Speed of Sound and Derived Properties of Ethyl Nonanoate | Journal

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

pubs.acs.org/jced

Speed of Sound and Derived Properties of Ethyl Nonanoate Taotao Zhan, Ying Zhang, Qi Zhou, Junshuai Chen, Xiaopo Wang, Xiangyang Liu, and Maogang He* Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, Xi’an Jiaotong University, Xi’an, Shaanxi Province 710049, P. R. China

Downloaded via BUFFALO STATE on July 26, 2019 at 03:38:52 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

S Supporting Information *

ABSTRACT: Ethyl nonanoate is a promising component of biodiesel with a satisfactory cetane number and reactivity. The speeds of sound in ethyl nonanoate were measured by the Brillouin light scattering (BLS) method within the temperatures from 295.24 to 593.15 K and at pressures up to 10 MPa. The relative expanded uncertainty (k = 2) of our BLS experimental system is estimated to be less than 0.7%. The densities of ethyl nonanoate were measured using a vibrating tube densimeter at atmospheric pressure in the temperature range of 293.15− 353.15 K, and the absolute average relative deviation between the experimental densities and the literature data is 0.12%. For temperatures between 303.15 and 353.15 K and at pressures up to 10 MPa, these measurements were used to calculate densities, isobaric heat capacities, and indirect derivative properties including the isobaric thermal expansion, the isothermal compressibility, the isentropic compressibility, and the internal pressure. The comparison between the calculated isobaric heat capacities and the literature values shows a satisfactory agreement with an absolute average relative deviation of 0.18% and a maximum deviation of 0.38%. At the end, the dependences of internal pressure of ethyl nonanoate on temperature and pressure were found to be in accordance with those of ethyl caprylate and ethyl caprate.

1. INTRODUCTION With the rapid development of economy, the energy problem is becoming increasingly prominent, and the ecological environment is getting more and more deteriorated. Biodiesel blends generally exhibit better combustion performance and lower exhaust emissions than conventional diesel fuels.1,2 Biodiesel, as an alternative source of energy, has many significant advantages, especially in fuel properties, nontoxicity, biodegradability, availability, sustainability, and renewability.3,4 For example, the superior fuel properties of methyl decanoate have been emphasized by different researchers recently.5,6 Compared with methyl decanoate, ethyl nonanoate has a similar cetane number and even higher reactivity at the lowtemperature combustion conditions because of relatively low activation energy.7−9 In addition, ethyl nonanoate, as a medium-chain fatty acid ethyl ester and a yeast secondary metabolite, can significantly contribute to the fruity aroma of foods and beverages.10,11 For instance, Chinese quince fruits with a potent aroma have been confirmed to have a high abundance of ethyl nonanoate.12,13 The injection process is closely related to the content of nitrogen oxides in emissions, which is determined by the speed of sound and the density and derived properties of the fuel.14 The propagation of sound is an adiabatic process, so the speed of sound in biodiesel is essential to determine the injection timing. Besides, the density of fuel has a direct influence on the mass flow in the injection system and the output power of an engine.15,16 The internal pressure, defined as pint = (∂Uint/∂V)T © XXXX American Chemical Society

(Uint is the internal energy and V is the molar volume), is related to the cohesive forces acting in liquids and provides valuable information of molecular interactions in liquids, which is often used to determine the solubility parameter in the petroleum industry.17,18 Hence, the accurate knowledge of the speed of sound and the density and derived properties plays an important role in optimizing the design for injection systems and improving the energy conversion efficiency in engines.19−23 There are no available experimental speeds of sound in ethyl nonanoate in the literature. Previous measurements of the density of ethyl nonanoate under atmospheric pressure were presented by Ortega et al.24 at T = 298.15 K, Mumford et al.25 at T = 293.15 and 298.15 K, Senol et al.26 at T = 293.2 K, Albert27 at T = 293.15−453.15 K, and Perkin28 at T = 288.15, 298.15 K. Besides, Liu et al.29 carried out measurements of the heat capacity of ethyl nonanoate in the temperature range of 303−393 K at pressures up to 25 MPa. The Brillouin light scattering (BLS) method is an effective and promising measurement technique, especially suitable for high-temperature measurements, which has been used to measure the speed of sound in several fatty acid esters in our previous work.30−32 In this work, the speeds of sound in ethyl nonanoate measured by the BLS method are reported along Received: May 10, 2019 Accepted: July 10, 2019

A

DOI: 10.1021/acs.jced.9b00420 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

five isobaric lines from 0.1 to 10 MPa and in the temperature interval 295.24−593.15 K. Densities of ethyl nonanoate under atmospheric pressure were measured using a vibrating tube densimeter within the temperature range of 293.15 to 393.15 K. These measurements were used to calculate densities, isobaric heat capacities, and indirect derivative properties such as the isobaric thermal expansion, the isothermal compressibility, the isentropic compressibility, and the internal pressure in the temperature range of 303.15−353.15 K and at pressures up to 10 MPa.

