Measurement and Prediction of the Molar Heat Capacities of Liquid

Article pubs.acs.org/jced

Measurement and Prediction of the Molar Heat Capacities of Liquid Polyoxyethylene Glycol Monoalkyl Ethers (CnEm) Paweł Góralski* and Mariola Tkaczyk Departrment of Physical Chemistry, University of Łódź, Pomorska Street 165, 90-236 Łódź, Poland S Supporting Information *

ABSTRACT: The saturation heat capacities of eleven polyoxyethylene glycol monoalkyl ethers (CnEm) were measured by the calorimetric (DSC) method. The measurements were performed within the temperature range of (275.15 to 339.15) K by means of Micro DSCIII (Setaram) calorimeter. Assuming that the molar heat capacity (Cp,m) shows an additive character, the contributions to the Cp,m values of particular functional groups forming the compounds of CnEm series were calculated. Two models differing in the manner of molecule division into functional groups, i.e., first- and second-order additivity group contribution approach, were used. In the latter, not only the type of functional group but also its position and the closest neighborhood was taken into account. The average deviations between the experimental values of Cp and those estimated on the basis of the group contributions do not exceed 0.4 % for the compound of the series under investigation. The group contributions determined in this study make it possible to predict the molar heat capacity of monoethers CnEm within the temperature range of (270 to 350) K with an average error below 1 %.

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INTRODUCTION Molar heat capacity (Cp,m) is a quantity used for the calculations of many basic thermodynamic parameters used in science and technology. The databases of physicochemical parameters contain experimental values of the molar heat capacity of numerous groups of substances; however, there is still a lack of the values of Cp,m of many commonly used compounds. Molar heat capacity at a constant pressure is considered to be an additive quantity. The determination of Cp,m contributions of individual functional groups makes it possible to estimate the value of molar heat capacity of a selected compound that is devoid of experimental data. However, so far there is no universal method for the calculation of the group contributions being widely applicable to any family of compounds at any particular temperature interval.1 The best compatibility between experimental and estimated values of Cp,m is obtained if the group contributions are determined for a narrow group of compounds, preferably of homological series. In previous works, we measured molar heat capacities of compounds forming homological series of α,ω-substituted: halogenoalkanes,2 diols,3 diamines,4 and halogen-derivatives of benzene.5 The group contributions of Cp,m calculated on their basis allowed us to estimate the molar heat capacity as a function of temperature for this compounds with uncertainty below 1 %. Continuing these studies, we have extended them with polyoxyethylene glycol monoalkyl ethers with a general formula CnH2n+1(OCH2CH2)mOH. The often used abbreviation of these compounds is CnEm, where n is the number of carbon atoms in the hydrocarbon chain (hydrophobic tail) and m refers to the number of oxyethylene units (−OCH2CH2−) in the hydrophilic head of molecule. A great practical importance of © XXXX American Chemical Society

these nonionic amphiphils is connected with their specific molecular structure. In their asymmetric molecules, nonpolar, weakly polar and polar (hydroxyl) group are present. The coexistence of ether, hydroxyl, and hydrocarbon groups in the same molecule causes that they form stable homogeneous oil−water solutions with a high fraction of water (or oil), and for this reason they are very important industrial solvents. They are used in many production processes in: textile, pharmaceutical, cosmetic, food, agrochemical, and petrochemical industries. Also their properties such as: high chemical stability, low vapor pressure, low melting point, low toxicity, and viscosity decide about their practical applications. In this work, the saturation molar heat capacity of monoalkyl ethers of: ethylene glycol CnE1 (n = 2−4); diethylene glycol CnE2 (n = 1−4, 6); triethylene glycol CnE3 (n = 1, 8), and tetraethylene glycol monomethyl ether C1E4, were measured within the temperature range of (275.15 to 339.15) K by DSC method. An additional aim of the study was to determine the Cp contributions of groups forming the series of polyoxyethylene glycol ethers. This will make it possible to predict the molar heat capacity of CnEm compounds within the temperature range of (275.15 to 339.15) K that are devoid of experimental data. Received: January 14, 2015 Accepted: July 3, 2015

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DOI: 10.1021/acs.jced.5b00051 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Chemical Names, Source, and Purity of the Polyoxyethylene Glycol Monoalkyl Ethers under Investigation

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abbreviation

chemical name

source

CAS No.

molar mass/g·mol−1

mass fraction purity

C2E1 C3 E 1 C4 E 1 C1 E 2 C2 E 2 C3 E 2 C4 E 2 C6 E 2 C1 E 3 C8 E 3 C1 E 4

ethylene glycol ethyl ether ethylene glycol propyl ether ethylene glycol butyl ether diethylene glycol methyl ether diethylene glycol ethyl ether diethylene glycol propyl ether diethylene glycol butyl ether diethylene glycol hexyl ether triethylene glycol methyl ether triethylene glycol octyl ether tetraethylene glycol methyl ether

