Article pubs.acs.org/jced
Excess Molar Volumes for Three- and Four-Component Mixtures Simulating the Binary Mixture (Cyclohexane + Hexadecane) Kenneth N. Marsh*,†,‡ and Anthony Brown †
Centre for Energy, School of Mechanical and Chemical Engineering, The University of Western Australia, Crawley, Western Australia 6009, Australia ‡ Department of Chemical and Process Engineering, University of Canterbury, Christchurch 8041, New Zealand ABSTRACT: Excess molar volumes of mixtures of cyclohexane and pseudocyclohexane (an equimolar mixture of cyclopentane + cycloheptane) with hexadecane and various pseudohexadecanes (equimolar mixtures of tetradecane + octadecane, decane + docosane, or octane + tetracosane) have been measured at 313.15 K. The results for the multicomponent mixtures are compared with those for the binary mixtures and they show that n-alkanes obey, not quite within experimental uncertainty, an extended principle of congruence with cyclohexane as the other component, whereas mixtures of pseudocyclohexane with hexadecane do not obey the extended principle.
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INTRODUCTION
EXPERIMENTAL SECTION The source and purity of the materials are summarized in Table 1. They were used without further purification except for
1
The principle of congruence of Brønsted and Koefoed states that the properties of a multicomponent n-alkane mixtures should depend only on the average carbon number of the mixture. For example, an n-alkane mixture of pentane (C5) (1) + heptane (C7) (2) with x1+2 = 0.5 mixed with tetradecane (C14) (3) + (1 − x) octadecane (C18) (4) with x3+4 = 0.5 should have the same excess volume, density, excess enthalpy, and excess Gibbs energy as an equimolar mixture of hexane (C6) + hexadecane (C16) and all mixtures should have the same density as undecane (C11). This principle has been found to hold for n-alkane mixtures nearly within experimental uncertainty2−4 and holds to a lesser extent with other alkane substituted homologous series such as n-alkan-1-ols.5,6 In our earlier work,7 the principle was shown to hold for the excess volumes of three and four component mixtures simulating hexane + hexadecane to within 1 % relative at VEm (max) for hexane + hexadecane. For the excess enthalpy with similar mixtures, the agreement was within 2 % relative at HEm (max).7 Measurements have been made on mixtures of cycloalkanes with pseudocycoloalkanes by Letcher et al.,8 and it was concluded that cycloalkanes did not satisfy the principle of congruence to the same extent as n-alkanes. In this work, the hypothesis that an extended principle can be applied to pseudocycloalkane mixtures with n-alkanes was tested. Also tested was the hypothesis that a pseudo-n-alkane (for example an equimolar mixture of tetradecane + octadecane) behaves the same as hexadecane when mixed with an arbitrary second component. © XXXX American Chemical Society
Table 1. Source and Mole Fraction Purity of Materials
a
chemical name
source
puritya
analysis methodb
cyclopentane cyclohexane cycloheptane octane decane tetradecane hexadecane octadecane docosane tetracosane
Fluka Fluka Fluka BDH Sigma Sigma Sigma Fluka Fluka Sigma
0.998 0.999 0.998 0.997 0.999 0.996 0.994 0.989 0.997 0.997
GC GC GC GC GC GC GC GC GC GC
Samples were used as received. bGas−liquid chromatography.
passing through a column of activated alumina. The purities were determined with a Varian GLC using a flame ionization detector with a 20 m capillary SE-30 column with splitter. The pseudoalkanes and pseudocycloalkanes were prepared as described previously.7 Briefly, the mixtures were prepared by mass in a flask containing a ground glass stopper with the mass of the less volatile component being determined first and then Special Issue: Memorial Issue in Honor of Anthony R. H. Goodwin Received: April 9, 2015 Accepted: July 3, 2015
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DOI: 10.1021/acs.jced.5b00331 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 2. Density, Molar Mass, and Molar Volume of the Pure Fluids and Pseudocyclohexane and Various Pseudohexadecanes with Mole Fraction x of the Component with the Lowest Molar Mass at p = 0.1 MPaa component
x
ρ/g·cm−3
M/g·mol−1
Vm/cm3·mol−1
T/K
cyclohexane cyclohexane (TRC TDE)10 pseudocyclohexane (5,7) hexadecane hexadecane (TRC TDE)10 pseudohexadecane (14,18) pseudohexadecane (10,22) pseudohexadecane (8,24) pseudohexadecane (8,24)
1 1 0.4999 1 1 0.5001 0.5001 0.5000 0.5000
0.7598 ± 0.0001 0.7597 ± 0.0001
84.156
110.761
84.164 226.448
298.154
226.445 226.435 226.448 226.448
298.56 298.37 299.10 298.43
313.15 313.15 313.15 313.15 313.15 313.15 313.15 315.65 313.15
0.7595 ± 0.0001 0.7598 ± 0.0002 0.7584 0.7589 0.7571 0.7588
a Numbers in brackets are the carbon number of the compounds in the pseudomixture. Standard uncertainties u are u(x) = 0.0002, u(T) = 0.01 K, and the combined standard uncertainties with a 95 % confidence level (k = 2) for u(ρ) = 0.0001 g·cm−3.
