Speed of Sound, Density, and Related Thermodynamic Excess

Article pubs.acs.org/jced

Speed of Sound, Density, and Related Thermodynamic Excess Properties of Binary Mixtures of 2‑Pyrrolidone and N‑Methyl-2-pyrrolidone with Acetonitrile and Chloroform Mikhail A. Varfolomeev,† Ilnaz T. Rakipov,† Boris N. Solomonov,† and Wojciech Marczak*,†,‡ †

Department of Physical Chemistry, Kazan Federal University, Kremlevskaya Str. 18, 420008 Kazan, Russian Federation Institute of Occupational Medicine and Environmental Health, Kościelna 13, 41-200 Sosnowiec, Poland

‡

ABSTRACT: Densities and speeds of sound were measured for binary mixtures of 2-pyrrolidone or N-methyl-2-pyrrolidone with acetonitrile or chloroform at temperatures of (293.15 to 323.15) K and at atmospheric pressure, with uncertainties of 0.5 kg·m−3 and 0.5 m·s−1, respectively. From the measured speeds and densities, isentropic compressibilities and molar excesses of volume, isentropic compression, and thermal expansion were calculated. All of the excesses are negative, which is due to the geometries of the molecules and changes in the hydrogen bonding upon mixing. In the simplest case of the N-methyl-2-pyrrolidone + acetonitrile system, the negative excesses result only from the different sizes of the molecules because the components are incapable of forming either self- or cross-associates. For the other systems, the net effects of the formation and/or dissociation of the hydrogen bonds lead to bigger negative excesses of molar volume and thermal expansion. The negative excesses of compression are probably caused mainly by filling of the gaps between the big lactam molecules with the smaller acetonitrile or chloroform molecules, while the formation of the hydrogen-bonded cross-associates plays a minor role.

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INTRODUCTION

The CH3 group on the ring nitrogen atom prevents the N-methyl-2-pyrrolidone molecule from acting as a proton donor. The weaker intermolecular attractions are manifested by the fact that the normal boiling temperature of N-methyl-2-pyrrolidone is lower than that of 2-pyrrolidone by 43 K (475.2 K7 vs 518.2 K9) as well as by lower standard vaporization enthalpies. Although estimations of the latter are fairly scattered for each of the two compounds, the difference is evident. The NIST values8 of ΔvapH0 vary from (54.88 ± 0.13) kJ·mol−1 to 61.9 kJ·mol−1 for N-methyl-2-pyrrolidone10,11 and from (68.7 ± 1.5) kJ·mol−1 to (73.6 ± 1.3) kJ·mol−1 for 2-pyrrolidone.10,12 Compressibility and other speed-of-sound-related quantities for binary systems containing the two lactams are not wellknown. Attention has been focused mainly on mixtures involving relatively strong hydrogen bonds, e.g., those with alcohols13,14 and water.3,15,16 Systems with weak hydrogen bonds have hardly ever been studied. In the present work, we report volumetric properties and compressibilities for four binary systems, (2-pyrrolidone or N-methyl-2-pyrrolidone) + (acetonitrile or chloroform), at different temperatures over the full concentration ranges of the mixtures. To the best of our knowledge, the speeds of sound for these systems have not been reported to date, except for 2-pyrrolidone + acetonitrile at one temperature (303.15 K).17 No hydrogen bonds occur in the

2-Pyrrolidone and N-methyl-2-pyrrolidone are polar, highboiling solvents that are used in different fields of industry in their pure states and in mixtures with various organic compounds. They present favorable media for organic syntheses, electrochemical processes, and extraction of low-molecular-mass aromatic substances. 2-Pyrrolidone is also used as a precursor for the production of some polymers and drugs.1 The −NH−CO− group in the 2-pyrrolidone molecule resembles the peptide bond in amino acids, making it a convenient model for studies of hydrogen-bonded systems that are important from the biological point of view. 2-Pyrrolidone is a highly associated liquid, but there are still different opinions about the nature of the self-association. The results of IR studies have been interpreted as evidencing the presence of cyclic dimers, trimers, and oligomers.2 On the other hand, density functional theory (DFT) calculations and attenuated total reflectance IR spectra point to cyclic dimers only.3 Calculations at the DFT/B3LYP and HF levels of theory led to the conclusion that cyclic dimers are more stable than open dimers in the gas and liquid phases and even in solutions in dioxane (relative dielectric permittivity ε = 2.21) and water (ε = 78.54).4 In the cyclic dimer, 2-pyrrolidone molecules favor the lactam form. The stabilization energies of dimers containing either one or two lactim tautomers are lower.5 2-Pyrrolidone forms various complexes with water, acting as an acceptor and donor of protons to hydrogen bonds through the CO and N−H groups, respectively.6 © XXXX American Chemical Society

Received: June 9, 2015 Accepted: February 17, 2016

A

DOI: 10.1021/acs.jced.5b00474 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Characteristics of the Chemicals Used in the Experiment and Densities (ρ) and Speeds of Sound (u) at T = 298.15 K ρ/kg·m−3

chemical name

source

purification method

final massfraction purity

analysis method a

mass fraction of water·100

measured

2-pyrrolidone

Aldrich

0.98

distillation

0.999

GC

0.02

1107.35

N-methyl-2-pyrrolidoneb

Aldrich Aldrich

0.98 0.98

distillation distillation

0.999 0.999

GC GC

0.02 0.02

1027.79 1028.07

acetonitrileb

Aldrich Aldrich Aldrich

0.98 0.98 0.98

distillation distillation distillation

0.999 0.999 0.999

GC GC GC

0.02 0.02 0.02 0.02

776.61 776.62 1478.02 1479.07

chloroform

a

initial massfraction purity

u/m·s−1

literature c

1106.97 1107.019d 1107.397e 1027.894e 1028.01f 1028.23c 1028.3g 1028.31d 776.60h 776.62i 1472.435j 1478.16k 1478.8l 1478.9m

measured

literature

1632.9

1633.95c 1633.2d 1633.3e 1545.1e 1545.25f 1546.06c 1545.2g 1545.1d 1277.7h 1278.9i 983.58j 983.68k 983l 984m

