Densities of Cresols and Linear Alkane Mixtures at High Pressure

Article pubs.acs.org/jced

Densities of Cresols and Linear Alkane Mixtures at High Pressure O. Elizalde-Solis,† D. García-Fuentes,‡ S. Á lvarez-Badillo,‡ A. Zúñiga-Moreno,‡ L. E. Camacho-Camacho,‡ and L. A. Galicia-Luna*,‡ †

Departamento de Ingeniería Química Petrolera, ESIQIE, Instituto Politécnico Nacional, UPALM, Edif. 8, 2° piso, Lindavista, C.P. 07738, México, D. F., México ‡ Laboratorio de Termodinámica, SEPI-ESIQIE, Instituto Politécnico Nacional, UPALM, Ed. Z, Secc. 6, 1ER piso, Lindavista, C.P. 07738, México, D.F., México ABSTRACT: This work reports experimental densities for o-, m-, and p-cresol and the m-cresol (x) + o-cresol (1 − x) mixture at x = 0.4891 and heptane (x) + undecane (1 − x) mixtures at x = 0.0, 0.05, 0.2346, 0.5063, 0.7482, and 0.9511, in the compressed liquid region from (313 to 363) K and from (1 to 25) MPa. Vibrating periods of each fluid or mixture under study were carried out in a commercial vibrating tube densimeter from Anton Paar. Then, their corresponding densities were obtained by relating density and vibrating periods of water and nitrogen or water and R134a as reference fluids with the vibrating period of the concerning fluids. Uncertainties for the measured properties are estimated to be ρ ± 0.2 kg·m−3, p ± 0.008 MPa, T ± 0.02 K, and x ± 0.0005. Experimental densities were represented within the experimental uncertainty using an empirical equation of six parameters. Thermodynamic-derived properties were also computed from this equation. Excess molar volumes for the binary mixtures of cresols and linear alkanes are negative. Extrapolated densities for the pure components and mixtures at atmospheric pressure are in agreement with the literature data. with accurate measurements on volumetric properties of fluids of environmental and industrial interest. Pure compound densities of cresols and undecane are presented. A mixture of m-cresol + o-cresol and the binary system heptane + undecane is also reported.

1. INTRODUCTION Accurate density for fluids is required for diverse applications in science and industry. Additionally, some properties derived from density can give more information about the volumetric behavior of fluids and their mixtures. For example, excess molar volume gives information about volume changes upon mixing, and these can be related to the spatial disposition of the molecules that form the mixture, usually closely connected with their size and shape. Hydrocarbon mixtures are important for their relevance in the petroleum industry. Mixtures of liquid alkanes have been studied for mixtures composed for pentane up to decane; however mixtures having a heavier alkane are less common in the literature. For pure alkanes there are many different works with efforts to describe their volumetric behavior. A summarization of references where experimental densities at high pressure of heptane and undecane are reported can be found in the work by Cibulka and Hnedkovský.1 On the other hand volumetric properties for cresols are scarce in the literature; these are very toxic materials, but they have a wide variety of uses as solvents, disinfectants, or intermediates in the production of numerous other substances. These compounds are presented in coal tar, fragrances, antioxidants, dyes, pesticides, and some resins.2,3 Their densities are higher than water. Density data at high pressure have been reported for m-cresol by Chang and Lee,4 Chang et al.,5 Randzio et al.,6 Siddiqi and Teja,7 and Belinskii and Ergopulo.8 Besides, Cibulka et al.9 reported the parameters for a Tait type equation for the calculation of m-cresol densities. These parameters were obtained by the evaluation and correlation of data reported in the literature. The vibrating tube densimeter is a suitable apparatus that can provide with reliable measurements.10 This work is a continuation of the effort to provide © 2013 American Chemical Society

2. EXPERIMENTAL SECTION 2.1. Materials. Cresols and linear alkanes were purchased from Sigma-Aldrich and were used as received without a further purification stage. Certified purities and CAS numbers are listed in Table 1. Table 1. Purity of Chemicals certified purity chemical name

source

CAS

mole fraction

o-cresol m-cresol p-cresol heptane undecane

Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich Sigma-Aldrich

95-48-7 108-39-4 106-44-5 142-82-5 1120-21-4

0.999 0.99 0.9986 0.999 0.997

2.2. Experimental Procedure. The experimental apparatus and procedure have been described in previous published researches.11,12 The apparatus is based on the static-synthetic Received: January 11, 2013 Accepted: May 30, 2013 Published: June 25, 2013 2163

dx.doi.org/10.1021/je400055v | J. Chem. Eng. Data 2013, 58, 2163−2175

Journal of Chemical & Engineering Data

Article

Table 2. Experimental Densities for o-Cresola T/K = 313.20

T/K = 323.16

T/K = 333.10

T/K = 343.06

T/K = 352.99

p/MPa

ρf/kg·m−3

p/MPa

ρf/kg·m−3

p/MPa

ρf/kg·m−3

p/MPa

ρf/kg·m−3

p/MPa

ρf/kg·m−3

1.022 2.031 3.017 4.012 5.018 6.010 7.005 8.006 9.004 10.005

1027.5 1028.1 1028.7 1029.2 1029.8 1030.4 1030.9 1031.5 1032.0 1032.6

1.013 2.039 3.007 4.009 5.005 6.004 6.999 8.008 9.002 10.005

1018.7 1019.3 1019.9 1020.5 1021.1 1021.7 1022.2 1022.8 1023.4 1024.0

1.010 2.033 3.009 4.014 5.004 5.998 7.000 8.009 9.004 10.010

1009.9 1010.5 1011.1 1011.8 1012.4 1013.0 1013.6 1014.2 1014.8 1015.4

1.023 2.024 3.015 4.003 5.009 6.005 7.008 8.003 8.999 10.004

1000.8 1001.6 1002.2 1002.9 1003.6 1004.2 1004.8 1005.5 1006.1 1006.7

1.043 2.000 3.034 4.015 5.033 6.007 7.016 8.006 9.015 10.014

991.9 992.6 993.3 994.0 994.6 995.3 996.0 996.7 997.3 998.0

Standard uncertainties are: u(x1) = 5·10−4 mol·mol−1, u(T) = 0.02 K, and u(p) = 0.002 MPa. The combined expanded uncertainty is Uc(ρf) = 0.2 kg·m−3 with 0.95 level of confidence (k ≈ 2). a

Table 3. Experimental Densities for m-Cresola T/K = 313.22

T/K = 322.90

T/K = 332.61

T/K = 342.27

T/K = 352.06

T/K = 361.90

p/MPa

ρf/kg·m−3

p/MPa

ρf/kg·m−3

p/MPa

ρf/kg·m−3

p/MPa

ρf/kg·m−3

p/MPa

ρf/kg·m−3

p/MPa

ρf/kg·m−3

1.001 2.012 3.024 4.007 4.992 6.027 7.013 8.000 9.008 10.014 11.015 12.040 13.022 14.023 15.002 16.009 17.020 18.021 19.016 20.026 21.024 22.026 23.030 24.017 25.019

1019.1 1019.8 1020.3 1020.9 1021.4 1022.0 1022.6 1023.1 1023.7 1024.3 1024.8 1025.4 1026.0 1026.4 1026.9 1027.5 1028.0 1028.5 1029.0 1029.6 1030.1 1030.7 1031.1 1031.6 1032.2

1.014 2.041 3.002 4.014 5.012 6.022 7.020 8.018 9.020 10.005 11.018 12.019 13.017 14.010 15.022 16.000 17.011 18.018 19.018 20.009 21.019 22.019 23.006 24.012 25.019