The measurement apparatus applied to study the speed of sound in ethyl nonanoate has been described in detail in previous papers.36,37 Here, only the measurement procedure and related instruments are introduced briefly. A continuouswave diode-pumped solid-state laser (Cobolt Samba) is applied as the light source, and the wavelength of the laser beam is 532 nm (λ0) with an uncertainty of 0.03 nm. The probing beam will get reflected by a mirror on the rotatable table by an incident angle (ΘEx) of 11° with an uncertainty of 9″. Finally, to obtain the spectrum of the filtered scatted light with an uncertainty in the frequency shift (Δω) of 0.005, a photon counting head (Hamamatsu H8259-01) and a data acquisition card (DAQ card, NI-PCI6221) were used. According to Bragg’s law and the relationship between the speed of sound and the frequency shift,34 the speed of sound can be obtained by

2. EXPERIMENTAL SECTION 2.1. Materials. The ethyl nonanoate sample was supplied by Aladdin Reagents, and the specified mass fraction purity analyzed through gas chromatography is higher than 0.988. Table 1 shows the details of the sample description.33 The

c ≈ ωsλ 0 sin(ΘEx )−1

Table 1. Selected Physical and Chemical Properties of Ethyl Nonanoate material

ethyl nonanoate

CAS number molecular formula molecular weight (g mol−1) critical temperature (K) boiling point (K) flash point (K) mass purity supplier purification method

123-29-5 C11H22O2 186.29 663.9 ± 0.433 500.15 228.7 >0.988 Aladdin Reagent Inc. used as supplied

(1)

where λ0 = 532 nm, ΘEx = 11°, and ωs = Δω/2π. The approximate calculation in eq 1 results in a relative uncertainty of 0.0015.34 The frequency shift (Δω) between the Brillouin (anti-Brillouin) peak and the central Rayleigh peak can be determined from the spectrum of the scattered light that is shown in Figure 1. For the entire measurement range, the temperatures measured by a Fluke Corporation platinum resistance thermometer kept stable within the limits of ±0.015 K, and the pressures measured by a digital manometer (Rosemount, 3051S, 0−20 MPa) were stabilized within ±0.002 MPa. Each experimental data was independently measured three times with a reproducibility of 0.001, and the average value was finally adopted. The uncertainties in the temperature and pressure and reproducibility were also taken into account. Consequently, the expanded relative uncertainty of our BLS experimental system with a confidence level of 95% (coverage factor, k = 2) is estimated to be 0.7%. According to the NIST GUM,38 the uncertainty evaluation for temperature, pressure, and the speed of sound is summarized in Table 2. The uncertainty caused by impurities is also significant, which can be considered a Type B error and equals to the impurity divided by the square root of 3.39 With a purity of 0.988, the standard uncertainty caused by impurities is estimated to be 0.007 in this work. Hence, the expanded relative uncertainty for the reported speed of sound values with a confidence level of 95% (coverage factor, k = 2) is estimated to be 1.6%.

ethyl nonanoate sample was filtered through membrane filters with the pore size of 0.22 μm before filling the sample cell, which can prevent the granular impurities from entering the sample cell. 2.2. Measurement of the Speed of Sound. The speed of sound was measured in a sample cell designed for working up to 15 MPa using the Brillouin light scattering (BLS) method. The BLS method based on an analysis of the scattered light originating from bulk fluids is mainly concerned about the Brillouin peak, the anti-Brillouin peak, and the central Rayleigh peak in the spectrum. The detailed and comprehensive description of the fundamental principles of the BLS method used in the measurement of the speed of sound can be found in the specialized literature.34,35

Figure 1. Count rate variation with time. B



Article

Table 2. Experimental Uncertainties in Temperature, Pressure, and the Speed of Sound source of uncertainty

value

platinum resistance, u1 temperature stability, u2 temperature measurement circuits, u3 standard uncertainty, uc(T)

0.010 K 0.015 K 0.002 K

pressure transmitter, u4 pressure stability, u5 pressure measurement circuits, u6 pressure control system, u7 standard uncertainty, uc(p)

0.010 0.002 0.020 0.025

wavelength, ur(λ0) incident angle, ur(ΘEx) Brillouin frequency shift, ur(ωs) temperature, ur(T) pressure, ur(p) reproducibility, ur(r) approximate process in eq 1, ur(a) relative combined uncertainty, ur(c)

0.03 nm 9″ 5.55 MHz

MPa MPa MPa MPa

1.2 m s−1

probability distribution

2.0 1.0 √3

1.0 1.0 1.0

0.005 0.015 0.001 0.016

K K K K

2.0 1.0 √3 √3

1.0 1.0 1.0 1.0

0.005 0.002 0.012 0.014 0.019

MPa MPa MPa MPa MPa

3.760 × 10−5 4.500 × 10−4 0.002 0.001 0.002 0.001 0.0015 0.0035

√3 1.0 1.0

1.0 1.0

uncertainty

1.0 1.0

yz zz zz zz z {

(5)

where ycal,i is the ith values calculated from the corresponding fitting correlation and yexp,i is the ith data of our experimental results. The adjustable parameters in eq 2 were calculated by the least-squares method with an absolute average relative deviation of 0.26% and a maximum deviation of 0.70%. As can be seen, the maximum deviation between the experimental data and the empirical correlation is much smaller than the experimental uncertainty. 3.2. Derived Properties. The measurements of the speed of sound were used to calculate the density, isobaric heat capacity, and indirect derivative properties such as the isobaric thermal expansion, the isothermal compressibility, the isentropic compressibility, and the internal pressure in the temperature range of 303.15−353.15 K and at pressures up to 10 MPa. The change of density (Δρ) at a constant temperature with respect to pressure from p1 to p2 can be calculated by the following well-known relationship

3. RESULTS AND DISCUSSION 3.1. Experimental Speeds of Sound. The experimental speeds of sound in ethyl nonanoate were measured at temperatures from 295.24 to 593.15 K and along six isobaric lines from 0.1 to 10 MPa, which are presented in Table 3 and Figure 2. With increasing temperature, the speed of sound first approximately linearly decreases at low temperature and then decreases a little rapidly at high temperature and becomes more and more sensitive to the variation of pressure. The experimental speeds of sound were fitted by an empirical correlation40 A + A1T + A 2 T 2 + A3T 3 + B1p + B2 p2 + B3p3 1 = 0 2 1 + CT + Dp c (2)

