Measurement of the Critical Properties of the Ternary Systems Hexane

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Measurement of the Critical Properties of the Ternary Systems Hexane + Heptane + Octane and Octane + Nonane + Decane Using a Flow Apparatus Mao-gang He,* Yang Liu, Nan Xin, Ying Zhang, and Xiangyang Liu Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, Xi’an Jiaotong University, Xi’an, Shaanxi Province 710049, P. R. China ABSTRACT: The critical temperatures (Tc) and critical pressures (pc) of ternary mixtures of hexane + heptane + octane and octane + nonane + decane were measured by a flow apparatus. The critical points are visually determined by observing the critical opalescence. The expanded uncertainties with 0.95 level of confidence in critical temperature and pressure were estimated to be 0.4 K and 0.01 MPa, respectively. The relative expanded uncertainty with 0.95 level of confidence in mole fraction was estimated to be 0.012. The experimental data are correlated by Cibulka’s and Singh’s expressions for the ternary contribution.

1. INTRODUCTION Critical properties are important design and characterization parameters for both practical and theoretical research. Fluids in the supercritical area have many favorable characteristics for applications in many processes, such as separation, material processing, chemical reactions, and so forth.1−5 The processes applying supercritical fluids usually involve two or more components. To use the advantages of supercritical fluids, mixtures in many processes should be a single phase. Therefore, the critical locus is very important to estimate the phase behavior of the mixtures. Critical properties are also important for theoretical research; these properties can be commonly used for calculating pvT properties, transport properties, and the prediction of thermodynamic property based on the corresponding states principle. In order to improve the accuracy of prediction and extend the range of applicability of predictive equations of state, experimental data for critical points of mixtures are necessary. Many experimental data of critical properties of ternary mixtures have been published,6−17 but the data are still lacking. C6−C10 normal alkanes are fundamental materials in chemical engineering and are the main components of fuel, which are widely used in power machines, for example, internal engine and aviation aircraft. The critical parameters of their mixtures are necessary for some applications. In this work, we use a flow apparatus to determine the critical properties of ternary mixtures of hexane + heptane + octane and octane + nonane + decane. The binary systems of these alkanes were measured in our previous work.18 For a ternary system, it is impractical to measure the critical properties over the whole composition range. Therefore, we selected 36 points for each ternary system with different mass © 2015 American Chemical Society

compositions. The mixtures measured in this work are all thermally stable.

2. EXPERIMENTAL SECTION 2.1. Materials. Compounds used in this work were purchased from commercial sources and used without any further purification. The purities and the suppliers of the compounds are listed in Table 1. Table 1. Suppliers and Purities of the Used Chemicals chemical

mass puritya

supplier

hexane heptane octane nonane decane

>0.990 >0.990 >0.990 >0.990 >0.990

Tianjin Guangfu Tianjin Guangfu Tianjin Guangfu Tianjin Guangfu Tianjin Guangfu

a The purities were specified by the supplier, and no purification was applied to the samples.

2.2. Apparatus and Experimental Procedure. A flowtype view apparatus was designed in our previous work to determine the critical properties based on the works of Roess19 and Rosenthal and Teja.20 The experimental apparatus used in this study is shown in Figure 1. A detailed description of the apparatus and experimental procedure was presented in our previous work.18 In brief, the fluid flows through a view Received: December 15, 2014 Accepted: November 30, 2015 Published: December 8, 2015 12

DOI: 10.1021/je501134s J. Chem. Eng. Data 2016, 61, 12−18

Journal of Chemical & Engineering Data

Article

Figure 1. Experimental system of the low-residence time flow method. ST, sample tank; DP, dual piston pump; V, valve; VP, vacuum pump; PH, preheater; TC, thermocouple; PRT, platinum resistance thermometer; PT, pressure transducer; BV, back pressure valve.