Sigma Aldrich Lancaster Aldrich Aldrich Aldrich Aldrich Aldrich Fluka Bachem Alfa Aesar

110-80-5 2807-30-9 111-76-2 111-77-3 111-90-0 6881-94-3 112-34-5 112-59-4 112-35-6 19327-38-9 23783-42-8

90.1222 104.148 118.176 120.148 134.175 148.202 162.229 190.283 164.202 262.39 208.255

0.99 0.994 0.99 0.99 0.99 0.99 ≥0.99 0.98 ≥0.97 0.985 0.98

Table 2. Comparison of the Experimentala and Literature Data of Molar Heat Capacities (Cp,m/J·mol−1·K−1) at Different Temperatures

EXPERIMENTAL SECTION Chemicals. The names, source, and purities of the investigated compounds are presented in Table 1. All compounds were used without further purification. Before measurements the chemicals were dried for several days with activated molecular sieves (type 4Ǻ from Lancaster) and degassed in an ultrasonic stream. Water used as a Cp reference was deionized, triple distilled and then degassed by heating under vacuum. The samples and cells were filled and stored in a drybox over phosphorus pentoxide. Apparatus and Procedure. The measurements of the saturation molar heat capacities (Csat) were carried out by means of a high sensitivity differential scanning calorimeter based on the Tian-Calvet principle (Micro DSC III − Setaram). The so-called continuous with reference method (with water as a reference) was used. The values of specific heat capacity of water in the temperature range (273.15 to 335.15) K were taken from Zabransky et al.6 The details of apparatus and measuring procedure are described elsewhere.7 Both heating and cooling sequences with a scanning rate of 0.25 K·min−1 were used to determine Cp The measuring cell, with a total volume of 1.02 mL was filled with such amount of liquid as to provide the vapor space volume at about 10 % of cell volume. Such a small vapor space makes it unnecessary to take into account a correction of the evaporation of liquid during the experiment. Due to the low vapor pressure of the liquids in the experimental conditions, the measured values of saturation heat capacity can be considered as isobaric heat capacity (Csat = Cp) since the difference between these values is many times smaller than the measurement error. The use of this procedure for liquids being Cp references, allowed us to obtain the capacity values with the apparatus error being at a level of 0.15 %. In reality, the total error of the values determined is higher, which is mainly connected with the type and quantity of impurities present in the substances under investigation. Purification by distillation often fails to remove impurities with a similar chemical nature, e.g. isomers. The specific heat capacities of this type of impurities have similar values (± 10 %) to those of the compounds studied, therefore their presence does not significantly affect the values of Cp measured. One can assume that 1 % of such impurities generate not more than ± 0.1 % error of the specific heat capacity measured. However, a particular attention should be paid to remove even trace quantities of water, whose Cp is considerably higher. Therefore we estimate that the total relative measurement error for the compounds with purity degree ≥ 0.99 amounts to 0.4 % and for the remaining ones 0.6 %. A Sartorius RC 210D balance (with an accuracy of 2·10−5 g) was used to determine the sample mass. The comparison of the experimental and literature Cp data is presented in Table 2

Cp,m/J·mol−1·K−1 substance

temperature/K

this work

literature

C2E1

298.15 313.15 298.15 313.15 298.15 313.15 298.15 298.15 315.00 335.00 298.15 298.15 313.15 298.15

211.1 216.5 241.4 248.0 273.0 280.5 267.4 301.7 336.0 344.7 360.2 421.0 428.0 356.6

211.37b, 210.8c, 210.3d 217.2b, 216.11e 244.3d, 241.6c 247.98e 273.0f, 272.05g, 273.1c, 273.3h 281.5d, 280.17g, 280.6h 271.1i 301i 333.1j 342.6j 354.89k 423.30l 431.63l 357.05m

C3E1 C4E1 C1E2 C2E2 C3E2 C4E2 C6E2 C1E3 a

Standard uncertainty u is u(T) = 0.05 K. The combined expanded uncertainty Uc is Uc(Cp,m) = 0.004·Cp,m for C2E1, C3E1, C4E1, C1E2, C2E2, C3E2, C4E2, and Uc(Cp,m) = 0.006Cp,m for C6E2, C1E3 (0.95 level of confidence). bRef 8. cRef 9. dRef 10. eRef 11. fRef 12. gRef 13. hRef 14. iRef 15. jRef 16. kRef 17. lRef 18. mRef 19.

and graphically as percent deviations at different temperatures in Figures 1 to 3.