Δρ =

where A0, A1, A2, A3, B1, B2, B3, C, and D are adjustable parameters, which are given in Table 5. The relative deviation, the absolute average relative deviation (AARD), and the maximum deviation (MD) are introduced to assess the performances of the fitting correlations, which are defined as

∫p

1

p2

2 y ij 1 jj + αp T zzzdp ≈ jj 2 z jc c p zz k {

∫p

1

p2

αp2T 1 p d + Δp cp c2

(3)

ρ(kgm−3) = a0 + a1T + a 2T 2 AARD(%) =

100 N

N

∑ i

1−

ycal, i yexp, i

(6)

where αp = −(1/ρ)(∂ρ/∂T)p is the isobaric thermal expansion and Δp = p2 − p1 is the computational step-length. The computation procedure proposed by Sun et al.41 was adopted. To initiate the computation procedure, the densities of ethyl nonanoate in the temperature interval of 293.15−353.15 K and at atmospheric pressure were measured. The experimental densities are given in Tables 4 and 5, which were fitted by the empirical polynomial

ycal, i yexp, i

sensitivity coefficient

ij ycal, i j MD(%) = 100Maxjjjj 1 − jj yexp, i k

2.3. Density Measurement. The density of ethyl nonanoate under atmospheric pressure was measured within the temperature range of 293.15−393.15 K by means of a vibrating tube densimeter Anton Paar DMA 5000 M. The relative combined expanded uncertainty in density is estimated to be 0.0015 (coverage factor k = 2, the level of confidence is 0.95).

RD(%) = 100 1 −

divisor

Temperature normal normal rectangular normal Pressure normal normal rectangular rectangular normal Speed of Sound rectangular normal normal normal normal normal normal

(7)

where the fitting parameters a0 = 1.09349 × 10 , a1 = −7.32650 × 10−1, and a2 = −1.59357 × 10−4 were obtained from a least-squares method. The mean deviation, MD, and 3

(4) C



Article

Table 3. Experimental Speeds of Sound in Ethyl Nonanoatea T (K)

p (MPa)

c (m s−1)

100Ur(c)

T (K)

p (MPa)

c (m s−1)

100Ur(c)

T (K)

p (MPa)

c (m s−1)

100Ur(c)

295.67 303.48 313.77 323.68 334.94 343.51 354.18 364.18 371.99 381.89 391.89 405.01 413.84 422.07 432.93 443.70 452.83 464.19 471.88 482.75 295.53 303.26 313.14 324.85 333.21 343.24 352.22 363.30 371.91 384.30 391.75 403.31 412.98 421.83 431.53 442.94 452.50 462.68 471.87 482.55 493.00 502.95 513.20 522.13 533.35 543.62 552.71 562.08 571.96 295.41 303.22 313.56 324.78 332.93 342.88 351.94 362.97 372.73

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0

1303.3 1273.9 1224.9 1183.3 1142.9 1107.8 1065.4 1028.8 1003.0 965.2 932.1 884.0 861.2 827.6 797.1 767.3 739.6 703.5 683.0 652.6 1318.3 1278.4 1242.7 1195.5 1163.1 1123.8 1085.5 1046.0 1012.3 971.3 939.5 902.3 870.1 842.1 808.9 779.7 750.6 720.1 693.4 665.4 637.4 607.9 581.3 555.5 519.4 491.0 458.7 428.6 387.2 1327.1 1296.2 1252.4 1204.3 1175.1 1137.2 1098.9 1063.9 1024.3

3.3 3.3 3.2 3.1 3.1 3.0 2.9 2.9 2.9 2.8 2.8 2.7 2.7 2.6 2.6 2.5 2.5 2.5 2.4 2.4 3.3 3.3 3.2 3.1 3.1 3.0 3.0 2.9 2.9 2.8 2.8 2.7 2.7 2.6 2.6 2.6 2.5 2.5 2.5 2.4 2.4 2.4 2.3 2.3 2.3 2.2 2.2 2.2 2.2 3.4 3.3 3.2 3.2 3.1 3.1 3.0 2.9 2.9

381.96 391.81 403.46 412.73 422.02 432.05 443.11 452.88 462.31 471.80 482.56 492.57 502.65 512.83 522.31 533.60 542.72 552.52 562.48 571.78 582.39 591.81 295.35 303.41 314.03 323.64 334.21 343.12 353.27 361.97 371.77 381.51 391.70 403.82 413.05 421.50 431.84 443.15 452.65 462.49 471.86 482.62 492.67 503.42 512.90 522.36 533.69 542.91 552.72 562.32 572.37 582.01 592.38 295.29 303.30 313.45 322.95 334.21

3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 7.0 7.0 7.0 7.0 7.0

995.2 961.1 921.8 893.7 862.5 827.6 796.4 771.1 743.5 718.5 691.9 660.7 635.1 609.6 583.9 552.1 528.8 500.5 468.4 435.9 393.3 351.2 1336.6 1298.0 1262.6 1215.5 1185.0 1153.6 1106.1 1078.7 1046.8 1011.2 974.2 929.8 904.2 875.4 850.9 814.1 786.9 763.0 737.7 709.2 681.7 655.5 633.5 609.3 581.4 553.5 527.6 499.9 472.0 439.9 398.5 1342.4 1307.0 1266.0 1231.4 1191.7

2.8 2.8 2.7 2.7 2.7 2.6 2.6 2.5 2.5 2.5 2.4 2.4 2.4 2.4 2.3 2.3 2.3 2.3 2.2 2.2 2.2 2.1 3.4 3.3 3.2 3.2 3.1 3.1 3.0 3.0 2.9 2.9 2.8 2.8 2.7 2.7 2.6 2.6 2.6 2.5 2.5 2.5 2.4 2.4 2.4 2.4 2.3 2.3 2.3 2.3 2.2 2.2 2.2 3.4 3.3 3.3 3.2 3.1