Table 2. Experimental Uncertainties in Critical Temperature, Critical Pressure, and Mole Fraction PRT, u1 temperature measurement circuit, u2 temperature control system, u3 measurement repeatability, urep combined standard uncertainty, uc expanded uncertainty U (0.95 level of confidence) pressure transducer, u1 pressure measurement circuit, u2 pressure control system, u3 measurement repeatability, urep combined standard uncertainty, uc expanded uncertainty U (0.95 level of confidence) mole number of first component, u1 mole number of first component, u2 mole number of first component, u3 purity, uP combined standard uncertainty, uc relative expanded uncertainty Ur (0.95 level of confidence)

In this study, the experimental procedure for ternary mixtures is same as the procedure for pure substances and binary mixtures. Before the measurement, the sample was degassed and well-mixed. The system was evacuated by a vacuum pump. At the beginning of critical point measurement, the experimental cell temperature was set higher than the estimated critical temperature. The degassed sample was pumped into the system, entering the bottom of the tube and exiting through the top. As the sample was pumped through the system, it was seen to flash to vapor inside the tube. When the pressure increased, this effect was no longer visible. When the temperature was close to the critical point, the gas−liquid meniscus became faint and eventually vanished at the critical point. During this process, the critical opalescence could be observed. After the critical point was exceeded, the critical opalescence disappeared, and only one transparent phase was left. Then, the cell was cooled slowly. With the temperature decreased to the critical value, the critical opalescence reappeared; the color went from colorless to yellow, to red−yellow, and to black. Then the gas−liquid meniscus reappeared, and two phases formed. At the points the meniscus disappeared and reappeared, the system was assumed to reach the critical points. Care was taken to adjust the position of the meniscus. When the critical opalescence steadily appeared near the end of the PRT, the temperature measured by the PRT was assumed to be the critical temperature, and the pressure was noted as well. The critical point of the material was visually observed at three or four flow rates. For each measurement, the whole process was repeated at least three times, and the average values were taken as the experimental data. After every measurement, the system was purged with nitrogen. In this work, the ternary mixtures were all thermally stable. The used sample was determined again, and the results show well agreement with the results in the first measurements, which mean there are no overall composition changes. 2.3. Assessment of Experimental Uncertainties. The expanded uncertainties in critical temperature and critical pressure can be given by21

temperature/K 0.02 0.001 0.005 0.2 0.2 0.4 pressure/kPa 1.25 0.2 0.8 5 5.2 10.4 mole fraction 0.0001 0.0001 0.0001 0.006 0.006 0.012

cell with heating and pressuring, critical point are determined by observing the disappearance and reappearance of the meniscus. In this process, the critical temperature and pressure can be obtained at the same time. The pressure can be regulated exactly with the temperature remains constant, which reduce the uncertainty of pressure effectively. The measurement can be carried out up to 10 MPa for pressure and 773 K for temperature. The temperature is measured by a PRT, which is installed into the tube directly. The pressure is measured by a Rosemount pressure transmitter. The mass of compounds is measured by an electronic balance. The instrument of the experimental system mainly includes a temperature sensor (Fluke 5608-12 PRT, 0.02 K), pressure transmitter (Rosemount 3051S; 0−10 MPa, 0.025%), digital multimeter (Keithley 2002), dual piston pump (LabAlliance 1500, flow control: 0.001 mL/min), temperature controller (Shimaden FP23, PID: 0.1), and electronic balance (Mettler Toledo ME204, 0.001 g).

U = kuc = k

∑ (ui)2

(1)

where ui is the standard uncertainty of each influencing factor, uc is the combined standard uncertainty composed by each 13



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Table 3. Critical Temperatures and Critical Pressures of Ternary System: Hexane + Heptane + Octanea Tc/K

a

pc/MPa

x1

x2

this workb

Cibulka’s equation

Singh’s equation

this workb


Singh’s equation

0.1267 0.1250 0.1234 0.1218 0.1202 0.1187 0.1172 0.1158 0.2457 0.2425 0.2395 0.2365 0.2336 0.2307 0.2279 0.3577 0.3533 0.3489 0.3447 0.3406 0.3365 0.4634 0.4578 0.4523 0.4470 0.4418 0.5632 0.5566 0.5501 0.5438 0.6577 0.6501 0.6428 0.7472 0.7388 0.8321

0.1089 0.2150 0.3183 0.4189 0.5170 0.6126 0.7058 0.7968 0.1056 0.2086 0.3089 0.4067 0.5022 0.5952 0.6861 0.1025 0.2025 0.3001 0.3953 0.4882 0.5788 0.0996 0.1969 0.2918 0.3844 0.4749 0.0969 0.1915 0.2839 0.3741 0.0943 0.1864 0.2764 0.0918 0.1815 0.0895