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RESULTS AND DISCUSSION In the continuous method used in this work, the experiment result is a set of 2750 values of Cp,m comprising the whole temperature range (from 275.13 to 339.15) K. For each examined liquid, the measurements were repeated 2 to 4 times, each time exchanging the content of the measurement cell. The series, for which the results did not differ more than 0.15 % constituted the base for averaging. A complete set of molar heat capacity data for the given substance (all the results for all series) were described with a common polynomial expressing the dependence of molar heat capacity on temperature (eq 1). Cp , m = A 0 + A1(T /100) + A 2 (T /100)2

(1)

Table 3 presents the values of Cp,m averaged in this way with a 2 K step and additionally at 298.15 K. The experimental data of specific heat capacity are listed in Table S1 in the Supporting Information. Polynomial coefficients Ai (eq 1) and the average deviations (δCp,m) of the experimental values from the calculated with polynomial are listed in Table 4. B



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Figure 1. Deviation of experimental heat capacities Cp,m from literature values for some polyoxyethylene glycol monoalkyl ethers: ▲, C2E1, ref 10; □, C2E1, ref 11; △, C1E2, ref 15; ■, C2E2, ref 15; ●, C4E2, ref 17; ○, C1E3, ref 19.

Figure 3. Deviation of experimental heat capacities Cp,m from literature values for: □, C3E1, ref 11; ▲, C3E2, ref 16; ●, C6E2, ref 18.

A more effective quantity that may be used for the analysis is specific heat capacity. Figure 4 (right axis, empty symbols) shows the temperature dependence of the specific heat capacity for the same derivatives of polyoxyethylene glycol monoalkyl ethers. In this case, clear changes in the slope of Cp = f(T) connected with a change in the polyoxyethylene chain length m are seen. A change in the hydrocarbon chain length n does not systematically affect the value of specific heat capacity and its temperature dependence. With an increase in the oxyethylene chain length m, the slope of the function discussed decreases as well as the values of specific heat capacity at higher temperature. In the same order (C1E1 > C1E2 > C1E3 > C1E4), there decreases the number of hydroxyl groups per mass unit which are capable to hydrogen bond formation as proton donors. It is believed that the heat capacity being a temperature derivative of entropy {Cp = T(dS/dT)p} determines the susceptibility of structure to temperature changes. From IR spectroscopic measurements22 it follows that owing to the stability of gauche conformation of oxyethylene group, the five-member rings (for m = 1) with intramolecular H-bonds are more stable than the eight-member ones (for m > 1). The density of such bonds in the mass unit is the highest for compounds with m = 1, and it decreases with increasing m. Maybe the opening of such cyclic structures constitutes an additional factor disturbing the liquid structure with increasing temperature and influences the heat capacity of the compound investigated. Group Contributions of Molar Heat Capacity. In the compounds of the CnEm series, the presence of four functional groups: CH3, CH2, −O−, and −OH can be distinguished. Assuming in the first approximation (simple model, SM) that the group heat capacity does not depend on its vicinity, the molar heat capacity of each of the compounds can be presented at the given temperature as follows:

Figure 2. Deviation of experimental heat capacities Cp,m from literature values for C4E1: △, ref 10; □, ref 13; ▲, ref 14; ●, ref 27.

Figure 4 (left axis, full symbols) shows the temperature dependence of molar heat capacity for selected compounds with the shortest hydrocarbon chain, i.e., C1Em (m = 1−4) and C2E1. For both the compounds presented in the diagram and all the remaining, the dependence Cp,m = f(T) increases almost linearly with a slightly differing slopes. It is the molar mass value (M) that decides about the mutual location of curves in the diagram. Compounds belonging to common family (homologous series) with a higher molar mass always have higher values of Cp,m. For CnEm compounds, it is not important whether an increase in M is connected with an increase in n or m. This is shown in Figure 5 presenting the correlation between Cp,m and M for two selected temperatures: (298.15 and 328.15) K. This figure also shows the values of Cp,m taken from literature19−21 for C1E5 (M = 252.30 g·mol−1), C6E4 (M = 278.39 g·mol−1), and for C6E5 (M = 322.40 g·mol−1). The linear dependence Cp,m = f(M) is characterized by a high regression coefficient (R = 0.999).

