(283.15 to 363.15) K at Pressures up to 66 MPa - American Chemical

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P−ρ−T Data for 1‑Butanol and Isobutyl Alcohol from (283.15 to 363.15) K at Pressures up to 66 MPa Gustavo A. Iglesias-Silva,* Micael Bravo-Sánchez, and Alejandro Estrada-Baltazar Departamento de Ingeniería Química, Instituto Tecnológico de Celaya Celaya, Gto., CP 38010, Mexico

Christian Bouchot Christian Bouchot SEPI ESIQIE IPN, EDIF. 8 3ER Piso, UPALM Zacatenco, C.P. 07738, México D.F. Mexico

Kenneth R. Hall Kenneth R. Hall Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, Texas 77843-3122, United States ABSTRACT: We present densities of pure 1-butanol and isobutyl alcohol from (283.15 to 363.15) K at pressures up to 66 MPa. We have measured densities using a vibrating tube densimeter. We use a forced path calibration method since this method depends mainly upon the mechanical properties of the cell. Experimental measurements of n-heptane have been measured to test the reliability of the apparatus. These measurements agree with a reference equation of state within 0.1 %. The new experimental densities of 1-butanol and isobutyl alcohol agree within 0.2 % with densities from the literature.

1. INTRODUCTION Accurate experimental densities at high pressure are important for the development of theories or the development of equations of state. Also they are useful for the design of high pressure equipment in the industry. In this work we have measured the density of 1-butanol and isobutyl alcohol using a vibrating tube densimeter from (283.15 to 363.15) K at pressures up to 66 MPa. We have calibrated the densimeter considering parameters from the material of the cell. This allows a better stability in the calibration and one can cover a higher range in pressure and temperature. To test the reliability of the apparatus, we measure densities of n-heptane from (283.15 to 363.15) K at pressures up to 66 MPa. We compare these densities with the reference equation of state from REFPROP.1

Table 1. Sample Information source

CAS No.

water n-heptane 1-butanol isobutanol

Fermont Fermont Sigma-Aldrich Fermont

7732-18-5 142-82-5 71-36-3 78-83-1

a

initial purity mole purification analysis fraction method methoda 0.9995 0.999 0.999 0.998

none none none none

GC GC GC GC

Gas chromatograph analysis provided by the supplier.

oscillation frequency of the tube. The assumption is that the sample volume trapped between the oscillation nodes is constant. The setup of the apparatus consists of a discharge− charged, a control temperature/pressure, and a data acquisition sections. Figure 1 shows a schematic of the apparatus. The first section consists of the vibrating tube cell (DMA 512P, Anton Paar), which is charged through a high pressure generator (model 62-6-10, HiP). The pressure pump is connected to the feed tank using stainless steel high pressure tubing. This system is also used to discharge the sample by means of a vacuum

2. EXPERIMENTAL SECTION This paper presents isothermal density data for 1-butanol and isobutyl alcohol at (283.15 to 363.15) K, at pressures up to 66 MPa. The 1-butanol and isobutyl alcohol came from SigmaAldrich having a purity of 0.999 and 0.998 mole fractions, respectively. Table 1 shows the purity and sources of the samples. The vibrating tube densimeter uses an indirect method to obtain the density at a given pressure and temperature from the © 2015 American Chemical Society

chemical name

Received: November 10, 2014 Accepted: March 1, 2015 Published: March 13, 2015 1076

DOI: 10.1021/je5010214 J. Chem. Eng. Data 2015, 60, 1076−1090

Journal of Chemical & Engineering Data

Article

Figure 1. Schematic of the apparatus: FC, frequency counter; PP, pressure pump; T, thermometer; RB, recirculating bath; F, feed; PI, pressure indicator; PT pressure transducer; VI, vacuum indicator; VC, vacuum pump.

Figure 3. Percentage density deviations for water from eq 2: ●, 283.15 K; ▲ 293.15 K; ◆, 303.15 K; ○, 313.15 K; △, 323.15 K; ◊, 333.15 K; ■, 343.15 K; □, 353.15 K; ▼, 363.15 K.

Figure 2. Percentage deviation of oscillation period at vacuum from eq 7.

pump (DS-102, Varian). The cell is a Hastelloy C-256 U-tube with a platinum resistance thermometer inside a thermostatic jacket. The total internal volume of the tube is 1.5 cm3. The second section encompasses the pressure generator which it is used to control manually the pressure in the DMA 512P cell. The pressure is measured using two pressure transducers (DRUCK, DPI 145). One transducer is used to measure the pressure from (0.1 to 35) MPa with an uncertainty of 0.004 MPa while another transducer is used to measure from 35 to 69 with an uncertainty of 0.008 MPa. The temperature in the cell is controlled using a circulating bath (Polyscience) and the temperature in the cell is measured with a Pt-100 thermometer (HartScientific, 1502A) with an uncertainty of 0.01 K on ITS-90. In the last section, data acquisition of the frequency is done using a vibrating tube densimeter (DMA 5000, Anton Paar). All devices are placed in a metallic structure and each one of them has its own section with vibration isolation pads. Vibrating Tube Calibration. There exists a great variety of calibration methods for the vibrating tube densimeter based

upon the first order spring model. In this work, we have used the forced path calibration method2 (FPCM). This model presents various advantages over other models: (a) reduce the dependence of the density data with the reference substances; (b) the model parameters are related to the mechanical properties of the measurement cell; (c) the density uncertainty remains of the same order in greater temperature and pressure intervals; and (d) the calibration can be used in different phases. We use the equation for the FPCM proposed by Bouchot and Richon3 ρ (T , P ) =

⎫ M 0 ⎧ K (T , P ) τ 2(T , P) ⎬ ⎨ − 1 Vi (T , P) ⎩ K (T , P = 0) τ 2(T , P = 0) ⎭ (1)

where ρ is the density of the fluid; Vi(T,P) is the internal volume of the tube; M0 is the vibrating mass of the tube under vacuum; K is the transversal stiffness of the tube; and τ is the oscillating period. Bouchot and Richon3 consider the geometry 1077


P/MPa

0.1010 0.2676 0.5508 0.8786 0.9913 2.0202 2.9148 4.9465 7.0348 9.0216 9.9919 11.9587 15.0112 18.0474 20.0454 22.0565 25.0441 28.0463 30.0517 32.0548 32.9713 32.9996 34.0165 34.9595 37.9430 40.0040 42.0579 44.9399 48.0224 49.9964 51.9818 54.9650 57.9493 59.9964 62.0254 64.9975 65.9710 0.1008 0.3160 0.5696 0.8607 1.0888 2.1097

T/K

283.152 283.152 283.151 283.154 283.153 283.152 283.153 283.153 283.152 283.153 283.152 283.151 283.152 283.151 283.154 283.155 283.152 283.152 283.154 283.151 283.151 283.152 283.153 283.152 283.152 283.153 283.153 283.152 283.154 283.152 283.152 283.153 283.152 283.154 283.151 283.153 283.156 313.152 313.155 313.155 313.156 313.153 313.153

0.692398 0.692646 0.692799 0.693177 0.693192 0.694161 0.694997 0.696597 0.698638 0.700052 0.700869 0.702480 0.704783 0.706965 0.708637 0.709841 0.712000 0.714050 0.715435 0.716688 0.717342 0.717432 0.718012 0.718734 0.720455 0.721755 0.723102 0.724839 0.726526 0.727851 0.728904 0.730736 0.732407 0.733467 0.734345 0.735980 0.736499 0.666870 0.667185 0.667234 0.667671 0.668002 0.669053

ρ/g·cm−3

288.152 288.150 288.151 288.150 288.153 288.152 288.150 288.152 288.151 288.150 288.150 288.151 288.152 288.151 288.152 288.152 288.151 288.151 288.151 288.150 288.151 288.152 288.151 288.152 288.150 288.150 288.152 288.150 288.153 288.151 288.150 288.150 288.154 288.154 288.150 288.150 288.150 318.152 318.155 318.156 318.156 318.155 318.155

T/K 0.1020 0.3913 0.5544 0.8827 0.9891 2.0575 2.9178 5.0414 7.0888 9.0186 10.0399 12.0716 15.0014 17.9682 20.0676 22.0196 25.0015 28.0257 30.0347 32.0840 33.0500 33.0962 34.0356 35.0770 37.9929 40.0408 42.0228 44.9793 48.0451 50.0676 52.0320 55.0769 58.0040 59.9875 61.9736 64.9416 66.0254 0.1007 0.3363 0.5909 0.8910 1.1057 1.9291

P/MPa 0.688224 0.688682 0.688232 0.689214 0.688618 0.689559 0.690931 0.692738 0.693960 0.695614 0.696278 0.698584 0.700836 0.703230 0.704758 0.705649 0.707645 0.709735 0.711006 0.712959 0.713818 0.713930 0.714067 0.714575 0.716378 0.717608 0.718735 0.720398 0.723180 0.724245 0.724841 0.726211 0.729214 0.729723 0.731101 0.731745 0.732751 0.662812 0.663228 0.663443 0.663766 0.663940 0.664905

ρ/g·cm−3 293.152 293.156 293.156 293.152 293.156 293.155 293.155 293.155 293.156 293.155 293.155 293.155 293.155 293.156 293.156 293.154 293.156 293.154 293.156 293.156 293.150 293.155 293.155 293.154 293.156 293.155 293.155 293.154 293.156 293.156 293.156 293.155 293.151 293.156 293.157 293.156 293.152 323.152 323.150 323.155 323.156 323.155 323.152

T/K 0.1005 0.3052 0.4764 0.8251 1.0452 1.9717 3.0606 5.0110 7.0968 9.0421 10.0357 11.9465 14.9406 17.8886 19.9916 21.9871 24.9832 27.9860 29.9758 32.2324 33.1508 33.1497 34.0989 34.9996 38.0265 40.0810 42.0992 45.0682 48.0215 50.0845 52.0324 54.9655 58.0719 60.0183 61.9622 64.9910 66.0452 0.1023 0.2961 0.5284 0.9207 0.9942 2.0069

P/MPa 0.683714 0.684504 0.684708 0.684796 0.685167 0.685978 0.686787 0.688859 0.690796 0.692394 0.693252 0.694459 0.697266 0.698789 0.701345 0.701769 0.704200 0.706659 0.708599 0.710098 0.710425 0.710401 0.710557 0.711530 0.712948 0.714898 0.716347 0.718234 0.720258 0.721322 0.722789 0.724479 0.726215 0.727310 0.728261 0.729973 0.730500 0.658378 0.658710 0.658782 0.659343 0.659429 0.660610

ρ/g·cm−3

Table 2. Pressure−Density−Temperature Experimental Measurements for n-Heptanea 298.152 298.154 298.156 298.155 298.156 298.154 298.154 298.154 298.155 298.156 298.152 298.156 298.156 298.156 298.155 298.153 298.155 298.156 298.156 298.156 298.150 298.156 298.155 298.156 298.152 298.152 298.154 298.150 298.154 298.153 298.156 298.151 298.152 298.152 298.153 298.151 298.156 328.152 328.153 328.156 328.155 328.152 328.155