al.9 to within 0.005 cm3·mol−1 in the overlap region. With the dilution method, the uncertainty varies as the volume of the second component is added. For the measurements reported here, the maximum values of the excess volumes are of the order of 0.6 cm3·mol−1. The uncertainty in VE at a 95 % confidence limit is high at low mole fractions: at xi = 0.02 δVE/ VE ≈ 0.02 (δVE ≈ 0.0002 cm3·mol−1), whereas at xi ≈ 0.5 δVE/ VE ≈ 0.007 (δVE ≈ 0.005 cm3·mol−1).
the more volatile component was added with the amounts calculated to give a mixture that just filled the flask and had a mole fraction of each component of (0.5000 ± 0.0002). Mass measurements were corrected to mass in vacuo. To avoid bubble formation during density and excess volume measurements, the pure fluids and the mixture were degassed by three freeze−thaw cycles, using liquid nitrogen, with vacuum applied during each freeze step, prior to loading the liquids into the pycnometer or dilatometer. This method of degassing ensured that there was minimal change in the mole fraction of the mixture. Densities of the pure cyclohexane, hexadecane, and the three pseudohexadecane mixtures were measured with a pycnometer having a precision calibrated 1 mm capillary containing a reference mark. The volume at the reference was (11.454 ± 0.003) cm3 at (298.150 ± 0.005) K determined from an average of three calibrations with water. The volume of the pycnometer at other temperatures was calculated from the known thermal expansion of glass. For density measurements, the height of the fluid relative to the reference mark was measured to ± 0.02 mm with a cathetometer. The estimated uncertainties in the densities at a 0.95 confidence level was 0.0001 g·cm−3. The density of the pseudohexane mixture was not reported as changes in the composition due to evaporation of the volatile materials during transfer from the preparation vessel to the pycnometer would have resulted in an incorrect density measurement. The majority of measurements were made at (313.15 ± 0.01) K except for the pseudohexadecane mixture prepared from octane + tetracosane which was made at (315.65 ± 0.01) K as that binary mixture was a solid at 313.15 K. The water thermostat was controlled to ± 0.001 K. Temperatures were measured with a platinum resistance thermometer calibrated on IPTS-68 and then adjusted to IPS-90. For measurements on cyclohexane + pseudohexadecane (equimolar C8 + C24), the whole apparatus as well as the equimolar C8 + C24 mixture added to the upper volume in the first run and subsequently added to the buret in the second run had to be kept in an enclosure heated to a temperature greater than 320 K and then immediately transferred to the thermostat held at 315.65 K to prevent solidification of the equimolar C8 +C24 mixture. Excess volume measurements were made with a dilatometer whose operation has been described in detail.9 The volume of the bulb was (18.959 ± 0.009) cm3 and the buret consisting of 110 mm of 5 cm bore and 240 mm of 10 mm bore calibrated precision glass tubing giving the dilatometer a total volume of 41.5 cm3. Measurements on the test mixtures benzene (1) + cyclohexane (2) at 298.15 K agreed with the results of Stokes et