343.31 353.32 362.59 373.26 383.69 391.74 403.36 412.81 422.00 431.88 443.00 452.64 462.34 471.86 482.58 492.66 502.91 512.78 522.19 533.43 542.79 552.61 562.40 572.13 582.26 592.79 295.24 303.18 313.08 323.39 332.89 343.10 352.39 363.00 373.24 383.17 391.74 403.47 412.73 421.98 431.86 443.02 452.68 462.43 471.95 482.62 492.48 503.08 512.80 522.38 533.52 542.76 552.76 562.45 572.32 582.35 593.15

7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0

1157.3 1114.4 1085.6 1045.8 1011.5 985.8 943.9 917.8 891.0 861.7 835.6 805.0 783.1 756.6 727.2 704.9 681.8 655.0 631.9 605.6 583.0 558.1 532.0 504.6 473.6 438.3 1348.5 1318.0 1283.3 1246.8 1208.8 1170.1 1135.0 1106.9 1068.4 1037.3 1009.8 968.6 936.6 916.0 888.7 860.3 835.1 804.8 783.4 759.9 735.7 709.9 689.4 662.0 637.0 619.6 596.5 574.7 549.0 525.5 495.3

3.1 3.0 3.0 2.9 2.9 2.8 2.8 2.7 2.7 2.7 2.6 2.6 2.6 2.5 2.5 2.5 2.4 2.4 2.4 2.4 2.3 2.3 2.3 2.3 2.2 2.2 3.4 3.3 3.3 3.2 3.2 3.1 3.0 3.0 3.0 2.9 2.9 2.8 2.8 2.7 2.7 2.7 2.6 2.6 2.6 2.5 2.5 2.5 2.4 2.4 2.4 2.4 2.3 2.3 2.3 2.3 2.2

a

Ur(c) is the relative combined expanded uncertainty (for a state point). Expanded uncertainties for temperature and pressure are U(T) = 0.016 K and U(p) = 0.038 MPa, respectively. The level of confidence is 0.95 (k = 2). D



Article

Figure 2. Experimental speeds of sound in ethyl nonanoate: pink, half-filled square: p = 0.1 MPa; golden, left-pointing, half-filled triangle: p = 1.0 MPa; yellow, half-filled circle: p = 3.0 MPa; green, upright, half-filled triangle: p = 5.0 MPa; blue, upright half-filled pentagon: p = 7.0 MPa; and purple, half-filled hexagon: p = 10.0 MPa. Solid line, calculated with eq 6.

Figure 3. Comparison of density for ethyl nonanoate as a function of temperature between our calculated results and the literature values: pink, half-filled square: Ortega et al.;24 golden, half-filled rhombus: Mumford et al.;25 green, upright, half-filled triangle: Senol et al.;26 blue, right-pointing, half-filled triangle: Albert;27 and purple, half-filled hexagon: Perkin.28

Table 4. Experimental Densities at Atmospheric Pressure and in the Temperature Range of 293.15−353.15 Ka

computation procedure were measured by Liu et al.29 and were correlated by

T (K)

ρ (kg m−3)

T (K)

ρ (kg m−3)

293.15 298.15 303.15 313.15

865.02 860.89 856.75 848.43

323.15 333.15 343.15 353.15

840.09 831.73 823.33 814.88

m

c p (Jkg −1K−1) = 0

where bl are the fitting parameters, which are listed in Table 7. The simultaneous step-by-step integration was started with the initial values c(T), ρ(T), and cp(T) at reference pressure p0 = 0.1 MPa. Because the isobaric heat capacity is extremely insensitive to pressure, the approximate relationship eq 6 is sufficiently accurate and the step-length Δp was taken as 0.1 MPa.41−43 The calculated densities ρ(T) at every specific pressure were fitted by eq 7. The isobaric heat capacities at a constant temperature under p1 and p2 were calculated by the following thermodynamic relationship

The standard uncertainty for temperature is u(T) = 0.05 K, and the relative combined expanded uncertainty (coverage factor k = 2, the level of confidence is 0.95) in density is Ur(ρ) = 0.0015.

Table 5. Coefficients of Equations 2 and 11 and Deviations from the Regression Line value

A0 A1 A2 A3 B1 B2 B3 C D deviations AARD% MD%

7.140 × 10−7 −5.284 × 10−9 1.827 × 10−11 −1.721 × 10−14 −2.374 × 10−9 1.001 × 10−10 −5.589 × 10−11 −1.645 × 10−3 8.331 × 10−2 2.6 × 10−1 7.0 × 10−1

Tammann−Tait equation

value

E F0 F1 F2

7.97189 × 102 4.36284 × 106 −1.61571 × 106 1.60552 × 105

(8)

l=0

a

parameter

∑ blT l

c p(p2 ) ≈ c p(p1 )‐(T /ρ)[αp2 + (∂αp/∂T )p ]Δp

(9)

where cp(p1) and cp(p2) are the isobaric heat capacities at p1 and p2, respectively. The calculated results of the isobaric heat capacity and density are presented in Table 6. The calculated isobaric heat capacities were fitted by the polynomial expression m

c p(Jkg −1K−1) =

n

∑ ∑ cijT ip j i=0 j=0

6.0 × 10−3 2.0 × 10−2

(10)

where cij are the fitting parameters, which are given in Table 7. The backward stepwise rejection procedure was applied to reduce the number of nonzero coefficients. The comparison between the correlation of the isobaric heat capacity and the literature values29 shows a satisfactory agreement with an AARD of 0.18% and an MD of 0.38%, which is shown in Figure 4. The pρT data were correlated by a modified Tammann−Tait equation as recommended by Dzida et al.43 É ÅÄÅ ij p + F(T ) yzÑÑÑÑ ÅÅ j z Ñ Å ρ(T , p) = ρ0 (T , p0 )/ÅÅÅ1 − E lnjjj zzÑÑ j p + F(T ) zzÑÑÑ ÅÅ (11) ÅÇ k 0 {ÑÖ

