J. Chem. Thermodyn. 2013, 65, 174−183. (5) Comuñas, M. J. P.; Bazile, J. P.; Baylaucq, A.; Boned, C. Density of Diethyl Adipate using a New Vibrating Tube Densimeter from (293.15 to 403.15) K and up to 140 MPa. Calibration and Measurements. J. Chem. Eng. Data 2008, 53, 986−994. (6) Lagourette, B.; Boned, C.; Saint-Guirons, H.; Xans, P.; Zhou, H. Densimeter calibration method versus temperature and pressure. Meas. Sci. Technol. 1992, 3, 699−703. I


Liquid Density of Mixtures of Methyl Nonafluorobutyl Ether (HFE-7100

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