Thermophysical and volumetric properties of mixtures {carvacrol + ethanol} at several temperatures and atmospheric pressure

Journal Pre-proofs Thermophysical and volumetric properties of mixtures {carvacrol + ethanol} at several temperatures and atmospheric pressure José F. Martínez-López, Juan I. Pardo, José S. Urieta, Ana M. Mainar PII: DOI: Reference:

S0021-9614(19)30873-0 https://doi.org/10.1016/j.jct.2019.106042 YJCHT 106042

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J. Chem. Thermodynamics

Received Date: Revised Date: Accepted Date:

3 October 2019 19 December 2019 29 December 2019

Please cite this article as: J.F. Martínez-López, J.I. Pardo, J.S. Urieta, A.M. Mainar, Thermophysical and volumetric properties of mixtures {carvacrol + ethanol} at several temperatures and atmospheric pressure, J. Chem. Thermodynamics (2019), doi: https://doi.org/10.1016/j.jct.2019.106042

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Thermophysical and volumetric properties of mixtures {carvacrol + ethanol} at several temperatures and atmospheric pressure. José F. Martínez-López1,*, Juan I. Pardo2, José S. Urieta2, Ana M. Mainar2 1

Group of Applied Thermodynamics and Surfaces (GATHERS), Aragon Food Institute (IA2),

Universidad de Zaragoza, Facultad de Ciencias, Zaragoza 50009, Spain 2

Group of Applied Thermodynamics and Surfaces (GATHERS), Aragon Institute for Engineering

Research (I3A), Universidad de Zaragoza, Facultad de Ciencias, Zaragoza 50009, Spain CORRESPONDING AUTHOR FOOTNOTE Email: [email protected]. Fax: +34 976 761 202. Phone +34 629 573 446 ABSTRACT Experimental molar heat capacities at atmospheric pressure have been determined for the mixture {carvacrol + ethanol} every 10 K in the temperature interval (298.15-328.15) K and over the entire composition range with a Calvet type calorimeter. Densities, necessary for determining isobaric heat capacities, and ultrasonic speed of sound have been also measured at the same conditions. From these properties isobaric thermal expansivities, isentropic compressibilities, isothermal compressibilities, internal pressures and isochoric molar heat capacities have been calculated. Furthermore, in order to complete our thermophysical study the corresponding excess properties have been calculated and discussed in terms of molecular interactions. Finally, excess molar isobaric heat capacities have been calculated with COSMO-RS and compared to the experimental values. KEYWORDS: {carvacrol + ethanol} mixture, isobaric molar heat capacity, density, speed of sound, isochoric molar heat capacity, COSMO-RS

1. Introduction The thermodynamic behaviour of binary mixtures containing the main component of a vegetable extract and a short chain alkanol, such as ethanol or propan-1-ol, results interesting for the design of extraction processes with supercritical CO2 as those alkanols are added as cosolvents to CO2 to increase the polarity of the final solvent [[1]]. In addition, scarce thermodynamic property data for natural compounds are found in literature. For this reason, in earlier papers [[2]-[3]] we reported values of thermodynamic properties for binary mixtures of a monoterpenoid with a short chain alkanol. In this sense, it would be useful to extend these studies to the mixture of carvacrol with ethanol. Carvacrol (2-Methyl-5-(propan-2-yl) phenol) is a monocyclic monoterpenoid that is present in the essential oil of thyme and oregano varieties such as Origanum vulgare and Lippia graveolens. Some studies have recently proven that carvacrol possesses antinociceptive as well as antiinflammatory activity [[4]], a fact which can widen its field of applications. Besides the interest of thermodynamic properties for the extraction processes mentioned above, new experimental data for the mixtures of carvacrol with ethanol would provide a more complete knowledge about mixtures of phenolic compounds with alkanols. Therefore, in this work values of experimental isobaric molar heat capacities for binary mixtures of carvacrol with ethanol, at four temperatures (298.15, 308.15, 318.15 and 328.15) K and atmospheric pressure over the entire composition range are reported. Also, both densities and ultrasonic speeds of sound have been measured at the same experimental conditions of temperature, pressure and composition. From these experimental measurements, isobaric thermal expansivities, isentropic compressibilities, isothermal compressibilities, internal pressures and isochoric molar heat capacities have been calculated at the same experimental conditions. Furthermore, excess

properties have been determined for the mixtures. The solvation model COSMO-RS [[5][6]-[7]] has been applied in order to evaluate its ability to predict the isobaric excess molar heat capacity.

2. Experimental 2.1 Materials The chemicals used were carvacrol and ethanol. Also, ultrapure water produced by a Milli-Q Plus device from Millipore was used to perform the measurements. Table 1 shows their description.

TABLE 1 Sample description. Chemical name

Source

Purity

Purification method

Analysis method

Carvacrol

Aldrich

0.997a

None

GCc

Ethanol

VWR

0.997a,b

None

GCc

Water

Laboratory

Ultrapured

None

Electrical resistivity

a

Mole fraction purity. Water content(mole fraction) x < 0.003 provided by the supplier c Gas-Chromatography from the supplier. d Resistivity: 18.2 M·cm b

2.2 Equipments and procedure Molar heat capacities at atmospheric pressure were experimentally determined by means of a Calvet type calorimeter, Setaram C80 (France). A detailed description of the equipment, the method followed for calorimetric determination as well as the calibration and validation procedure have been reported elsewhere [[8]].