1011.2 1011.8 1012.4 1013.0 1013.6 1014.2 1014.7 1015.3 1015.9 1016.4 1017.0 1017.6 1018.2 1018.7 1019.3 1019.8 1020.4 1020.9 1021.4 1022.0 1022.6 1023.1 1023.6 1024.1 1024.7

1.018 2.014 3.003 4.030 5.000 6.022 7.020 8.020 9.003 10.014 11.012 12.000 13.000 14.028 15.028 16.023 17.000 18.008 19.000 20.001 21.013 22.010 23.007 24.000 25.008

1003.3 1004.0 1004.5 1005.2 1005.8 1006.4 1006.9 1007.5 1008.1 1008.7 1009.3 1009.9 1010.4 1011.0 1011.6 1012.2 1012.7 1013.3 1013.9 1014.4 1014.9 1015.5 1016.0 1016.6 1017.1

2.018 2.999 3.998 4.976 5.984 7.059 8.070 8.967 9.994 10.921 11.964 12.971 13.954 14.960 15.941 16.963 17.992 18.963 19.996 21.003 21.974 22.968 24.051 24.971

995.8 996.4 997.0 997.6 998.3 998.9 999.7 1000.2 1000.8 1001.4 1002.1 1002.6 1003.2 1004.0 1004.3 1005.1 1005.8 1006.2 1006.7 1007.5 1008.0 1008.7 1009.2 1009.7

1.951 2.979 4.034 4.966 5.929 7.014 8.011 8.921 9.982 10.938 11.975 12.999 13.907 14.981 15.966 16.996 17.984 18.991 20.005 21.038 22.019 23.001 24.029 24.969

988.5 989.1 989.8 990.3 990.9 991.6 992.2 992.8 993.4 994.0 994.6 995.3 995.8 996.5 997.1 997.7 998.3 998.9 999.5 1000.1 1000.6 1001.2 1001.8 1002.3

1.990 3.001 4.024 5.019 6.014 7.025 8.019 9.010 9.978 11.019 12.038 13.020 14.021 15.006 15.970 16.988 17.991 19.016 20.042 20.983 22.034 23.021 24.011 24.912

980.5 981.2 981.8 982.5 983.1 983.7 984.4 985.0 985.6 986.3 986.9 987.6 988.2 988.8 989.4 990.1 990.7 991.4 992.0 992.6 993.3 993.9 994.6 995.1

Standard uncertainties are: u(x1) = 5·10−4 mol·mol−1, u(T) = 0.02 K, and u(p) = 0.002 MPa. The combined expanded uncertainty is Uc(ρf) = 0.2 kg·m−3 with a 0.95 level of confidence (k ≈ 2). a

method coupled to the vibrating tube technique. It is mainly constituted by a variable volume cell which contains the mixture or pure component and the vibrating tube densimeter (Anton Paar, 512P) for measuring the oscillation period of sample. The experiment starts with the washing of the cell, vibrating tube densimeter (VTD), and all the circuit by using organic solvents and carbon dioxide. Afterward, the cell was filled with the pure component and degassed to eliminate the presence of light components. For the binary mixture, each degassed component was fed to the evacuated cell from separate autoclaves. The components with low and high vapor pressure are added in that order. The mass of each component was known by successive loadings by using a comparator balance (Sartorius, MCA 1200).

The cell with the sample under study was placed into the air bath (Spame) and connected to the VTD which is thermally regulated by a liquid bath (Polyscience, 9510). Temperature was measured by calibrated platinum resistance probes 100-Ω (Thermo-est). Pressure was registered in a pressure transducer (Sedeme, 250) previously calibrated. Both instruments are connected to digital indicators. After degassing all the circuit where the pure compound or mixture will flow, the temperature is set to the desired value, and the sample from the cell was fed to the VTD. A piston allows adjusting pressure; this is displaced by a pressurizing system which uses nitrogen and a (HiP) syringe pump. The vibrating period of the fluid or sample (τf) under study at a specific temperature (T) and pressure (p) is registered after equilibrium conditions are reached. This condition is achieved 2164



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Table 4. Experimental Densities for p-Cresola T/K = 312.90

T/K = 322.78

T/K = 332.54

T/K = 342.37

T/K = 352.15

T/K = 361.90

p/MPa

ρf/kg·m−3

p/MPa

ρf/kg·m−3

p/MPa

ρf/kg·m−3

p/MPa

ρf/kg·m−3

p/MPa

ρf/kg·m−3

p/MPa

ρf/kg·m−3

1.002 2.016 3.017 4.016 5.002 6.010 7.000 8.006 9.001 10.002 11.006 12.002 13.015 14.007 15.006 16.019 17.004 18.011 19.009 20.005 21.008 22.004 23.023 24.004 25.006

1019.4 1020.0 1020.6 1021.1 1021.7 1022.2 1022.8 1023.3 1023.9 1024.4 1024.9 1025.5 1026.0 1026.6 1027.1 1027.6 1028.1 1028.6 1029.2 1029.7 1030.2 1030.7 1031.2 1031.7 1032.2

1.019 2.015 3.002 4.013 5.011 6.018 7.022 8.001 9.015 10.006 11.002 12.018 13.002 14.016 15.001 16.000 17.001 18.029 19.015 20.011 21.022 22.002 23.006 24.010 25.023

1011.6 1012.2 1012.8 1013.4 1013.9 1014.5 1015.1 1015.7 1016.3 1016.8 1017.4 1017.9 1018.4 1019.0 1019.5 1020.1 1020.6 1021.2 1021.7 1022.2 1022.8 1023.3 1023.8 1024.4 1024.9

1.040 2.019 3.013 4.019 5.001 6.001 7.002 8.041 9.000 10.001 11.006 12.001 13.008 14.004 15.003 16.015 17.011 18.014 19.014 20.009 21.013 22.007 23.000 24.001 25.032

1003.7 1004.3 1005.0 1005.6 1006.2 1006.8 1007.5 1008.1 1008.7 1009.2 1009.7 1010.4 1010.9 1011.5 1012.1 1012.7 1013.3 1013.9 1014.4 1014.9 1015.4 1016.0 1016.6 1017.1 1017.7

1.001 2.002 3.004 4.025 5.036 6.032 7.001 8.020 9.003 10.002 11.036 12.001 13.020 14.019 15.007 16.000 17.022 18.014 19.033 20.005 21.005 22.010 22.962 24.021 25.017

995.7 996.4 997.1 997.7 998.2 998.8 999.3 999.9 1000.6 1001.3 1001.9 1002.6 1003.2 1003.9 1004.5 1005.1 1005.6 1006.2 1006.8 1007.4 1007.9 1008.4 1009.0 1009.7 1010.2

1.023 2.007 3.000 4.003 5.001 6.009 7.001 8.037 9.008 10.040 11.006 12.001 13.001 14.009 15.000 16.010 17.028 18.020 19.045 20.018 21.038 22.000 23.065 24.024 25.039

987.9 988.5 989.1 989.8 990.4 991.1 991.7 992.4 993.0 993.7 994.3 994.9 995.5 996.2 996.8 997.4 998.0 998.6 999.3 1000.0 1000.5 1001.1 1001.8 1002.4 1002.9

1.017 1.991 3.004 4.027 4.992 6.000 7.033 8.010 9.001 9.998 10.994 11.976 12.949 14.010 15.017 15.992 16.992 18.007 19.034 19.992 21.000 22.059 23.020 24.014 25.002

979.6 980.3 981.0 981.5 982.3 983.1 983.6 984.4 985.0 985.8 986.5 987.0 987.7 988.3 989.0 989.6 990.3 990.8 991.6 992.1 992.9 993.4 994.1 994.8 995.3