T/K 0.1023 0.3054 0.4937 0.8545 1.0126 1.9809 3.1678 5.0676 7.0653 9.1209 10.1066 11.9702 15.2197 17.9841 20.1278 22.0042 25.0805 28.0402 30.0891 32.0339 33.1128 33.0927 33.9243 35.2166 38.0969 40.1613 42.0285 45.0209 48.1066 50.0681 52.0197 55.0160 57.9309 59.9144 62.0363 65.0175 66.1184 0.1008 0.2899 0.5010 0.8975 0.9941 1.9888

P/MPa 0.679807 0.680336 0.680581 0.680896 0.680891 0.681933 0.682970 0.684841 0.686383 0.688480 0.689119 0.689977 0.693294 0.694869 0.696696 0.699062 0.701290 0.703578 0.704725 0.706093 0.707026 0.706936 0.706971 0.707884 0.709948 0.711975 0.713324 0.715087 0.717001 0.718317 0.719461 0.721123 0.723027 0.724031 0.725393 0.726954 0.727501 0.653868 0.654182 0.654211 0.654815 0.655012 0.656162

ρ/g·cm−3 303.152 303.152 303.151 303.155 303.153 303.151 303.156 303.153 303.156 303.156 303.156 303.155 303.155 303.156 303.154 303.154 303.155 303.156 303.156 303.154 303.151 303.152 303.151 303.154 303.155 303.151 303.153 303.153 303.155 303.153 303.151 303.151 303.151 303.154 303.152 303.151 303.154 333.152 333.156 333.154 333.155 333.156 333.154

T/K 0.1007 0.3041 0.4989 0.9006 0.9791 1.9776 2.9649 4.9304 7.0456 8.8582 10.0139 11.9751 15.0436 18.0213 19.9744 21.9196 24.9917 27.9334 29.9904 31.9578 32.8621 33.1117 34.0807 34.9799 37.9510 39.9035 42.0138 44.8962 47.9514 50.0653 52.0726 55.0745 57.9893 59.9786 62.0524 64.9882 66.0297 0.1004 0.3035 0.5326 0.8978 1.0030 1.9872

P/MPa 0.675559 0.675598 0.675770 0.675904 0.676053 0.677270 0.678337 0.680060 0.682343 0.683448 0.684334 0.686610 0.689150 0.692198 0.693813 0.695403 0.697736 0.699906 0.701007 0.702727 0.703514 0.703900 0.704468 0.705109 0.707216 0.708418 0.709635 0.711236 0.713224 0.714711 0.715915 0.717452 0.719654 0.720537 0.721855 0.723925 0.724328 0.649302 0.649622 0.649653 0.650259 0.650554 0.651687

ρ/g·cm−3 308.152 308.155 308.153 308.150 308.154 308.151 308.151 308.151 308.155 308.153 308.153 308.150 308.156 308.150 308.152 308.151 308.152 308.151 308.154 308.152 308.152 308.151 308.154 308.156 308.152 308.153 308.155 308.154 308.155 308.154 308.155 308.152 308.153 308.155 308.154 308.154 308.156 338.152 338.154 338.155 338.153 338.155 338.156

T/K 0.1050 0.2743 0.4941 0.8033 1.0395 1.9167 2.9807 4.9902 6.9649 8.8643 9.8631 12.0086 15.0687 17.8498 19.9302 21.9883 25.0122 27.9552 29.9062 31.9287 32.9414 32.8859 34.0108 34.9493 37.9712 40.0114 41.9981 45.0166 48.0334 50.0436 51.9774 54.9819 58.0089 60.0300 61.9848 64.9805 66.0878 0.1004 0.3098 0.5616 0.8985 1.0141 2.0002

P/MPa

0.671006 0.671143 0.671318 0.671687 0.672093 0.672909 0.674097 0.676132 0.678143 0.679887 0.680761 0.682857 0.685368 0.687815 0.689488 0.691177 0.693658 0.695718 0.696905 0.698302 0.698960 0.699002 0.700438 0.701078 0.703176 0.704309 0.705614 0.707854 0.709906 0.711265 0.712584 0.714563 0.716265 0.717688 0.718959 0.720569 0.721543 0.644915 0.645161 0.645341 0.645924 0.646212 0.647409

ρ/g·cm−3

Journal of Chemical & Engineering Data Article

1078


P/MPa

3.1370 5.1118 6.9218 9.2107 10.2093 12.0197 15.0586 17.9211 19.9319 22.0582 24.8616 27.8687 29.9568 32.1071 32.9803 33.0022 33.9812 35.0454 38.1266 39.9969 41.9784 44.9463 47.8797 50.0208 52.0974 54.9240 58.0815 59.9322 62.0040 64.9541 66.1131 0.1051 0.2973 0.5203 0.9117 1.0177 1.9946 2.9683 4.9948 6.9766 9.0026 10.0604 12.0245

T/K

313.155 313.152 313.151 313.155 313.151 313.151 313.150 313.150 313.151 313.155 313.150 313.152 313.152 313.154 313.153 313.154 313.153 313.155 313.154 313.156 313.153 313.155 313.154 313.156 313.154 313.152 313.155 313.153 313.154 313.155 313.154 343.152 343.151 343.152 343.151 343.150 343.153 343.152 343.151 343.152 343.154 343.152 343.153

Table 2. continued

0.670192 0.672198 0.674169 0.676379 0.677309 0.679079 0.681665 0.684308 0.686100 0.687733 0.690068 0.692385 0.693806 0.695430 0.696141 0.696147 0.697086 0.697948 0.700098 0.701327 0.702778 0.704758 0.706851 0.708330 0.709812 0.711549 0.713474 0.714707 0.716103 0.717814 0.718367 0.640758 0.640918 0.641218 0.641765 0.641938 0.643242 0.644553 0.647152 0.649726 0.652141 0.653267 0.655625

ρ/g·cm−3

318.152 318.156 318.156 318.153 318.155 318.150 318.156 318.154 318.155 318.155 318.156 318.156 318.155 318.156 318.152 318.155 318.156 318.156 318.152 318.155 318.156 318.153 318.154 318.156 318.156 318.155 318.154 318.152 318.156 318.155 318.151 348.152 348.156 348.155 348.150 348.155 348.153 348.150 348.150 348.156 348.156 348.155 348.156

T/K 2.9332 5.0208 6.9267 8.9890 10.0745 11.8960 14.8001 18.1024 19.9851 22.0937 24.8728 27.9094 29.9975 31.9571 33.0156 33.1796 34.1103 35.0476 37.8384 40.0925 41.9960 44.8840 47.9444 49.9502 52.0373 54.9442 57.9723 59.9225 61.9300 65.0218 66.0275 0.1003 0.2917 0.4622 0.8598 0.9742 1.9749 3.0511 5.0940 7.0502 9.0032 10.0254 12.1869

P/MPa 0.665972 0.668355 0.670309 0.672331 0.673533 0.675253 0.678075 0.681046 0.682727 0.684679 0.686865 0.689380 0.691196 0.692414 0.693259 0.693331 0.694119 0.694934 0.697046 0.698439 0.699600 0.701561 0.703663 0.705200 0.706412 0.708215 0.710506 0.711605 0.712850 0.714898 0.715438 0.636109 0.636475 0.636505 0.637192 0.637393 0.638781 0.640295 0.643002 0.645632 0.648038 0.649256 0.651830

ρ/g·cm−3 323.153 323.154 323.154 323.153 323.155 323.155 323.154 323.151 323.153 323.155 323.154 323.156 323.156 323.155 323.156 323.152 323.154 323.153 323.155 323.156 323.155 323.156 323.153 323.150 323.153 323.152 323.150 323.152 323.154 323.152 323.156 353.152 353.150 353.155 353.152 353.152 353.156 353.154 353.150 353.152 353.154 353.151 353.151

T/K 2.9666 4.9962 7.0421 9.0299 10.0897 11.9137 15.1107 17.9807 20.0378 21.9949 24.9934 27.9584 30.0546 32.0792 33.0674 33.1032 34.0808 35.1130 37.9528 40.0470 42.0111 44.9369 48.0254 49.9335 52.1143 54.9635 58.0449 60.0498 62.1310 64.9987 66.1312 0.1005 0.3360 0.5726 0.9260 1.0164 2.1134 2.9921 4.9639 7.0009 9.0623 10.0050 12.1275

P/MPa 0.661806 0.663968 0.666276 0.667858 0.669742 0.670973 0.674373 0.677251 0.678710 0.680737 0.683213 0.685975 0.687083 0.689177 0.689946 0.689972 0.690434 0.691624 0.693659 0.695097 0.696516 0.698783 0.700814 0.702105 0.703681 0.705509 0.707475 0.708827 0.710008 0.711842 0.712551 0.631649 0.631995 0.632233 0.632774 0.632950 0.634631 0.635919 0.638644 0.641284 0.643911 0.645176 0.647788

ρ/g·cm−3 328.151 328.151 328.155 328.154 328.155 328.156 328.156 328.156 328.156 328.156 328.151 328.150 328.153 328.153 328.150 328.154 328.153 328.150 328.150 328.152 328.153 328.150 328.150 328.150 328.153 328.150 328.151 328.150 328.150 328.150 328.150 358.152 358.155 358.155 358.151 358.154 358.156 358.154 358.151 358.156 358.156 358.155 358.154

T/K 2.9967 5.0134 6.9749 9.0170 10.0400 12.2096 15.0548 18.0613 20.2790 22.0129 24.9241 27.9792 29.9583 32.0595 33.0655 33.1072 34.0134 35.0296 38.0098 39.9690 41.9588 44.9526 47.9775 49.9265 51.9969 54.9466 57.9387 59.9909 61.9815 65.0316 66.0462 0.1004 0.2641 0.5084 0.9268 1.0139 2.0839 3.0212 4.9300 6.9935 9.0302 10.0727 12.1368

P/MPa 0.657408 0.659794 0.662023 0.664204 0.665257 0.667562 0.670204 0.673216 0.675247 0.676775 0.679489 0.682036 0.683395 0.685102 0.685969 0.685992 0.687010 0.687796 0.690025 0.691415 0.692865 0.695094 0.697371 0.698804 0.700259 0.702284 0.704221 0.705640 0.707057 0.708835 0.709499 0.626935 0.627168 0.627316 0.628098 0.628327 0.629903 0.631365 0.634077 0.637086 0.639755 0.641066 0.643735

ρ/g·cm−3 333.155 333.150 333.152 333.153 333.153 333.156 333.155 333.156 333.156 333.151 333.156 333.154 333.151 333.150 333.153 333.156 333.150 333.151 333.150 333.151 333.153 333.152 333.150 333.152 333.150 333.152 333.150 333.152 333.150 333.152 333.151 363.152 363.155 363.154 363.154 363.155 363.155 363.155 363.152 363.156 363.156 363.155 363.152