1544.6 1545.5

1278.9 1278.6 984.6 984.3

Gas chromatography. bChemicals from two batches. cPapamatthaiakis et al.15 dGeorge and Sastry.16 eDávila et al.3 fKimura et al.18 gBlanco et al.19 Geppert-Rybczyńska and Sitarek.20 iGonzález et al.21 jBhatia et al.22 kVarfolomeev et al.23 lThamsen.24 mAral.25

h

Table 2. Experimental Densities and Speeds of Sound, Isentropic Compressibilities (eq 1), and Molar Excesses of Volume, Isentropic Compression, and Thermal Expansion (eq 7) for the Binary System 2-Pyrrolidone (1) + Acetonitrile (2) at Atmospheric Pressure (p = 100 kPa)a T

ρ

u

κS·1010

VEm·106

KES,m·1014

EEp,m·109

x1

K

kg·m−3

m·s−1

Pa−1

m3·mol−1

m3·mol−1·Pa−1

m3·mol−1·K−1

0 0 0 0 0 0 0.1025 0.1025 0.1025 0.1025 0.1025 0.1025 0.1865 0.1865 0.1865 0.1865 0.1865 0.1865 0.3069 0.3069 0.3069 0.3069 0.3069 0.3069 0.3976 0.3976 0.3976 0.3976 0.3976 0.3976 0.4974 0.4974 0.4974 0.4974 0.4974

298.155 303.155 308.155 313.154 318.155 323.156 298.155 303.155 308.154 313.155 318.155 323.156 298.153 303.154 308.155 313.155 318.155 323.157 298.149 303.154 308.154 313.154 318.156 323.156 298.149 303.154 308.155 313.156 318.155 323.156 298.155 303.154 308.155 313.156 318.156

776.609 771.183 765.722 760.231 754.709 749.150 827.196 821.985 816.754 811.493 806.204 800.887 864.997 859.946 854.873 849.779 844.673 839.540 913.434 908.581 903.718 898.840 893.944 889.032 946.686 941.969 937.251 932.515 927.770 923.008 979.551 974.979 970.394 965.800 961.200

1278.88 1258.99 1239.11 1219.27 1199.47 1179.61 1311.16

7.8730 8.1808 8.5057 8.8482 9.2096 9.5930 7.0320

−0.2223

1337.00 1317.82 1298.80 1280.10 1261.42 1242.81 1380.17 1362.30 1344.44 1326.65 1308.81 1290.49 1414.40 1396.82 1379.34 1361.93 1344.59 1327.32 1451.90 1434.85 1417.72 1400.66 1383.69

6.4673 6.6960 6.9345 7.1814 7.4403 7.7117 5.7472 5.9305 6.1219 6.3213 6.5304 6.7542 5.2802 5.4410 5.6079 5.7814 5.9618 6.1495 4.8428 4.9819 5.1271 5.2777 5.4339

−0.2347 −0.2485 −0.2635 −0.2792 −0.2953 −0.3122 −0.3789 −0.4002 −0.4226 −0.4461 −0.4714 −0.4977 −0.4793 −0.5058 −0.5337 −0.5631 −0.5940 −0.6260 −0.5340 −0.5620 −0.5918 −0.6227 −0.6551 −0.6889 −0.5171 −0.5443 −0.5728 −0.6026 −0.6339

−2.76 −2.89 −3.03 −3.17 −3.32 −3.47 −4.11 −4.36 −4.61 −4.87 −5.14 −5.41 −5.13 −5.44 −5.74 −6.02 −6.29 −6.54 −5.51 −5.78 −6.05 −6.33 −6.62 −6.92 −5.32 −5.57 −5.83 −6.10 −6.37

B

−0.3326 −0.3620 −0.3948 −0.4326 −0.4739 −0.5194 −0.4362 −0.4788 −0.5249 −0.5754 −0.6300 −0.6861 −0.4733 −0.5179 −0.5667 −0.6198 −0.6777 −0.7410 −0.4681 −0.5122 −0.5595 −0.6110 −0.6670



Article

Table 2. continued T x1

K

0.4974 0.6050 0.6050 0.6050 0.6050 0.6050 0.6050 0.6950 0.6950 0.6950 0.6950 0.6950 0.6950 0.7932 0.7932 0.7932 0.7932 0.7932 0.7932 0.8972 0.8972 0.8972 0.8972 0.8972 0.8972

323.156 298.153 303.154 308.156 313.154 318.155 323.156 298.154 303.154 308.155 313.156 318.155 323.156 298.155 303.154 308.156 313.155 318.155 323.156 298.153 303.154 308.155 313.155 318.155 323.155

ρ kg·m

κS·1010

u −3

956.587 1012.169 1007.721 1003.268 998.811 994.350 989.880 1036.849 1032.505 1028.154 1023.800 1019.441 1015.077 1061.579 1057.326 1053.072 1048.817 1044.559 1040.298 1085.626 1081.458 1077.290 1073.125 1068.960 1064.798