The calorimeter has a measurement and a reference cell, both with an effective volume of 14 cm3 for the sample, which are connected in opposition in such a way that non-desired effects that could affect the measurement cell are cancelled by the reference cell that would be also identically affected. Concerning to the procedure, the incremental temperature mode (step method) was used. Specifically, the temperature was increased 10 K in every step with a heating rate of 0.1 K·min-1 followed by an isothermal delay of 9000 s. To carry out a measurement, three runs are necessary. In all of them the reference cell was filled with air at atmospheric pressure. The measurement cell was filled with air in the first run, whereas it was filled with ultrapure water in the second run and with a sample of the liquid (pure compound or mixture) whose heat capacity was to be determined in the third run. Water was chosen as the reference liquid due to the high accuracy with which their heat capacity values are known [[9]]. Then, molar heat capacity is calculated through the equation

C P,m,sample  C P,m,water

M sample ρ water (Q3 - Q1 ) M water ρsample (Q2 - Q1 )

(1)

where CP,m is the molar heat capacity, M is the molar mass,  is the density and Q1, Q2 and Q3 are the heats exchanged in the first, second and third runs, respectively. The equipment was checked by measuring the molar heat capacity of heptane and comparing the results with the values in the critical selection of Zábranský et al. [[10]] and the relative expanded uncertainty (coverage factor k = 2) in the molar heat capacity is estimated to be ±0.008. Densities for water [[11]] were taken from the literature whereas densities for carvacrol and its mixtures at 0.101 MPa (atmospheric pressure) were measured by means of a vibrating tube densimeter Anton Paar DMA 5000 M. The expanded uncertainty (k = 2) for density is estimated to be better than ±0.7 kg·m-3. The densimeter was calibrated using ultrapure water and ambient air. Speed of sound was experimentally determined by means of a sound analyser Anton Paar DSA

5000 at a frequency of approximately 3 MHz. This apparatus, which was adjusted with dry air and ultrapure water at each temperature and atmospheric pressure, leads to repeatability for the measured properties of ±0.1 m·s-1, being the estimated standard uncertainty ±0.5 m·s-1 for the values of speed of sound. For determining the preceding properties, samples of the mixtures of carvacrol and ethanol were prepared by weighing using a Mettler-Toledo analytical balance, model AB265-S, with a precision of ±10-4 g. Hence, the expanded uncertainty (k = 2) in the mole fraction was estimated to be less than ±0.0005.

3. Results and discussion 3.1. Pure liquid components. Experimental values of densities, speeds of sound and isobaric molar heat capacities for the pure components at the working temperatures are reported in table 2. In this same table available literature values [Error! Bookmark not defined.,Error! Bookmark not defined.,[12]-] for ethanol are included for comparison. For carvacrol a comparison of density values with those found in the literature [[22][23][24]-[25]] can be found in figure 1.

TABLE 2 Experimental and literature densities, , speeds of sound, u, and isobaric molar heat capacities, C P ,m , for the pure liquid compounds at T = (298.15, 308.15, 318.15, 328.15) K and atmospheric pressure P = (0.101±0.002) MPa. Compound

 / kg·m-3

Exp.a Carvacrol Ethanol

972.46 785.19

u / m·s-1 Lit. Exp.b Lit. T/K = 298.15 1431.4 785.01d 1142.7 1142.72e

C P ,m / J·mol-1·K-1 Exp.c 325.1 112.3

Lit. 112.34f

785.10g 785.11i 785.11h 785.14e 785.20k 785.20l 785.22m 785.25n 785.46o

a

Carvacrol Ethanol

964.88 776.53

Carvacrol Ethanol

957.19 767.72

Carvacrol Ethanol

949.42 758.69

T/K = 308.15 1400.0 d 776.34 1109.5 776.44g 776.44h 776.48e 776.57m T/K = 318.15 1368.8 767.53d 1076.3 767.62h 767.63g 767.68e T/K = 328.15 1337.7 758.57d 1042.7 758.60h 758.62g 758.61i 758.65e

1142.88g 1143i 1143.84j

112.0h

e

1108.81 1109.16g 1109.92j

1075.23e 1075.80g

1041.87e 1042.79g 1043i

329.7 116.6

335.0 121.5

339.3 126.4

116.38f 116.4h

120.79f 121.0h

125.59f 125.6h

Measured with a densimeter Anton Paar DMA 5000 M, standard uncertainty u is u(T) = ±0.01 K,

and the combined expanded uncertainty Uc is Uc() = ±0.7 kg·m-3 with 0.95 level of confidence (k ≈ 2). b

Measured with a sound analyzer Anton Paar DSA 5000, standard uncertainty u is u(T) = ±0.01 K,

and the combined expanded uncertainty Uc is Uc(u) = ±0.5 m·s-1 with 0.95 level of confidence (k ≈ 2). c

Measured with a Calvet calorimeter Setaram C80. Relative combined expanded uncertainty Ur is Ur

( C P ,m ) = ±0.008 with 0.95 level of confidence (k ≈ 2). d

Ref [Error! Bookmark not defined.]; eRef [Error! Bookmark not defined.]; fRef [Error! Bookmark not

defined.]; gRef [Error! Bookmark not defined.]; hRef. [2]; iRef [Error! Bookmark not defined.]; jRef

[Error! Bookmark not defined.]; kRef. [Error! Bookmark not defined.]; lRef. [Error! Bookmark not

defined.];

m

Ref. [Error! Bookmark not defined.]; nRef. [Error! Bookmark not defined.]; oRef. [Error!