T/K 3.0234 4.9974 7.0024 9.0320 10.2095 12.0111 15.0084 17.9919 20.0359 22.0336 25.0271 28.0399 30.0156 32.0671 32.9769 33.0727 34.0859 35.0754 37.8937 40.1109 41.9468 44.9740 47.9356 49.9196 51.9533 54.8759 58.0572 59.9927 62.0486 64.9704 66.0050 0.1041 0.3340 0.6017 0.8929 1.0347 1.9860 2.9404 4.9792 6.9202 8.9648 9.9595 11.9707

P/MPa 0.653063 0.655338 0.657844 0.660047 0.661268 0.663322 0.666206 0.669217 0.671108 0.672882 0.675678 0.678188 0.679579 0.681185 0.681946 0.682004 0.683474 0.684235 0.686324 0.687848 0.689191 0.691567 0.693899 0.695372 0.696893 0.699008 0.700988 0.702482 0.703927 0.705650 0.706481 0.622138 0.622474 0.622649 0.623267 0.623668 0.625081 0.626678 0.629757 0.632642 0.635395 0.636563 0.639421

ρ/g·cm−3 338.154 338.154 338.156 338.156 338.152 338.156 338.150 338.155 338.153 338.150 338.150 338.156 338.155 338.156 338.152 338.156 338.155 338.151 338.156 338.155 338.154 338.153 338.152 338.153 338.151 338.156 338.152 338.151 338.156 338.151 338.151

T/K 2.9361 5.0186 6.9173 9.0469 10.0336 11.9594 14.8849 17.9558 19.9270 22.0411 25.0262 27.9755 29.9937 31.9489 32.8815 32.8815 33.9374 35.0124 37.9621 39.9869 41.9899 44.9782 47.9714 49.9986 52.1272 54.9922 57.9399 60.0138 62.0735 65.0119 66.0568

P/MPa

0.648694 0.651205 0.653552 0.656063 0.657126 0.659361 0.662203 0.665481 0.667369 0.669319 0.672169 0.674704 0.676134 0.677899 0.678515 0.678499 0.679921 0.680879 0.683240 0.684582 0.686092 0.688463 0.690744 0.692380 0.693976 0.696066 0.697820 0.699459 0.700918 0.702688 0.703550

ρ/g·cm−3


1079


a

1080

14.9275 17.9752 19.9850 22.0328 25.0905 28.0447 30.0820 32.1696 33.0533 33.0968 34.0341 35.0301 37.9432 40.0123 41.9722 44.9273 47.9079 50.0589 52.0262 54.9185 57.9862 59.9444 61.9665 65.0699 66.0592

343.154 343.154 343.153 343.155 343.154 343.154 343.151 343.155 343.150 343.152 343.156 343.155 343.155 343.154 343.155 343.152 343.153 343.155 343.150 343.156 343.156 343.153 343.152 343.151 343.153

0.658769 0.661975 0.664000 0.666001 0.668930 0.671724 0.673379 0.675296 0.676043 0.676076 0.676976 0.677808 0.680185 0.681817 0.683353 0.685751 0.688000 0.689668 0.691103 0.693158 0.695230 0.696690 0.697921 0.699939 0.700533

ρ/g·cm−3

348.155 348.156 348.154 348.152 348.156 348.155 348.154 348.154 348.156 348.154 348.153 348.155 348.151 348.155 348.156 348.152 348.150 348.154 348.154 348.153 348.155 348.156 348.150 348.152 348.154

T/K 14.7920 17.8990 20.1114 22.1634 25.0998 28.0801 30.1489 32.1613 32.9416 32.9352 33.9586 35.0446 37.9374 40.0256 42.0658 45.0506 47.9147 49.9498 52.1668 55.0219 57.9453 60.0300 62.0633 64.9416 66.1534

P/MPa 0.654622 0.658098 0.660386 0.662539 0.665329 0.668108 0.670002 0.671799 0.672463 0.672452 0.673504 0.674428 0.676834 0.678502 0.680230 0.682511 0.684825 0.686336 0.688088 0.690168 0.692261 0.693748 0.695106 0.696910 0.697788

ρ/g·cm−3 353.153 353.150 353.150 353.150 353.154 353.154 353.151 353.154 353.153 353.152 353.156 353.153 353.152 353.150 353.153 353.151 353.151 353.152 353.151 353.155 353.155 353.153 353.156 353.153 353.156

T/K 14.9542 17.9774 19.9370 21.8936 24.9082 27.8503 29.9362 31.8760 32.9110 32.9608 33.9637 34.9454 37.9131 40.1428 42.0673 45.0017 48.0292 50.1451 52.0822 55.1322 57.9803 60.0984 62.0425 65.0627 66.0243

P/MPa

Standard uncertainties are u(ρ) = 0.0004 g·cm−3, u(P) = 0.008 MPa, u(T) = 0.01 K.

P/MPa

T/K

Table 2. continued 0.651028 0.654406 0.656492 0.658507 0.661562 0.664482 0.666345 0.668022 0.668934 0.669075 0.670126 0.670985 0.673509 0.675336 0.677003 0.679292 0.681775 0.683478 0.685052 0.687213 0.689013 0.690731 0.692223 0.694154 0.694802

ρ/g·cm−3 358.154 358.152 358.156 358.153 358.154 358.152 358.155 358.151 358.150 358.154 358.152 358.153 358.152 358.153 358.154 358.156 358.153 358.150 358.152 358.152 358.155 358.150 358.152 358.153 358.151

T/K 14.9049 17.9654 20.1620 22.1746 25.0594 28.0352 30.0019 31.9777 32.7926 33.0393 33.8500 35.0265 37.8723 40.0374 42.1001 45.0540 47.9581 50.0379 52.0807 55.0734 57.9184 60.0427 62.0665 64.9861 66.1086

P/MPa 0.646944 0.650491 0.652870 0.654965 0.657993 0.660974 0.662532 0.664488 0.665093 0.665404 0.666525 0.667567 0.669996 0.671748 0.673454 0.675954 0.678424 0.680129 0.681850 0.684059 0.685685 0.687680 0.689111 0.691283 0.692023

ρ/g·cm−3 363.155 363.153 363.154 363.156 363.155 363.152 363.152 363.152 363.153 363.153 363.151 363.152 363.151 363.154 363.152 363.156 363.152 363.151 363.154 363.151 363.153 363.152 363.155 363.155 363.155

T/K 14.9355 17.9733 19.9399 21.9329 24.8722 27.9927 30.0623 31.9611 33.0533 33.0326 33.9995 35.0283 37.9192 39.9160 42.0155 44.9868 47.9472 50.0503 52.0226 54.9404 57.9165 59.9800 62.0429 64.9241 66.0884

P/MPa 0.642887 0.646544 0.648708 0.650806 0.654024 0.657078 0.659006 0.660630 0.661633 0.661606 0.663017 0.664030 0.666495 0.668059 0.669917 0.672551 0.675063 0.676807 0.678457 0.680815 0.682780 0.684625 0.686168 0.688267 0.689169

ρ/g·cm−3 T/K

P/MPa

ρ/g·cm−3




Article

at P = 0, and we correlated them as

and the mechanical properties of the tube to obtain ⎛ M ⎞⎛ ⎡ ⎞⎧ ⎪ ⎛ Δr 4(T , P) ⎞ 1 ⎢⎜ 4 ⎟⎨ ρF (T , P) = ⎜⎜ 0 ⎟⎟⎜ 2 ⎟ ⎪ ⎝ Lref 0 ⎠⎝ πri (T , P)δL ⎠⎩⎢⎣⎝ Δr (T , P = 0) ⎠

τ(T , P = 0) = 3719.36 + 3.73326·10‐1T + 2.25992·10−4T 2 (7)

Figure 2 shows the relative deviation of the equation with the experimental oscillating period. Then, we use eq 7 to obtain the gradient, (∂τ/∂T). Laznickova and Huemer7 have shown that this point is more stable and independent of time. In our apparatus the standard deviation of replicate measurements at vacuum taken over a period of 400 min is 0.006 μs. Finally the oscillating period at vacuum and at any temperature is corrected using the gradient

⎫ γ ⎞⎞⎤ τ 2(T , P) ⎛ ⎪ ⎛ ⎬ × exp⎜ −3P ⎜γ1 + 2 P ⎟⎟⎥ 2 − 1⎪ ⎝ ⎝ 2 ⎠⎠⎦⎥ τ (T , P = 0) ⎭ (2)

where τ(T,P) is the oscillating period at different temperatures and pressures; Lref0 is the length of the tube at vacuum and at reference temperature; and δL is the correction of the tube length due to temperature and pressure. In eq 2, the radii differences are Δr 4(T , P) = re4 − ri4

τ(T , P = 0) = τ(Tref , P = 0) +

4 Δr 4(T , P = 0) = re0 − ri04

and

where e and i stand for external and internal radiuses of the vibrating tube, respectively. The radii at vacuum are calculated as Bouchot and Richon3 but with the linear dilation coefficient of Hastelloy C-276 α(T ) = 8.78646 + 13.942541· 10−3T − 1.65722· 10‐5T 2 (4)

where the temperature is in K and the linear dilation coefficient is in μm/(m·K). In this work we use ri00 = 0.1073 cm and re00 = 0.1588 cm. For the calculation of the internal and external radius at different pressures and temperatures, we calculate the radiuses using the Lamé equations4 as formulated by Bouchot and Renon.3 The only difference with their equation is that we have included a reference pressure rj0 +

{

r j20 + 4 1 −

rj =

{

2 i0

2 e 0 ref 2 i0

)}( )( )( )}

( 1 −E υ )( r Pr −−r r P

2 1−

2 e0

( 1 −E υ

1+υ E

2 2 ri0 (P − Pref )re0 2 re0 − ri02

)

dρ =

2 ri02P − re0 Pref

⎛ ∂ρ ⎞2 2 2 ⎟ (dx) + dρ app ∂x ⎠ y

∑ ⎜⎝ x

2 re0 − ri02

for j = i or e

(8)

The oscillating period at a reference temperature is a local point chosen within a cloud of point of the isotherm. This point will be selected such as it is in the middle of the dispersion of the oscillating period. Once the expression for the oscillating period at vacuum is obtained, then the calibration parameters are obtained by a curve fitting of eq 2. We measured the oscillating period of the vibrating tube with HPLC water from (283.15 to 363.15) K and at pressures up to 66 MPa. Density values are taken from the standard reference equation of state of water developed by Wagner and Pruss.8 This equation has an uncertainty in density of less than 0.02% in the liquid region. The final values for the calibration parameters are M0/Lref0 = 0.331997·10−1 kg·m−1; γ1 = 9.97685·10−6 MPa−1; and γ2 = 1.06102·10−12 MPa−2. Figure 3 shows the quality of the calibration by comparing the densities from the calibration with the densities from the equation of state.8 The uncertainty in the experimental density measurements is calculated using a propagation error formula9

(3)

+ 8.1353·10−9T 3

⎛ ∂τ ⎞ ⎜ ⎟ (T − T ) ref ⎝ ∂T ⎠

(9)

(5)

where E is the temperature dependence Young modulus5 in MPa of Hastelloy C-276 given by E = 2.05· 105 + 121167.04 ⎡ 1 ⎢ ×⎢ − 1354.196 exp ⎢⎣ exp 298.15 − 1