Table 5. Optimized Parameters and Deviations for Density of Cresols Using eq 2 Tmin/K Tmax/K pmin/MPa pmax/MPa N d1/MPa·m3·kg−1 d2/m3·kg−1 d3/MPa d4/MPa·K−1 d5/MPa·K−1/2 d6 AAD/% bias/% SDV/% RMS/%

o-cresol

m-cresol

p-cresol

m-cresol (x) + o-cresol (1 − x) x = 0.4891

313.20 352.99 1.010 10.014 50 −5.1451 −0.01750 −5872.54 −7.205 −94.23 −20.99 2.7·10−3 1.2·10−6 3.5·10−3 3.5·10−3

313.22 361.9 1.001 25.019 147 −0.9558 −0.00239 −1421.15 −0.167 22.32 −2.986 7.6·10−3 −1.0·10−6 1.0·10−2 1.0·10−2

312.9 361.9 1.001 25.039 150 −1.3407 −0.00447 −1424.92 −1.935 −30.89 −5.329 5.6·10−3 −4.4·10−6 7.6·10−3 7.6·10−3

313.19 362.91 0.998 25.036 150 −1.2118 −0.00386 −1505.39 −1.2073 −6.36 −4.655 2.9·10−3 −3.4·10−4 3.6·10−3 3.6·10−3

fluids for determining alkane densities. Since cresols have higher vibrating periods than water and nitrogen, we decided to use R134a (1,1,1,2-tetrafluoroethane) and water as calibration fluids.

when τ, T, and p are stable within the instruments uncertainties. Variables are monitored in a personal computer by connecting all of the instruments to a data acquisition system. Pressure is increased with the pressurizing system to register vibrating periods at different pressure isothermally. Once measurements were obtained at fixed temperature, it was again set to another value up to cover all the studied range of temperature and pressure. The density of the fluid or mixture (ρf) is calculated by relating its vibrating period with the density and vibrating periods of reference fluids at the same conditions of temperature and pressure using eq 1. Water and nitrogen were used as reference

ρf (p , T , τ ) = ρA (p , T ) +

[τf2(p , T ) − τA2(p , T )][ρA (p , T ) − ρB (p , T )] τA2(p , T ) − τB2(p , T )

(1)

where the subscript f denotes the fluid, reference fluids are named in subscripts as A and B. Density data for water and nitrogen were calculated using the equations of state reported in the literature.13,14 In the case of the refrigerant R134a, it was taken 2165



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from the National Institute of Standards and Technology database.15 The experimental uncertainties for temperature, pressure, composition and density are within ± 0.02 K, ± 0.002 MPa, ± 5·10−4 mole fraction, and ± 0.2 kg·m−3, respectively. These were obtained according to the error propagation law as suggested by NIST.16

3. RESULTS AND DISCUSSION 3.1. Cresols. Densities for cresols were measured in the compressed liquid region. Data for o-cresol are reported from (313.20 to 352.99) K and (1 to 10) MPa in Table 2. In the case of results for m-cresol, and p-cresol, these are summarized in Tables 3 and 4 in the ranges of (313.22 to 361.99) K and (1 to 25) MPa. Density behavior is proportional to pressure changes at fixed temperature; on the contrary, it decreases when temperature is increased keeping pressure as constant. The magnitude of density for the different cresols increase in the following order: o-cresol > p-cresol > m-cresol; nevertheless, p-cresol, and m-cresol have close density values. Density data were correlated using a six-parameter equation: ρf =

d3 − d4T + d5T1/2 + d6p d1 + d 2p

Figure 1. Residuals for densities of p-cresol calculated with the sixparameter equation. ●, 312.90 K; ○, 322.78 K; ▼, 332.54 K; △, 342.37 K; ■, 352.15 K; □, 361.90 K.

Density measurements for a binary mixture consisting of m-cresol (x) + o-cresol (1−x) at x = 0.4891 were performed in the ranges of (313.19 to 362.91) K and (1 to 25) MPa. Values are listed in Table 6; these are within those corresponding to pure components of m-cresol and o-cresol. Density behavior of this mixture is shown in Figure 2. Excess molar volumes were also calculated: these were negative, but the order of magnitude is too low (−5.5·10−5 to −9.0·10−5) m3·kmol−1 for the studied temperature. Taking into account the obtained uncertainty of ±2·10−5 m3·kmol−1, error bars cross each other between each isothermal data. High pressure density data for cresols are reported for m-cresol by Chang and Lee,4 Chang et al.,5 Randzio et al.,6 and Siddiqi and Teja.7 We took the advantage of eq 2 and parameters listed in Table 5 to perform comparison between our calculated data and reference values reported at (318.2, 323.15, 333.15, 338.2, 348.15, and 353.15) K. Density residuals are depicted in Figure 3. As can be observed, data from this work agree with those reported by Chang et al.,5 Randzio et al.,6 and Siddiqi and Teja7 according to the reported uncertainty in this work and the reported on each reference. Systematic deviations were found when our calculated data were compared with those reported by Chang and Lee4 which are out of the experimental uncertainty. Deviations are attributed to the used calibration fluids (water and nitrogen) by Chang and Lee4 which induce an error since their vibrating periods are lower than mcresol. The comparison with the data sets of Siddiqi and Teja7 at 338.2 is lower than 0.4 kg·m−3; nevertheless, deviations are higher at 318.2 K in the order of 8.6 kg·m−3. On the contrary, densities for m-cresol using the Tait equation were used to compare against our related data sets. Parameters for this equation are reported by Cibulka et al.9 which were optimized from volumetric properties database available in the literature. Residuals are plotted in Figure 4. It is important to point out that the RMSD is reported to be 0.23 kg·m−3 for the correlated data in ref 9 using the Tait equation. Therefore, higher deviations (>1.2 kg·m−3) are observed at higher temperatures (352.06 and 361.90) K. Densities of o-cresol and p-cresol are not reported in the literature at high pressure. The only available data are published at atmospheric pressure in a wide range of temperature; then, we extrapolated our data for these fluids at this pressure and compared with the literature data within our interval of

(2)

Parameters (di) were obtained using the Levenberg−Marquardt least-squares optimization algorithm with the following objective function: ⎡ ρ exp − ρ cal ⎤ fj fj ⎥ S = ∑ ⎢⎢ exp ⎥ ρ fj j=1 ⎣ ⎦ N

(3)

Optimized parameters from eq 2 for each pure component are listed in Table 5 as well as its corresponding statistical deviations between experimental and calculated densities. The absolute average deviation is expressed as: AAD/% =

1 N−1

N

∑ j=1

⎛ ρ exp − ρ cal ⎞ fj fj ⎟ 100⎜⎜ ⎟ ρfexp j ⎝ ⎠

(4)

The bias: 1 bias/% = N

⎡ ⎛ ρ exp − ρ cal ⎞⎤ f f ∑ ⎢⎢100⎜⎜ j exp j ⎟⎟⎥⎥ ρf j=1 ⎢ j ⎠⎥⎦ ⎣ ⎝ N

(5)

The standard deviation:

SDV/% =

1 N−z

⎡ ⎛ ρ exp − ρ cal ⎞⎤2 f f ∑ ⎢⎢100⎜⎜ j exp j ⎟⎟⎥⎥ ρf j=1 ⎢ j ⎠⎥⎦ ⎣ ⎝ N

(6)

It is influenced by the number of parameters (z) from eq 2. Finally the root-mean-square deviation is obtained as:

RMSD/% =

1 N

⎡ ⎛ ρ exp − ρ cal ⎞⎤2 f f ∑ ⎢⎢100⎜⎜ j exp j ⎟⎟⎥⎥ ρf j=1 ⎢ j ⎠⎥⎦ ⎣ ⎝ N

(7)

According to the values of these deviations, density data were represented within the experimental uncertainty using the sixparameter equation as can be observed in Figure 1 for p-cresol. 2166