Bookmark not defined.]

The table only collects a selection from the huge amount of data reported for the density of ethanol, especially at 298.15 K. It can be seen that the values cover a quite wide interval. Our values show a very good agreement with some of the literature data, including previous measurements carried out by the authors [Error! Bookmark not defined.,Error! Bookmark not defined.]. In any case, all of the values are within the range of the expanded standard uncertainty of density which actually corresponds to the density of ethanol when taking into account its purity. A good agreement is also found for speeds of sound. Referring to isobaric molar heat capacities a more thorough comparison can be found in an earlier paper [Error! Bookmark not defined.].

FIGURE 1. Comparison of experimental densities, , for pure carvacrol (■) with literature values: (●) Carpenter and Easter 298.15 K [22]; () Gardner et al. [23]; (▼) Schaaffs [24] and (▲) Leeke et al. [25] at several temperatures. The line corresponds to the fitting of the experimental values.

About the density of carvacrol, it must be said that only Leeke et al. [25] provide the method of measurement (“density bottle technique”) and a value for purity of the sample (99 %). Neither

Gardner et al. [23] nor Carpenter and Easter [22] or Schaaffs [24] provide the method for measuring the density. The sample of Gardner et al. [23] is the product of a synthesis and it is said to be perfectly pure whereas the sample of Carpenter and Easter [22] is separated from the oil of Spanish Origanum through two reactions and no statement about its purity is done. It can be seen in figure 1 that our density values, when extrapolated, are in quite good agreement with that of Gardner et al. [23] and exhibit very good concordance with that of Schaaffs [24]. On the other hand, our density value at 298.15 K deviates noticeably from the only value at that temperature, reported by Carpenter and Easter [22]. Finally, our values, when interpolated, agree quite well with that of Leeke et al. [25] at 313 K but show a great deviation at 323 K. Given the scarcity of literature data and the lack of information about purity and measurement method, the comparison does not provide a definite result. In reference to the speed of sound, only one value has been found for carvacrol in the literature [3]. At 293.15 K, Schaaffs reported a value of 1475 m·s-1 whereas the extrapolation of our experimental values to that temperature leads to a very different value of 1447 m·s-1.

3.2. Experimental, calculated and excess properties. 3.2.1 Experimental and calculated properties. Experimental values of density, , and speed of sound, u, as well as calculated values of isobaric thermal expansivity,  P , for the mixtures {carvacrol (1) + ethanol (2)} in the entire composition range, are reported in table 3. The isobaric thermal expansivities were obtained at a given composition, x1 , from  (T) data by means of the following equation

P 

1 Vm

 ∂Vm  1       ∂T   -    T  P  P

(2)

where Vm stands for molar volume and T for temperature. Density values were fitted to temperature using a second degree polynomial that was subsequently derived to determine the isobaric thermal expansivities. A comparison of the values obtained for pure ethanol with several reported in the literature can be found in table S.2 in the Supplementary Information. In general, a good agreement is observed.

TABLE 3 Mole fraction, x1 , volume fraction, 1  density, , speed of sound, u, and isobaric thermal expansivity,  P , for the mixture {carvacrol (1) + ethanol (2)} at T = (298.15, 308.15, 318.15, 328.15) K and atmospheric pressure P = (0.101±0.002) MPa. x1 u / m · s-1  P / kK-1 / kg·m-3 1  T/K = 298.15 1.090 0 0 785.19 1142.7 1.054 0.0494 0.1204 810.26 1183.4 1.030 0.0999 0.2261 831.86 1218.9 0.991 0.2021 0.4001 866.48 1276.2 0.967 0.3038 0.5346 892.34 1317.9 0.945 0.4028 0.6397 911.78 1347.9 0.925 0.4995 0.7243 926.97 1370.3 0.905 0.6009 0.7986 939.83 1388.6 0.886 0.7037 0.8621 950.52 1403.7 0.869 0.7917 0.9091 958.19 1414.4 0.850 0.9014 0.9601 966.28 1425.1 0.842 0.9401 0.9764 968.80 1427.9 0.830 1 1 972.46 1431.4 T/K = 308.15 0 0 776.53 1109.5 1.126 0.0494 0.1200 801.70 1150.1 1.089 0.0999 0.2256 823.38 1185.6 1.062 0.2021 0.3993 858.15 1242.8 1.020 0.3038 0.5338 884.14 1284.5 0.993 0.4028 0.6390 903.70 1314.5 0.967 0.4995 0.7237 918.99 1336.9 0.944 0.6009 0.7980 931.94 1355.5 0.921 0.7037 0.8617 942.71 1370.8 0.900 0.7917 0.9089 950.45 1381.9 0.882 0.9014 0.9600 958.62 1393.1 0.860 0.9401 0.9763 961.18 1396.2 0.852 1 1 964.88 1400.0 1.126