Cp , m =

∑ niCp,i i

(2)

where ni defines the number of particular groups: CH3, CH2, −O−, and −OH, while Cp,i is their heat capacity. The molar heat capacity of the substance under study depends on temperature and is described by the secondary polynomial. C



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Table 3. Saturated Molar Heat Capacities (Cp,m/J·mol−1·K−1) of Examined Liquid Compounds for T = (275.13 to 339.15) Ka Cp/J·mol−1·K−1

a

Cp,m/J·mol−1·K−1

T/K

C2E1

C3E1

C4 E 1

C1E2

C2E2

T/K

C3E2

C4E2

C6 E 2

C1E3

C8E3

C1E4

275.15 277.15 279.15 281.15 283.15 285.15 287.15 289.15 291.15 293.15 295.15 297.15 298.15 299.15 301.15 303.15 305.15 307.15 309.15 311.15 313.15 315.15 317.15 319.15 321.15 323.15 325.15 327.15 329.15 331.15 333.15 335.15 337.15 339.15

203.3 204.0 204.6 205.3 205.9 206.6 207.3 208.0 208.6 209.3 210.0 210.7 211.1 211.4 212.1 212.8 213.6 214.3 215.0 215.7 216.5 217.2 218.0 218.7 219.5 220.2 221.0 221.8 222.6 223.3 224.1 224.9 225.7 226.5

231.6 232.4 233.3 234.1 235.0 235.8 236.6 237.5 238.3 239.2 240.1 240.9 241.4 241.8 242.7 243.5 244.4 245.3 246.2 247.1 248.0 248.9 249.8 250.7 251.6 252.5 253.4 254.3 255.2 256.1 257.1 258.0 258.9 259.9

261.7 262.6 263.6 264.6 265.6 266.6 267.6 268.5 269.5 270.5 271.5 272.5 273.0 273.5 274.5 275.5 276.5 277.5 278.5 279.5 280.5 281.5 282.5 283.5 284.5 285.5 286.5 287.5 288.5 289.6 290.6 291.6 292.6 293.6

261.9 262.3 262.7 263.2 263.6 264.1 264.6 265.1 265.6 266.1 266.6 267.1 267.4 267.6 268.2 268.7 269.3 269.8 270.4 271.0 271.6 272.2 272.8 273.4 274.0 274.7 275.3 276.0 276.6 277.3 278.0 278.7 279.4 280.1

296.5 296.8 297.2 297.6 298.0 298.5 298.9 299.4 299.9 300.4 300.9 301.4 301.7 301.9 302.5 303.1 303.7 304.3 304.9 305.5 306.2 306.9 307.5 308.2 309.0 309.7 310.4 311.2 312.0 312.8 313.6 314.4 315.2 316.1

275.15 277.15 279.15 281.15 283.15 285.15 287.15 289.15 291.15 293.15 295.15 297.15 298.15 299.15 301.15 303.15 305.15 307.15 309.15 311.15 313.15 315.15 317.15 319.15 321.15 323.15 325.15 327.15 329.15 331.15 333.15 335.15 337.15 339.15

321.3 322.0 322.6 323.3 324.0 324.7 325.4 326.1 326.8 327.5 328.2 329.0 329.4 329.7 330.5 331.3 332.0 332.8 333.6 334.4 335.2 336.0 336.9 337.7 338.5 339.4 340.3 341.1 342.0 342.9 343.8 344.7 345.6 346.5

351.2 351.9 352.7 353.4 354.2 354.9 355.7 356.5 357.3 358.1 359.0 359.8 360.2 360.6 361.5 362.4 363.3 364.2 365.1 366.0 366.9 367.9 368.8 369.8 370.8 371.8 372.8 373.8 374.8 375.8 376.9 377.9 379.0 380.1

411.2 412.0 412.8 413.6 414.4 415.3 416.1 417.0 417.9 418.7 419.6 420.5 421.0 421.4 422.3 423.2 424.2 425.1 426.0 427.0 428.0 428.9 429.9 430.9 431.9 432.9 433.9 434.9 436.0 437.0 438.0 439.1 440.2 441.2

352.2 352.6 352.9 353.2 353.6 353.9 354.3 354.7 355.1 355.5 355.9 356.3 356.6 356.8 357.2 357.7 358.1 358.6 359.1 359.6 360.1 360.6 361.2 361.7 362.2 362.8 363.4 364.0 364.5 365.1 365.8 366.4 367.0 367.6

563.7 564.5 565.2 566.0 566.9 567.7 568.6 569.5 570.4 571.3 572.2 573.2 573.7 574.2 575.2 576.2 577.3 578.4 579.5 580.6 581.7 582.9 584.1 585.3 586.5 587.7 589.0 590.3 591.6 592.9 594.3 595.6 597.0 598.4

445.4 445.6 445.8 446.0 446.2 446.5 446.8 447.1 447.4 447.7 448.1 448.4 448.6 448.8 449.2 449.6 450.0 450.5 451.0 451.5 452.0 452.5 453.0 453.6 454.2 454.8 455.4 456.0 456.6 457.3 458.0 458.7 459.4 460.1

Standard uncertainty u is u(T) = 0.05 K. The combined expanded uncertainty Uc is Uc(Cp,m) = 0.004Cp,m for C2E1, C3E1, C4E1, C1E2, C2E2, C3E2, C4E2, and Uc(Cp,m) = 0.006· Cp,m for C6E2, C1E3, C8E3, C1E4 (0.95 level of confidence).