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Table 6. Experimental Densities for m-Cresol (x) + o-Cresol (1 − x) Mixture at x = 0.4891a T/K = 313.19

T/K = 323.14

T/K = 333.08

T/K = 343.04

T/K = 352.98

T/K = 362.91

p/MPa

ρf/kg·m−3

p/MPa

ρf/kg·m−3

p/MPa

ρf/kg·m−3

p/MPa

ρf/kg·m−3

p/MPa

ρf/kg·m−3

p/MPa

ρf/kg·m−3

1.020 2.041 3.049 4.014 5.025 6.012 7.014 8.027 9.004 10.008 11.008 12.039 13.005 14.031 15.024 16.041 17.007 18.005 19.012 20.003 21.015 22.002 23.025 24.014 24.998

1023.8 1024.3 1024.9 1025.5 1026.0 1026.6 1027.1 1027.7 1028.3 1028.8 1029.3 1029.9 1030.4 1031.0 1031.5 1032.1 1032.6 1033.1 1033.6 1034.1 1034.7 1035.2 1035.7 1036.2 1036.7

0.998 2.038 3.068 4.028 5.041 6.017 7.027 8.018 9.048 9.99 11.013 12.02 13.038 14.016 15.002 16.013 17.008 17.999 19.009 20.015 21.009 22.03 23.005 24.03 25.001

1015.4 1016.0 1016.6 1017.1 1017.8 1018.3 1018.9 1019.5 1020.1 1020.6 1021.2 1021.8 1022.4 1022.9 1023.5 1024.0 1024.6 1025.1 1025.6 1026.2 1026.7 1027.3 1027.8 1028.4 1028.9

1.027 2.064 3.013 4.032 5.013 6.028 6.994 8.018 9.011 10.024 11.006 12.018 13.008 14.004 15.01 16.037 17.017 18.003 19.007 20.044 21.05 22.033 23.055 24.061 25.034

1007.0 1007.6 1008.2 1008.8 1009.4 1010.1 1010.6 1011.3 1011.9 1012.5 1013.0 1013.7 1014.2 1014.8 1015.4 1016.0 1016.6 1017.1 1017.7 1018.3 1018.9 1019.4 1020.0 1020.6 1021.1

1.023 2.058 3.018 4.014 5.041 6.017 7.021 8.015 9.002 10.007 11.005 12.048 13.009 14.021 15.007 16 16.997 18.007 19.007 20.018 21.021 22.047 23.001 24 25.036

998.4 999.0 999.7 1000.3 1001.0 1001.6 1002.3 1002.9 1003.5 1004.1 1004.8 1005.4 1006.0 1006.6 1007.2 1007.9 1008.4 1009.1 1009.7 1010.2 1010.8 1011.4 1011.9 1012.5 1013.1

1.044 2.022 3.013 4.033 5.025 6.022 6.987 8.002 9.015 10.002 11.021 12.02 12.989 13.995 14.994 16.022 17.008 17.98 19.028 20.008 21.015 22.078 23.014 24.059 25.032

990.0 990.6 991.3 992.0 992.6 993.3 993.9 994.7 995.3 996.0 996.6 997.2 997.9 998.5 999.1 999.8 1000.4 1001.0 1001.7 1002.3 1002.9 1003.5 1004.2 1004.8 1005.4

1.053 2.013 3.019 4.022 5.041 6.004 6.993 8.006 9.004 9.999 10.996 11.992 13.011 14.001 15.009 16.01 17.013 18.019 19.009 20.041 21.009 22.009 23.019 24.028 25.029

981.5 982.2 982.9 983.6 984.3 985.0 985.7 986.3 987.0 987.7 988.3 989.0 989.7 990.3 991.0 991.7 992.3 993.0 993.6 994.3 994.9 995.5 996.2 996.8 997.5

Standard uncertainties are: u(x1) = 5·10−4 mol·mol−1, u(T) = 0.02 K, u(p) = 0.002 MPa. The combined expanded uncertainty is Uc(ρf) = 0.2 kg·m−3 with a 0.95 level of confidence (k ≈ 2). a

Figure 2. Experimental density (ρ) for m-cresol (x) + o-cresol (1 − x) system: Black and open symbols denote ∼313.20 K and ∼352.67 K, respectively. (▼, ▽) x = 0.0; (●, ○) x = 0.4891; (■, □)x = 1.0.

Figure 3. Density residuals for m-cresol between experimental reference data (●, 323.15 K ref 4; ○, 348.15 K ref 4; ▼, 333.15 K ref 5; △, 353.15 K ref 6; ■, 338.2 K ref 7) and those calculated from this work using eq 2.

temperature as shown in Figures 5 and 6. Differences between our extrapolated data and those measured at atmospheric pressure vary within ± 1.8 kg·m−3 for p-cresol and ±1.5 kg·m−3 for o-cresol. Our extrapolated densities for p-cresol and o-cresol using eq 2 are not able to represent the density data for both components from literature17−20 within the experimental uncertainty except for few data reported by Yang et al.18 and Bhatia et al.20 Thermodynamic derived properties were calculated from eq 2. The isobaric expansivity is obtained from the derivative of the density function with respect to the temperature at constant

pressure {αp = −(1/ρm)(∂ρm/∂T)p}, the isothermal compressibility is the derivative of the density function with respect to pressure at constant temperature {κT = −(1/ρm)(∂ρm/∂p)T}, and the thermal pressure coefficient is the ratio of these two variables {γV = αp/κT} and the internal pressure {pi = T γV − p}. Behavior of these variables with respect to pressure changes are plotted in Figures 7 and 8 for o-cresol and m-cresol, respectively. αp and κT values are proportional to temperature changes at fixed pressure; it also increases if pressure is low at constant temperature. The opposite behavior is observed for γV and pi. 2167



Article

Figure 7. Isobaric expansivity (αp, open symbols) and isothermal compressibility (κT, black symbols) behavior of o-cresol with respect to pressure changes. (○, ●) 313.20 K; (▽, ▼) 323.16 K; (□, ■) 333.10 K; (◇, ◆) 343.06 K; (△, ▲) 352.99 K.

Figure 4. Density residuals for m-cresol. Experimental data from this work against calculated data using Tait equation from ref 9: ○, 313.22 K; ▽, 322.90 K; □, 332.61 K; ◇, 342.27 K; △, 352.06 K; ☆, 361.90 K.

Figure 8. Thermal pressure coefficient (γV, open symbols) and internal pressure (pi, black symbols) behavior of m-cresol with respect to pressure changes. (○, ●) 313.22 K; (▽, ▼) 323.16 K; (□, ■) 333.10 K; (◇, ◆) 343.06 K; (△, ▲) 352.99 K; (☆, ★) 361.90 K.

Figure 5. Density residuals for p-cresol at atmospheric pressure between experimental data from literature (●, ref 17; ○, ref 18; △, ref 19; ▼, ref 20) and extrapolated data from this work calculated with eq 2.

reported in Tables 7 to 11 in the compressed liquid region. Compositions for this system were prepared at x = 0.0, 0.05, 0.2346, 0.5063, 0.7482, and 0.9511 mole fraction. Measurements are reported isothermally from (313 to 363) K in the pressure range of (1 to 25) MPa. As expected, density values are proportional to pressure changes and inversely proportional to temperature changes; besides, as the presence of heptane increases, density is low due to the lower carbon chain and pure component density compared with undecane. Experimental results at fixed composition were represented using eq 2; therefore, the optimized parameters di are independent of T and p within the studied conditions. Good agreement was found between experimental and calculated densities; their residuals are within the experimental uncertainty. Parameters and statistical deviations are reported in Table 13 for each composition. Experimental density data reported from Tables 2 to 4 and 6 to 12, were also optimized using a Tait-like equation.21 The obtained statistical deviations were higher than the obtained with eq 2. Moreover, we have used the empirical six-parameter equation because it represents a series of experimental density data (see for instance ref 11) with low deviations and its practical use which does not need a reference state. Therefore, this justifies the use of the empirical eq 2.