0 0.0494 0.0999 0.2021 0.3038 0.4028 0.4995 0.6009 0.7037 0.7917 0.9014 0.9401 1

0 0.1196 0.2250 0.3985 0.5330 0.6382 0.7230 0.7975 0.8613 0.9086 0.9599 0.9762 1

0 0.0494 0.0999 0.2021 0.3038 0.4028 0.4995 0.6009 0.7037 0.7917 0.9014 0.9401 1

0 0.1193 0.2243 0.3976 0.5321 0.6374 0.7223 0.7969 0.8609 0.9083 0.9597 0.9761 1

T/K = 318.15 767.72 792.99 814.76 849.69 875.83 895.51 910.91 923.96 934.83 942.63 950.87 953.47 957.19 T/K = 328.15 758.69 784.07 805.94 841.06 867.37 887.19 902.71 915.88 926.84 934.72 943.05 945.67 949.42

1076.3 1116.4 1151.5 1208.5 1250.3 1280.8 1303.6 1322.7 1338.5 1350.0 1361.6 1364.8 1368.8

1.163 1.124 1.095 1.051 1.020 0.990 0.963 0.938 0.915 0.894 0.870 0.861 0.847

1042.7 1081.9 1116.7 1174.0 1216.9 1248.5 1272.2 1291.7 1307.4 1318.6 1329.9 1333.2 1337.7

1.201 1.161 1.129 1.082 1.047 1.013 0.983 0.955 0.930 0.907 0.880 0.871 0.857

Standard uncertainty u is u(T) = ±0.01 K, and the combined expanded uncertainties Uc are Uc ( x1 ) = ±0.0005, Uc( 1 ) = ±0.001 Uc() = ±0.7 kg·m-3, Uc(u) = ±0.5 m·s-1 and Uc(  P ) = ±0.002 kK-1 with 0.95 level of confidence (k ≈ 2).

The molar isobaric heat capacities, C P ,m , have been experimentally determined in the entire composition range and at the temperature interval (298.15 - 328.15) K. Their values are gathered in table 4. They have been depicted in Figure S.1 (Supplementary Information) and fitted to the mole fraction of carvacrol at each temperature. The values of the adjustable parameters can be found in table S.1 along with the standard deviation of the fitting (Supplementary Information).

TABLE 4 Mole fraction, x1 , molar isobaric heat capacity, C P ,m , isentropic compressibility,  S , isothermal compressibility,  T , internal pressure, Pint , and molar isochoric heat capacity, CV , m , for the mixture {carvacrol (1) + ethanol (2)} and the pure compounds at T = (298.15, 308.15, 318.15, 328.15) K and atmospheric pressure P = (0.101±0.002) MPa. x1 C P ,m / J·mol-1·K-1  S / TPa-1  T / TPa-1 Pint / MPa-1 CV , m / J·mol-1·K-1 0 0.0494 0.0999 0.2021 0.3038 0.4028 0.4995 0.6009 0.7037 0.7917 0.9014 0.9401 1

112.3 123.4 134.6 156.2 177.4 197.3 216.2 236.6 256.9 274.0 296.7 307.1 325.1

0 0.0494 0.0999 0.2021 0.3038 0.4028 0.4995 0.6009 0.7037 0.7917 0.9014 0.9401 1

116.6 127.7 138.9 161.0 182.4 202.6 222.1 242.2 262.0 279.8 301.7 312.4 329.7

0 0.0494 0.0999 0.2021 0.3038 0.4028 0.4995 0.6009 0.7037 0.7917 0.9014

121.5 132.9 144.2 166.6 188.2 208.6 228.0 248.3 268.9 286.5 309.0

T/K = 298.15 975.3 881.2 809.1 708.6 645.2 603.6 574.6 551.8 533.9 521.7 509.6 506.2 501.9 T/K = 308.15 1046.2 943.0 864.0 754.4 685.5 640.4 608.8 584.1 564.5 551.0 537.5 533.7 528.8 T/K = 318.15 1124.4 1011.9 925.6 805.9 730.4 680.8 646.0 618.6 597.0 582.1 567.3

1161.5 1023.0 924.8 791.3 713.4 658.0 618.2 590.4 569.4 554.2 540.5 536.0 530.2

279.8 307.1 331.9 373.2 404.0 428.3 445.8 456.7 463.8 467.5 468.7 468.3 466.6

94.0 105.4 116.1 136.6 155.8 173.8 191.8 207.8 222.9 235.4 247.6 252.4 258.9

1246.3 1096.11 989.01 844.11 761.25 700.76 657.76 627.64 604.5 587.89 572.12 567.26 561.02

278.3 306.0 330.7 372.4 401.9 425.3 442.0 452.0 458.9 462.0 463.0 462.5 460.5

97.7 109.1 120.2 141.9 159.9 178.4 195.9 211.1 226.0 237.4 251.1 256.3 262.4

1332.4 1173.9 1059.1 904.1 814.3 748.1 700.9 668.0 643.0 624.0 607.0

277.5 304.6 328.8 369.6 398.4 421.0 437.0 446.4 452.7 455.8 455.9

101.8 113.3 124.4 145.4 163.2 181.7 199.2 214.0 228.4 241.5 253.9

0.9401 1

319.0 335.0

0 0.0494 0.0999 0.2021 0.3038 0.4028 0.4995 0.6009 0.7037 0.7917 0.9014 0.9401 1

126.4 137.7 149.3 171.9 193.5 213.9 233.5 253.8 274.4 292.2 314.6 324.0 339.3

563.1 557.6 T/K = 328.15 1212.4 1089.7 995.0 862.7 778.6 723.2 684.5 654.5 631.2 615.3 599.5 594.9 588.6

601.4 595.0

455.4 453.0

259.3 266.0

105.9 117.3 128.7 149.3 166.9 184.0 201.8 217.6 231.6 244.6 257.7 262.0 269.8 Standard uncertainty u is u(T) = ±0.1 K, the combined expanded uncertainties are, Uc is Uc( x1 ) = 1441.2 1264.0 1137.2 968.5 870.7 799.6 748.0 711.4 684.2 663.0 643.3 637.4 629.0