−1

−1

m·s

Pa

1366.78 1492.87 1476.04 1459.19 1442.44 1425.68 1408.89 1526.13 1509.49 1492.43 1475.54 1458.66 1441.83 1561.59 1545.17 1528.70 1512.33 1496.08 1479.93 1598.14 1582.07 1565.91 1549.80 1533.78 1517.86

5.5960 4.4331 4.5547 4.6812 4.8120 4.9479 5.0894 4.1410 4.2506 4.3667 4.4862 4.6103 4.7388 3.8629 3.9613 4.0635 4.1688 4.2772 4.3889 3.6065 3.6944 3.7856 3.8797 3.9766 4.0763

VEm·106 m ·mol 3

−1

−0.6664 −0.4875 −0.5117 −0.5372 −0.5638 −0.5918 −0.6209 −0.4152 −0.4360 −0.4576 −0.4801 −0.5034 −0.5277 −0.3068 −0.3219 −0.3378 −0.3543 −0.3714 −0.3891 −0.1677 −0.1757 −0.1841 −0.1928 −0.2019 −0.2114

KES,m·1014 −1

m ·mol ·Pa 3

EEp,m·109 −1

−0.7280 −0.4282 −0.4674 −0.5095 −0.5552 −0.6045 −0.6576 −0.3637 −0.3965 −0.4300 −0.4667 −0.5062 −0.5489 −0.2686 −0.2927 −0.3183 −0.3460 −0.3762 −0.4089 −0.1444 −0.1581 −0.1722 −0.1872 −0.2034 −0.2209

m ·mol−1·K−1 3

−6.65 −4.74 −4.97 −5.21 −5.45 −5.70 −5.96 −4.07 −4.24 −4.41 −4.58 −4.76 −4.95 −2.98 −3.10 −3.23 −3.35 −3.48 −3.61 −1.57 −1.64 −1.71 −1.78 −1.85 −1.93

The standard uncertainties u are u(x1) = 5 × 10−5, u(T) = 0.05 K, and u(p) = 1 kPa, and the combined expanded uncertainties Uc are Uc(ρ) = 0.5 kg·m−3, Uc(u) = 0.5 m·s−1, Uc(κS) = 2 × 10−13 Pa−1, Uc(VEm) = 5 × 10−10 m3·mol−1, Uc(EEp,m) = 1 × 10−11 m3·mol−1·K−1, and Uc(KES,m) = 5 × 10−18 m3·mol−1·K−1 (0.95 level of confidence). a

Table 3. Experimental Densities and Speeds of Sound, Isentropic Compressibilities (eq 1), and Molar Excesses of Volume, Isentropic Compression, and Thermal Expansion (eq 7) for the Binary System 2-Pyrrolidone (1) + Chloroform (2) at Atmospheric Pressure (p = 100 kPa)a T

ρ

u

κS·1010

VEm·106

KES,m·1014

EEp,m·109

x1

K

kg·m−3

m·s−1

Pa−1

m3·mol−1

m3·mol−1·Pa−1

m3·mol−1·K−1

0 0 0 0 0 0 0.1002 0.1002 0.1002 0.1002 0.1990 0.1990 0.1990 0.1990 0.1990 0.3019 0.3019 0.3019 0.3019 0.3019 0.4027 0.4027 0.4027 0.4027 0.4027

293.151 295.153 297.152 298.154 303.154 308.156 293.152 298.155 303.155 308.155 293.153 295.152 298.154 303.154 308.154 293.149 295.152 298.154 303.154 308.156 293.153 295.152 298.155 303.154 308.154

1487.520 1483.736 1479.933 1478.024 1468.468 1458.850 1457.636 1449.068 1440.461 1431.811 1424.667 1421.543 1416.869 1409.065 1401.222 1388.179 1385.334 1381.099 1374.002 1366.883 1350.998 1348.405 1344.531 1338.048 1331.553

1001.53

6.7021

984.65 967.76 950.87 1033.39 1017.36 1001.46 985.52 1074.62

6.9784 7.2711 7.5814 6.4242 6.6675 6.9220 7.1909 6.0782

−0.1205 −0.1422 −0.1679 −0.1962 −0.2417

1059.56 1043.95 1028.33 1124.85

6.2866 6.5119 6.7488 5.6933

1109.78 1094.68 1079.46 1179.01

5.8790 6.0735 6.2785 5.3249

1164.48 1149.51 1134.39

5.4849 5.6559 5.8360

−0.3418 −0.3639 −0.3873 −0.4120 −0.5135 −0.5265 −0.5480 −0.5858 −0.6250 −0.5984 −0.6146 −0.6415 −0.6868 −0.7344 −0.6238 −0.6414 −0.6700 −0.7182 −0.7690

−4.30 −4.55 −4.81 −5.07 −6.75 −6.94 −7.22 −7.70 −8.19 −8.41 −8.58 −8.85 −9.31 −9.78 −9.01 −9.19 −9.46 −9.92 −10.39

C

−0.2829 −0.3235 −0.3686 −0.3402 −0.3884 −0.4414 −0.4991 −0.3914 −0.4462 −0.5031 −0.5648