(

)

1

( 1354.196 ) T

⎤ ⎥ ⎥ − 1 ⎥⎦

(6)

and υ is the Poisson coefficient.5 In this work, υ is considered temperature independent and equal to 0.307. Equation 6 represents the experimental Young modulus within the experimental relative uncertainty (1 %) suggested byVarshni.6 The calibration procedure consists of measuring the oscillation period at vacuum in the temperature range of interest, and also of estimating the calibration parameters (M0/Lref 0), γ1, and γ2. Laznickova and Huemer7 and Bouchot and Renon3 indicate that if one uses vacuum conditions as a reference point, the calibration not only depends upon temperature but also of time. To correct the instability of the calibration with time, we follow the procedure given by Laznickova and Huemer.7 We measure the oscillating period at different temperatures and

Figure 4. Percentage density deviations of experimental measurements of n-heptane from REFPROP1 equation of state: ●, 283.15 K;, 288.15 K; ▼, 293.15 K;, 298.15 K; ■, 303.15 K; □, 308.15 K; ◆, 313.15 K; ◊, 318.15 K; ▲, 323.15 K; ▽, 328.15 K; ⬢ 333.15 K; ⬡, 338.15 K; dotted circle, 343.15 K; dotted diamond, 348.15 K; dotted triangle up, 353.15 K; dotted triangle down, 358.15 K; dotted square, 363.15 K. 1081


P/MPa

0.1012 0.2676 0.5508 0.8786 0.9913 2.0202 2.9148 4.9465 7.0348 9.0216 9.9919 11.959 15.011 18.047 20.045 22.057 25.044 28.046 30.052 32.971 32.970 34.017 34.960 37.943 40.004 42.058 44.940 48.022 49.996 51.982 54.965 57.949 59.996 62.025 64.998 65.971

0.1031 0.3160 0.5696 0.8607 1.0888 2.1097

T/K

283.157 283.152 283.151 283.154 283.153 283.152 283.153 283.153 283.152 283.153 283.152 283.151 283.152 283.151 283.154 283.155 283.152 283.152 283.154 283.151 283.152 283.153 283.152 283.152 283.153 283.153 283.152 283.154 283.152 283.152 283.153 283.152 283.154 283.151 283.153 283.156

313.154 313.155 313.155 313.156 313.153 313.153

1082

0.794254 0.794433 0.794643 0.794888 0.795074 0.795902

0.817825 0.817937 0.818140 0.818388 0.818415 0.819134 0.819722 0.821145 0.822538 0.823807 0.824485 0.825705 0.827609 0.829455 0.830642 0.831928 0.833615 0.835368 0.836501 0.838117 0.838092 0.838557 0.839141 0.840737 0.841811 0.842896 0.844325 0.845954 0.846902 0.847942 0.849358 0.850826 0.851847 0.852740 0.854215 0.854690

ρ/g·cm−3

288.151 288.150 288.151 288.150 288.153 288.152 288.150 288.152 288.151 288.150 288.150 288.151 288.152 288.151 288.152 288.150 288.152 288.151 288.151 288.151 288.150 288.151 288.151 288.152 288.150 288.150 288.152 288.150 288.153 288.151 288.150 288.150 288.154 288.154 288.150 288.150 288.150 318.153 318.154 318.155 318.156 318.156 318.155

T/K 0.0785 0.3913 0.5544 0.8827 0.9891 2.0575 2.9178 5.0414 7.0888 9.0186 10.040 12.072 15.001 17.968 20.068 20.693 22.020 25.002 28.026 30.035 32.084 33.050 34.036 35.077 37.993 40.041 42.023 44.979 48.045 50.068 52.032 55.077 58.004 59.988 61.974 64.942 66.025 0.0727 0.1501 0.3363 0.5909 0.8910 1.1057

P/MPa 0.813612 0.813840 0.813953 0.814204 0.814282 0.815033 0.815651 0.817160 0.818541 0.819847 0.820583 0.821910 0.823877 0.825720 0.826976 0.827380 0.828211 0.829984 0.831832 0.832896 0.834074 0.834714 0.835152 0.835674 0.837311 0.838449 0.839459 0.841064 0.842655 0.843734 0.844696 0.846251 0.847666 0.848618 0.849542 0.850930 0.851488 0.790456 0.790516 0.790675 0.790894 0.791160 0.791334

ρ/g·cm−3 293.155 293.156 293.156 293.152 293.156 293.155 293.155 293.155 293.156 293.155 293.155 293.155 293.155 293.156 293.156 293.154 293.156 293.154 293.151 293.156 293.156 293.150 293.155 293.154 293.156 293.155 293.155 293.154 293.156 293.156 293.156 293.155 293.151 293.156 293.157 293.156 293.152 323.153 323.150 323.155 323.156 323.155 323.152

T/K 0.0911 0.3052 0.4764 0.8251 1.0452 1.9717 3.0606 5.0110 7.0968 9.0421 10.036 11.947 14.941 17.889 19.992 21.987 24.983 27.986 28.066 29.976 32.232 33.151 34.099 35.000 38.027 40.081 42.099 45.068 48.022 50.085 52.032 54.966 58.072 60.018 61.962 64.991 66.045 0.0950 0.2961 0.5284 0.9207 0.9942 2.0069

P/MPa 0.810528 0.810686 0.810810 0.811053 0.811221 0.811916 0.812720 0.814074 0.815616 0.816992 0.817626 0.818963 0.820924 0.822832 0.824147 0.825417 0.827251 0.829060 0.829163 0.830110 0.831521 0.832036 0.832526 0.833078 0.834783 0.835959 0.837008 0.838658 0.840192 0.841310 0.842308 0.843810 0.845282 0.846257 0.847209 0.848649 0.849224 0.786145 0.786326 0.786535 0.786888 0.786944 0.787814

ρ/g·cm−3

Table 3. Pressure−Density−Temperature Experimental Measurements for 1-Butanola 298.155 298.154 298.156 298.155 298.156 298.154 298.154 298.154 298.155 298.156 298.152 298.156 298.156 298.156 298.155 298.153 298.155 298.156 298.156 298.156 298.150 298.155 298.156 298.152 298.152 298.154 298.155 298.150 298.154 298.153 298.156 298.151 298.152 298.152 298.153 298.151 298.156 328.154 328.153 328.156 328.155 328.152 328.155

T/K 0.0981 0.3054 0.4937 0.8545 1.0126 1.9809 3.1678 5.0676 7.0653 9.1209 10.107 11.970 15.220 17.984 20.128 22.004 25.081 28.040 30.089 32.030 33.113 33.924 35.217 38.097 40.161 42.029 42.359 45.021 48.107 50.068 52.020 55.016 57.931 59.914 62.036 65.018 66.118 0.0979 0.2899 0.5010 0.8975 0.9941 1.9888

P/MPa 0.806282 0.806450 0.806599 0.806874 0.806992 0.807747 0.808637 0.810040 0.811550 0.813012 0.813670 0.814957 0.817234 0.819076 0.820445 0.821641 0.823550 0.825420 0.826686 0.827814 0.828365 0.828845 0.829575 0.831213 0.832357 0.833462 0.833614 0.835052 0.836745 0.837797 0.838835 0.840375 0.841819 0.842826 0.843934 0.845412 0.845919 0.781987 0.782179 0.782371 0.782733 0.782825 0.783741

ρ/g·cm−3 303.156 303.152 303.151 303.155 303.153 303.151 303.156 303.153 303.156 303.156 303.156 303.155 303.155 303.156 303.154 303.154 303.155 303.156 303.156 303.154 303.151 303.152 303.151 303.154 303.155 303.151 303.153 303.153 303.155 303.153 303.151 303.151 303.151 303.154 303.152 303.151 303.154 333.156 333.156 333.154 333.155 333.156 333.154

T/K 0.1000 0.3041 0.4989 0.9006 0.9791 1.9776 2.9649 4.9304 7.0456 8.8582 10.014 11.975 15.044 18.021 19.974 21.920 24.992 27.933 29.990 31.958 32.862 33.112 34.081 34.980 37.951 39.904 42.014 44.896 47.951 50.065 52.073 55.075 57.989 59.979 62.052 64.988 66.030 0.0877 0.3035 0.5326 0.8978 1.0030 1.9872

P/MPa 0.802125 0.802278 0.802435 0.802733 0.802787 0.803554 0.804300 0.805792 0.807335 0.808638 0.809449 0.810901 0.812956 0.814973 0.816207 0.817555 0.819440 0.821256 0.822537 0.823711 0.824267 0.824372 0.824900 0.825355 0.827164 0.828270 0.829398 0.831035 0.832781 0.833864 0.834942 0.836525 0.838099 0.839130 0.840165 0.841599 0.842119 0.779482 0.779691 0.779903 0.780245 0.780346 0.781249

ρ/g·cm−3 308.156 308.155 308.153 308.150 308.154 308.151 308.151 308.151 308.155 308.153 308.153 308.150 308.156 308.150 308.152 308.151 308.152 308.151 308.154 308.152 308.151 308.152 308.154 308.156 308.152 308.153 308.155 308.154 308.155 308.154 308.155 308.152 308.153 308.155 308.154 308.154 308.156 338.155 338.154 338.155 338.153 338.155 338.156

T/K 0.0852 0.2743 0.4941 0.8033 1.0395 1.9167 2.9807 4.9902 6.9649 8.8643 9.8631 12.009 15.069 17.850 19.930 21.988 25.012 27.955 29.906 31.929 32.886 32.941 34.011 34.949 37.971 40.011 41.998 45.017 48.033 50.044 51.977 54.982 58.009 60.030 61.985 64.981 66.088 0.0809 0.3098 0.5616 0.8985 1.0141 2.0002

P/MPa

0.798155 0.798317 0.798504 0.798750 0.798954 0.799642 0.800489 0.802048 0.803548 0.804962 0.805692 0.807267 0.809400 0.811315 0.812759 0.814131 0.816144 0.817999 0.819191 0.820410 0.820911 0.821059 0.821636 0.822224 0.823987 0.825154 0.826392 0.828081 0.829748 0.830856 0.831933 0.833542 0.835036 0.836098 0.837136 0.838691 0.839237 0.775106 0.775333 0.775578 0.775911 0.776019 0.776987

ρ/g·cm−3



P/MPa

3.1370 5.1118 6.9218 9.2107 10.209 12.020 15.059 17.921 19.932 22.058 24.862 27.869 29.957 32.107 32.980 33.002 33.981 35.045 38.127 39.997 41.978 44.946 47.880 50.021 52.097 54.924 58.082 59.932 62.004 64.954 66.113 0.0737 0.2973 0.5203 0.9117 1.0177 1.9946 2.3325 2.9683 4.9948 6.9766 9.0026 10.060

T/K

313.155 313.152 313.151 313.155 313.151 313.151 313.150 313.150 313.151 313.155 313.150 313.152 313.152 313.154 313.153 313.154 313.153 313.155 313.154 313.156 313.153 313.155 313.154 313.156 313.154 313.152 313.155 313.153 313.154 313.155 313.154 343.153 343.151 343.152 343.151 343.150 343.153 343.152 343.152 343.151 343.152 343.154 343.152