560.24 557.23 554.49 551.77 548.76 545.79 542.86 539.91 554.66 551.62 548.23 545.08 542.37 540.04 538.07 548.28 545.01 542.19 539.13 536.09 533.96 542.16 538.67 536.37 533.51 531.07 536.29 533.29 529.57 527.03 529.57 526.56 523.61 523.17 520.23 517.04

560.25 557.31 554.43 551.59 548.75 545.88 542.97 540.01 554.25 551.24 548.33 545.49 542.66 539.81 536.89 548.18 545.12 542.22 539.38 536.55 533.70 542.03 538.97 536.07 533.25 530.42 535.85 532.80 529.91 527.10 529.64 526.61 523.74 523.41 520.41 517.17

560.30 557.31 554.40 551.43 548.55 545.68 542.76 539.92 554.43 551.28 548.21 545.30 542.56 539.70 536.93 548.40 545.19 542.10 539.30 536.72 533.88 542.33 539.07 536.02 533.39 530.77 536.07 532.81 530.01 527.42 529.81 526.65 523.95 523.45 520.45 517.25

2.657 2.686 2.713 2.738 2.752 2.773 2.788 2.798 2.760 2.779 2.798 2.809 2.821 2.830 2.838 2.842 2.850 2.861 2.873 2.883 2.901 2.900 2.910 2.918 2.922 2.924 2.950 2.956 2.958 2.959 2.997 2.987 2.981 3.022 3.007 3.018

2.658 2.691 2.717 2.739 2.757 2.773 2.786 2.794 2.751 2.778 2.798 2.814 2.826 2.835 2.841 2.830 2.850 2.864 2.873 2.879 2.881 2.896 2.909 2.916 2.919 2.919 2.951 2.957 2.958 2.954 2.994 2.993 2.987 3.023 3.016 3.037

2.659 2.690 2.715 2.736 2.755 2.772 2.785 2.794 2.756 2.779 2.795 2.810 2.825 2.837 2.845 2.837 2.851 2.859 2.870 2.882 2.888 2.904 2.909 2.912 2.920 2.926 2.956 2.954 2.956 2.959 2.995 2.990 2.989 3.022 3.015 3.037

x1 and x2 represent the mole fractions of hexane and heptane. bExpanded uncertainties Ur(x) = 0.012, U(Tc) = 0.4 K, and U(pc) = 0.01 MPa.

0.95 level of confidence in mole fraction in this work are estimated to be less than 0.4 K, 0.01 MPa, and 0.012, respectively, as shown in Table 2.

uncertainty of the influencing factor. In this study, the confidence coefficient of the compound uncertainty k is taken to be 2, and the level of confidence is 0.95. The mole fraction x is calculated by xi =

ni n1 + n2 + n3

3. RESULTS AND DISCUSSION For a ternary system, it is impractical to measure the critical properties over the whole composition range. Therefore, we selected 36 points for each ternary system by different mass compositions. The critical temperatures and critical pressures of hexane + heptane + octane and octane + nonane + decane are shown in Tables 3−4 and Figures 2−5. We correlated ternary mixtures by assuming that the ternary critical state is the sum of the ideal contributions, the pseudo-excess contribution for the binary parts, and a further pseudo-excess contribution for the ternary part. To facilitate data treatment of ternary mixtures, it is necessary to acquire data regarding all binary pairs. The pure substances of the five alkanes and the binary systems hexane + heptane, hexane + octane, heptane + octane, octane + nonane, octane + decane, and nonane + decane were measured in our previous work,18

(2)

where n1, n2, and n3 are the mole numbers of three components. The expanded uncertainty in mole fraction is given by ⎛ ∂x ⎞2 2 ⎛ ∂x ⎞2 2 ⎛ ∂x ⎞2 2 Ux = kur = k ⎜ ⎟ un + u p2 ⎟ un 2 + ⎜ ⎟ un1 + ⎜ ⎝ ∂n2 ⎠ ⎝ ∂n1 ⎠ ⎝ ∂n3 ⎠ 3 (3)

where un1, un2, and un3 are the uncertainties of n1, n2, and n3, and up is the uncertainty caused by chemical purity. The expanded uncertainties with 0.95 level of confidence in critical temperature, critical pressure, and the relative expanded uncertainty with 14