Figure 6. Density residuals for o-cresol at atmospheric pressure between experimental data from the literature (●, ref 17; ○, ref 19; ▼, ref 20) and extrapolated data from this work calculated with eq 2.

3.2. Heptane (x) + Undecane (1 − x). Experimental density data for the binary heptane (x) + undecane (1−x) system are 2168



Article

Table 7. Experimental Densities for Undecanea T/K = 313.15

T/K = 323.10

T/K = 333.02

T/K = 342.09

T/K = 352.93

T/K = 362.91

p/MPa

ρf/kg·m−3

p/MPa

ρf/kg·m−3

p/MPa

ρf/kg·m−3

p/MPa

ρf/kg·m−3

p/MPa

ρf/kg·m−3

p/MPa

ρf/kg·m−3

1.000 2.001 3.001 4.000 5.000 6.001 7.000 8.000 9.000 10.000 11.000 12.000 13.000 14.001 15.000 16.000 17.000 18.000 19.000 20.000 21.001 22.000 23.000 24.000 25.000

726.6 727.3 728.0 728.7 729.5 730.2 731.0 731.8 732.6 733.4 734.1 734.9 735.7 736.4 737.2 737.9 738.7 739.4 740.0 740.7 741.3 742.0 742.6 743.2 743.7

1.000 2.000 3.000 4.000 5.001 6.000 7.000 8.000 9.000 10.001 11.000 12.000 13.000 14.000 15.001 16.000 17.000 18.000 19.000 20.000 21.000 22.000 23.000 24.000 25.000

719.0 719.8 720.6 721.4 722.2 723.0 723.8 724.6 725.5 726.3 727.1 727.9 728.7 729.5 730.3 731.1 731.9 732.6 733.3 734.0 734.7 735.4 736.0 736.7 737.3

1.000 2.001 3.000 4.000 5.000 6.000 7.000 8.001 9.000 10.000 11.000 12.000 13.000 14.000 15.000 16.000 17.000 18.000 19.000 20.000 21.000 22.000 23.000 24.000 25.000

711.3 712.1 713.0 713.8 714.7 715.5 716.4 717.3 718.1 719.0 719.9 720.7 721.5 722.4 723.2 724.0 724.8 725.6 726.3 727.1 727.8 728.5 729.2 729.9 730.5

1.000 2.000 3.001 4.000 5.000 6.000 7.000 8.000 9.000 10.000 11.000 12.000 13.000 14.000 15.000 16.000 17.000 18.000 19.000 20.000 21.000 22.000 23.000 23.999 25.000

703.9 704.8 705.8 706.7 707.6 708.5 709.4 710.4 711.2 712.2 713.1 714.0 714.8 715.7 716.6 717.4 718.2 719.1 719.9 720.6 721.4 722.2 722.9 723.6 724.3

1.000 2.000 3.001 4.000 5.000 6.000 7.001 8.000 9.000 10.001 11.000 12.000 13.000 14.000 15.000 16.000 17.000 18.000 19.000 20.000 21.000 22.000 23.000 24.000 25.000

696.5 697.4 698.4 699.4 700.4 701.4 702.3 703.3 704.3 705.2 706.2 707.1 708.0 709.0 709.8 710.7 711.6 712.5 713.3 714.1 715.0 715.7 716.5 717.3 718.0

1.000 2.001 3.000 4.000 5.001 6.001 7.001 8.000 9.000 10.000 11.000 12.001 13.000 14.001 15.001 16.001 17.001 18.000 19.001 20.000 21.000 22.000 23.000 24.000 25.000

688.8 689.9 691.0 692.0 693.1 694.1 695.2 696.2 697.2 698.2 699.2 700.2 701.1 702.1 703.0 704.0 704.9 705.8 706.6 707.5 708.4 709.2 710.0 710.9 711.6


Table 8. Experimental Densities for the Heptane (x) + Undecane (1 − x) Mixture at x = 0.05a ρf/kg·m−3 p/MPa

313.15 K

323.12 K

333.09 K

343.02 K

352.96 K

362.92 K

1.001 2.001 3.000 4.000 5.000 6.000 7.000 8.001 9.000 10.000 11.000 12.000 13.000 14.000 15.000 16.000 17.000 18.000 19.000 20.000 21.000 22.001 23.000 24.000 25.000

724.3 725.1 726.0 726.8 727.6 728.4 729.2 730.0 730.8 731.6 732.3 733.1 733.8 734.5 735.2 735.9 736.6 737.3 738.0 738.7 739.3 740.0 740.6 741.3 741.9

716.7 717.6 718.5 719.4 720.3 721.1 722.0 722.8 723.6 724.5 725.3 726.1 726.8 727.6 728.4 729.1 729.9 730.6 731.3 732.0 732.7 733.4 734.1 734.8 735.4

709.1 710.1 711.0 712.0 712.9 713.8 714.7 715.6 716.5 717.3 718.2 719.0 719.9 720.7 721.5 722.3 723.1 723.8 724.6 725.4 726.1 726.8 727.6 728.3 729.0

701.5 702.5 703.6 704.6 705.5 706.5 707.5 708.4 709.3 710.2 711.1 712.0 712.9 713.8 714.6 715.5 716.3 717.1 717.9 718.7 719.5 720.3 721.1 721.8 722.6

694.0 695.1 696.1 697.2 698.2 699.2 700.2 701.2 702.2 703.2 704.1 705.1 706.0 706.9 707.8 708.7 709.6 710.4 711.3 712.1 712.9 713.8 714.6 715.4 716.2

686.5 687.6 688.7 689.8 690.9 692.0 693.0 694.1 695.1 696.1 697.1 698.1 699.1 700.0 701.0 701.9 702.8 703.7 704.6 705.5 706.4 707.3 708.1 708.9 709.8


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Table 9. Experimental Densities for the Heptane (x) + Undecane (1 − x) Mixture at x = 0.2346a T/K = 313.16

T/K = 323.15

T/K = 333.09

T/K = 343.06

T/K = 352.99

T/K = 362.91

p/MPa

ρf/kg·m−3

p/MPa

ρf/kg·m−3

p/MPa

ρf/kg·m−3

p/MPa

ρf/kg·m−3

p/MPa

ρf/kg·m−3

p/MPa

ρf/kg·m−3

1.000 2.001 3.000 4.001 5.000 6.000 7.000 8.000 9.000 10.000 11.001 12.000 13.000 14.000 15.000 16.000 17.000 18.000 19.000 20.000 21.000 22.000 23.000 24.000 25.000

716.5 717.4 718.3 719.2 720.0 720.8 721.7 722.5 723.3 724.1 724.8 725.6 726.4 727.1 727.8 728.6 729.3 730.0 730.7 731.4 732.1 732.7 733.4 734.0 734.7

1.000 2.000 3.000 4.001 5.001 6.001 7.001 8.000 9.000 10.000 11.000 12.000 13.000 14.000 15.000 16.001 17.000 18.000 19.000 20.000 21.033 22.034 23.036 24.037 25.039

708.9 709.9 710.8 711.7 712.6 713.5 714.4 715.2 716.1 716.9 717.7 718.5 719.4 720.1 720.9 721.7 722.5 723.2 724.0 724.7 725.4 726.1 726.9 727.5 728.2

1.004 2.004 3.003 4.003 5.003 6.003 7.003 8.002 9.002 10.002 11.002 12.002 13.001 14.001 15.002 16.002 17.002 18.002 19.001 20.002 21.035 22.036 23.038 24.039 25.041