Article


K

0.5022 0.5022 0.5022 0.5022 0.5022 0.6054 0.6054 0.6054 0.6054 0.6054 0.6970 0.6970 0.6970 0.6970 0.6970 0.7992 0.7992 0.7992 0.7992 0.7992 0.9000 0.9000 0.9000 0.9000 0.9000 1 1 1 1 1 1 1 1

293.154 295.152 298.154 303.154 308.154 293.156 295.151 298.153 303.159 308.154 293.152 295.153 298.153 303.155 308.155 293.153 295.152 298.159 303.154 308.155 293.153 295.152 298.158 303.154 308.155 293.151 298.153 301.155 303.154 308.154 313.155 318.156 323.156

ρ kg·m

κS·1010

u −3

1313.309 1310.935 1307.378 1301.432 1295.474 1272.912 1270.721 1267.473 1262.003 1256.522 1235.751 1233.711 1230.665 1225.575 1220.479 1194.433 1192.542 1189.718 1184.995 1180.277 1152.994 1151.230 1148.604 1144.208 1139.819 1111.441 1107.352 1104.885 1103.258 1099.168 1095.081 1090.998 1086.918

−1

−1

m·s

Pa

1238.71

4.9624

1223.68 1208.60 1193.47 1307.24

5.1081 5.2603 5.4194 4.5972

1292.92 1278.23 1263.13 1374.49

4.7197 4.8498 4.9881 4.2834

1358.87 1343.07 1327.08 1457.34

4.4005 4.5234 4.6524 3.9420

1442.25 1426.55 1411.03 1548.79

4.0409 4.1468 4.2554 3.6157

1533.33 1517.29 1501.54 1649.30 1632.93

3.7030 3.7963 3.8913 3.3076 3.3867

1616.67 1600.51 1584.49 1568.57 1552.77

3.4680 3.5516 3.6373 3.7254 3.8158

VEm·106 m ·mol 3

−1

−0.6106 −0.6284 −0.6565 −0.7043 −0.7542 −0.5413 −0.5567 −0.5835 −0.6267 −0.6706 −0.4135 −0.4267 −0.4478 −0.4837 −0.5208 −0.2971 −0.3064 −0.3221 −0.3470 −0.3738 −0.1558 −0.1604 −0.1691 −0.1819 −0.1960

KES,m·1014 −1

m ·mol ·Pa 3

−0.4086 −0.4591 −0.5143 −0.5746 −0.3871 −0.4375 −0.4907 −0.5461 −0.3358 −0.3729 −0.4125 −0.4547 −0.2518 −0.2822 −0.3121 −0.3456 −0.1402 −0.1572 −0.1730 −0.1912

EEp,m·109 −1

m ·mol−1·K−1 3

−8.99 −9.15 −9.38 −9.78 −10.18 −8.39 −8.46 −8.57 −8.75 −8.94 −6.75 −6.86 −7.02 −7.30 −7.59 −4.86 −4.93 −5.03 −5.20 −5.38 −2.57 −2.60 −2.65 −2.72 −2.80


N-methyl-2-pyrrolidone + acetonitrile system, while in the three other systems hydrogen-bonded cross-associates exist, as well as self-associates in those containing 2-pyrrolidone. We tried to correlate the excess properties, i.e., those of volume, isobaric thermal expansion, and isentropic compression, with the propensity of the mixture components to hydrogenbond.

The solutions were prepared by weighing the components in glass bottles, in a manner reported in a previous work.23 The uncertainty in the mole fraction was estimated to be 5 × 10−5 from the combined balance accuracy and sample size. Apparatus. The density and speed of sound were measured with an Anton Paar DSA 5000 apparatus. The frequency of the ultrasonic wave was 3 MHz. The resolutions of the density and speed measurements were 1 × 10−3 kg·m−3 and 1 × 10−2 m·s−1, respectively. Unknown and probably different impurities in the “pure” liquid samples affected the measurement results in a way that is difficult to estimate. A comparison of the speeds and densities for the same compound from different production batches led to combined uncertainties of 5 × 10−1 kg·m−3 for the density and 5 × 10−1 m·s−1 for the speed of sound. The former is the half of the range for the most unfavorable case of chloroform (cf. Table 1). Since the densities reported in Table 1 characterize the chemicals used, they were reported with the numbers of significant digits sufficient to this end, which are greater by one than those resulting from the total uncertainty. The instrument was calibrated with water and dry air following the manufacturer’s instructions. Details were reported in the previous work.23

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EXPERIMENTAL SECTION Chemicals. 2-Pyrrolidone and N-methyl-2-pyrrolidone were dried over 4 Å molecular sieves and distilled under reduced pressure in an inert atmosphere. Chloroform was washed thoroughly with water, dried with calcium chloride, and distilled over P2O5. Samples of chloroform were used immediately after purification. Acetonitrile was dried with P2O5 and distilled afterward from anhydrous K2CO3 in order to remove traces of phosphorus oxide. An Agilent 7890B gas chromatograph with a flame ionization detector was used to check the purities of the studied compounds. Traces of water were determined by Karl Fischer titration. The purities of the chemicals and a comparison of the measured densities and speeds of sound with the literature data3,15,16,18−25 are reported in Table 1. D



Article

Table 4. Experimental Densities and Speeds of Sound, Isentropic Compressibilities (eq 1), and Molar Excesses of Volume, Isentropic Compression, and Thermal Expansion (eq 7) for the Binary System N-Methyl-2-pyrrolidone (1) + Acetonitrile (2) at Atmospheric Pressure (p = 100 kPa)a T