Table 4. Saturated Molar Heat Capacities (Cp,m/J·mol−1·K−1) of Examined Liquid Compounds at T = (275.13 to 339.15) Ka

a

substance

A0/J·mol−1·K−1



δ/J·mol−1·K−1

C2E1 C3E1 C4E1 C1E2 C2E2 C3E2 C4E2 C6E2 C1E3 C8E3 C1E4

161.12 151.17 138.85 285.69 395.08 311.41 364.91 381.34 405.64 659.27 588.56

−1.6313 17.150 40.347 −38.776 −89.811 −25.439 −45.618 −18.475 −54.700 −106.95 −112.93

6.1667 4.3934 1.5586 10.945 19.615 10.552 14.772 10.654 12.825 26.245 22.133

0.15 0.14 0.12 0.26 0.33 0.36 0.34 0.29 0.41 0.54 0.43

exp δ = (1/ni)∑i|Ccalc p − Cp |.

The basis for the calculation of parameters Bi of eq 3 for each of the groups are Cp,m data determined in this study. As each of the compounds studied contains always one CH3 and one −OH group, the separation of the contributions made by these groups is impossible. Therefore, to the database used, we added

Hence the dependence of heat capacity on temperature of particular groups can be also presented in the form of secondary polynomial: Cp , i = B0 + B1(T /100) + B2 (T /100)2

(3) D



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Table 6. Average Relative Deviation (ARD, Eq 4) and Percent Deviation (PD) of Cp,m Estimation for Compounds Forming the Database for the Group Contribution Calculations for T = (275.15 to 339.15) K simple model compound C2E1c C3E1c C4E1c C1E2c C2E2c C3E2c C4E2c C6E2c C1E3c C8E3c C1E4c

Figure 4. Temperature dependence of molar heat capacity Cp,m, full symbols, and specific heat capacity Cp, empty symbols of polyoxyethylene glycol monoalkyl ethers: ▲, △, C1E1 (ref 11); ★, ☆, C2E1; ○, ●, C1E2; ◊, ⧫, C1E3; ▽, ▼, C1E4.

C1E1C1b,d C1E2C1b,e C1E3C1b,f C1E5C1b,g overall

second-order model

ARD/%

a

PD /%

ARD/%

PDa/%

0.27 0.20 0.47 0.59 0.68 0.25 0.17 0.43 0.48 0.13 0.35 0.58 0.40 0.38 0.10 0.37

−0.33 to +0.27 −0.13 to +0.21 −0.67 to +0.21 0.50 to +0.75 −0.47 to −1.19 0.16 to +0.44 −0.16 to +0.36 0.21 to +0.71 0.37 to +0.57 −0.05 to −0.31 −0.25 to −0.62

0.19 0.21 0.58 0.09 0.31 0.48 0.24 0.36 0.32 0.17 0.31 0.85 0.37 0.42 0.31 0.47

−0.16 to +0.42 −0.30 to +0.34 −0.81 to +0.11 0.05 to +0.21 −0.08 to −0.86 0.48 to +0.44 −0.16 to +0.36 −0.04 to +0.46 0.14 to +0.63 0.22 to +0.40 −0.22 to −0.56

exp exp b Percent deviation PD = 100·[(Ccalc p − Cp )/Cp ]. T = 298.15 K only. Experimental data of heat capacities from: This work. dRef 9, 19, 23, 29, and 30. eRef 23, 24, 26, and 29. fRef 19, 23, 25, 29, and 31. gRef 19. a c

However, this does not exclude the possibility of calculating all the parameters Bi of eq 3 for the temperature range (275.15 to 339.15) K. The same procedure was used assuming that the heat capacity of CH2 group placed between two carbons (C−CH2−C) differs from that neighboring with oxygen and carbon atoms (C−CH2−O) (second order model, SOM). In this model, the compounds studied comprise five different groups: −CH3, C−CH2−C, C−CH2−O, −O−, −OH. The parameters Bi calculated for simple model (eq 3) and Ci for second order model (analogous equation as eq 3) are shown in Table 5. These parameters have not any universal character and can be used only for the estimation of the heat capacity of compounds belonging to CnEm series. The correctness of the estimation of heat capacity on the basis of calculated group contributions, was tested through the comparison of estimated and experimental values. For each compound, the values of PD (minimum and maximum percent deviation) and ARD (average relative deviation) was calculated for the whole temperature range:

Figure 5. Molar heat capacity of polyoxyethylene glycol monoalkyl ethers as a function of molar mass. Full symbols, 298.15 K; empty symbols, 328.15 K. ▼, ref 19; ▲, △, ref 20; ■, □, ref 21, regression lines.