273.3 301.2 325.6 366.4 394.6 415.8 431.2 440.2 446.1 448.9 449.0 448.3 446.7

±0.0005, Uc(  S ) = ±1.4 TPa-1, Uc(  T ) = ±4 TPa-1 and Uc( Pint ) = ±1 MPa and the relative combined expanded uncertainties Ur are Ur ( C P ,m ) = ±0.008 and Ur ( CV , m ) = ±0.016 with 0.95 level of confidence (k ≈ 2) Furthermore, with the aim to provide the corresponding values for isochoric molar heat capacities, CV , m , both isentropic,  S , and isothermal,  T , compressibilities, have also been obtained from the experimentally determined magnitudes. The isentropic compressibility,  S , was obtained from the density, , and the speed of sound values, u, through the Newton-Laplace equation

S 

1  u2

(3)

The isothermal compressibility,  T , was obtained by means of the following exact thermodynamic relation, which is considered [[26]] as one of the most important equations in thermophysics

T   S 

T Vm  P2 C P,m

(4)

The internal pressure, Pint , was determined by using the equation

Pint  T

P -P T

(5)

being P the pressure. Values of the internal pressure for pure ethanol are compared with literature ones at 298.15 and 308.15 K in table S.2 in the Supplementary Information. The molar isochoric heat capacity, CV , m , was obtained from the thermodynamic relation

CV , m  C P,m

S T

(6)

It is worthy to remark that the use of experimentally accurate values of molar isobaric heat capacities, isobaric expansivities and speeds of sound, provides an indirect and attractive method for determining CV , m . In fact, the majority of the isochoric heat capacity data for liquids reported in the literature has been obtained indirectly through the application of Equation (6) [26]. The values of all of these properties are listed in table 4.

3.2.2. Excess properties Excess properties, YE, (all pseudo-excess as well) were calculated as:

Y E  Y M - Y id

(7)

where YM represents the actual value of the property and Yid the value of the same property for an ideal solution. The ideal values for every property have been obtained through the following

equations that include (equation 15) the exact formula derived by Benson and Kiyohara [[27]] for the ideal isentropic compressibility

Vmid  x1 Vm,1  x2 Vm,2

(8)

1 2

 1 u id   id id    S   

(9)

 id  1 1  2  2  Sid

 1  S,1  2  S,2

(10)

  

2 2 id id  V  P,  V  P, 1 2 Vm  P  T  1 m,1  2 m,2 CidP,m C P,m,2  C P,m,1

2



(11)

 Pid  1  P,1  2  P,2

(12)

CPid,m  x1 CP,m,1  x2 CP,m,2

(13)

Tid  1 T,1  2 T,2

(14)

Pintid

 Pid  T id - P T

(15)

 Sid  Tid

(16)

CVid, m

id  C P, m

where xi is the mole fraction of component i, i  xi

Vm,i Vmid

the volume fraction of component i, and

subindices 1 and 2 indicate the property for pure compounds 1 and 2, respectively, in all cases.

The values of the excess properties have been listed in Tables S.3 and S.4 of the Supplementary Information. Excess properties values considered in this study, excepting excess molar heat capacities, were fitted to the Redlich–Kister equation

N

Y E   1 (1 -  1 )  A i (2 1 -1)i

(17)

i 0



xi

i , that is, the mole fraction or volume fraction of component i, and Ai are

adjustable coefficients that appear listed in table 5 along with the corresponding standard fitting deviations, , whose definition is





1

m E  E 2 2   Yexp - Ycal   j 1     mn      



(18)

where the subscripts exp and cal indicate the experimental and calculated values, respectively, m is the number of experimental points, and n is the number of coefficients used in the fitting equation. Mole fractions have been used for excess molar volumes whereas volume fractions have been used for the remaining excess properties as in these cases the value of the property for the ideal solution is dependent on the volume fractions. Isobaric and isochoric excess molar heat capacities have been adjusted by using the skewed form of the Redlich–Kister equation. N

 Ai

(2 x1 -1) i

Y E  x1 (1 - x1 ) i  0 M 1   B j (2 x1 -1) j

(19)

j 0

where xi is the mole fraction Ai and Bi are adjustable coefficients which can be found in table 5 along with the corresponding standard fitting deviations defined by equation 18. The fitting curves have been included in the corresponding figures. Excess molar volumes, VmE , were directly obtained from the densities by means of the equation

1 1      x2 M 2  1 - 1  VmE  x1 M 1      2    1  

(20)

and their values appear represented in figure 2.

FIGURE 2. Excess molar volumes, VmE , for the mixture {carvacrol (1) + ethanol (2)} as a function of carvacrol mole fraction, x1 , at the temperatures: (●) 298.15 K; () 308.15 K; (□) 318.15 K; and (▼) 328.15 K along with the Redlich-Kister fitting curves (equation 17).