ρ

u

κS·1010

VEm·106

KES,m·1014

EEp,m·109

x1

K

kg·m−3

m·s−1

Pa−1

m3·mol−1

m3·mol−1·Pa−1

m3·mol−1·K−1

0 0 0 0 0 0 0 0.0997 0.0997 0.0997 0.0997 0.0997 0.0997 0.0997 0.2019 0.2019 0.2019 0.2019 0.2019 0.2019 0.2019 0.2953 0.2953 0.2953 0.2953 0.2953 0.2953 0.2953 0.4033 0.4033 0.4033 0.4033 0.4033 0.4033 0.4033 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.5645 0.5645 0.5645 0.5645 0.5645 0.5645 0.5645 0.6971 0.6971 0.6971 0.6971 0.6971 0.6971 0.6971 0.7909

293.151 298.151 303.154 308.154 313.154 318.156 323.156 293.151 298.149 303.154 308.154 313.154 318.155 323.156 293.151 298.153 303.154 308.154 313.155 318.155 323.156 293.151 298.155 303.154 308.154 313.154 318.155 323.156 293.151 298.150 303.154 308.154 313.154 318.156 323.155 293.150 298.154 303.154 308.155 313.155 318.155 323.156 293.151 298.152 303.153 308.155 313.154 318.156 323.156 293.151 298.154 303.154 308.155 313.154 318.156 323.156 293.151

781.989 776.616 771.178 765.719 760.223 754.702 749.144 826.597 821.365 816.101 810.812 805.495 800.149 794.775 865.011 859.919 854.802 849.665 844.503 839.318 834.109 895.168 890.188 885.193 880.180 875.146 870.091 865.017 925.343 920.480 915.600 910.709 905.801 900.875 895.938 948.634 943.847 939.067 934.271 929.461 924.640 919.805 962.588 957.857 953.126 948.386 943.637 938.874 934.100 987.869 983.231 978.597 973.957 969.311 964.657 959.996 1002.678

1278.58 1258.41 1238.27 1218.16 1198.07 1178.00

7.8766 8.1884 8.5173 8.8644 9.2312 9.6193

1311.57 1291.84 1271.98 1252.16 1232.38 1212.63

7.0775 7.3424 7.6229 7.9180 8.2289 8.5566

1345.36 1325.69 1306.01 1286.39 1266.83 1247.32

6.4249 6.6566 6.9002 7.1557 7.4240 7.7059

1375.00 1355.43 1335.85 1316.35 1296.92 1277.56

5.9417 6.1490 6.3667 6.5944 6.8330 7.0829

1407.57 1387.91 1367.73 1347.57 1327.39 1307.52

5.4833 5.6699 5.8698 6.0795 6.3000 6.5287

1434.37 1414.85 1394.79 1374.74 1354.79 1335.03

5.1496 5.3196 5.5019 5.6928 5.8923 6.0999

1450.83 1430.68 1410.42 1390.25 1370.21 1350.35

4.9598 5.1258 5.3005 5.4829 5.6731 5.8710

1483.74 1463.63 1443.44 1423.32 1403.28 1383.41

4.6199 4.7702 4.9279 5.0925 5.2643 5.4429

E

−0.1669 −0.1752 −0.1843 −0.1938 −0.2038 −0.2143 −0.2252 −0.2715 −0.2851 −0.2993 −0.3145 −0.3304 −0.3471 −0.3644 −0.3346 −0.3508 −0.3679 −0.3861 −0.4050 −0.4248 −0.4455 −0.3787 −0.3957 −0.4140 −0.4333 −0.4534 −0.4744 −0.4964 −0.3803 −0.3962 −0.4142 −0.4329 −0.4523 −0.4727 −0.4939 −0.3668 −0.3817 −0.3983 −0.4159 −0.4343 −0.4534 −0.4731 −0.3064 −0.3179 −0.3308 −0.3444 −0.3587 −0.3737 −0.3893 −0.1760

−0.1478 −0.1642 −0.1811 −0.1999 −0.2207 −0.2436 −0.2462 −0.2711 −0.2983 −0.3284 −0.3618 −0.3986 −0.2984 −0.3277 −0.3598 −0.3954 −0.4347 −0.4780 −0.3239 −0.3541 −0.3838 −0.4162 −0.4513 −0.4912 −0.3165 −0.3459 −0.3749 −0.4063 −0.4409 −0.4794 −0.2972 −0.3210 −0.3463 −0.3741 −0.4049 −0.4391 −0.2410 −0.2591 −0.2782 −0.2990 −0.3217 −0.3467

−1.60 −1.74 −1.86 −1.96 −2.06 −2.14 −2.20 −2.65 −2.79 −2.94 −3.09 −3.25 −3.41 −3.57 −3.13 −3.33 −3.53 −3.71 −3.88 −4.05 −4.20 −3.38 −3.56 −3.74 −3.92 −4.11 −4.31 −4.51 −3.25 −3.43 −3.61 −3.80 −3.99 −4.18 −4.39 −2.86 −3.16 −3.41 −3.61 −3.77 −3.88 −3.95 −2.21 −2.44 −2.64 −2.81 −2.95 −3.05 −3.13 −1.50



Article


K

0.7909 0.7909 0.7909 0.7909 0.7909 0.7909 0.8906 0.8906 0.8906 0.8906 0.8906 0.8906 0.8906 1 1 1 1 1 1 1

298.155 303.154 308.154 313.155 318.154 323.156 293.151 298.151 303.154 308.154 313.154 318.155 323.156 293.151 298.149 303.154 308.155 313.155 318.155 323.157