AARD from the regression line are 0.004 kg m−3, 0.07 and 0.05%, respectively. The densities of ethyl nonanoate measured in this work are in a good agreement with the literature data, which is shown in Figure 3. The AARD between our experimental densities and the literature data is equal to 0.02, 0.13, 0.15, 0.02, and 0.37% for results reported by Ortega et al.,24 Mumford et al.,25 Senol et al.,26 Albert,27 and Perkin,28 respectively. The density reported by Perkin28 is extremely lower than other density data because of the large uncertainty of the magnetic rotary method used by Perkin.28 The isobaric heat capacities in the investigated temperature range at atmospheric pressure needed to initiate the

where ρ0 is the density at atmospheric pressure p0 as a function of temperature. E is the fitting parameter, and F(T) can be calculated from the second-order polynomial: F(T) = F0 + F1(T/100) + F2(T/100) 2. The fitting parameters and E



Article

Table 6. Calculated Densities and Isobaric Heat Capacities of Ethyl Nonanoate at Pressures up to 10 MPa and in the Temperature Range of 303.15−353.15 K T (K)

p (MPa)

ρ (kg m−3)

cp (J kg−1 m−3)

T (K)

p (MPa)

ρ (kg m−3)

cp (J kg−1 m−3)

T (K)

p (MPa)

ρ (kg m−3)

cp (J kg−1 m−3)

303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

856.7 852.6 848.4 844.3 840.1 835.9 831.7 827.5 823.3 819.1 814.9 857.4 853.3 849.2 845.0 840.9 836.7 832.5 828.4 824.2 820.0 815.8

1987 2009 2031 2052 2072 2092 2112 2131 2149 2168 2186 1986 2008 2030 2051 2071 2091 2111 2130 2148 2167 2185

303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15

3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0

858.9 854.8 850.7 846.6 842.5 838.4 834.3 830.2 826.1 822.0 817.8 860.4 856.3 852.3 848.2 844.2 840.1 836.1 832.0 827.9 823.9 819.8

1985 2007 2028 2049 2070 2090 2109 2128 2147 2165 2183 1983 2005 2027 2048 2068 2088 2107 2126 2145 2163 2181

303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15

7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0

861.8 857.8 853.8 849.8 845.8 841.8 837.8 833.8 829.8 825.7 821.7 863.9 860.0 856.0 852.1 848.1 844.2 840.3 836.3 832.4 828.5 824.6

1982 2004 2025 2046 2067 2086 2106 2125 2143 2161 2179 1980 2002 2024 2044 2065 2084 2104 2122 2141 2159 2177

deviations are presented in Table 5. The isobaric thermal expansion αp obtained from ρ(T) dependence and the isentropic compressibility, κs = 1/(ρc2), obtained from the experimental speeds of sound and the calculated densities are given in Table 8. The isothermal compressibility can be calculated by the following well-known relationship44

Table 7. Coefficients of Equations 8 and 10 and Deviations from the Regression Line parameter b0 b1 b2 b3

deviations AARD% MD%

bl 2.53737 2.24453 7.06214 7.26535

× × × ×

5.9 × 10−2 2.8 × 10−1

104 102 10−1 10−4

parameter

cij

c00 c01 c02 c10 c11 c12 c20 c21

−1.91985 × 102 −3.00386 × 10−1 −2.51205 × 10−2 9.984872 × 100 2.21720 × 10−3 1.20969 × 10−4 −9.10546 × 10−3 −1.26229 × 10−5

κT = κs +

Tαp2 ρc p

(12)

where κT is defined as ρ(p) dependence in the form of (1/ ρ)(∂ρ/∂p)T, whose values are listed in Table 8. The internal pressure is related to the isobaric thermal expansion and the isothermal compressibility in the following way45

8.4 × 10−4 1.5 × 10−2

pint =

T · αp κT

−p

(13)

The results of the calculation are presented in Table 8 and Figure 5. The dependences of internal pressure of ethyl nonanoate on temperature and pressure are similar to those of alkanes, dibromoalkanes, ethyl caprylate, and ethyl caprate.46−48 The internal pressure of ethyl nonanoate decreases with increasing temperature, and increases sharply under low pressure, and has a slowly increasing tendency under pressures between 3 and 10 MPa with increasing pressure. The internal pressure is very sensitive to the speed of sound that is not precise enough in this work, so only a trend of slow increase of the internal pressure under pressures between 3 and 10 MPa can be shown roughly in Figure 5. Figure 4. Comparison of specific isobaric heat capacity for ethyl nonanoate as a function of temperature between our calculated results and the literature values: pink, half-filled square: Liu et al.29 at p = 0.1 MPa; green, upright, half-filled triangle: Liu et al.29 at p = 5.0 MPa; and purple, half-filled hexagon: Liu et al.29 at p = 10.0 MPa.