TABLE 5 Redlich-Kister (equation 17) and skewed Redlich-Kister (equation 19) fitting parameters for the excess molar volumes, VmE , excess speeds of sound, u E , excess isentropic compressibilites,  SE , E excess isothermal compressibilities,  TE , excess internal pressures, Pint , excess isobaric

expansivities,  PE , excess isobaric molar heat capacitites, CPE, m , and excess isochoric molar heat capacitites, CVE,m , of the mixture {carvacrol (1) + ethanol (2)} at T = (298.15, 308.15, 318.15, 328.15) K and atmospheric pressure P = (0.101±0.002) MPa. VmE /106 m3·mol-1 A0 A1

T/K = 298.15 -2.81 1.05

T/K = 308.15 -2.87 1.10

T/K = 318.15 -2.94 1.14

T/K = 328.15 -3.03 1.18

-0.37 0.004 T/K = 298.15 283.63 87.05 19.96 0.6 T/K = 298.15 -336.78 47.88 0.4 T/K = 298.15 -353.65 75.44 0.7 T/K = 298.15

-0.41 0.004 T/K = 308.15 283.98 84.52 16.43 0.6 T/K = 308.15 -367.85 58.49 0.4 T/K = 308.15 -389.87 82.24 0.6 T/K = 308.15

-0.44 0.005 T/K = 318.15 280.61 87.61 19.57 0.6 T/K = 318.15 -398.85 62.52 0.4 T/K = 318.15 -427.07 83.24 0.4 T/K = 318.15

-0.48 0.005 T/K = 328.15 281.68 101.14 20.34 0.2 T/K = 328.15 -438.36 55.57 0.2 T/K = 328.15 -472.91 71.93 0.4 T/K = 328.15

A0 A1 A2



126.05 44.17 2.68 0.4

128.72 41.59 -2.31 0.4

129.30 41.09 -1.48 0.3

131.73 46.13 -2.78 0.2

106· α P /K-1

T/K = 298.15

T/K = 308.15

T/K = 318.15

T/K = 328.15

A0 A1 A2 A3

-48.01 29.15 -0.33 0.00 0.5

-55.03 19.83 -7.24 0.00 0.4

-62.14 9.70 -17.91 0.00 0.2

-70.67 7.71 -25.32 -22.50 0.4

T/K = 298.15

T/K = 308.15

T/K = 318.15

T/K = 328.15

-8.08 -24.86 4.65 -0.84 0.3 T/K = 298.15

-3.50 -26.60 -1.11 -0.79 0.4 T/K = 308.15

-0.11 -26.53 6.01 -0.81 0.2 T/K = 318.15

3.42 -26.30 8.81 -0.84 0.2 T/K = 328.15

-16.91 -12.01 8.53 -0.98 0.2

-12.78 -12.80 6.54 -0.97 0.1

-9.17 -13.37 10.83 -0.98 0.1

-5.63 -14.82 6.99 -0.86 0.1

A2



E

u /m·s-1 A0 A1 A2  E  S /TPa-1 A0 A1



 TE

/TPa-1 A0 A1



E Pint

/MPa-1

E



CPE, m

/J·mol-1·K-1 A0 A1 A2 B1



CVE,m

/ J·mol-1·K-1 A0 A1 A2 B1



E and VmE , CPE, m , and CVE,m have been fitted with respect to mole fraction. u E ,  SE ,  TE , Pint

α PE

have been fitted with respect to volume fraction.

As shown in figure 2, excess molar volumes are negative over the entire composition range and their values slightly decrease as the temperature increases, at a given mole fraction x1 . The minima are located at x1 ≈ 0.4. Considering only mixtures of ethanol with compounds with alcohol function, this behavior has been also reported for mixtures of ethanol with diols [[28]-[31]] or glycerol [[32]] or glycols or glycol derivatives [17,[33]]. Negative values of excess molar volume have been also obtained when compounds similar to carvacrol such as cresols (methylphenols) have been mixed with alkanols [[34]-[37]]. In this way, mixtures of p-cresol with methanol [34] or alkanols from C3 to C8 [35], m-cresol with methanol [36] and o-cresol, m-cresol and p-cresol with ethanol [37] exhibit negative excess molar volumes in the entire composition range, in a temperature interval similar to ours. But the values are lower for the mixtures of carvacrol. The excess molar volumes of the mixtures of cresols with methanol or ethanol also decrease as the temperature rises. The negative values of excess molar volume indicate a better packing of the molecules in the mixture with respect to that of the pure compounds and the quite high absolute values obtained would point to the formation of strong interactions between carvacrol and ethanol, an explanation also proposed for mixtures of cresol with alkanols [34-37]. It is well known that ethanol molecules form hydrogen bonds. On the other hand, carvacrol has a boiling point of 510.8 K [[38]] whereas that of 1,2-dimethyl-4-(1-methylethyl) benzene where the hydroxyl group of carvacrol is substituted by a methyl group is 474.95 K [[39]]. This significant difference can be attributed also to the formation of hydrogen bonds between the molecules of carvacrol. Then, it can be supposed that hydrogen bonds between the hydroxyl groups of ethanol and carvacrol as well as between the

hydroxyl group of ethanol and the -cloud of carvacrol are formed when carvacrol and ethanol are mixed and their energetic effects would prevail over the endothermic breaking of hydrogen bonds in the pure compounds, leading to a global exothermic mixing process. This is supported by the fact that the mixtures of o-cresol and m-cresol with ethanol are strongly exothermic with a minimum excess enthalpy at 298.15 K of about -1652.17 and -1227.7 J·mol-1 [[40]], respectively. In any case, steric effects cannot be discarded to have influence on the excess molar volume given the great difference in the shape and size of the molecules involved. Moreover, another fact that backs up the formation of hydrogen bonds between carvacrol and ethanol can be found in the behaviour of excess molar volume values with temperature and from the related property, the excess isobaric expansivity,  PE , which can be expressed [[41]] by the equation

 PE 

1 Vmid

  V E   E  m  -  P Vm    T  P 

The values of  PE are represented in figure 3.