701.3 702.3 703.3 704.2 705.2 706.1 707.0 708.0 708.9 709.7 710.6 711.5 712.3 713.2 714.0 714.8 715.6 716.4 717.2 718.0 718.8 719.5 720.3 721.0 721.8

1.010 2.010 3.010 4.011 5.011 6.011 7.012 8.012 9.012 10.013 11.013 12.014 13.014 14.014 15.015 16.016 17.016 18.017 19.017 20.018 21.051 22.053 23.055 24.057 25.059

693.6 694.6 695.7 696.7 697.7 698.7 699.7 700.6 701.6 702.5 703.5 704.4 705.3 706.2 707.0 707.9 708.8 709.6 710.4 711.3 712.1 712.9 713.7 714.5 715.2

1.015 2.016 3.016 4.017 5.018 6.019 7.020 8.020 9.021 10.022 11.022 12.023 13.024 14.025 15.026 16.027 17.028 18.030 19.030 20.031 21.066 22.068 23.071 24.073 25.076

685.9 687.0 688.1 689.2 690.2 691.3 692.3 693.3 694.4 695.3 696.3 697.3 698.2 699.2 700.1 701.0 701.9 702.8 703.7 704.5 705.4 706.3 707.1 707.9 708.7

1.023 2.024 3.026 4.027 5.028 6.029 7.031 8.032 9.033 10.035 11.036 12.037 13.038 14.040 15.041 16.043 17.044 18.046 19.047 20.049 21.083 22.086 23.089 24.092 25.095

678.2 679.4 680.6 681.7 682.8 683.9 685.0 686.1 687.1 688.2 689.2 690.2 691.2 692.2 693.2 694.1 695.1 696.0 696.9 697.8 698.8 699.6 700.5 701.4 702.2



313.12 K

323.11 K

333.04 K

343.01 K

352.96 K

362.94 K

2.001 3.000 4.000 5.000 6.000 7.000 8.001 9.000 10.000 11.000 12.000 13.000 14.000 15.000 16.000 17.001 18.000 19.000 20.000 21.001 22.050 23.000 24.000 25.000

703.7 704.6 705.6 706.5 707.4 708.2 709.1 709.9 710.8 711.6 712.4 713.2 714.0 714.8 715.6 716.3 717.1 717.8 718.5 719.2 720.0 720.6 721.3 722.0

695.8 696.8 697.8 698.8 699.7 700.7 701.6 702.5 703.4 704.3 705.1 706.0 706.8 707.6 708.5 709.3 710.1 710.8 711.6 712.4 713.1 713.9 714.6 715.3

688.0 689.0 690.1 691.1 692.1 693.1 694.1 695.0 696.0 696.9 697.8 698.7 699.6 700.5 701.4 702.2 703.1 703.9 704.7 705.6 706.3 707.1 707.9 708.7

680.1 681.2 682.3 683.4 684.5 685.5 686.5 687.6 688.6 689.5 690.5 691.5 692.4 693.4 694.3 695.2 696.1 697.0 697.8 698.7 699.5 700.4 701.2 702.0

672.2 673.4 674.6 675.7 676.8 677.9 679.0 680.1 681.2 682.2 683.2 684.2 685.2 686.2 687.2 688.1 689.1 690.0 690.9 691.8 692.7 693.6 694.5 695.3

664.4 665.6 666.8 668.0 669.2 670.4 671.5 672.6 673.8 674.8 675.9 677.0 678.0 679.1 680.1 681.1 682.1 683.1 684.0 685.0 685.9 686.9 687.8 688.7


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Table 11. Experimental Densities for the Heptane (x) + Undecane (1−x) Mixture at x = 0.7482a ρf/kg·m−3 p/MPa

313.15 K

323.12 K

333.05 K

343.03 K

352.97 K

362.91 K

1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.000 11.000 12.000 13.000 14.000 15.000 16.000 17.000 18.000 19.000 20.000 21.000 22.000 23.000 24.000 25.000

687.4 688.4 689.4 690.4 691.3 692.3 693.2 694.1 695.0 695.9 696.8 697.6 698.5 699.3 700.1 700.9 701.7 702.5 703.3 704.0 704.8 705.5 706.2 707.0 707.7

679.1 680.2 681.3 682.3 683.4 684.4 685.4 686.4 687.3 688.3 689.2 690.1 691.1 691.9 692.8 693.7 694.5 695.4 696.2 697.0 697.8 698.6 699.4 700.1 700.9

670.8 672.0 673.1 674.3 675.4 676.4 677.5 678.6 679.6 680.6 681.6 682.6 683.6 684.5 685.4 686.4 687.3 688.2 689.0 689.9 690.8 691.6 692.4 693.2 694.0

662.4 663.6 664.9 666.1 667.2 668.4 669.5 670.6 671.7 672.8 673.9 674.9 675.9 677.0 678.0 678.9 679.9 680.8 681.8 682.7 683.6 684.5 685.4 686.2 687.1

654.0 655.3 656.6 657.8 659.1 660.3 661.5 662.7 663.9 665.0 666.1 667.2 668.3 669.4 670.5 671.5 672.5 673.5 674.5 675.5 676.5 677.4 678.3 679.2 680.2

645.5 646.9 648.3 649.6 650.9 652.2 653.5 654.7 656.0 657.2 658.4 659.5 660.7 661.8 662.9 664.0 665.1 666.2 667.2 668.3 669.3 670.3 671.3 672.2 673.2


densities at (30 and 40) MPa accurately. The uncertainty reported for authors are: ± 0.3 kg·m−3 by Valencia et al.,22 ± 1.5 kg·m−3 by Doolittle,23 and ± 0.75 kg·m−3 by Landau and Würflinger.24 The maximum residuals between literature and our data are 0.48 kg·m−3, 1.0 kg·m−3, and 0.53 kg·m−3, respectively. On the other hand, parameters for the Tait equation to represent undecane densities are reported by Cibulka and Hěndkovský.1 Then, we compared these calculated values with our corresponding data. Residuals are depicted in Figure 10. The

Experimental densities for undecane reported in the open literature22−24 using a different apparatus are compared with our calculated results (eq 2) in Figure 9. Residuals are reported in the

Figure 9. Density residuals for undecane. Calculated data are from this work using the six-parameter equation and experimental data are from the literature: (●, 303.15 K; ▼, 323.15 K; ■, 373.15 K) for Doolittle.23 +, 313.25 K for Landau and Würflinger.24 ○, 313.15 K; ▽, 318.15 K; □, 323.15 K for Valencia et al.22

range of (303.15 to 373.15) K. Good agreement was found between both sets of data based on the experimental uncertainties claimed in the different sources even at pressures higher than 25 MPa; the error bars cross each other. The empirical six-parameter equation is also capable to extrapolate

Figure 10. Density residuals for undecane. Experimental data from this work against calculated data using Tait equation from ref 1: ○, 313.15 K; ▽, 323.10 K; □, 333.02 K; ◇, 342.09 K; △, 352.93 K; ☆, 362.91 K. Dotted lines refer to our experimental uncertainty. 2171



Article


313.14 K

323.09 K

333.01 K

342.97 K

352.90 K

362.87 K

1.001 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.000 11.000 12.000 13.000 14.001 15.001 16.000 17.001 18.001 19.000 20.000 21.001 22.000 23.001 24.000 25.000

671.7 672.8 673.9 674.9 676.0 677.0 678.0 679.0 680.0 680.9 681.8 682.7 683.6 684.5 685.4 686.3 687.1 687.9 688.7 689.5 690.3 691.1 691.9 692.6 693.3

663.1 664.3 665.4 666.6 667.7 668.8 669.9 670.9 672.0 673.0 674.0 675.0 675.9 676.9 677.8 678.7 679.6 680.5 681.4 682.3 683.1 683.9 684.8 685.6 686.3