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Table 4. Critical Temperatures and Critical Pressures of Ternary System: Octane + Nonane + Decanea Tc/K

a

pc/MPa

x1

x2

this workb


Singh’s equation

this workb


Singh’s equation

0.1203 0.1190 0.1178 0.1166 0.1154 0.1142 0.1131 0.1120 0.2350 0.2326 0.2302 0.2279 0.2257 0.2235 0.2213 0.3445 0.3411 0.3377 0.3344 0.3311 0.3280 0.4492 0.4448 0.4405 0.4363 0.4321 0.5493 0.5441 0.5389 0.5338 0.6452 0.6392 0.6332 0.7371 0.7304 0.8253

0.1072 0.2121 0.3148 0.4154 0.5140 0.6106 0.7053 0.7981 0.1047 0.2072 0.3077 0.4061 0.5026 0.5972 0.6899 0.1023 0.2026 0.3008 0.3972 0.4916 0.5843 0.1000 0.1981 0.2943 0.3886 0.4812 0.0979 0.1939 0.2880 0.3804 0.0958 0.1898 0.2820 0.0938 0.1859 0.0919

610.51 608.16 606.40 603.56 602.55 600.34 598.82 595.57 606.22 603.29 601.11 599.68 598.54 596.66 594.98 601.72 598.03 596.11 594.48 594.13 591.89 596.19 593.91 591.57 589.58 588.88 591.14 588.97 587.92 585.07 587.08 584.10 582.95 581.23 579.97 576.92

610.07 607.33 605.26 603.62 602.15 600.57 598.58 595.91 604.18 600.95 598.90 597.53 596.36 594.93 592.81 598.38 594.79 592.76 591.56 590.57 589.15 592.92 589.20 587.28 586.29 585.45 587.92 584.35 582.73 582.05 583.39 580.29 579.19 579.25 576.96 575.42

611.22 608.68 606.38 604.29 602.32 600.29 598.17 595.55 606.20 603.47 601.24 599.48 598.00 596.21 593.57 601.20 598.37 596.29 595.02 593.74 591.56 596.21 593.36 591.75 590.84 589.03 591.28 588.78 587.52 586.06 586.47 584.34 582.88 581.78 579.89 577.02

2.218 2.247 2.280 2.286 2.312 2.337 2.345 2.338 2.267 2.295 2.328 2.347 2.352 2.376 2.372 2.320 2.348 2.374 2.395 2.384 2.405 2.372 2.385 2.415 2.427 2.419 2.420 2.430 2.435 2.452 2.448 2.454 2.477 2.478 2.483 2.500

2.224 2.248 2.272 2.295 2.317 2.334 2.346 2.349 2.283 2.303 2.325 2.348 2.369 2.383 2.387 2.334 2.351 2.372 2.392 2.407 2.413 2.381 2.396 2.414 2.428 2.434 2.424 2.437 2.449 2.455 2.462 2.471 2.476 2.492 2.495 2.509

2.230 2.255 2.277 2.297 2.314 2.328 2.339 2.343 2.282 2.303 2.325 2.346 2.362 2.373 2.378 2.324 2.343 2.367 2.386 2.397 2.402 2.365 2.385 2.406 2.419 2.423 2.408 2.427 2.442 2.446 2.450 2.464 2.469 2.485 2.491 2.506

x1 and x2 represent the mole fractions of octane and nonane. bExpanded uncertainties Ur (x) = 0.012, U(Tc) = 0.4 K, and U(pc) = 0.01 MPa.

with the coefficients for the Redlich−Kister equation22 shown in Table 5. We use Cibulka’s23 and Singh’s24 equations to describe the critical temperature and pressure of the ternary system. Cibulka:

Singh and Sharma: n

Tc,123 = x1Tc,1 + x 2Tc,2 + x3Tc,3 + n

+

n

Tc,123 = x1Tc,1 + x 2Tc,2 + x3Tc,3 +

∑ a12,kx1x2(2x1 − 1)

k−1

∑ a23,kx2x3(2x2 − 1)

+

k=1

∑ a13,kx1x3(2x1 − 1)

n

+

(4)

n

+

∑ b12,kx1x2(2x1 − 1)k− 1

+ x1x 2x3(β1 + β2x1 + β3x 2)