4. CONCLUSIONS The experimental speeds of sound in ethyl nonanoate were measured by the Brillouin light scattering method in the examined temperature range T = 295.24−593.15 K and along six isobaric lines at p = 0.1, 1.0, 3.0, 5.0, 7.0, and 10.0 MPa. The measured speeds of sound were fitted by an empirical F


p (MPa)

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0

T (K)

303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15

0.968 0.974 0.981 0.988 0.995 1.002 1.008 1.016 1.023 1.030 1.037 0.963 0.969 0.976 0.982 0.989 0.995 1.002 1.009 1.015 1.022 1.029 0.951 0.957 0.963 0.968 0.974 0.980 0.986 0.992 0.998 1.005 1.011

αp·103 (K−1) 0.891 0.923 0.957 0.992 1.029 1.068 1.109 1.151 1.195 1.241 1.290 0.875 0.907 0.939 0.974 1.010 1.048 1.087 1.128 1.171 1.216 1.263 0.851 0.881 0.912 0.945 0.979 1.015 1.052 1.091 1.132 1.174 1.218

κT·109 (Pa−1) 0.724 0.752 0.782 0.813 0.846 0.880 0.916 0.953 0.992 1.033 1.076 0.710 0.738 0.766 0.797 0.829 0.862 0.897 0.933 0.971 1.011 1.053 0.690 0.717 0.744 0.773 0.803 0.835 0.868 0.903 0.939 0.976 1.016

κs·109 (Pa−1) 329.3 325.2 321.0 316.6 312.2 307.6 303.0 298.3 293.5 288.7 283.9 332.6 328.5 324.2 319.8 315.3 310.8 306.1 301.3 296.6 291.7 286.9 335.7 331.6 327.4 323.0 318.5 313.9 309.3 304.5 299.8 295.0 290.1

pint·10−6 (Pa−1) 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15

T (K) 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0

p (MPa) 0.940 0.945 0.950 0.955 0.961 0.966 0.971 0.977 0.982 0.988 0.993 0.929 0.933 0.938 0.943 0.947 0.952 0.957 0.962 0.967 0.972 0.977 0.913 0.917 0.921 0.925 0.929 0.933 0.937 0.941 0.945 0.949 0.953

αp·103 (K−1) 0.837 0.866 0.896 0.927 0.960 0.994 1.029 1.066 1.105 1.145 1.187 0.827 0.854 0.883 0.913 0.944 0.977 1.011 1.047 1.083 1.122 1.161 0.805 0.831 0.858 0.886 0.916 0.946 0.978 1.011 1.045 1.081 1.118

κT·109 (Pa−1) 0.680 0.706 0.732 0.760 0.789 0.819 0.851 0.884 0.919 0.955 0.992 0.674 0.698 0.724 0.751 0.779 0.808 0.838 0.870 0.903 0.937 0.973 0.658 0.681 0.705 0.730 0.757 0.784 0.813 0.842 0.873 0.906 0.939

κs·109 (Pa−1)

335.2 331.2 327.1 322.8 318.4 313.9 309.3 304.7 300.0 295.3 290.6 333.5 329.6 325.6 321.4 317.2 312.8 308.3 303.8 299.3 294.7 290.0 333.7 329.9 326.0 321.9 317.7 313.5 309.1 304.7 300.2 295.7 291.2

pint·10−6 (Pa−1)

Table 8. Calculated Isobaric Thermal Expansion Coefficients, Isothermal Compressibilities, Isentropic Compressibilities, and Internal Pressures of Ethyl Nonanoate at Pressures up to 10 MPa and in the Temperature Range of 303.15−353.15 K

Journal of Chemical & Engineering Data Article

G



■

correlation that correlates 1/c2 as a function of temperature and pressure, resulting in an AARD of 0.26% and an MD of 0.70%. The densities of ethyl nonanoate in the temperature interval 293.15−353.15 K and at atmospheric pressure were measured by means of a vibrating tube densimeter The absolute average relative deviation between the experimental densities and the literature data is 0.12%, and the experimental densities were fitted by a quadratic polynomial with a mean average of 0.004 kg m−3. In the temperature range of 303.15− 353.15 K and pressures up to 10 MPa, the comparison between the calculated isobaric heat capacities and the literature values shows a satisfactory agreement with an AARD of 0.18% and an MD of 0.38%. In the investigated range, the internal pressure of ethyl nonanoate decreases with increasing temperature and increases with increasing pressure, which is in accordance with that of ethyl caprylate and ethyl caprate.

ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.9b00420. Literature isobaric heat capacities at atmospheric pressure and temperatures (T) (Table S1); schematic of the experimental optical setup for the speed of sound (Figure S1); control and measurement systems of temperature and pressure (Figure S2) (PDF)