ρ kg·m

κS·1010

u −3

998.089 993.514 988.935 984.350 979.759 975.164 1018.291 1013.762 1009.245 1004.726 1000.205 995.681 991.156 1032.250 1027.794 1023.332 1018.871 1014.410 1009.948 1005.483

−1

−1

m·s

Pa

1503.33 1483.15 1462.85 1442.63 1422.44 1402.37

4.4332 4.5757 4.7253 4.8814 5.0444 5.2143

1524.80 1505.08 1485.25 1465.50 1445.91 1426.45

4.2427 4.3741 4.5118 4.6552 4.8039 4.9584

1544.64 1525.29 1505.97 1486.79 1467.78 1448.90

4.0779 4.2003 4.3276 4.4595 4.5960 4.7375

VEm·106 m ·mol 3

−1

KES,m·1014 −1

m ·mol ·Pa 3

−0.1829 −0.1916 −0.2009 −0.2107 −0.2207 −0.2314 −0.1601 −0.1638 −0.1693 −0.1750 −0.1811 −0.1875 −0.1943

EEp,m·109 −1

m ·mol−1·K−1 3

−0.1693 −0.1806 −0.1921 −0.2047 −0.2178 −0.2320

−1.61 −1.74 −1.86 −1.99 −2.12 −2.25 −0.87 −0.96 −1.06 −1.15 −1.25 −1.35 −1.46

−0.1044 −0.1117 −0.1187 −0.1262 −0.1347 −0.1436


Table 5. Experimental Densities and Speeds of Sound, Isentropic Compressibilities (eq 1), and Molar Excesses of Volume, Isentropic Compression, and Thermal Expansion (eq 7) for the Binary System N-Methyl-2-pyrrolidone (1) + Chloroform (2) at Atmospheric Pressure (p = 100 kPa)a T x1

K

0 0 0 0 0.1061 0.1061 0.1061 0.1061 0.1079 0.1079 0.1079 0.1079 0.2054 0.2054 0.2054 0.2054 0.2994 0.2994 0.2994 0.2994 0.4032 0.4032 0.4032 0.4032 0.4961 0.4961 0.4961 0.4961 0.6006 0.6006

293.151 298.154 303.159 308.154 293.151 298.159 303.154 308.153 293.144 298.145 303.144 308.145 293.152 298.153 303.154 308.154 293.155 298.144 303.143 308.145 293.153 298.154 303.154 308.155 293.151 298.153 303.154 308.152 293.151 298.153

ρ kg·m

κS·1010

u −3

1488.550 1479.070 1469.517 1459.910 1438.959 1430.504 1422.000 1413.446 1437.791 1429.339 1420.852 1412.319 1390.745 1383.073 1375.364 1367.626 1345.236 1338.242 1331.204 1324.138 1294.056 1287.661 1281.238 1274.788 1249.813 1243.851 1237.894 1231.598 1201.325 1195.783

−1

−1

m·s

Pa

1000.94 984.33 967.53 950.62 1049.98 1033.57 1016.32 999.25 1051.57 1034.93 1018.32 1001.81 1098.57 1082.07 1065.24 1048.29 1146.04 1130.17 1114.10 1098.07 1198.37 1181.94 1165.23 1148.51 1248.43 1231.87 1215.16 1198.58 1307.85 1290.68

6.7053 6.9780 7.2694 7.5798 6.3036 6.5438 6.8083 7.0855 6.2897 6.5319 6.7871 7.0550 5.9580 6.1751 6.4075 6.6538 5.6598 5.8503 6.0521 6.2634 5.3810 5.5591 5.7484 5.9469 5.1337 5.2979 5.4708 5.6519 4.8666 5.0201 F

VEm·106 m ·mol 3

−1

−0.4059 −0.4285 −0.4511 −0.4752 −0.3950 −0.4162 −0.4393 −0.4640 −0.5996 −0.6337 −0.6697 −0.7078 −0.6966 −0.7397 −0.7849 −0.8325 −0.6289 −0.6765 −0.7256 −0.7766 −0.5606 −0.6067 −0.6562 −0.6842 −0.4435 −0.4851

KES,m·1014 −1

m ·mol ·Pa 3

−0.1534 −0.1737 −0.1883 −0.2090 −0.1601 −0.1781 −0.2004 −0.2288 −0.2466 −0.2768 −0.3090 −0.3455 −0.2965 −0.3388 −0.3860 −0.4408 −0.2907 −0.3311 −0.3751 −0.4254 −0.2773 −0.3171 −0.3615 −0.4105 −0.2458 −0.2795

EEp,m·109 −1

m ·mol−1·K−1 3

−4.37 −4.53 −4.69 −4.86 −4.08 −4.43 −4.78 −5.14 −6.62 −7.01 −7.41 −7.82 −8.41 −8.84 −9.28 −9.72 −9.33 −9.67 −10.01 −10.36 −9.39 −9.75 −10.13 −10.48 −8.17 −8.41



Article


K

0.6006 0.6006 0.6854 0.6854 0.6854 0.6854 0.7986 0.7986 0.7986 0.7986 1 1 1 1

303.154 308.154 293.153 298.152 303.154 308.154 293.153 298.145 303.145 308.145 293.154 298.145 303.145 308.146

ρ kg·m

κS·1010

u −3

1190.221 1184.644 1163.121 1157.849 1152.567 1147.276 1114.368 1109.428 1104.477 1099.520 1032.513 1028.066 1023.611 1019.153