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RESULTS AND DISCUSSION The densities of the pure fluids and pseudomixtures are listed in Table 2. The density of cyclohexane and hexadecane agree within the assigned uncertainties of the critically evaluated values derived using a dynamic data evaluation performed within the NIST/TRC ThermoData Engine accessing the NIST/TRC Source database.10 The densities of the various pseudohexadecanes are close to the density of hexadecane indicating that the principal hold for the densities. The excess volumes for the mixtures listed in Table 3 were fit by a least-squares regression to eq 1 using the routine in Excel and confirmed using a web based nonlinear regression package11 n
VmE/(cm 3·mol−1) = x(1 − x) ∑ aix i i=0
(1)
The coefficients of eq 1 are listed in Table 4 along with the standard deviations in VE. Excess volumes for cyclohexane (1) + pseudohexadecane (equimolar C8 + C24) (2) measured at 315.65 K were compared with the results for hexane + hexadecane by adjusting the constant a1 in eq 1 for hexane + hexadecane. This adjustment was calculated by assuming that the temperature variation in VE was linear in temperature and that the temperature dependence for this system was the same as for cyclohexane (1) + hexadecane (2). For this system the values of VE at x2 = 0.5 are (0.629, 0.628, and 0.646) cm3·mol−1 at 298.15 K (refs 12, 13, and 14, respectively), 0.600 cm3·mol−1 at 303.15 K (ref 15), and 0.567 cm3·mol−1 at 313.15 K (this work), giving a difference of 0.008 cm3·mol−1 between 313.15 K and 315.65 K at x2 = 0.5. El-Banna and El-Batouti16 measured densities over the temperature range from 283 K to 313 K, but their densities and excess volumes are clearly wrong. The excess volumes are all negative with a value interpolated from their Figure 1 at x1 ≈ 0.5 of −1.1 cm3·mol−1 at 298.15 K and −0.6 cm3·mol−1 at 313.15 K. The unusual feature of their results is that VE values calculated from the densities reported in their Table 2 do not B
DOI: 10.1021/acs.jced.5b00331 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 3. Excess Molar Volumes VE at p = 0.1 MPa of Cyclohexane and Pseudocyclohexane with Hexadecane and Various Pseudohexadecanes with Mole Fraction x1 of the Component or Mixture with the Lowest Molar Massa x1
VE/cm3·mol−1
0.00830 0.03441 0.08390 0.1372 0.2221 0.3029 0.3641 0.4199 0.4911 0.5316 0.5632
0.0132 0.0531 0.1341 0.2074 0.3185 0.4088 0.4671 0.5136 0.5593 0.5779 0.5878
0.0117 0.0420 0.1024 0.1334 0.2193 0.3183 0.3959 0.4643 0.5264 0.5659 0.6048
0.0188 0.0648 0.1522 0.1948 0.3074 0.4172 0.4871 0.5364 0.5687 0.5815 0.5887
0.0326 0.0633 0.0985 0.1309 0.2414 0.3497 0.4354 0.4962 0.5420 0.5814
0.0510 0.0976 0.1472 0.1911 0.3297 0.4409 0.5073 0.5427 0.5601 0.5728
0.0169 0.0459 0.0991 0.1432 0.2309 0.3265 0.4171 0.4856 0.5509 0.5906 0.6325
0.0349 0.0768 0.1488 0.2072 0.3191 0.4221 0.5009 0.5455 0.5754 0.5860 0.5893
0.0051 0.0305 0.0657 0.1081 0.1416 0.2226 0.2881 0.3571 0.4100 0.4629 0.5095
0.0008 0.0211 0.0561 0.0951 0.1232 0.1880 0.2297 0.2669 0.2889 0.3060 0.3164
VE/cm3·mol−1
x1
x1
VE/cm3·mol−1
0.8303 0.8736 0.8928 0.9106 0.9242 0.9453 0.9634 0.9801 0.9880 0.9948
0.4675 0.3939 0.3535 0.3105 0.2747 0.2130 0.1518 0.0860 0.0532 0.0230
0.8574 0.8718 0.8918 0.9202 0.9408 0.9592 0.9778 0.9866 0.9941 0.9994
0.4206 0.3941 0.3529 0.2833 0.2242 0.1637 0.0913 0.0545 0.0243 0.0021