Table 5. Coefficients of Group Contributions of Heat Capacity (Eq 3)a simple model (SM) group −CH3

−CH2−

second-order model (SOM) group

B0 B1 B2 B0 B1

95.337 −57.568 12.715 18.286 4.1730

−CH3

C−CH2−C C−CH2−O

−O− −OH a

B0 B1 B1

65.856 −12.740 17.921

−O− −OH

C0 C1 C2 C0 C1 C0 C1 C0 C1 C1

96.852 −57.674 12.715 18.356 4.0360 17.721 5.1544 66.409 −14.266 16.598

ARD/% =

100 ni

∑ i

exp (C pcalc , m − C p , m)

C pexp ,m

(4)

where ni is the number of single Cp,m data (in the case of temperature dependence, the calculations were made every two steps). The comparison of the ARD and PD values for all the compounds examined in this study and for the test set of compounds (that did not constitute the database used for calculation of the group contributions) are listed in Tables 6 and 7. From the data presented it follows that for monoalkyl ether polyoxyethylene glycols, the average deviation of Cp,m estimation does not exceed 1 % for each compound. The simple model of the group additivity described by eight constants for four functional groups is equally correct as the second order model required 10 parameters for five functional groups. In the case of CnEm compounds being the database of calculation, the

Units: B0, C0/J·mol−1·K−1, B1, C1/J·mol−1·K−2, B2, C2/J·mol−1·K−3.

the literature data of heat capacities of three diethers C1E1C1,9,19,23,29,30 C1E2C1,23,24,26,29 and C1E3C1,19,23,25,29,31 in which the −OH group is absent. Due to the lack of Cp,m data as a function of temperature, the values refer only to 298.15 K. E



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Table 7. Average Relative Deviation (ARD, Eq 4) of Cp,m Estimation for Test Set of Compounds Not Used in the Database for Group Contributions Calculation

a

compound

Cp,m data from references

temperature range/K

ARD/% simply model

ARD/% SOM model

ARDa/%

ARDb/%

C2E1 C2E1 C3E1 C4E1 C4E1 C4E1 C6E2 C6E4 C1E5 C6E5 C2E1C1 C2E1C2 C1E1C3 C3E1C3 C4E1C1 C4E2C4 C1E4C1 C1E5C1

11 10 11 10 27 13 18 20 19 21 9 9 9 9 9 29 23, 28, 29 19

300.6−328.3 283.15−313.15 300.6−328.3 277.15−328.15 280.0−300.0 277.15−348.15 273.15−328.15 280.15−333.15 298.15 283.15−328.15 298.15 298.15 298.15 298.15 298.15 298.15−323.15 298.15 298.15

0.10 0.22 0.26 0.77 0.11 0.43 0.18 0.23 0.01 0.66 1.48 2.82 1.28 1.47 0.29 1.46 0.38 0.10

0.15 0.21 0.27 0.76 0.12 0.50 0.20 0.39 0.11 0.39 0.82 1.33 1.75 2.50 0.58 2.18 0.35 0.47

1.25 3.01 1.59 2.84 3.22 2.13 2.97 2.03 1.95 2.55 0.83 3.15 1.49 0.59 0.14 0.43 0.50 0.42

1.14 1.62 1.81 2.62 2.51 2.23 2.71 1.98 0.31 2.76 2.60 0.16 4.21 2.46 2.20 1.26 2.18 2.05

Group contributions taken from ref 32. bGroup contributions taken from ref 33 and 34.

Table 8. Estimated Molar Heat Capacity at 298.15 K and Coefficients of Polynomial (1) for the Temperature Dependence of (Cp,m/J·mol−1·K−1) of Several Liquid Polyoxyethylene Glycol Monoalkyl Ethers with a Temperature Range (270 to 350) K

a

abbreviation

chemical name

Cp,m/J·mol−1·K−1




ARDa/%

C5E1 C6E1 C7E1 C8E1 C5E2 C7E2 C8E2 C2E3 C3E3 C4E3 C5E3 C6E3 C7E3 C2E4 C3E4 C4E4 C5E4 C7E4 C8E4 C1E5 C2E5 C3E5 C4E5 C5E5 C7E5 C8E5

ethylene glycol pentyl ether ethylene glycol hexyl ether ethylene glycol heptyl ether ethylene glycol octyl ether diethylene glycol pentyl ether diethylene glycol heptyl ether diethylene glycol octyl ether triethylene glycol ethyl ether triethylene glycol propyl ether triethylene glycol butyl ether triethylene glycol pentyl ether triethylene glycol hexyl ether triethylene glycol heptyl ether tetraethylene glycol ethyl ether tetraethylene glycol propyl ether tetraethylene glycol buthyl ether tetraethylene glycol pentyl ether tetraethylene glycol heptyl ether tetraethylene glycol octyl ether pentaethylene glycol methyl ether pentaethylene glycol ethyl ether pentaethylene glycol propyl ether pentaethylene glycol buthyl ether pentaethylene glycol pentyl ether pentaethylene glycol heptyl ether pentaethylene glycol octyl ether