∑ b12,kx1x2(2x1 − 1)k− 1 k=1 n

∑ b23,kx2x3(2x2 − 1)k− 1 + ∑ b13,kx1x3(2x1 − 1)k− 1 k=1

k=1

+ x1x 2x3(β1 + β2x1(x 2 − x3) + β3x12(x 2 − x3)2 )

k=1 n

∑ b23,kx2x3(2x2 − 1)k− 1 + ∑ b13,kx1x3(2x1 − 1)k− 1 k=1

(6)

n

pc,123 = x1pc,1 + x 2pc,2 + x3pc,3 +

k=1

n

pc,123 = x1pc,1 + x 2pc,2 + x3pc,3 +

k=1

+ x1x 2x3(α1 + α2x1(x 2 − x3) + α3x12(x 2 − x3)2 )

k−1

+ x1x 2x3(α1 + α2x1 + α3x 2)

k=1 n

∑ a23,kx2x3(2x2 − 1)k− 1 + ∑ a13,kx1x3(2x1 − 1)k− 1 k=1

k=1 n

n

+

k−1

∑ a12,kx1x2(2x1 − 1)k− 1

(7)

where Tc,i and pc,i are the critical temperature and pressure of component i; here we use the values we measured in our previous work,18 which are shown in Table 6; n is set as 3 in the correlation, xi is the mole fraction of component i; aij,k and bij,k are

k=1

(5) 15



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Figure 2. Experimental critical temperatures for the hexane + heptane + octane system. The critical surface is generated using the Cibulka’s equation: red ○, this work; blue line, Cibulka’s correlation.

Figure 5. Experimental critical pressures for the octane + nonane + decane system. The critical surface is generated using the Cibulka’s equation; red ○, this work; blue line, Cibulka’s correlation.

Table 5. Coefficients of Redlich−Kister Equations18 binary mixtures

a1/K

hexane + heptane 6.195 hexane + octane 20.620 heptane + octane 4.868 octane + nonane 1.810 octane + decane 15.401 nonane + decane 4.986

a2/K

a3/K

−0.740 1.279 0.360 0.232 1.629 5.543

−2.397 0.372 −0.063 7.033 6.483 6.101

b1/MPa b2/MPa b3/MPa 0.203 0.519 0.164 0.217 0.369 0.201

0.043 0.203 0.009 −0.005 0.096 0.026

0.159 0.153 0.086 0.276 0.258 0.094

Table 6. Experimental Critical Temperatures and Pressures for Pure Compounds18 experimental critical dataa

Figure 3. Experimental critical pressures for the hexane + heptane + octane system. The critical surface is generated using the Cibulka’s equation: red ○, this work; blue line, Cibulka’s correlation. a

compounds

Tc/K

pc/MPa

hexane heptane octane nonane decane

507.79 540.14 568.92 594.52 617.73

3.033 2.736 2.496 2.278 2.106

Expanded uncertainties U(Tc) = 0.4 K and U(pc) = 0.01 MPa.

α and β and the RMSD for the ternary mixtures are summarized in Table 7. The agreements of Cibulka’s and Singh’s equations to the data are comparable. The two equations for the hexane + heptane + octane system both have correlation coefficients (R2) above 0.99, for critical temperature and critical pressure. The maximum average absolute deviations are 0.047% for critical temperature and 0.151% for critical pressure. The two equations for the octane + nonane + decane system both have correlation coefficients (R2) above 0.99 for critical temperatures and above 0.98 for critical pressures. The maximum average absolute deviations were 0.10% for critical temperature and 0.28% for critical pressure. The critical temperatures and critical pressures obtained in this work are shown in Figures 6−9 as relative deviations from the values predicted from in eqs 4−7. The plots in the low temperature range are for ΔTc of hexane + heptane + octane, and those in the high temperature range are for ΔTc of octane + nonane + decane. Otherwise the plots in high pressure range are for Δpc of hexane + heptane + octane and those in the low range Δpc of octane + nonane + decane. Most of the

Figure 4. Experimental critical temperatures for the octane + nonane + decane system. The critical surface is generated using the Cibulka’s equation: red ○, this work; blue line, Cibulka’s correlation.

the coefficients of the Redlich−Kister equation for each binary, which are shown in Table 6; and α and β are the ternary parameters for temperatures and pressures, respectively. The values of 16