■

REFERENCES

(1) Zheng, M.; Mulenga, M. C.; Reader, G. T.; Wang, M.; Ting, D. S. K.; Tjong, J. Biodiesel engine performance and emissions in low temperature combustion. Fuel 2008, 87, 714−722. (2) Giakoumis, E. G.; Rakopoulos, C. D.; Dimaratos, A. M.; Rakopoulos, D. C. Exhaust emissions of diesel engines operating under transient conditions with biodiesel fuel blends. Prog. Energy Combust. Sci. 2012, 38, 691−715. (3) Escobar, J. C.; Lora, E. S.; Venturini, O. J.; Yáñez, E. E.; Castillo, E. F.; Almazan, O. Biofuels: Environment, technology and food security. Renewable Sustainable Energy Rev. 2009, 13, 1275−1287. (4) Nigam, P. S.; Singh, A. Production of liquid biofuels from renewable resources. Prog. Energy Combust. Sci. 2011, 37, 52−68. (5) Knothe, G.; Cermak, S. C.; Evangelista, R. L. Cuphea Oil as Source of Biodiesel with Improved Fuel Properties Caused by High Content of Methyl Decanoate. Energy Fuels 2009, 23, 1743−1747. (6) Li, Z.; Wang, W.; Huang, Z.; Oehlschlaeger, M. A. Autoignition of Methyl Decanoate, a Biodiesel Surrogate, under High-Pressure Exhaust Gas Recirculation Conditions. Energy Fuels 2012, 26, 4887− 4895. (7) Hotard, C.; Tekawade, A.; Oehlschlaeger, M. A. Constant volume spray ignition of C9-C10 biodiesel surrogates: Methyl decanoate, ethyl nonanoate, and methyl decenoates. Fuel 2018, 224, 219−225. (8) Schwartz, W. R.; McEnally, C. S.; Pfefferle, L. D. Decomposition and Hydrocarbon Growth Processes for Esters in Non-Premixed Flames. J. Phys. Chem. A 2006, 110, 6643−6648. (9) Coniglio, L.; Bennadji, H.; Glaude, P. A.; Herbinet, O.; Billaud, F. Combustion chemical kinetics of biodiesel and related compounds (methyl and ethyl esters): Experiments and modeling-Advances and future refinements. Prog. Energy Combust. Sci. 2013, 39, 340−382. (10) Hu, K.; Jin, G. J.; Mei, W. C.; Li, T.; Tao, Y. S. Increase of medium-chain fatty acid ethyl ester content in mixed H. uvarum/S. cerevisiae fermentation leads to wine fruity aroma enhancement. Food Chem. 2018, 239, 495−501. (11) Lu, Y.; Voon, M. K.; Huang, D.; Lee, P. R.; Liu, S. Q. Combined effects of fermentation temperature and pH on kinetic changes of chemical constituents of durian wine fermented with Saccharomyces cerevisiae. Appl. Microbiol. Biotechnol. 2017, 101, 3005−3014. (12) Pico, J.; Hansen, Å. S.; Petersen, M. A. Comparison of the volatile profiles of the crumb of gluten-free breads by DHE-GC/MS. J. Cereal Sci. 2017, 76, 280−288. (13) Choi, J. Y.; Lee, S. M.; Lee, H. J.; Kim, Y. S. Characterization of aroma-active compounds in Chinese quince (Pseudocydonia sinensis Schneid) by aroma dilution analyses. Food Res. Int. 2018, 105, 828− 835. (14) Szybist, J. P.; Boehman, A. L.; Taylor, J. D.; McCormick, R. L. Evaluation of formulation strategies to eliminate the biodiesel NOx effect. Fuel Process. Technol. 2005, 86, 1109−1126. (15) Alptekin, E.; Canakci, M. Characterization of the key fuel properties of methyl ester−diesel fuel blends. Fuel 2009, 88, 75−80. (16) Tat, M. E.; Gerpen, J. H. V. The specific gravity of biodiesel and its blends with diesel fuel. J. Am. Oil Chem. Soc. 2000, 77, 115− 119. (17) Zorębski, E.; Musiał, M.; Dzida, M. Relation between temperature−pressure dependence of internal pressure and intermolecular interactions in ionic liquids-Comparison with molecular liquids. J. Chem. Thermodyn. 2019, 131, 347−359. (18) Verdier, S.; Andersen, S. I. Internal pressure and solubility parameter as a function of pressure. Fluid Phase Equilib. 2005, 231, 125−137. (19) Boehman, A. L.; Morris, D.; Szybist, J. The impact of the bulk modulus of diesel fuels on fuel injection timing. Energy Fuels 2004, 18, 1877−1882. (20) Lopes, A. F. G.; Talavera-Prieto, M. d. C.; Ferreira, A. G. M.; Santos, J. B.; Santos, M. J.; et al. Portugal, A. T. G. Speed of sound in pure fatty acid methyl esters and biodiesel fuels. Fuel 2014, 116, 242− 254.

Figure 5. Internal pressure of ethyl nonanoate as a function of pressure at several temperatures: pink, half-filled square: T = 303.15 K; golden, left-pointing, half-filled triangle: T = 313.15 K, yellow, halffilled circle: T = 323.15 K; green, upright, half-filled triangle: T = 333.15 K; blue, upright half-filled pentagon: T = 343.15 K; and purple, half-filled hexagon: T = 353.15 K.

■

Article

AUTHOR INFORMATION

Corresponding Author

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

Maogang He: 0000-0002-2364-2140 Funding

This work was supported by the National Natural Science Foundation of China (NSFC No. 51576161). Notes

The authors declare no competing financial interest. H



Article

from 273.15 to 333.1 5 K and up to 280 MPa. Phys. Chem. Liq. 1988, 18, 107−116. (42) Dzida, M.; Prusakiewicz, P. The effect of temperature and pressure on the physicochemical properties of petroleum diesel oil and biodiesel fuel. Fuel 2008, 87, 1941−1948. (43) Ż arska, M.; Bartoszek, K.; Dzida, M. High pressure physicochemical properties of biodiesel components derived from coconut oil or babassu oil. Fuel 2014, 125, 144−151. (44) Carlos R. Reis, J.; Blandamer, M. J.; Davis, M. I.; Douhéret, Gr. The concepts of non-Gibbsian and non-Lewisian properties in chemical thermodynamics. Phys. Chem. Chem. Phys. 2001, 3, 1465− 1470. (45) Dzida, M. Speeds of sound, densities, isobaric thermal expansion, compressibilities, and internal pressures of heptan-1-ol, octan-1-ol, nonan-1-ol, and decan-1-ol at temperatures from (293 to 318) K and pressures up to 100 MPa. J. Chem. Eng. Data 2007, 52, 521−531. (46) Dzida, M.; Cempa, M. Thermodynamic and acoustic properties of (heptane+dodecane) mixtures under elevated pressures. J. Chem. Thermodyn. 2008, 40, 1531−1541. (47) Chorążewski, M.; Skrzypek, M. Thermodynamic and Acoustic Properties of 1,3-Dibromopropane and 1,5-Dibromopentane within the Temperature Range From 293 K to 313 K at Pressures up to 100MPa. Int. J. Thermophys. 2009, 31, 26−41. (48) Dzida, M.; Jężak, S.; Sumara, J.; Ż arska, M.; Góralski, P. HighPressure Physicochemical Properties of Ethyl Caprylate and Ethyl Caprate. J. Chem. Eng. Data 2013, 58, 1955−1962.