Table 3. continued

0.796707 0.798292 0.799704 0.801445 0.802164 0.803525 0.805716 0.807720 0.809082 0.810550 0.812410 0.814438 0.815731 0.817091 0.817674 0.817783 0.818214 0.818819 0.820760 0.821817 0.822973 0.824676 0.826390 0.827556 0.828677 0.830321 0.831994 0.832960 0.834048 0.835652 0.836222 0.769631 0.769853 0.770070 0.770459 0.770563 0.771497 0.771830 0.772434 0.774313 0.776117 0.777941 0.778847

ρ/g·cm−3

318.155 318.152 318.156 318.156 318.153 318.155 318.150 318.156 318.154 318.155 318.155 318.156 318.156 318.155 318.156 318.152 318.156 318.156 318.152 318.155 318.156 318.153 318.154 318.156 318.156 318.155 318.154 318.152 318.156 318.155 318.151 348.150 348.156 348.155 348.150 348.155 348.153 348.150 348.150 348.156 348.156 348.155 348.156

T/K 1.9291 2.9332 5.0208 6.9267 8.9890 10.075 11.896 14.800 18.102 19.985 22.094 24.873 27.909 29.998 31.957 33.016 34.110 35.048 37.838 40.093 41.996 44.884 47.944 49.950 52.037 54.944 57.972 59.923 61.930 65.022 66.028 0.0888 0.2917 0.4622 0.8598 0.9742 1.9749 3.0511 5.0940 7.0502 9.0032 10.025 12.187

P/MPa 0.792026 0.792866 0.794556 0.796098 0.797678 0.798523 0.799896 0.802072 0.804461 0.805780 0.807257 0.809191 0.811139 0.812541 0.813824 0.814458 0.815009 0.815630 0.817415 0.818817 0.819890 0.821648 0.823402 0.824565 0.825741 0.827433 0.829016 0.830120 0.831241 0.832785 0.833327 0.765578 0.765770 0.765945 0.766355 0.766465 0.767461 0.768513 0.770529 0.772352 0.774145 0.775087 0.777001

ρ/g·cm−3 2.9666 4.9962 7.0421 9.0299 10.090 11.914 15.111 17.981 20.038 21.995 24.993 27.958 30.055 32.079 33.067 34.081 35.113 37.953 40.047 42.011 44.937 48.025 49.934 52.114 54.964 58.045 60.050 62.131 64.999 66.131 0.0862 0.3360 0.5726 0.9260 1.0164 2.1134 2.9921 4.9639 7.0009 9.0623 10.005 12.128

353.154 353.150 353.155 353.152 353.152 353.156 353.154 353.150 353.152 353.154 353.151 353.151

P/MPa

323.153 323.154 323.154 323.153 323.155 323.155 323.154 323.151 323.153 323.155 323.154 323.156 323.156 323.155 323.156 323.154 323.153 323.155 323.156 323.155 323.156 323.153 323.150 323.153 323.152 323.150 323.152 323.154 323.152 323.156

T/K

1083

0.760995 0.761273 0.761533 0.761914 0.762008 0.763181 0.764106 0.766051 0.768126 0.770136 0.771015 0.772980

0.788632 0.790328 0.792001 0.793564 0.794392 0.795800 0.798229 0.800333 0.801815 0.803198 0.805264 0.807280 0.808674 0.809955 0.810610 0.811155 0.811773 0.813623 0.814861 0.816075 0.817856 0.819642 0.820799 0.821994 0.823594 0.825293 0.826448 0.827565 0.829093 0.829687

ρ/g·cm−3 328.151 328.151 328.155 328.154 328.155 328.156 328.156 328.156 328.156 328.156 328.151 328.150 328.153 328.153 328.150 328.154 328.153 328.150 328.150 328.152 328.153 328.150 328.150 328.150 328.153 328.150 328.151 328.150 328.150 328.150 328.150 358.156 358.155 358.155 358.151 358.154 358.156 358.154 358.151 358.156 358.156 358.155 358.154

T/K 2.9967 5.0134 6.9749 9.0170 10.040 12.210 15.055 18.061 20.279 22.013 24.924 27.979 29.958 32.060 33.066 33.107 34.013 35.030 38.010 39.969 41.959 44.953 47.978 49.927 51.997 54.947 57.939 59.991 61.982 65.032 66.046 0.0951 0.2641 0.5084 0.9268 1.0139 2.0839 3.0212 4.9300 6.9935 9.0302 10.073 12.137

P/MPa 0.784660 0.786446 0.788150 0.789881 0.790727 0.792522 0.794783 0.797122 0.798799 0.800057 0.802164 0.804324 0.805680 0.807104 0.807772 0.807703 0.808285 0.808989 0.810915 0.812181 0.813311 0.815144 0.816959 0.818128 0.819320 0.821045 0.822658 0.823770 0.824890 0.826439 0.826965 0.755754 0.755935 0.756190 0.756640 0.756732 0.757886 0.758947 0.760980 0.763142 0.765202 0.766290 0.768259

ρ/g·cm−3 333.155 333.150 333.152 333.153 333.153 333.156 333.155 333.156 333.156 333.151 333.156 333.154 333.151 333.150 333.156 333.150 333.151 333.150 333.151 333.153 333.152 333.152 333.150 333.152 333.150 333.152 333.150 333.152 333.150 333.152 333.151 363.152 363.155 363.154 363.154 363.155 363.155 363.155 363.155 363.152 363.156 363.156 363.155

T/K 3.0234 4.9974 7.0024 9.0320 10.210 12.011 15.008 17.992 20.036 22.034 25.027 28.040 30.016 32.067 33.073 34.086 35.075 37.894 40.111 41.947 44.974 45.490 47.936 49.920 51.953 54.876 58.057 59.993 62.049 64.970 66.005 0.0940 0.3340 0.6017 0.8929 0.9616 1.0347 1.9860 2.9404 4.9792 6.9202 8.9648 9.9595

P/MPa 0.782177 0.783921 0.785686 0.787401 0.788367 0.789847 0.792251 0.794568 0.796123 0.797567 0.799667 0.801782 0.803156 0.804524 0.805134 0.805827 0.806492 0.808332 0.809759 0.810938 0.812823 0.813093 0.814509 0.815727 0.816927 0.818691 0.820500 0.821547 0.822689 0.824293 0.824853 0.752456 0.752741 0.753061 0.753404 0.753487 0.753567 0.754594 0.755648 0.757840 0.759821 0.761886 0.762855

ρ/g·cm−3 338.154 338.154 338.156 338.156 338.152 338.156 338.150 338.155 338.153 338.150 338.150 338.156 338.155 338.156 338.152 338.155 338.151 338.156 338.155 338.154 338.153 338.152 338.153 338.151 338.156 338.152 338.151 338.156 338.151 338.151 338.156

T/K 2.9361 5.0186 6.9173 9.0469 10.034 11.959 14.885 17.956 19.927 22.041 25.026 27.976 29.994 31.949 32.882 33.937 35.012 37.962 39.987 41.990 44.978 47.971 49.999 52.127 54.992 57.940 60.014 62.074 65.012 66.057 67.534

P/MPa

0.777859 0.779821 0.781550 0.783457 0.784276 0.785981 0.788349 0.790925 0.792473 0.794077 0.796362 0.798446 0.799911 0.801318 0.801907 0.802603 0.803345 0.805345 0.806717 0.808025 0.809926 0.811881 0.813099 0.814375 0.816085 0.817865 0.819058 0.820252 0.821872 0.822451 0.823221

ρ/g·cm−3



a

1084

12.025 14.928 17.975 19.985 22.033 25.091 28.045 30.082 32.170 33.097 34.034 35.030 37.943 40.012 41.972 44.927 47.908 50.059 52.026 54.919 57.986 59.944 61.967 65.070 66.059

343.153 343.154 343.154 343.153 343.155 343.154 343.154 343.151 343.155 343.152 343.156 343.155 343.155 343.154 343.155 343.152 343.153 343.155 343.150 343.156 343.156 343.153 343.152 343.151 343.153

0.780506 0.782929 0.785398 0.786983 0.788560 0.790858 0.793012 0.794441 0.795891 0.796546 0.797101 0.797771 0.799701 0.801058 0.802307 0.804186 0.806033 0.807349 0.808534 0.810240 0.812021 0.813181 0.814212 0.815911 0.816518

ρ/g·cm−3

348.155 348.156 348.154 348.152 348.156 348.155 348.154 348.154 348.156 348.154 348.153 348.155 348.151 348.155 348.156 348.152 348.150 348.154 348.154 348.153 348.155 348.156 348.150 348.152

T/K 14.792 17.899 20.111 22.163 25.100 28.080 30.149 32.161 32.942 33.959 35.045 37.937 40.026 42.066 45.051 47.915 49.950 52.167 55.022 57.945 60.030 62.063 64.942 66.153

P/MPa 0.779258 0.781843 0.783649 0.785270 0.787550 0.789800 0.791333 0.792797 0.793364 0.793985 0.794751 0.796729 0.798192 0.799570 0.801465 0.803304 0.804611 0.805991 0.807759 0.809531 0.810761 0.811961 0.813608 0.814319

ρ/g·cm−3 353.153 353.150 353.150 353.150 353.154 353.154 353.151 353.154 353.152 353.156 353.153 353.152 353.150 353.153 353.151 353.151 353.152 353.151 353.155 353.155 353.153 353.156 353.153 353.156

T/K 14.954 17.977 19.937 21.894 24.908 27.850 29.936 31.876 32.961 33.964 34.945 37.913 40.143 42.067 45.002 48.029 50.145 52.082 55.132 57.980 60.098 62.043 65.063 66.024

P/MPa


P/MPa

T/K

Table 3. continued 0.775544 0.778173 0.779792 0.781405 0.783869 0.786199 0.787797 0.789263 0.790048 0.790701 0.791423 0.793571 0.795172 0.796559 0.798550 0.800525 0.801944 0.803184 0.805077 0.806879 0.808146 0.809275 0.811071 0.811636

ρ/g·cm−3 358.154 358.150 358.152 358.156 358.153 358.154 358.152 358.155 358.151 358.150 358.152 358.153 358.152 358.153 358.154 358.156 358.153 358.150 358.152 358.152 358.155 358.150 358.152 358.153 358.152

T/K 14.905 17.041 17.965 20.162 22.175 25.059 28.035 30.002 31.978 32.793 33.850 35.027 37.872 40.037 42.100 45.054 47.958 50.038 52.081 55.073 57.918 60.043 62.067 64.986 66.109

P/MPa 0.770903 0.772871 0.773738 0.775665 0.777415 0.779849 0.782278 0.783844 0.785370 0.786010 0.786716 0.787554 0.789731 0.791310 0.792749 0.794810 0.796761 0.798154 0.799474 0.801393 0.803161 0.804453 0.805674 0.807407 0.808067

ρ/g·cm−3 363.152 363.155 363.153 363.154 363.156 363.155 363.152 363.152 363.152 363.153 363.151 363.152 363.151 363.154 363.152 363.156 363.152 363.151 363.154 363.151 363.153 363.152 363.155 363.155 363.155