−1

−1

m·s

m ·mol 3

Pa

1273.46 1256.29 1359.76 1342.10 1324.20 1306.24 1430.75 1412.95 1395.08 1377.29 1564.74 1545.48 1526.13 1506.88

VEm·106

5.1809 5.3485 4.6500 4.7949 4.9480 5.1084 4.3837 4.5149 4.6521 4.7945 3.9557 4.0724 4.1945 4.3212

KES,m·1014

−1

−1

m ·mol ·Pa 3

−0.5277 −0.5716 −0.3306 −0.3642 −0.3994 −0.4359 −0.2071 −0.2297 −0.2534 −0.2781

EEp,m·109 −1

−0.3176 −0.3613 −0.2166 −0.2445 −0.2749 −0.3089 −0.1557 −0.1774 −0.2018 −0.2299

m ·mol−1·K−1 3

−8.66 −8.90 −6.60 −6.88 −7.16 −7.45 −4.43 −4.63 −4.84 −5.05


The isentropic compressibilities and excesses of molar volume, thermal expansion, and isentropic compression were calculated in a way similar to that described in detail in the previous paper.23 The calculations are shortly outlined below for the readers’ convenience. The isentropic compressibility, κS, is given by the Laplace formula:

κS = ρ−1u−2

(1)

The dependences of the logarithm of the specific volume (ν ≡ ρ−1) and of the speed of sound (u) on temperature (T) were approximated by the following equation: 3

y = y298.15 +

∑ ai ϑi

(2)

i=1 −1

where y = ln[ν/(cm ·g )] for the specific volume or y = u/(m·s−1) for the speed, ϑ = T/K − 298.15, y298.15 is the value of the respective function at T = 298.15 K, and ai are the empirical coefficients. The values of y298.15 and ai calculated by the leastsquares method are reported in Tables 6 and 7. For the data sets with only four pairs of values available, a second-order polynomial was applied (i.e., eq 2 with a3 = 0). The F test was used to reject statistically insignificant coefficients. The coefficient of thermal expansion, αp, and the molar expansion, Ep,m, at constant pressure were calculated from eq 2 for the volume: 3

Figure 1. Speed of sound in the system 2-pyrrolidone (1) + acetonitrile (2) at T = 303.15 K: ●, this work; △, Mehta and Sharma.17

■

RESULTS The measured speeds of sound (u) and densities (ρ) for the four binary systems (2-pyrrolidone or N-methyl-2-pyrrolidone) + (acetonitrile or chloroform) are reported in Tables 2−5. The good agreement between the speeds of sound in the 2-pyrrolidone + acetonitrile system at 303.15 K measured in this work and by Mehta and Sharma17 is illustrated in Figure 1. Because of the high vapor pressure of chloroform, the systems containing this solvent were studied at temperatures up to 308 K rather than up to 323 K as for the mixtures with acetonitrile. We decided to report the raw results with the number of significant digits corresponding to the measurements resolution because of the requirements of further calculations, especially those of the isobaric thermal expansibility. High precision of the data is crucial for proper fitting of the volume− temperature relationship. Since the expansibility is the temperature derivative of the volume logarithm, systematic errors in the volume are less important in this respect. Systematic errors in the experimental densities and speeds may also be at least partially canceled in the calculations of the thermodynamic excess functions.

3

αp ≡ V −1(∂V /∂T )p =

∑ iai ϑi− 1 i=1

(3)

and Ep ,m ≡ (∂Vm/∂T )p = αpVm

(4)

where Vm is the molar volume of the system: Vm = (x1M1 + x 2M 2)ν

(5)

in which x is the mole fraction, M is the molar mass, and the subscripts 1 and 2 stand for the binary mixture components. In this work “1” denotes 2-pyrrolidone or N-methyl-2-pyrrolidone and “2” denotes acetonitrile or chloroform. G



Article

Table 6. Coefficients in eq 2 for the Specific Volumes of the Binary Systems (2-Pyrrolidone or N-Methyl-2-pyrrolidone) + (Acetonitrile or Chloroform) and Standard Errors of the Fits (δ) system

range of T/K

x1

C4H7NO (1) + C2H3N (2)

298−323

0 0.1025 0.1865 0.3069 0.3976 0.4974 0.6050 0.6950 0.7932 0.8972 1 0 0.1002 0.1990 0.3019 0.4027 0.5022 0.6054 0.6970 0.7992 0.9000 1a 0 0.0997 0.2019 0.2953 0.4033 0.4999 0.5645 0.6971 0.7909 0.8906 1 0 0.1061 0.1079 0.2054 0.2994 0.4032 0.4961 0.6006 0.6854 0.7986 1

C4H7NO (1) + CHCl3 (2)

293−308

C5H9NO (1) + C2H3N (2)

293−323

C5H9NO (1) + CHCl3 (2)

a

293−308

ln[ν298.15/(cm3·g−1)]

a1·103

a2·106

a3·108

0.2528117 0.1897094 0.1450253 0.0905451 0.0547904 0.0206563 −0.0120980 −0.0361897 −0.0597608 −0.0821593 −0.1019737 −0.3907121 −0.3709265 −0.3484554 −0.3228807 −0.2960472 −0.2680259 −0.2370237 −0.2075566 −0.1737182 −0.1385480

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.0000021 0.0000026 0.0000020 0.0000003 0.0000022 0.0000010 0.0000010 0.0000005 0.0000008 0.0000004 0.0000003 0.0000016 0.0000000 0.0000039 0.0000040 0.0000030 0.0000017 0.0000069 0.0000019 0.0000037 0.0000041