654.4 655.7 656.9 658.2 659.4 660.5 661.7 662.8 663.9 665.0 666.1 667.1 668.2 669.2 670.2 671.2 672.1 673.1 674.0 674.9 675.8 676.7 677.6 678.5 679.3

645.7 647.0 648.4 649.7 650.9 652.2 653.4 654.6 655.8 657.0 658.1 659.2 660.3 661.4 662.5 663.5 664.5 665.6 666.6 667.5 668.5 669.4 670.4 671.3 672.2

636.9 638.4 639.8 641.1 642.5 643.8 645.1 646.4 647.7 648.9 650.1 651.3 652.5 653.6 654.8 655.9 657.0 658.0 659.1 660.1 661.2 662.2 663.2 664.1 665.1

628.1 629.7 631.1 632.6 634.0 635.4 636.8 638.2 639.5 640.8 642.1 643.4 644.6 645.8 647.0 648.2 649.3 650.5 651.6 652.7 653.8 654.9 655.9 656.9 658.0


Table 13. Optimized Parameters and Deviations for Density of Heptane (x) + Undecane (1 − x) Using eq 2 x Tmin/K Tmax/K pmin/MPa pmax/MPa N d1/MPa·m3·kg−1 d2/m3·kg−1 d3/MPa d4/MPa·K−1 d5/MPa·K−1/2 d6 AAD/% bias/% SDV/% RMS/%

0.0 313.15 362.91 1.000 25.000 150 −1.8607 −0.01273 −2501.66 0.6940 77.362 −10.837 2.4·10−2 −1.5·10−5 8.9·10−4 8.8·10−4

0.0500 313.15 362.92 1.001 25.000 150 −2.4562 −0.01838 −2452.48 −1.6253 9.419 −15.449 1.1·10−3 −1.1·10−4 1.2·10−3 1.2·10−3

0.2346 313.16 362.91 1.000 25.095 150 −2.2405 −0.01675 −2022.80 −2.1123 −13.681 −14.014 1.4·10−3 −2.0·10−5 1.4·10−3 1.4·10−3

estimated RMSD is reported to be 0.344 kg·m−3 for the correlated data in ref 1 using the Tait equation. In consequence, higher deviations are observed at pressures lower than 15 MPa for 342.09 K and above 15 MPa for 352.93 K. In summary, we have shown the results of the calculated densities using both the empirical six-parameter and a Tait-like equation. The lower deviations were obtained using the first equation; however, it is important to point out that it concerns to a specific interval of temperature and pressure conditions. Additionally, deviations are shown to be systematic in both cases; this trend is common to be found when data are inadequately fitted by the equation. Therefore, additional calculations can be

0.5063 313.12 362.94 1.000 25.000 150 −2.3956 −0.01920 −2277.55 −1.9426 −0.6767 −15.793 1.4·10−3 4.0·10−4 1.4·10−3 1.4·10−3

0.7482 313.15 362.91 1.000 25.000 150 −2.2976 −0.02061 −1852.56 −2.9443 −36.526 −16.547 1.8·10−3 −8.9·10−5 1.8·10−3 1.8·10−3

0.9511 313.14 362.87 1.001 25.000 150 −2.0269 −0.01974 −1728.77 −2.3645 −20.957 −15.531 2.5·10−3 7.6·10−4 3.0·10−3 3.1·10−3

performed since the Tait-like equation could probably represent with better agreement densities of other fluids in a different range of temperature and pressure. Thermodynamic derived properties (isobaric expansivity αp, isothermal compressibility κT, thermal pressure coefficient γV, and internal pressure pi) are reported from Tables 8 to 11. These were calculated by solving the above-mentioned derivatives based on the empirical equation (eq 2) using optimized parameters reported in Table 13. Behavior of these four properties is presented with isopleths as a function of pressure changes. The corresponding values for heptane were calculated from the reported density values in a previous research by 2172



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Quevedo-Nolasco et al.12 Isobaric expansivity and isothermal compressibility are depicted in Figures 11 and 12 at ∼362.9 K, these variables tend to low values as the mixture is compressed at constant composition. On the contrary, thermal pressure coefficient and internal pressure values increase if pressure is increased as observed in Figures 13 and 14 at 313.1 K.

Figure 11. Isobaric expansivity (αp) for heptane (x) + undecane (1 − x) mixtures with respect to pressure changes at ∼362.9 K. ●, x = 0; ○, x = 0.05; ▼, x = 0.2346; △, x = 0.5063; ■, x = 0.7482; □, x = 0.9511; ◆, x = 1.

Figure 14. Internal pressure (pi) for heptane (x) + undecane (1 − x) mixtures with respect to pressure changes at ∼313.1 K. ●, x = 0; ○, x = 0.05; ▼, x = 0.2346; △, x = 0.5063; ■, x = 0.7482; □, x = 0.9511; ◆, x = 1.

Excess molar volumes were calculated using the following expression: VE =

⎡ x MW (1 − x)MWC11H24 ⎤ MWf C7H16 ⎥ −⎢ + ⎥⎦ ⎢⎣ ρC H ρf ρC H 7 16 11 24

(8)

where MW represents the molecular weight, the molecular weight of the mixture MWf = xMWC7H16 + (1 − x) MWC11H24 depends on the mole fraction composition for heptane x and undecane (1 − x), and subscripts C7H16 and C11H24 denote heptane and undecane, respectively. Excess molar volumes exhibit negative behavior and as the mixture is compressed the excess molar values tend to zero as observed in Figure 15 at 333.09 K; the maximum negative values

Figure 12. Isothermal compressibility (κT) for heptane (x) + undecane (1 − x) mixtures with respect to pressure changes at ∼362.9 K. ●, x = 0; ○, x = 0.05; ▼, x = 0.2346; △, x = 0.5063; ■, x = 0.7482; □, x = 0.9511; ◆, x = 1.

Figure 13. Thermal pressure coefficient (γv) for heptane (x) + undecane (1 − x) mixtures with respect to pressure changes at ∼313.1 K. ●, x = 0; ○, x = 0.05; ▼, x = 0.2346; △, x = 0.5063; ■, x = 0.7482; □, x = 0.9511; ◆, x = 1.

Figure 15. Excess molar volume (VE) for heptane (x) + undecane (1 − x) at 333.09 K. ●, 2 MPa; ○, 5 MPa; ▼, 10 MPa; △, 15 MPa; ■, 20 MPa; □, 25 MPa. 2173



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are observed at equimolar composition for each isobar. On the other hand, if temperature is increased, the mixture is expanded and excess molar volumes are more negative. Our experimental density data measured at 313.15 K for this binary system were extrapolated at atmospheric pressure using eq 2 and the corresponding parameters from Table 13. These results are depicted in Figure 16 as a function of heptane