T/K 11.971 14.936 17.973 19.940 21.933 24.872 27.993 30.062 31.961 33.033 34.000 35.028 37.919 39.916 42.016 44.987 47.947 50.050 52.023 54.940 57.917 59.980 62.043 64.924 66.088

P/MPa 0.764806 0.767534 0.770255 0.771991 0.773696 0.776146 0.778673 0.780285 0.781745 0.782563 0.783178 0.783945 0.786081 0.787488 0.788986 0.791029 0.793030 0.794458 0.795718 0.797589 0.799479 0.800724 0.802008 0.803734 0.804418

ρ/g·cm−3 T/K

P/MPa

ρ/g·cm−3



P/MPa

0.0894 0.2899 0.4782 0.4899 0.9302 1.0273 2.1721 2.9929 4.9938 6.9069 8.9957 10.003 12.183 14.910 17.915 20.110 22.168 24.886 27.713 30.148 32.117 33.086 33.288 34.077 35.107 38.030 39.967 41.406 44.591 48.034 49.830 51.952 54.994 57.756 59.886 61.822 64.894 66.072

0.0829 0.3168 0.4918 0.8909

T/K

283.154 283.156 283.150 283.152 283.153 283.152 283.150 283.151 283.152 283.150 283.151 283.152 283.153 283.151 283.150 283.151 283.151 283.150 283.150 283.151 283.150 283.152 283.150 283.150 283.155 283.153 283.156 283.156 283.154 283.156 283.156 283.157 283.152 283.155 283.155 283.154 283.154 283.156

313.151 313.151 313.153 313.154

1085

0.787400 0.787607 0.787767 0.788108

0.809726 0.810056 0.810123 0.810142 0.810437 0.810557 0.811348 0.811865 0.813245 0.814669 0.816167 0.816885 0.818287 0.820439 0.822056 0.823875 0.825177 0.826625 0.828290 0.829717 0.830745 0.831522 0.831507 0.832073 0.832469 0.834322 0.835340 0.835909 0.837752 0.839700 0.840462 0.841796 0.843308 0.844723 0.845575 0.846524 0.848158 0.848566

ρ/g·cm−3

288.152 288.153 288.156 288.155 288.154 288.152 288.153 288.151 288.153 288.154 288.152 288.156 288.154 288.152 288.152 288.151 288.154 288.151 288.151 288.150 288.154 288.155 288.159 288.156 288.150 288.156 288.154 288.154 288.150 288.151 288.153 288.152 288.154 288.153 288.155 288.156 288.154 288.156 288.150 318.157 318.152 318.153 318.156

T/K 0.0853 0.3511 0.5493 0.7186 0.9283 1.1323 1.9316 3.4339 5.0239 6.8939 8.4064 9.9591 12.498 13.061 15.159 16.159 17.078 19.062 20.120 21.983 22.948 24.955 27.092 29.078 31.002 33.729 36.056 38.602 40.698 42.984 44.991 46.862 49.740 53.748 55.203 57.016 60.810 62.338 65.611 0.1285 0.3683 0.5894 0.8582

P/MPa 0.806159 0.806381 0.806494 0.806519 0.806632 0.807006 0.807420 0.808429 0.809620 0.810983 0.812175 0.813184 0.814345 0.815035 0.815414 0.816818 0.817715 0.818283 0.819399 0.820300 0.821319 0.821837 0.823174 0.824509 0.825774 0.826936 0.828477 0.829859 0.831363 0.832313 0.833694 0.834848 0.835692 0.837321 0.839369 0.840129 0.841135 0.843086 0.844144 0.783253 0.783457 0.783667 0.783902

ρ/g·cm−3 293.153 293.152 293.158 293.157 293.151 293.156 293.156 293.159 293.156 293.156 293.152 293.151 293.156 293.153 293.157 293.150 293.156 293.153 293.155 293.159 293.156 293.158 293.158 293.156 293.154 293.155 293.157 293.156 293.156 293.152 293.152 293.151 293.153 293.156 293.156 293.156 293.156 293.156 293.156 323.155 323.151 323.150 323.151

T/K 0.0634 0.1945 0.3104 0.4635 0.6626 1.0597 2.0371 2.9220 3.4315 5.2988 5.3678 5.9793 7.1114 8.0314 9.9685 12.279 14.057 16.110 18.001 20.853 22.118 24.057 25.922 27.187 30.253 32.967 34.602 38.051 40.103 42.984 44.913 47.933 50.078 52.135 55.036 58.004 60.107 62.061 66.037 0.0621 0.3380 0.5575 0.9173

P/MPa 0.802054 0.802316 0.802406 0.802612 0.802599 0.802921 0.803747 0.804089 0.804593 0.805894 0.806019 0.806327 0.807238 0.807842 0.809474 0.811587 0.812743 0.814191 0.815385 0.817066 0.818157 0.819188 0.820412 0.821228 0.822999 0.824811 0.825683 0.827567 0.828763 0.830218 0.831278 0.833008 0.834047 0.835387 0.836790 0.838271 0.839502 0.840325 0.842335 0.778890 0.779159 0.779374 0.779697

ρ/g·cm−3

328.150 328.152 328.156 328.155

298.155 298.150 298.152 298.151 298.152 298.156 298.156 298.156 298.156 298.155 298.157 298.156 298.157 298.155 298.151 298.154 298.153 298.155 298.155 298.155 298.155 298.156 298.155 298.156 298.156 298.156 298.156 298.155 298.156 298.156 298.157 298.156 298.157 298.155 298.153 298.155 298.153

T/K

Table 4. Pressure−Density−Temperature Experimental Measurements for Isobutyl Alcohola

0.0965 0.3958 0.5150 0.9041

0.1224 0.1626 0.4055 0.6328 0.9564 1.1522 2.0463 3.0211 5.1074 6.9888 9.0443 9.9968 11.947 14.555 18.284 20.164 22.781 25.076 27.604 30.046 32.326 33.072 33.317 34.997 37.948 39.972 41.983 44.911 48.045 49.997 52.020 54.851 57.898 60.006 62.079 65.330 66.093

P/MPa

0.774907 0.775157 0.775262 0.775603

0.798281 0.798371 0.798562 0.798678 0.798832 0.799011 0.799798 0.800420 0.801927 0.803491 0.804777 0.805681 0.807140 0.809311 0.812068 0.813104 0.814894 0.816275 0.817904 0.819519 0.821055 0.821357 0.821248 0.822338 0.823936 0.825207 0.826345 0.827946 0.829528 0.830783 0.832399 0.833381 0.835245 0.836063 0.837121 0.838566 0.839052

ρ/g·cm-3

333.152 333.157 333.157 333.155

303.155 303.156 303.157 303.156 303.151 303.153 303.156 303.156 303.156 303.155 303.150 303.160 303.155 303.155 303.153 303.156 303.155 303.157 303.154 303.155 303.155 303.157 303.156 303.152 303.151 303.153 303.155 303.154 303.156 303.154 303.155 303.154 303.155 303.154 303.154 303.155 303.156

T/K

0.0957 0.2959 0.5745 0.9136

0.0506 0.2701 0.4644 0.7796 0.9744 1.9225 2.9450 4.9112 7.0586 9.0123 10.062 12.047 14.908 18.109 20.042 22.055 25.084 28.094 30.167 32.070 33.147 32.939 34.037 35.162 38.019 39.970 42.004 45.033 48.317 49.864 52.115 55.239 58.089 60.079 62.294 65.137 66.124

P/MPa

0.770629 0.770818 0.771110 0.771467

0.793736 0.793901 0.794084 0.794287 0.794496 0.795367 0.796031 0.797923 0.799569 0.801250 0.802346 0.803470 0.805823 0.808133 0.809402 0.811092 0.812578 0.815049 0.816191 0.817319 0.817694 0.817604 0.818139 0.818815 0.820574 0.821716 0.823024 0.824950 0.826769 0.827592 0.829036 0.830776 0.832479 0.833282 0.834706 0.835715 0.836430

ρ/g·cm−3

338.154 338.155 338.153 338.150

308.153 308.154 308.152 308.156 308.155 308.156 308.158 308.151 308.156 308.156 308.154 308.158 308.154 308.158 308.158 308.158 308.159 308.158 308.157 308.158 308.158 308.151 308.158 308.151 308.157 308.158 308.158 308.157 308.157 308.155 308.157 308.158 308.155 308.156 308.153 308.155 308.157 308.150

T/K

0.0725 0.2671 0.4965 0.8213

0.0967 0.2506 0.5622 0.7702 0.9919 2.1012 3.1951 5.2193 7.0830 9.1080 10.282 12.379 15.083 18.161 20.006 22.192 25.100 27.887 30.041 31.933 33.077 32.866 34.026 35.203 35.193 38.088 40.106 42.282 45.145 48.031 50.089 52.047 55.094 58.085 60.161 62.192 65.217 66.004

P/MPa

0.765803 0.766009 0.766255 0.766600

0.791579 0.791714 0.791995 0.792158 0.792349 0.793300 0.794224 0.795881 0.797398 0.799011 0.799926 0.801538 0.803575 0.805827 0.807165 0.808686 0.810705 0.812568 0.813990 0.815242 0.815959 0.815750 0.816482 0.817171 0.817245 0.818995 0.820225 0.821541 0.823251 0.824960 0.826126 0.827233 0.828952 0.830585 0.831729 0.832798 0.834405 0.834804

ρ/g·cm−3



1086

0.0556 0.1018 0.2773 0.4877 0.8816 1.0370 1.9414 3.0003 4.9570

0.9815 1.9396 2.9510 4.8891 6.8565 8.8869 10.029 11.886 14.927 17.845 20.040 21.942 24.894 28.132 29.974 32.058 33.053 33.131 34.040 35.162 37.952 40.011 41.939 45.098 47.966 49.918 52.024 54.951 58.062 60.202 62.187 65.050 66.082

313.150 313.153 313.151 313.155 313.152 313.154 313.153 313.155 313.155 313.155 313.155 313.150 313.150 313.155 313.153 313.155 313.156 313.156 313.156 313.152 313.150 313.151 313.153 313.150 313.151 313.155 313.150 313.151 313.155 313.155 313.156 313.150 313.150

343.150 343.152 343.150 343.151 343.151 343.150 343.151 343.153 343.150

P/MPa

T/K

Table 4. continued

0.761239 0.761279 0.761484 0.761699 0.762130 0.762294 0.763263 0.764362 0.766378

0.788182 0.789038 0.789905 0.791537 0.793195 0.794841 0.795770 0.797214 0.799577 0.801775 0.803389 0.804760 0.806850 0.809095 0.810333 0.811716 0.812371 0.812356 0.812940 0.813664 0.815444 0.816732 0.817878 0.819950 0.821512 0.822650 0.823857 0.825557 0.827336 0.828515 0.829599 0.831150 0.831700