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Table 7. Coefficients AAD and R2 of Cibulka’s and Singh’s Equations hexane + heptane + octane temperature α1/K α2/K α3/K RMSD/K AAD/% R2 pressure β1/MPa β2/MPa β3/MPa RMSD/MPa AAD/% R2

octane + nonane + decane

Cibulka’s

Singh’s

Cibulka’s

Singh’s

−19.3884 −0.8981 32.3253 0.33 0.047 0.9990

−12.6663 40.7807 695.3291 0.32 0.046 0.9991

−156.7074 158.1609 330.3831 0.73 0.100 0.9922

−5.5099 477.1353 1952.5443 0.76 0.087 0.9915

0.3341 0.0080 −0.1515 0.006 0.151 0.9958

0.1628 −0.4047 20.3534 0.005 0.130 0.9973

−1.8645 2.2324 2.8448 0.008 0.285 0.9875

−0.3164 3.9837 −16.4616 0.007 0.281 0.9889

Figure 8. Fractional deviations Δpc = pc(expt) − pc(calc) in the experimental critical pressures pc(expt) of ternary mixtures: hexane + heptane + octane, and octane + nonane + decane from values pc(calc) estimated from Cibulka’s correlation. ●, This work, with error bars representing the expanded uncertainty.

Figure 6. Fractional deviations ΔTc = Tc(expt) − Tc(calc) in the experimental critical temperatures Tc(expt) of ternary mixtures: hexane + heptane + octane, and octane + nonane + decane from values Tc(calc) estimated from Cibulka’s correlation. ●, This work, with error bars representing the expanded uncertainty.

Figure 9. Fractional deviations Δpc = pc(expt) − pc(calc) in the experimental critical pressures pc(expt) of ternary mixtures: hexane + heptane + octane, and octane + nonane + decane from values pc(calc) estimated from Singh and Sharma’s correlation. ●, This work, with error bars representing the expanded uncertainty.

deviations in the critical temperatures are between ±0.25%, with two deviations between 0.25% and 0.50% in each equation. All of the deviations in the critical pressures are between ±1%. The agreement between our experimental data and fitted data is satisfactory.

4. CONCLUSION As presented in this work, the critical temperatures (Tc) and critical pressures (pc) of ternary mixtures of hexane + heptane + octane and octane + nonane + decane were measured by a flow apparatus. The experimental values were correlated by Cibulka’s and Singh’s expressions for the ternary contribution equation. For the hexane + heptane + octane system, the maximum average absolute deviations were 0.047% for critical temperature and 0.151% for critical pressure. For the octane + nonane + decane system, the maximum average absolute deviations were 0.100% for critical temperature and 0.285% for critical pressure.

Figure 7. Fractional deviations ΔTc = Tc(expt) − Tc(calc) in the experimental critical temperatures Tc(expt) of ternary mixtures: hexane + heptane + octane, and octane + nonane + decane from values Tc(calc) estimated from Singh and Sharma’s correlation. ●, This work, with error bars representing the expanded uncertainty. 17



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containing propanol and alkanes using a flow view-type apparatus. J. Supercrit. Fluids 2016, 108, 35−44. (18) Liu, Y.; Zhang, Y.; He, M. G.; Xin, N. Determination of the critical properties of C6−C10 n-alkanes and their binary systems using a flow apparatus. J. Chem. Eng. Data 2014, 59, 3852−3857. (19) Roess, L. C. Determination of critical temperature and pressure of petroleum fractions by a flow method. J. Pet. Technol. 1936, 22, 665− 705. (20) Rosenthal, D. J.; Teja, A. S. The critical properties of n-alkanes using a low-residence time flow apparatus. AIChE J. 1989, 35, 1829− 1834. (21) BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP and OIML. Evaluation of measurement data. Guide to the expression of uncertainty in measurement; Joint Committee for Guides in Metrology, 2008 (22) Redlich, O.; Kister, A. T. Algebraic representation of thermodynamic properties and the classification of solutions. Ind. Eng. Chem. 1948, 40, 345−348. (23) Cibulka, I. Estimation of excess volume and density of ternary liquid mixtures of non-electrolytes from binary data. Collect. Czech. Chem. Commun. 1982, 47, 1414−1419. (24) Singh, P. P.; Sharma, V. K. Thermodynamics of ternary mixtures of non-electrolytes: excess volumes. Can. J. Chem. 1983, 61, 2321−2328.

AUTHOR INFORMATION

Corresponding Author

*Tel.: +86-29-8266-3863. Fax: +86-29-8266-8789. E-mail: [email protected]. Funding

This work was supported by the National Natural Science Fund for Distinguished Young Scholars of China (NSFC No. 51525604). Notes

The authors declare no competing financial interest.

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Measurement of the Critical Properties of the Ternary Systems Hexane

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