(21)

FIGURE 3. Excess isobaric expansivities,  PE , for the mixture {carvacrol (1) + ethanol (2)} as a function of carvacrol volume fraction, 1 , at the temperatures: (●) 298.15 K; () 308.15 K; (□) 318.15 K; and (▼) 328.15 K along with the Redlich-Kister fitting curves (equation 17).  V E  According to equation (21), the fact that  PE is negative means that the negative term  m    T P

prevails over the term  P VmE . Moreover, negative values of  PE suppose the presence of strong interactions between the components in the mixtures as it implies that as temperature increases the contraction experimented by the mixtures (molar volume of the mixture is minor than the ideal volume of the mixture) increases with temperature. This behaviour of excess volumes with temperature could be explained considering that an increase in temperature supposes an increasing rupture of hydrogen bonds in both pure components followed by new interactions between dissimilar components which are stronger compared to the mentioned ruptures. Then, the mixing process would become more exothermic as the temperature increases.

Excess speeds of sound, u E , are graphically represented in figure 4, where it can be seen that they are positive over the entire composition range. They scarcely change when the temperature is modified and show the maxima at 1 ≈ 0.6, that is, at x1 ≈ 0.4 which is the mole fraction where the minima for excess molar volumes are placed. The positive values for u E are in agreement with the negative values found for excess molar volumes because a minor distance between molecules would lead, as a consequence, to an enhancement in the sound propagation. Taken into account that the maxima for u

E

and the minima for VmE , appear at the same value

for mole fraction, (x1 = 0.4) it is clear the strait relation between both properties which is reinforced by the quite similar behaviour of both properties with temperature.

FIGURE 4. Excess speeds of sound, u E , for the mixture {carvacrol (1) + ethanol (2)} as a function of carvacrol volume fraction, 1 , at the temperatures: (●) 298.15 K; () 308.15 K; (□) 318.15 K; and (▼) 328.15 K along with the Redlich-Kister fitting curves (equation 17). The excess compressibilities, both isentropic,  SE , and isothermal,  TE , shown in figure 5, are negative over the whole composition range with minima placed at 1 ≈ 0.5, that is, at x1 ≈ 0.25. Negative values for  SE are indicative of strong interactions between dissimilar molecules. For both excess compressibilities their values clearly decrease as the temperature increases. These results are again in agreement with those of the excess molar volume because a closer packing of the molecules would lead to smaller compressibility values. The variation with the temperature of both compressibilities also agrees with that of the excess molar volume because, as the molecules approach, the free space diminishes between them so that it results more difficult to compress the mixture.

FIGURE 5. Excess isentropic compressibilities,  SE , and excess isothermal compressibilities,  TE , for the mixture {carvacrol (1) + ethanol (2)}as a function of carvacrol volume fraction, 1 , at the temperatures: (●) 298.15 K; () 308.15 K; (□) 318.15 K; and (▼) 328.15 K) along with the Redlich-Kister fitting curves (equation 17). Excess internal pressures, PintE , represented in figure 6, are positive in the entire composition range and they slightly increase when temperature rises. The maxima are located at 1 ≈ 0.6 which corresponds to x1 ≈ 0.4. The internal pressure is related to the cohesive energy density [[42]], that is, to the intermolecular interactions in a liquid (pure or mixture). Then, the positive values obtained would, in principle, indicate the presence of interactions between carvacrol and ethanol stronger than those in the pure compounds. This would be in agreement with the hypothesis of negative excess molar enthalpies due to hydrogen bonds between dissimilar molecules. But it must be pointed out that the relationship between internal pressure and cohesive energy density, which is quite direct for non-polar systems, is more complex when molecules interact through hydrogen bonds [42]. Then, the values of excess internal pressure are not sufficient proof to ascertain the formation of hydrogen bonds although they could be due to this kind of bonds. The variation with temperature, weak as it is, corresponds to what can be expected from the behaviour of the volumetric and acoustical properties.

FIGURE 6. Excess internal pressures, PintE , for the mixture {carvacrol (1) + ethanol (2)} as a function of carvacrol volume fraction, 1 , at the temperatures: (●) 298.15 K; () 308.15 K; (□) 318.15 K; and (▼) 328.15 K along with the Redlich-Kister fitting curves (equation 17).

Excess molar heat capacities at constant pressure, C PE, m , and at constant volume, CVE,m , are represented in figure 7. Both are sigmoidal shaped with positive values mainly for mixtures rich in ethanol and negative ones in the remaining composition range. This change in the sign of the excess heat capacities is not a usual behaviour but it has been observed for mixtures of dimethyl sulfoxide with propylene carbonate [[43]] or ethanol or butan-1-ol [[44]], for mixtures of cyclic ethers with alkanols [[45]] or cyclic ketones [[46],[47]] and also for mixtures of two alkanols [[48]-[50]]. All of these mixtures share the feature that both components have oxygenated functions capable of establish specific interactions, hydrogen bonds in most of the cases. But, apart from this, it is difficult to assess how this feature would determine a different variation of the strength of the interactions at different composition ranges as the temperature varies. In any case, the decrease of the excess molar enthalpy with increasing temperatures, C PE, m < 0, inferred from the behaviour of  PE would take place only in a part of the composition range. This points to the complexity of the phenomena occurring in the mixture and the consequent difficulty in interpreting the properties.