302.1 332.6 363.2 393.7 391.7 452.9 483.4 389.8 420.3 450.9 481.4 512.0 542.5 479.4 510.0 540.6 571.1 632.2 662.8 537.2 569.1 599.7 630.3 660.8 721.9 752.5

271.20 289.52 307.84 326.16 373.34 409.98 428.30 420.52 438.84 457.16 475.48 493.80 512.12 522.65 540.98 559.30 577.62 614.26 632.58 606.79 624.79 643.11 661.44 679.76 716.40 734.72

−27.560 −23.456 −19.351 −15.247 −31.736 −23.527 −19.422 −48.225 −44.121 −40.016 −35.912 −31.807 −27.703 −52.401 −48.296 −44.192 −40.087 −31.879 −27.774 −61.240 −56.577 −52.472 −48.368 −44.263 −36.054 −31.950

12.715 12.715 12.715 12.715 12.715 12.715 12.715 12.715 12.715 12.715 12.715 12.715 12.715 12.715 12.715 12.715 12.715 12.715 12.715 12.715 12.715 12.715 12.715 12.715 12.715 12.715

0.24 0.32 0.39 0.45 0.01 0.15 0.21 0.49 0.37 0.27 0.18 0.09 0.02 0.57 0.46 0.37 0.29 0.14 0.08 0.19 0.62 0.53 0.44 0.37 0.24 0.18

SM SM Average relative deviation ARD/% = (100/ni)∑i|(CSOM p,m − Cp,m)/Cp,m|.

model, the value being different by 0.56 % (295.6 J·mol−1·K−1). Thus, one can assume that the group contributions determined by us make it possible to predict the values of molar heat capacity of monoethers CnEm for (270 to 350) K with an average error far below 1 %. The use of group contributions calculated on the basis of Cp data of wide range of family of compounds,32−34 brings much less accurate results (Table 7).

total ARD for SOM model is lower by 0.06 % compared with SM model, while for test set of compounds it is higher by 0.09 %. For temperatures exceeding the range studied, we have found in literature13 only the value of Cp,m for C4E1 that at 348.15 K amounts to 297.24 J·mol−1·K−1. The estimated value of Cp,m with the use of simple model gives a result with a perfect agreement (297.18 J·mol−1·K−1), while with the use of SOM F