(21) Tat, M. E.; Gerpen, J. H. V.; Soylu, S.; Canakci, M.; Monyem, A.; Wormley, S. The speed of sound and isentropic bulk modulus of biodiesel at 21°C from atmospheric pressure to 35 MPa. J. Am. Oil Chem. Soc. 2000, 77, 285−289. (22) Tat, M. E.; Gerpen, J. H. V. Effect of temperature and pressure on the speed of sound and isentropic bulk modulus of mixtures of biodiesel and diesel fuel. J. Am. Oil Chem. Soc. 2003, 11, 1127−1130. (23) Kegl, B. Numerical analysis of injection characteristics using biodiesel fuel. Fuel 2006, 85, 2377−2387. (24) Ortega, J.; Placido, J.; Vidal, M. Thermodynamic properties of (an ethyl ester + an n-alkane). XI. HmE and VmE values for {xCH3(CH2)uCOOCH2CH3+ (1 - x)CH3(CH2)2v+1CH3} with u = 6, 7, 8, 10, 12, and 14, and v = (1 to 7). J. Chem. Thermodyn. 1999, 31, 151−176. (25) Mumford, S. A.; Phillips, J. W. C. The physical properties of some aliphatic compounds. J. Chem. Soc. 1950, 19, 75−84. (26) Senol, A.; Lalikoglu, M.; Bilgin, M. Modeling extraction equilibria of butyric acid distributed between water and tri-n-butyl amine/diluent or tri-n-butyl phosphate/diluent system: Extension of the LSER approach. Fluid Phase Equilib. 2015, 385, 153−165. (27) Albert, O. Viscosity measurements on homologous ester series with special regard to the relations of Thorpe and Roger. Z. Phys. Chem., Abt. A 1938, 182, 421−429. (28) Perkin, W. H. On the Magnetic Rotary Polarisation of Compounds in Relation to their Chemical Consitution; with Observations on the Preparation and Relative Densities of the Bodies Examined. J. Chem. Soc., Trans. 1884, 45, 421−580. (29) Liu, X.; Zhu, C.; Yang, F.; Su, C.; He, M. Experimental and correlational study of isobaric molar heat capacities of fatty acid esters: Ethyl nonanoate and ethyl dodecanoate. Fluid Phase Equilib. 2019, 479, 47−51. (30) Zhang, Y.; Zheng, X.; He, M.-G.; Chen, Y. Speed of Sound in Methyl Caprate, Methyl Laurate, and Methyl Myristate: Measurement by Brillouin Light Scattering and Prediction by Wada’s Group Contribution Method. Energy Fuels 2016, 30, 9502−9509. (31) Zheng, X.; Zhang, Y.; He, M.; Liang, L.; He, X. Speed of sound measurement and prediction of ethyl hexanoate and ethyl octanoate at temperatures from (293.15 to 473.15) K and pressures from (0.1 to 10) MPa. J. Chem. Thermodyn. 2016, 97, 1−8. (32) He, M.; Zheng, X.; Zhang, Y.; Chen, Y. Measurement of speed of sound and thermal diffusivity of ethyl heptanoate using light scattering method. Fluid Phase Equilib. 2017, 431, 75−81. (33) Morton, D. W.; Lui, M.; Young, C. L. The (gas + liquid) critical temperature of some ethers, esters, and ketones. J. Chem. Thermodyn. 1999, 31, 675−684. (34) Chu, B. Light Scattering Theory-Laser Light Scattering, 2nd ed.; Academic Press, 1991. (35) Will, S.; Froba, A. P.; Leipertz, A. Thermal diffusivity and sound velocity of toluene over a wide temperature range. Int. J. Thermophys. 1998, 19, 403−414. (36) Wang, S.; Zhang, Y.; He, M.-G.; Zheng, X.; Chen, L.-B. Thermal Diffusivity and Speed of Sound of Saturated Pentane from Light Scattering. Int. J. Thermophys. 2014, 35, 1450−1464. (37) Zhang, Y.; Chen, Y.; Zhan, T.; He, M. Measurement of the Speed of Sound in Near-Critical and Supercritical n-Heptane at Temperatures from (513.40 to 650.90) K and Pressures from (2.5 to 10.0) MPa. J. Chem. Eng. Data 2018, 63, 3331−3337. (38) Kuyatt, E. Guidelines for Evaluating and Expressing Uncertainty in NIST Measurement Results; NIST Technical Note 1297, 1994. (39) Gates, K.; Chang, N.; Dilek, I.; Jian, H.; Pogue, S.; Sreenivasan, U. The uncertainty of reference standards - a guide to understanding factors impacting uncertainty, uncertainty calculations, and vendor certifications. J. Anal. Toxicol. 2009, 33, 532−539. (40) Ndiaye, E. H. I.; Nasri, D.; Daridon, J. L. Speed of Sound, Density, and Derivative Properties of Fatty Acid Methyl and Ethyl Esters under High Pressure: Methyl Caprate and Ethyl Caprate. J. Chem. Eng. Data 2012, 57, 2667−2676. (41) Sun, T. F.; Ten Seldam, C. A.; Kortbeek, P. J.; Trappeniers, N. J.; Biswas, S. N. Acoustic and Thermodynamic Properties of Ethanol I


Speed of Sound and Derived Properties of Ethyl Nonanoate | Journal

Recommend Documents