ρ/g·cm−3

348.152 348.152 348.152 348.155 348.154 348.150 348.153 348.155 348.152

318.156 318.156 318.157 318.156 318.156 318.156 318.154 318.156 318.156 318.156 318.157 318.156 318.156 318.156 318.157 318.157 318.153 318.152 318.157 318.155 318.157 318.157 318.156 318.157 318.155 318.157 318.155 318.156 318.156 318.153 318.154 318.152 318.154

T/K

0.0940 0.2938 0.4819 0.7635 1.0110 1.9811 3.0732 5.0899 7.0346

1.0695 1.9791 2.9974 4.9426 6.9872 8.9675 9.8876 11.870 14.863 17.735 19.860 21.987 25.193 27.823 30.119 32.145 33.128 33.065 34.164 35.190 38.074 40.048 41.997 45.096 48.088 50.173 52.184 55.235 58.075 60.194 62.260 65.194 66.060

P/MPa

0.756672 0.756914 0.757128 0.757435 0.757701 0.758826 0.759880 0.762131 0.764092

0.784105 0.784923 0.785790 0.787513 0.789270 0.790929 0.791657 0.793265 0.795639 0.797848 0.799438 0.801004 0.803357 0.805216 0.806799 0.808205 0.808894 0.808852 0.809488 0.810134 0.812009 0.813265 0.814496 0.816426 0.818249 0.819491 0.820670 0.822460 0.824084 0.825273 0.826409 0.828017 0.828484

ρ/g·cm−3

353.150 353.150 353.150 353.150 353.151 353.150 353.151 353.152 353.153

323.156 323.155 323.154 323.153 323.155 323.151 323.150 323.151 323.151 323.151 323.150 323.152 323.150 323.154 323.154 323.154 323.151 323.150 323.150 323.151 323.153 323.150 323.153 323.155 323.156 323.153 323.154 323.155 323.152 323.153 323.152 323.152 323.155

T/K

0.0981 0.3058 0.3840 0.5585 0.9294 1.0737 2.0827 3.0259 5.0179

1.1178 2.1254 3.1548 5.1264 7.3668 9.0816 10.156 12.167 15.030 18.076 19.932 22.079 25.085 28.006 30.029 31.969 32.903 33.102 33.950 34.958 37.883 39.891 42.065 44.846 47.886 49.935 52.064 54.897 57.818 59.855 61.856 64.838 65.957

P/MPa

0.752221 0.752433 0.752511 0.752696 0.753125 0.753289 0.754432 0.755465 0.757656

0.779897 0.780833 0.781778 0.783557 0.785517 0.787010 0.787907 0.789544 0.791876 0.794274 0.795694 0.797333 0.799541 0.801644 0.803084 0.804431 0.805081 0.805154 0.805707 0.806425 0.808369 0.809680 0.811076 0.812852 0.814721 0.815968 0.817249 0.818944 0.820634 0.821787 0.822928 0.824600 0.825209

ρ/g·cm−3

358.150 358.152 358.155 358.151 358.153 358.151 358.151 358.150 358.150

328.154 328.156 328.155 328.153 328.156 328.156 328.155 328.150 328.156 328.156 328.156 328.158 328.150 328.153 328.151 328.154 328.156 328.155 328.154 328.150 328.153 328.156 328.150 328.155 328.156 328.156 328.156 328.152 328.151 328.155 328.154 328.156 328.150

T/K

0.0916 0.3049 0.5173 0.8501 1.0955 2.1016 3.2106 5.3242 7.1901

1.0306 2.0697 2.9993 5.0420 6.9367 8.8742 10.121 11.905 14.954 17.891 20.040 22.054 24.953 27.874 29.949 31.948 33.018 33.061 34.111 34.984 37.913 39.966 41.958 44.806 47.820 49.817 52.099 55.150 58.100 60.045 62.082 64.955 66.095

P/MPa

0.747694 0.747895 0.748147 0.748568 0.748835 0.750029 0.751303 0.753465 0.755483

0.775740 0.776794 0.777646 0.779515 0.781257 0.782985 0.784077 0.785621 0.788149 0.790513 0.792210 0.793773 0.795929 0.798098 0.799588 0.800996 0.801745 0.801681 0.802415 0.803007 0.805001 0.806346 0.807674 0.809500 0.811414 0.812637 0.814145 0.815995 0.817750 0.818881 0.820048 0.821692 0.822334

ρ/g·cm-3

363.152 363.152 363.150 363.150 363.150 363.153 363.153 363.153 363.155

333.156 333.156 333.156 333.157 333.152 333.154 333.152 333.155 333.155 333.157 333.157 333.155 333.156 333.156 333.155 333.155 333.152 333.157 333.156 333.157 333.156 333.157 333.155 333.156 333.153 333.154 333.153 333.153 333.153 333.154 333.154 333.152 333.152

T/K

0.0532 0.1255 0.3203 0.5625 0.8925 1.0013 1.9116 2.9773 4.9575

1.0695 2.1106 3.1000 5.0340 6.9656 8.9373 9.9951 11.970 14.915 17.954 19.985 22.033 24.923 27.922 29.996 31.986 32.928 33.031 34.001 35.030 37.925 39.862 41.792 44.782 47.830 49.895 51.876 54.830 58.116 59.975 61.974 65.057 66.042

P/MPa

0.742307 0.742405 0.742647 0.742935 0.743339 0.743446 0.744576 0.745832 0.748169

0.771621 0.772649 0.773622 0.775464 0.777259 0.779076 0.780005 0.781720 0.784255 0.786777 0.788397 0.790027 0.792261 0.794514 0.796045 0.797490 0.798124 0.798137 0.798837 0.799567 0.801558 0.802861 0.804162 0.806126 0.808087 0.809380 0.810610 0.812440 0.814429 0.815509 0.816676 0.818467 0.819039

ρ/g·cm−3 338.153 338.154 338.151 338.156 338.152 338.153 338.153 338.156 338.157 338.155 338.156 338.155 338.156 338.155 338.156 338.155 338.154 338.155 338.153 338.156 338.152 338.156 338.154 338.156 338.153 338.154 338.154 338.151 338.153 338.151 338.150 338.150 338.152 338.155

T/K 1.0077 2.0124 3.0391 5.0911 7.0185 8.9876 10.054 12.131 15.171 18.105 20.167 22.120 25.290 28.029 30.041 32.010 32.776 32.995 33.922 35.102 38.056 39.987 42.127 45.109 48.090 50.121 52.094 55.116 58.010 60.191 62.244 65.243 65.986 66.355

P/MPa

0.766796 0.767824 0.768845 0.770879 0.772739 0.774596 0.775578 0.777462 0.780113 0.782627 0.784349 0.785947 0.788465 0.790565 0.792069 0.793527 0.794103 0.794184 0.794869 0.795700 0.797798 0.799156 0.800629 0.802623 0.804572 0.805906 0.807168 0.809055 0.810837 0.812149 0.813373 0.815143 0.815583 0.815805

ρ/g·cm−3



a

1087

6.9561 8.9695 10.003 11.997 14.895 17.840 20.135 21.925 24.920 27.949 29.863 31.874 32.981 32.927 34.026 35.028 38.080 39.908 41.973 44.972 47.997 50.016 52.079 54.997 57.987 60.015 62.074 65.051 66.170

343.152 343.151 343.154 343.151 343.154 343.150 343.155 343.155 343.152 343.150 343.150 343.152 343.150 343.151 343.151 343.152 343.150 343.155 343.154 343.155 343.152 343.151 343.153 343.154 343.154 343.156 343.153 343.155 343.151

0.768377 0.770304 0.771264 0.773149 0.775758 0.778358 0.780417 0.781908 0.784349 0.786755 0.788238 0.789777 0.790602 0.790544 0.791305 0.792011 0.794257 0.795530 0.796980 0.799034 0.801072 0.802401 0.803724 0.805581 0.807460 0.808691 0.809959 0.811734 0.812401

ρ/g·cm−3

348.151 348.151 348.156 348.152 348.154 348.154 348.153 348.155 348.156 348.154 348.155 348.156 348.156 348.156 348.154 348.152 348.151 348.152 348.151 348.153 348.151 348.156 348.154 348.155 348.156 348.152 348.153 348.154 348.150

T/K 9.0525 9.9913 12.060 15.042 17.922 19.893 22.033 22.381 25.066 28.023 29.922 32.007 32.760 32.941 33.999 34.980 37.995 40.072 41.992 45.082 48.031 50.014 52.067 55.099 58.146 60.084 62.302 65.219 66.250

P/MPa 0.766106 0.767026 0.769030 0.771822 0.774408 0.776137 0.777985 0.778265 0.780513 0.782927 0.784471 0.786046 0.786619 0.786660 0.787493 0.788228 0.790467 0.791973 0.793388 0.795525 0.797589 0.798878 0.800261 0.802242 0.804186 0.805420 0.806758 0.808569 0.809201

ρ/g·cm−3 353.153 353.154 353.154 353.150 353.155 353.152 353.155 353.155 353.153 353.155 353.155 353.150 353.154 353.151 353.155 353.150 353.153 353.155 353.154 353.152 353.155 353.153 353.154 353.152 353.155 353.155 353.151 353.153 353.154 353.154

T/K 6.9578 8.9766 9.9903 11.934 14.917 18.020 19.983 22.060 24.899 27.951 29.947 31.942 32.982 33.037 33.907 35.053 37.939 39.830 41.863 44.753 47.880 49.780 51.876 55.023 55.678 57.869 59.971 62.015 64.989 66.151

P/MPa


P/MPa

T/K

Table 4. continued 0.759690 0.761781 0.762812 0.764803 0.767603 0.770471 0.772259 0.773965 0.776429 0.778961 0.780584 0.782185 0.782978 0.783002 0.783604 0.784493 0.786664 0.788076 0.789556 0.791642 0.793816 0.795140 0.796535 0.798765 0.799178 0.800594 0.801962 0.803245 0.805090 0.805820

ρ/g·cm−3 358.150 358.150 358.150 358.155 358.150 358.155 358.155 358.156 358.157 358.153 358.151 358.151 358.150 358.154 358.154 358.153 358.155 358.155 358.152 358.152 358.152 358.150 358.150 358.153 358.152 358.152 358.152 358.155 358.155

T/K 9.0743 10.165 12.208 13.986 15.000 17.866 20.104 22.005 25.079 27.962 30.131 32.076 33.039 32.938 33.914 34.978 37.986 39.996 42.079 45.119 48.100 49.987 52.101 54.983 58.017 60.055 62.083 65.016 66.339

P/MPa 0.757505 0.758644 0.760738 0.762552 0.763577 0.766293 0.768379 0.770073 0.772781 0.775177 0.776699 0.778299 0.779080 0.778904 0.779672 0.780530 0.782876 0.784402 0.785976 0.788207 0.790343 0.791672 0.793112 0.795084 0.797106 0.798438 0.799766 0.801626 0.802467

ρ/g·cm-3 363.150 363.152 363.150 363.153 363.150 363.154 363.151 363.151 363.154 363.155 363.155 363.153 363.151 363.153 363.155 363.150 363.150 363.152 363.150 363.150 363.151 363.152 363.150 363.151 363.150 363.152 363.153 363.152 363.155

T/K 6.9374 8.8929 10.033 11.914 14.908 17.925 19.995 21.953 24.962 27.932 30.163 32.029 33.151 33.315 34.086 35.189 37.932 40.070 41.883 44.755 48.054 50.037 51.977 55.048 57.990 60.071 62.073 64.996 66.050

P/MPa 0.750436 0.752564 0.753801 0.755769 0.758826 0.761773 0.763754 0.765578 0.768273 0.770858 0.772879 0.774439 0.775369 0.775421 0.776049 0.776934 0.779076 0.780754 0.782107 0.784308 0.786713 0.788134 0.789492 0.791627 0.793615 0.794972 0.796302 0.798178 0.798847

ρ/g·cm−3 T/K

P/MPa

ρ/g·cm−3




Article

where x represents either temperature, pressure, oscillation period at given T and P or oscillating period at vacuum, y is all others variables, dx is the experimental uncertainty, and dρapp is the apparatus uncertainty equal to 0.0001 g/cm3. Derivatives in eq 9 have been calculated numerically. The uncertainty of the oscillating period is equal to 0.033 μs. We have not considered the uncertainty due to the purity of the sample. Previously, it has been shown10 that the main contribution to the uncertainty of the density of a mixture is due to the apparatus uncertainty and the pressure uncertainty. The density uncertainty of our measurements ranges from (0.0002 to 0.0004) g/cm3.