Article

(10) Roux, G.; Perron, G.; Desnoyers, J. E. Model Systems for Hydrophobic Interactions: Volumes and Heat Capacities of nAlkoxyethanols in Water. J. Solution Chem. 1978, 7, 639−654. (11) Svoboda, V.; Zabransky, M.; Barta, M. Molar Heat Capacities of 2-Methoxyethanol, 2-Ethoxyethanol, and 2-propoxyethanol in the Temperature Range from 298 to 330 K. J. Chem. Thermodyn. 1991, 23, 711−712. (12) Malhotra, R.; Woolf, L. A. Thermodynamic Properties of 2Butoxyethanol at Temperatures from 288 to 348 K and Pressures from 0.1 to 380 MPa. J. Chem. Thermodyn. 1993, 25, 1189−1196. (13) Wojtczak, L.; Piekarski, H.; Tkaczyk, M.; Zasada, I.; Rychtelska, T. Application of Two-Point Scaling to the Pseudophases Coexistence. J. Mol. Liq. 2002, 95, 229−241. (14) Onken, U. Die Thermodynamischen Funktionen des Systems Wasser/Butylglykol. Z. Elektrochem. 1959, 63, 321−327. (15) Riddick J. A.; Bunger W. B.; Sakano T. K. Techniques of Chemistry. Organic Solvents. Physical Properties and Methods of Purification, Vol. 2; Wiley: New York, 1986. (16) Steele, W. V.; Chirico, R. D.; Knipmeyer, S. E.; Nguyen, A. Vapor Pressure of Acetophenone, (±)-1,2-Butanediol, (±)-1,3Butanediol, Diethylene Glycol Monopropyl Ether, 1,3-Dimethyladamantane, 2-Ethoxyethyl Acetate, Ethyl Octyl Sulfide, and Pentyl Acetale. J. Chem. Eng. Data 1996, 41, 1255−1268. (17) Cobos, J. C.; Casanova, C.; Roux-Desgranges, G.; Grolier, J.-P. E. Excess Properties of Mixtures of some n-Alkoxyethanols with Organic Solvents II. VmE and Cp,mE with di-n-Butylether at 298.15 K. J. Chem. Thermodyn. 1987, 19, 791−796. (18) Piekarski, H.; Tkaczyk, M.; Wasiak, M. Heat Capacity of Aqueous 2-(2-Hexyloxyethoxy)ethanol Solutions by Differential Scanning Calorimetry. Application of Two - point Scaling to Pseudophases Coexistence. J. Therm. Anal. Calorim. 2005, 82, 711− 718. (19) Schrodle, S.; Hefter, G.; Buchner, R. Effects of Hydration on the Thermodynamic Properties of Aqueous Ethylene Glycol Ether Solutions. J. Chem. Thermodyn. 2005, 37, 513−522. (20) Piekarski, H.; Tkaczyk, M. Heat Capacity and Phase Behavior of {C6E4+water} Solutions by DSC. J. Therm. Anal. Calorim. 2006, 83, 541−547. (21) Piekarski, H.; Tkaczyk, M. Heat Capacity and Phase Behaviour of Aqueous 2-(Hexyloxytetraethoxy)ethanol by DSC. Thermochim. Acta 2005, 428, 113−118. (22) Prabhumirashi, L. S. Self Association Behaviour of α-ω Diol Monoalkyl Ethers. J. Chem. Soc., Faraday Trans. 2 1978, 74, 1567− 1572. (23) Trejo, L. M.; Costas, M.; Patterson, D. Effect of Molecular Size on the W-shaped Excess Heat Capacities: Oxaalkane-Alkane Systems. J. Chem. Soc., Faraday Trans. 1991, 87, 3001−3008. (24) Kimura, F.; D’Arcy, P. J.; Sugamori, M. E.; Benson, G. C. Excess Enthalpies and Heat Capacities for 2,5,8-Trioxanonane + n-Heptane Mixtures. Thermochim. Acta 1983, 64, 149−154. (25) Tovar, C. A.; Carballo, E.; Cerdeiriña, C. A.; Romaní, L. Excess Molar Volumes and Excess Molar Heat Capacities of (2, 5, 8, 11Tetraoxadodecane + C4H8O2 Ester Isomers) at Several Temperatures. J. Chem. Thermodyn. 1997, 29, 1353−1361. (26) Tovar, A.; Carballo, E.; Cerdeiriña, C. A.; Romaní, L. Excess Molar Volumes and Excess Molar Heat Capacities of Mixtures Containing (Mono and Poly)ethers + Ethyl Acetate. J. Chem. Eng. Data 1997, 42, 1085−1089. (27) Atake, T.; Kawaji, H.; Tojo, K.; Kawasaki, K.; Ootsuka, Y.; Katou, M.; Koga, Y. Heat Capacities of Isomeric 2-Butoxyethanols from 280 to 300 K: Fusion and Glass Transition. Bull. Chem. Soc. Jpn. 2000, 73, 1987−1991. (28) Kriebel, M.; Loeffler, J. Thermodynamic Properties of the Binary System Difluoromonochloromethane (R22) − Tetraethylene Glycol Dimethyl Ether (E181). Kaeltetechnik 1965, 17, 266−271. (29) Burgdorf, R.; Zocholl, A.; Arlt, W.; Knapp, H. Thermophysical Properties of Binary Liquid Mixtures of Polyether and n-Alkane at 298.15 and 323.15 K: Heat of Mixing, Heat Capacity, Viscosity,

Table 8 shows the predicted values of molar heat capacity of twenty six monoalkyl ether of polyoxyethylene glycols at 298.15 K, for which there is a lack of the experimental Cp,m values in the literature. The constants of polynomial (1) listed in Table 8 permit the calculation of Cp,m as a function of temperature in the range of (270 to 350) K. The constants are the result of averaging both the models (SM and SOM). The average relative deviation of Cp,m between both models (ARD) for most of the compounds does not exceed 0.5 %. The possibility of the estimation of molar heat capacities of diethers is also possible but should be limited to 298.15 K. This is caused by the use, in calculations, of the contributions of the Cp,m data of diethers only at this temperature. The error of estimation for this group of compounds often exceed 1 % regardless of the model used. However, in many cases the experimental data of Cp,m are not free of error of a similar order.

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ASSOCIATED CONTENT

S Supporting Information *

Experimental data of saturated specific heat capacities (Cp /J·g−1·K−1) for some liquid polyoxyethylene glycol monoalkyl ethers for T = (275.13 to 339.15) K are listed in Table S1. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.5b00051.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 48 426355817. Fax: 48 426355822 Notes

The authors declare no competing financial interest.

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REFERENCES

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Measurement and Prediction of the Molar Heat Capacities of Liquid

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