cyclohexane (1) + hexadecane (2) T = 313.15 K 0.5900 0.5938 0.6216 0.5968 0.6527 0.5956 0.6834 0.5888 0.7073 0.5731 0.7163 0.5728 0.7223 0.5731 0.7489 0.5558 0.7508 0.5513 0.7749 0.5318 0.8022 0.5039 cyclohexane (1) + pseudohexadecane(14,18) (2) T = 313.15 K 0.6424 0.5888 0.6795 0.5828 0.7074 0.5729 0.7096 0.5712 0.7331 0.5597 0.7372 0.5567 0.7489 0.5496 0.7629 0.5383 0.7884 0.5152 0.8134 0.4868 0.8393 0.4498 cyclohexane (1) + pseudohexadecane(10,22) (2) T = 315.15 K 0.6144 0.5782 0.6474 0.5773 0.6798 0.5710 0.7030 0.5632 0.7118 0.5552 0.7247 0.5522 0.7378 0.5409 0.7491 0.5362 0.7817 0.5060 0.8006 0.4864 cyclohexane (1) + pseudohexadecane(8,24) (2) T = 315.65 K 0.6670 0.5863 0.6919 0.5794 0.7100 0.5724 0.7188 0.5565 0.7352 0.5611 0.7466 0.5399 0.7512 0.5520 0.7719 0.5211 0.7926 0.5020 0.8146 0.4775
0.8187 0.8398 0.8555 0.8771 0.9009 0.9336 0.9668 0.9815 0.9898 0.9986
0.4641 0.4345 0.4095 0.3734 0.3286 0.2426 0.1348 0.0763 0.0342 0.0031
0.8385 0.8616 0.8864 0.9000 0.9248 0.9481 0.9707 0.9859 0.9898 0.9935
0.4458 0.4085 0.3612 0.3311 0.2691 0.2007 0.1225 0.0618 0.0456 0.0294
Pseudocyclohexane (5,7) (1) + hexadecane (2) T = 315.15 K 0.5462 0.3218 0.5915 0.3227 0.6351 0.3186 0.6781 0.3115 0.7085 0.2999 0.7092 0.2992 0.7297 0.2915 0.7399 0.2853 0.7499 0.2819 0.7989 0.2495
0.8298 0.8649 0.8953 0.9243 0.9528 0.9650 0.9785 0.9831 0.9937 0.9974
0.2250 0.1924 0.1596 0.1228 0.0816 0.0623 0.0381 0.0195 0.0105 0.0043
C
DOI: 10.1021/acs.jced.5b00331 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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Table 3. continued a Numbers in brackets are the carbon number of the compounds in the pseudomixture. Standard uncertainties u are u(x) = 0.0005, u(T) = 0.01 K, and the combined standard uncertainties with a 95 % confidence level (k = 2) for u(VE) = 0.001 cm3·mol−1 at xi ≈ 0.1 and u(VE) = 0.005 cm3·mol−1 at xi ≈ 0.5.
Table 4. Coefficients to Eq 1 and Standard Deviation σ in VEa
a
system
T/K
a0
a1
a2
a3
a4
σ/cm3·mol−1
cyclohexane + hexadecane cyclohexane + hexadecaneb cyclohexane + pseudohexadecane (14,18) cyclohexane + pseudohexadecane (10,22) cyclohexane + pseudohexadecane (8,24) pseudocyclohexane (5,7) + hexadecane
313.15 315.65 313.15 313.15 315.65 313.15
1.7284 1.6979 1.5937 1.6583 1.8012 0.7970
−0.4844 −0.4844 0.3463 −0.4561 −1.9638 2.0393
5.9529 5.9529 3.4358 5.9063 11.1865 −4.7194
−8.8401 −8.8401 −5.5023 −8.8261 −15.7214 6.2375
6.2140 6.2140 4.6169 6.1135 9.2071 −2.5335
0.0018 0.0011 0.0032 0.0040 0.0026
Numbers in brackets are the carbon number of the compounds in the pseudomixture. bExtrapolated to T = 315.65 K as explained in text.
agree with the values in their Figure 1. The value calculated from the density at x1 ≈ 0.5 and T = 298.15 K using their eq 11 is ≈ −0.20 cm3·mol−1. Furthermore, the values calculated from their eq 12 using their coefficients from Table 3 do not agree with either the plot in their Figure 1, nor with the values calculated from their reported densities and their eq 11. Figure 1 is a plot of VE for cyclohexane + hexadecane at 313.15 K. In the overlap region the results from the two runs
Figure 3. Plot of 103 δVE (symbol blue ◆) as a function of x1 where δVE is the difference in the excess volumes VE for the mixture cyclohexane (1) + pseudohexadecane (10,22) (2) at T = 313.15 K and the value of VE calculated from the eq 1 for cyclohexane (1) + hexadecane (2) at T = 313.15 K with coefficients given in Table 4. Figure 1. Plot of excess volumes VE for cyclohexane (1) + hexadecane (2) at T = 313.15 K. Blue ◇, hexadecane into cyclohexane; red □, hexane into hexadecane. The line is calculated from eq 1 with coefficients from Table 4.