Table 5. Coefficients and Exponents of the Correlation, eq 11 i 1 2 3 4 1 2 3 4

3. RESULTS After the calibration is done, we measured the density of n-heptane to test the quality of the density measurements. The density of n-heptane is measured from (283.15 to 363.15) K and at pressures up to 66 MPa. Table 2 shows the density measurements. We compare this density measurements with an equation of state for n-heptane developed by Span and Wagner11 and formulated in the software REFPROP.1 The equation of state predicts the density of n-heptane with an uncertainty of approximately 0.2 % and up to 0.5 % at high pressures (max. 100 MPa). The new measurements are within the uncertainty of the reference equation of state as shown in Figure 4. Also, we have compared our results with experimental values considered reference values by Schilling et al.12 They measured the density of n-heptane from (233.15 to 393.15) K at pressures up to 30 MPa. They used a single-sinker densimeter based upon the Archimedes’ buoyancy principle and claim a total uncertainty of the density measurements of 0.02 % (level of confidence 95 %). Our measurements agree with these measurements within an average absolute percentage deviation of 0.04 % with a maximum deviation of 0.1 %. We have also measured the densities of 1-butanol and isobutyl alcohol from (283.15 to 363.15) K and at pressures up to 66 MPa. They are shown in Tables 3 and 4, respectively. We have represented the new measurements with 2

α r (τ , δ ) =

Ni

ti

1-Butanol 0.2978751·101 2.849 0.7241970·100 0.238 0.4320172·102 1.662 0.9947022·101 3.195 Isobutyl Alcohol 0.2979192·101 3.051 0.7005887·100 0.246 0.4157447·102 1.965 0.8281872·101 3.483

di

li

1 2 1 2

1 1

1 2 1 2

1 1

Figure 5. Percentage density deviations of experimental measurements of 1-butanol from eq 11: ●, 283.15 K; ○, 288.15 K; ▼, 293.15 K; △, 298.15 K; ■, 303.15 K; □, 308.15 K; ◆, 313.15 K; ◊, 318.15 K; ▲, 323.15 K; ▽, 328.15 K; ⬢ 333.15 K; ⬡, 338.15 K; dotted circle, 343.15 K; dotted diamond, 348.15 K; dotted triangle up, 353.15 K; dotted triangle down, 358.15 K; dotted square, 363.15 K.

4

∑ Niτ t δ d i

i

+

∑ Niτ t δ d

i=1

i

i=3

i

exp( −δ li) (10)

where αr is the dimensionless residual Helmholtz energy, τ = Tc/T, δ = ρ/ρc, and Ni, ti, di, and li are adjusting parameters. The pressure can be calculated from ⎛ ∂α r ⎞ ⎟ P = RTρ + RTρδ ⎜ ⎝ ∂δ ⎠τ

(11)

in which R = 8.314472 cm3·MPa·mol−1·K−1. The coefficients, Ni, and the exponents are obtained by curve fitting eq 11 to the experimental pressure, temperature, and density, and they are shown in Table 5. Figures 5 and 6 show the percentage deviation of the experimental density measurement from eq 11 for 1-butanol and isobutyl alcohol, respectively. We can predict the density of both substances using eq 11 within an average absolute percentage deviation of 0.05 %. The critical density and temperature of 1-butanol1 are 0.2668 g·cm−3 and 562.4 K, while that of isobutyl alcohol13 are 0.2722 g·cm−3 and 547.78 K, respectively. We have compared the density prediction from eq 11 with literature experimental densities. Experimental measurements of 1-butanol and isobutyl alcohol and comparison

Figure 6. Percentage density deviations of experimental measurements of isobutyl alcohol from eq 11: ●, 283.15 K; ○, 288.15 K; ▼, 293.15 K; △, 298.15 K; ■, 303.15 K; □, 308.15 K; ◆, 313.15 K; ◊, 318.15 K; ▲, 323.15 K; ▽, 328.15 K; ⬢ 333.15 K; ⬡, 338.15 K; dotted circle, 343.15 K; dotted diamond, 348.15 K; dotted triangle up, 353.15 K; dotted triangle down, 358.15 K; dotted square, 363.15 K.

with eq 11 are summarized in Tables 6 and 7. Although, 1-butanol densities have been measured previously, the stated uncertainty by the authors of their measurements is higher than our uncertainty as shown in Table 6. The percentage density 1088



Article

Table 6. Accuracy of Correlation in the Representation in the Liquid Density Data for 1-Butanol

a

ref

points

uncert.a

T range K

P range MPa

AAD %

bias %

this work Albert et al.15 Davila et al.16 Gates et al.17 Goluveb et al.14 Goluveb et al.18 Han et al.19 Ihmels and Gmehling20 Kato et al.21 Kubota et al.22 Kubota et al.23 Outcalt et al.24 Papaioannou et al.25 ́ Rodriguez et al.26 Sahli et al.27 Smyth et al.28 Torin-Ollarves et al.29 Troncoso et al.30 Ulbig et al.31 Vasilkovskaya et al.32 Wang et al.33 Wong et al.34 Zuniga-Moreno et al.35

625 9 126 9 44 45 10 150 10 95 52 60 10 8 16 9 113 11 8 22 6 21 297

0.0004 0.0002 0.0012 na 0.0008b 0.0008b 0.00005 0.0002 0.0001 0.0007 0.0007 0.0006 0.0001 0.0001 0.0007 0.0005 0.0007 na 0.0005b 0.0008b na 0.0001 0.0002

283 298 288 298 293 300 293 283 313 298 283 290 298 293 293 283 283 283 298 297 288 298 313

0.073 to 67.5 0.2 to 20.5 0.1 to 60 0.2 to 20.5 0.29 to 50.7 1 to 50 0.1 to 1 0.332 to 40 1 to 10 0.1 to 150 0.1 to 206 0.5 to 50 0.1 to 33.9 0.1 0.1 to 7 0.1 0.1 to 140 0.1 0.1 to 60 1.09 to 49.1 0.1 0.1 to 6.89 0.999 to 25.1

0.048 0.044 0.051 0.044 0.139 0.091 0.011 0.003 0.095 0.111 0.102 0.012 0.076 0.035 0.019 0.040 0.132 0.078 0.054 0.138 0.008 0.309 0.022

−0.007 −0.044 0.042 −0.044 −0.098 −0.039 −0.004 −0.018 −0.095 0.011 −0.095 −0.003 −0.076 −0.035 −0.017 −0.030 −0.132 −0.078 −0.054 −0.138 −6.·10−5 −0.295 −0.009

to to to to to to to to

363 348 358 348 330 350 333 363

to 333 to 348 to 350 to to to to to to to to to to

313 298 363 333 308 323 327 348 348 363

na: Not available. bStated by TRC Database36.

Table 7. Accuracy of Correlation in the Representation in the Liquid Density Data for Isobutyl Alcohol

a

ref

points

uncert.

T range K

P range MPa

AAD %

bias %

this work Fukuchi et al.37 Govuleb et al.18 Goluveb et al.14 Sahli et al.27 Vasilkovskaya et al.32

642 7 22 42 14 22

0.0004 0.0015a 0.0008a 0.0008a 0.0007 0.0008a

283 to 363 293 to 343 300, 350 293 to 330 293 to 298 297, 327

0.073 to 67.5 0.1 1 to 50 0.29 to 50.7 0.1 to 7 1.09 to 49.1

0.033 0.117 0.053 0.120 0.097 0.085

0.005 0.117 −0.053 −0.076 0.097 0.002

Stated by TRC Database36

0.12 % for the experimental measurements by Goluveb et al.14 Equation 11 correlates the densities of isobutyl alcohol within an average absolute percentage deviation of 0.033 %. Then, our density measurements should agree with literature values within an average absolute percentage deviation of 0.2 %.

deviation between the experimental measurements and eq 11 is calculated as ⎛ ρexp − ρcalc ⎞ ⎟ ·100. Δρ = ⎜ ρexp ⎠ ⎝

(12)

Using this definition, the average percentage deviation is AAD =

1 n pts

n pts

∑ |Δρi | i=1

4. CONCLUSIONS In this work, we have set up an apparatus with a vibrating tube densimeter capable of measuring the density of liquids from (283.15 to 363.15) K at pressures up to 70 MPa. The vibrating tube densimeter is a DMA 512 P cell and we have calibrated it using a procedure that contains physical characteristics of the cell. We use this calibration procedure because it has been proven that it is more stable with time. We measure the density of n-heptane to check the calibration. These measurements agree with the REFPROP equation of state and with experimental measurements considered standard within 0.1 %. We have measured the density of 1-butanol and isobutyl alcohol from (283.15 to 363.15) K at pressures up to 66 MPa. The new density measurements compare with the literature experimental densities within an average absolute percentage deviation of 0.2 %.

(13)

where npts is the number of experimental data. Also the bias is calculated using 1 bias = n pts

n pts

∑ Δρi i=1

(14)

The AAD and bias are listed in Table 6 for 1-butanol and for each author’s data set. Equation 11 produces values that agree with the density measurements within 0.2 %. Therefore, we expect that our measurements agree with the literature values within this value. For isobutyl alcohol, we found less available data in the literature. A comparison of these measurements with the values from eq 11 is shown in Table 7. The maximum average absolute percentage density deviation is 1089



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Article

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AUTHOR INFORMATION

Corresponding Author

*Tel: 011 52 461 611 7575. Fax: 011 52 461 611 7744. E-mail: [email protected]. Funding

The authors thank CONACyT and DGEST for the financial support through projects CB-2012-177920 and 5036.13-P, respectively. Notes

The authors declare no competing financial interest.

■

REFERENCES

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(283.15 to 363.15) K at Pressures up to 66 MPa - American Chemical

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