REFERENCES

(1) Cibulka, I.; Hěndkovský, L. Liquid Densities at Elevated Pressures of n-Alkanes from C5 to C16: A Critical Evaluation of Experimental Data. J. Chem. Eng. Data 1996, 41, 657−668. (2) Kennedy, L. J.; Vijaya, J. J.; Sekaran, G.; Kayalvizhi, K. Equilibrium, Kinetic and Thermodynamic Studies on the Adsorption of m-Cresol onto Micro- and Mesoporous Carbon. J. Hazard. Mater. 2007, 149, 134−143. (3) Chan, C. P.; Yuan-Soon, H.; Wang, Y. J.; Lan, W. H.; Chen, L. I.; Chen, Y. J.; Lin, B. R.; Chang, M. C.; Jeng, J. H. Inhibition of Cyclooxygenase Activity, Platelet Aggregation and Thromboxane B2 Production by Two Environmental Toxicants: m- and o-Cresol. Toxicology 2005, 208, 95−104. (4) Chang, J. S.; Lee, M. J. Densities of m-Cresol + m-Xylene and mCresol + Tetralin Mixtures at 298−348 K and up to 30 MPa. J. Chem. Eng. Data 1995, 40, 1115−1118. (5) Chang, J. S.; Lee, M. J.; Lin, H. M. Densities of m-Xylene + Diphenylmethane and m-Cresol + Diphenylmethane from 333 to 413 K and Pressures up to 30 MPa. J. Chem. Eng. Data 1997, 42, 574−579. (6) Randzio, S. L.; Lewis, E. A.; Eatough, D. J.; Hansen, L. D. Termophysical Properties of m-Cresol as a Function of Temperature (303 to 503 K) and Pressure. Int. J. Thermophys. 1995, 16, 883−900. (7) Siddiqi, S. A.; Teja, A. S. High Pressure Densities of Mixtures of Coal Chemicals. Chem. Eng. Commun. 1988, 72, 159−169. (8) Belinskii, B. A.; Ergopulo, E. V. Physical Properties of m-Cresol as Functions of Pressure, Temperature, and Density. Zh. Fiz. Khim. 1968, 42, 1520−1523. (9) Cibulka, I.; Hěndkovský, L.; Toshiharu, T. P-ρ-T Data of Liquids: Summarization and Evaluation. 4. Higher 1-Alkanols (C11, C12, C14, C16), Secondary, Tertiary, and Branched Alkanols, Cycloalkanols, Alkanediols, Alkanetriols, Ether Alkanols, and Aromatic Hydroxy Derivatives. J. Chem. Eng. Data 1997, 42, 415−433. (10) Schilling, G.; Kleinrahm, R.; Wagner, W. Measurement and Correlation of the (p, ρ, T) Relation of Liquid n-Heptane, n-Nonane, 2,4-Dichlorotoluene, and Bromobenzene in the Temperature Range from (233.15 to 473.15) K at Pressures up to 30 MPa for use as Density Reference Liquids. J. Chem. Thermodyn. 2008, 40, 1095−1105. (11) Quevedo-Nolasco, R.; de la Cruz-Hernández, L. A.; Galicia-Luna, L. A.; Elizalde-Solis, O. Volumetric Properties for the Binary Systems nHexane + n-Octane and n-Hexane + n-Decane at High Temperatures and Pressures. J. Chem. Eng. Data 2011, 56, 4226−4234. (12) Quevedo-Nolasco, R.; Galicia-Luna, L. A.; Elizalde-Solis, O. Compressed Liquid Densities for the (n-Heptane + n-Decane) and (nOctane + n-Decane) Systems from T = (313 to 363) K. J. Chem. Thermodyn. 2012, 44, 133−147. (13) Wagner, W.; Pruß, A. The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use. J. Phys. Chem. Ref. Data 2002, 31, 387−535. (14) Span, R.; Lemmon, E. W.; Jacobsen, R. T.; Wagner, W. A Reference Quality Equation of State for Nitrogen. Int. J. Thermophys. 1998, 19, 1121−1132. (15) Thermophysical Properties of Fluid Systems; http://webbook. nist.gov/chemistry/fluid/, 2011. (16) Taylor, B. N.; Kuyatt, C. E. Guidelines for evaluating and expressing the uncertainty of NIST measurement results. NIST Technical Note 1297, 1994 Edition. (17) Narendra, K.; Srinivasu, Ch.; Fakruddin, Sk.; Narayanamurthy, P. Excess Parameters of Binary Mixtures of Anisaldehyde with o-Cresol, mCresol and p-Cresol at T = (303.15, 308.15, 313.15, and 318.15) K. J. Chem. Thermodyn. 2011, 43, 1604−1611. (18) Yang, C.; Liu, Z.; Lai, H.; Ma, P. Excess Molar Volumes and Viscosities of Binary Mixtures of p-Cresol with Ethylene Glycol and Methanol at Different Temperature and Atmospheric Pressure. J. Chem. Eng. Data 2006, 51, 457−461. (19) Rosal, R.; Medina, I.; Forster, E.; MacInnes, J. Viscosities and Densities for Binary Mixtures of Cresols. Fluid Phase Equilib. 2003, 211, 143−150. (20) Bhatia, S. C.; Rani, R.; Bhatia, R.; Anand, H. Volumetric and Ultrasonic Behaviour of Binary Mixtures of 1-Nonanol with o-Cresol,

Figure 16. Density (ρ) behavior for heptane (x) + linear alkane (1 − x) mixtures at atmospheric pressure and 313.15 K. ●, C7H16 + C8H18 ref 25; ○, C7H16 + C10H22 ref 25; ▼, C7H16 + C11H24 extrapolated data in this work; △, C7H16 + C12H26 ref 25.

composition. Density behavior trends for heptane (x) + linear alkane (1−x) are also shown in this figure at the same conditions (atmospheric pressure and 313.15 K). Our extrapolated data for heptane + undecane agree with those trends reported by Fischer et al.25 for heptane + octane, heptane + decane, and heptane + dodecane.

4. CONCLUSIONS Novel experimental high pressure density data have been reported for o-cresol, m-cresol, p-cresol, undecane, and binary mixtures composed by m-cresol + o-cresol and heptane + undecane from (313 to 363) K. Our density data agree with the density data available in the literature except for some data points reported at atmospheric pressure. Excess molar volumes for cresols, and linear alkanes binary mixtures exhibit negative behavior; for the case of m-cresol + o-cresol mixture values for excess molar volumes are too low between (−5.5·10−5 and −9.0·10−5) m3·kmol−1 and near to zero; consequently these are within the uncertainty for this variable ± 2·10−5 m3·kmol−1. Thermodynamic derived properties were calculated with the six-parameter equation which represents reliable density values even at atmospheric pressure.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 52 55 5729-6000 ext. 55133. Fax: 52 55 5586-2728. Funding

The authors acknowledge Consejo Nacional de Ciencia y Tecnologiá and Instituto Politécnico Nacional for the financial support. Notes

The authors declare no competing financial interest. 2174



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m-Cresol, p-Cresol and Anisole at T = (293.15 and 313.15) K. J. Chem. Thermodyn. 2011, 43, 479−486. (21) Fandiño, O.; Lugo, L.; Comuñas, M. J. P.; Enriqueta, R. L.; Fernández, J. Temperature and Pressure Dependences of Volumetric Properties of two Poly(Propylene Glycol) Dimethyl Ether Lubricants. J. Chem. Thermodyn. 2010, 42, 84−89. (22) Valencia, J. L.; González-Salgado, D.; Troncoso, J.; Peleteiro, J.; Carballo, E.; Romaní, L. Thermophysical Characterization of Liquids using Precise Density and Isobaric Heat Capacity Measurements as a Function of Pressure. J. Chem. Eng. Data 2009, 54, 904−915. (23) Doolittle, A. K. Specific Volumes of n-Alkanes. J. Chem. Eng. Data 1964, 9, 275−279. (24) Landau, R.; Würflinger, A. PVT-Daten von Acetonitril, Undecan und Dodecan bis 3 kbar und −50°C. Druckadhängigkeit der Umwandlungsvolumina, -enthalpien und -entropien. Ber. Bunsenges. Phys. Chem. 1980, 84, 895−902. (25) Fischer, K.; Anders, C.; Gmehling, J. Densities and Excess Molar Volumes of 14 Binary Liquid Mixtures of Normal Alkanes (C6 or C7 + C8, C10, C12, C14, C16, C18, or C20) at 313.15 K. ELDATA Int. Electron. J. Phys.-Chem. Data 1999, 5, 19−38.

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Densities of Cresols and Linear Alkane Mixtures at High Pressure

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