agree within 0.002 cm3·mol−1. Figures 2, 3, and 4 are deviation plots of the difference in VE from the values calculated from the equation for VE for the mixture cyclohexane + hexadecane given in Table 4 and the experimental values for mixtures of
Figure 4. Plot of 103 δVE (symbol green Δ) as a function of x1 where δVE is the difference is the difference between the excess volumes VE for the mixture cyclohexane (1) + pseudohexadecane (8,24) (2) at T = 315.65 K from the value of VE calculated from the eq 1 for cyclohexane (1) + hexadecane (2) at 315.65 K with coefficients given in Table 4.
cyclohexane and the three pseudohexadecanes. Figure 2 shows that there is a difference of −0.008 cm3·mol−1 at x = 0.5 for an equimolar C14 + C18 mixture which is within the combined experimental uncertainty of ≈0.010 cm3·mol−1. For an equimolar C10 +C22 mixture (Figure 3), the difference at the same conditions is −0.020 cm3·mol−1, which is considerably greater than the combined experimental uncertainty. For the equimolar C8 + C24 mixture at 315.65 K (Figure 4), the overlap between the two runs is poor as explained above with the maximum difference being 0.014 cm3·mol−1. However, the
Figure 2. Plot of 103 δVE (symbol purple ◊) as a function of x1 where δVE is the difference between the excess volumes VE for the mixture cyclohexane (1) + pseudohexadecane (14,18) (2) at T = 313.15 K and the value of VE calculated from eq 1 for cyclohexane (1) + hexadecane (2) at T = 313.15 K with coefficients given in Table 4. D
DOI: 10.1021/acs.jced.5b00331 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
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maximum difference from the equation for cyclohexane + hexadecane is −0.010 cm3·mol−1, within the combined uncertainties. These measurements show that pseudohexadecane composed of mixtures of equimolar even-chain number nalkanes obey the principle of congruence. Previous results7 have shown that the excess volumes of pseudohexane (an equimolar mixture of pentane and heptane) + pseudohexadecane prepared from various even chain number n-alkanes also obey the principle with the difference from the binary alkane mixture being about 0.008 cm3·mol−1. Looi et al.2 measured both excess enthalpies and excess volumes for pseudohexadecane consisting of an equimolar mixture of tridecane + nonadecane and concluded that the principle held. A further application of the congruence principle is illustrated in the recent measurements of Ramos-Estrada et al.17 who reported density measurements on mixtures of pentane, octane, and nonane over a wide temperature range. The density data for mixtures at mole fractions corresponding to the intermediate pure alkanes show agreement with those pure alkanes almost within experimental uncertainty. It is concluded that multicomponent mixtures of nalkanes of both even and odd chain length in a non-n-alkane solvent (cyclohexane) would obey the principle of congruence almost with experimental uncertainty. For mixtures of pure n-alkanes with a pseudocyclohexane composed of an equimolar mixture of cyclopentane + cycloheptane (Figure 5), the difference in VE from the binary
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Figure 5. Plot of δVE (symbol red ◆) as a function of x1 where δVE is the difference between the excess volumes VE for the mixture pseudocyclohexane (5,7) (1) + hexadecane (2) at T = 313.15 K from the value of VE calculated from the eq 1 for cyclohexane (1) + hexadecane (2) at T = 313.15 K with coefficients given in Table 4.
mixture of cyclohexane + hexadecane at x = 0.5 is −0.28 cm3· mol−1, so clearly mixtures of cycloalkanes do not obey the principle of congruence. This lack could be attributed to cycloalkanes with different carbon numbers having different symmetry and different hindered rotations.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest. This work was completed at the University of New England, Armidale, NSW, Australia.
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ACKNOWLEDGMENTS The authors thank Dr. Thomas Hughes for help in finalizing the publication. E
DOI: 10.1021/acs.jced.5b00331 J. Chem. Eng. Data XXXX, XXX, XXX−XXX