On the other hand, the values of both properties increase as the temperature increase. This effect is quite marked for the minima that, in the case of C PE,m , from a value of -8.3 J·mol-1·K-1 at 298.15 K reach a value of -3.7 J·mol-1·K-1 at 328.15 K and somewhat similar occurs to CVE, m . As a result of this effect of the temperature, the composition range corresponding to positive values of both excess heat capacities is widened in such a way that, for C PE,m at 298.15 K that composition range extends until x1 ≈ 0.35 but at 328.15 K it covers up to x1 ≈ 0.55. Another feature due to the effect of the temperature is that the position of the maxima slightly shifts toward higher mole fractions of carvacrol at higher temperatures but a shift is not clearly observed for the position of the minima, which are placed at very high mole fractions of carvacrol.

FIGURE 7. Excess molar heat capacity, isobaric, C PE,m , and isochoric, CVE, m , at atmospheric pressure for the mixture {carvacrol (1) + ethanol (2)} as a function of carvacrol mole fraction, x1 ,

at the temperatures: (●) 298.15 K, () 308.15 K, (□) 318.15 K and (▼ ) 328.15 K along with the skewed Redlich-Kister fitting curves (equation 19).

3.3. Modelling of C PE,m with COSMO-RS. The COSMO-RS model has been applied to predict the excess molar heat capacity of the considered binary mixture. COSMO-RS, first introduced by Klamt [5] and afterwards refined [6-7], is a method that proceeds in two steps. First, DFT (density functional theory) calculations adjust the polarization charge density of the compound in the mixture. Then, statistical thermodynamics is applied to quantify the molecular interactions in the liquid phase using those polarization charge densities. A comparison of the results of COSMO-RS with experimental data shows that the model performs very poorly for the mixture of carvacrol and ethanol. Details about the model application and the results can be found in the Supplementary Information.

Conclusions The molar heat capacity at atmospheric pressure of the mixture {carvacrol (1) + ethanol (2)} has been determined in the temperature interval (298.15-328.15) K over the whole composition range. Densities and speeds of sound have been also experimentally measured for this mixture at the same conditions of temperature, pressure and composition. From densities, speeds of sound and isobaric molar heat capacities, the isobaric thermal expansivities, both isentropic and isothermal compressibilities and internal pressures have been obtained as well as isochoric molar heat capacities. Excess properties have been calculated for all the preceding quantities. Excess molar volumes are negative in the entire composition range. This implies better packing of molecules after the mixing process. Their great absolute values would indicate stronger

interactions, mainly hydrogen bonds, between dissimilar molecules than in the pure compounds. Then excess molar enthalpies would be presumably negative for this mixture. Also the variation of excess molar volumes as the temperature changes, becoming more negative as temperature increases at a given mole fraction, agrees with the negative values determined for excess isobaric expansivity that points to more negative excess molar enthalpies with rising temperatures. Both excess isentropic and isothermal compressibilities are negative in the entire composition range whereas the excess speeds of sound are positive which is in accordance with a better packing after mixing process. Moreover, the behaviour with temperature of both excess isothermal and isentropic compressibilities, at a given composition of the mixture, indicates lower compressibilities as temperature rises, which is in agreement with the behavior found by excess molar volumes. On their hand, the excess internal pressures are positive in the whole composition range. As they are related to the cohesive energy density, their values point to stronger interactions between carvacrol and ethanol than those existing in the pure compounds. Both excess isobaric and isochoric molar heat capacities are sigmoidal shaped being positive in compositions richer in ethanol and negative in the remaining composition range. These excess properties increase as the temperature rises. The COSMO-RS model has been applied to predict the excess molar heat capacity of the mixture {carvacrol (1) + ethanol (2)}. Although the model is able to slightly reproduce the unusual sigmoidal shaped behaviour of the excess molar heat capacities and their variation with temperature, from a quantitative point of view the prediction shows important deviations (up to 30 %) for the positive values and even greater for the negative ones.

Acknowledgements

The authors thank the financial support of MINECO-FEDER (Project CTQ2015-64049-C3-2R) and also of Gobierno de Aragón-FSE-FEDER “Construyendo Europa desde Aragón” (Group E39_17R).

José F. Martínez-López: Investigation, Formal analysis, Writing-original draft, Writing - Review & Editing Juan I. Pardo: Investigation, Formal analysis, Writing - Review & Editing José S. Urieta: Resources, Writing - Review & Editing Ana M. Mainar: Funding acquisition, Project administration

Declaration of interests

☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

Highlights Thermophysical and volumetric properties of mixtures {carvacrol + ethanol} at several temperatures and atmospheric pressure José F. Martínez-López, Juan I. Pardo, José S. Urieta and Ana M. Mainar Group of Applied Thermodynamics and Surfaces (GATHERS), Aragon Institute for Engineering Research (I3A), Universidad de Zaragoza, Facultad de Ciencias, Zaragoza 50009, Spain

 C P ,m , 

  P ,  S ,  T , Pint and CV , m

 C PE,m 

C PE,m



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