1.39280 1.25527 1.16550 1.06010 0.99311 0.93271 0.87803 0.83746 0.80081 0.76789 0.73956 1.28879 1.18491 1.10107 1.02568 0.96280 0.90833 0.85996 0.82654 0.79279 0.76439

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.00040 0.00049 0.00037 0.00010 0.00041 0.00018 0.00018 0.00009 0.00016 0.00007 0.00006 0.00035 0.00001 0.00074 0.00077 0.00058 0.00032 0.00132 0.00037 0.00070 0.00080

1.878 1.496 1.167 0.850 0.788 0.645 0.500 0.454 0.365 0.277 0.214 1.684 1.313 0.939 0.841 0.693 0.621 0.718 0.432 0.379 0.313

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.015 0.019 0.014 0.010 0.016 0.007 0.007 0.003 0.006 0.003 0.002 0.052 0.001 0.114 0.118 0.090 0.050 0.203 0.056 0.108 0.122

0.2528200 0.1967877 0.1509135 0.1163173 0.0828579 0.0577806 0.0430532 0.0169062 0.0019027 −0.0136751 −0.0274145 −0.3914193 −0.3580347 −0.3572068 −0.3243106 −0.2913499 −0.2528310 −0.2181971 −0.1788034 −0.1465664 −0.1038405 −0.0276754

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.0000041 0.0000006 0.0000007 0.0000004 0.0000009 0.0000023 0.0000009 0.0000007 0.0000022 0.0000020 0.0000002 0.0000007 0.0000030 0.0000006 0.0000006 0.0000007 0.0000004

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.00074 0.00011 0.00013 0.00008 0.00016 0.00040 0.00016 0.00013 0.00039 0.00036 0.00004 0.00013 0.00055 0.00012 0.00012 0.00012 0.00007

0.034 0.016 0.006 0.011 0.007 0.019 0.024 0.019 0.018 0.017 0.002 0.019 0.082 0.017 0.018 0.018 0.010

0.0000006 0.0000007 0.0000005 0.0000004

± ± ± ±

0.00011 0.00012 0.00009 0.00007

1.905 1.492 1.286 1.049 0.916 0.778 0.573 0.488 0.492 0.416 0.407 1.803 1.512 1.278 1.114 0.959 0.928 0.761 0.746 0.573 0.482 0.398

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

± ± ± ±

1.39222 1.27753 1.18662 1.12012 1.05790 1.01274 0.98752 0.94267 0.91728 0.89165 0.86742 1.28587 1.18501 1.18518 1.11185 1.04979 0.99534 0.95571 0.92829 0.91147 0.89229 0.86671

± ± ± ±

0.017 0.018 0.013 0.010

δ·106 2.3 2.9 2.2 0.3 2.4 1.1 1.1 0.5 0.9 0.4 0.3 2.7 0.0 5.7 5.9 4.5 2.5 10.2 2.8 5.4 6.1

0.23 ± 0.03

7.7 1.0 1.3 0.7 1.6 4.2 1.4 1.1 4.1 3.8 0.4 0.9 4.1 0.9 0.9 0.9 0.5 −b 0.8 0.9 0.6 0.5

0.19 ± 0.05 0.15 ± 0.04

0.43 ± 0.08 0.27 ± 0.06

The same coefficients as for the system with C2H3N. bFit based on two series of measurements.

Modified Redlich−Kister polynomials23 were applied to approximate the excess functions:

The molar isentropic compression is given by KS ,m ≡ −(∂Vm/∂p)S = κSVm

(6)

ZmE = x1x 2

with κS calculated using eq 1. The thermodynamic excesses of the molar volume, thermal expansion, and isentropic compression were calculated from the definition ZmE = Zm − Zmid

4

2

∑ ∑ aij(x2 − x1)i ϑ j (8)

i=0 j=0 −1

−1

−1

where Z = V·10 /(m ·mol ) or Z = KS·10 /(m ·mol ·Pa ). In seven cases out of eight (three sets of data for the excess volume and four sets for the excess compression), the coefficients aij were calculated by least-squares fitting of eq 8. Since the excess molar thermal expansion is given by the derivative 6

(7)

where Z = V, Ep, or KS and the superscript “id” denotes the ideal mixture. The functions Zidm were calculated in the strict thermodynamic way,23 applying molar isobaric heat capacities of the pure substances taken from the literature for 2-pyrrolidone,26 N-methyl-2-pyrrolidone,27 acetonitrile,28 and chloroform.29 Isentropic compressibilities and the excesses of molar volume, thermal expansion, and isentropic compression are reported in Tables 2−5.

3

EpE,m = (∂VmE/∂T )p

15

3

(9)

VEm

the coefficients aij for may be used to calculate the EEp,m function as well. However, the calculation results for the excess molar volume of N-methyl-2-pyrrolidone + chloroform turned out to be unsatisfactory: either the VEm(x1, T) function was too simple H



Article

Table 7. Coefficients in eq 2 for the Speeds of Sound in the Binary Systems (2-Pyrrolidone or N-Methyl-2-pyrrolidone) + (Acetonitrile or Chloroform) and Standard Errors of the Fits (δ) system

range of T/K

x1

u298.15/(m·s−1)

a1

C4H7NO (1) + C2H3N (2)

298−323

0 0.1865 0.3069 0.3976 0.4974 0.6050 0.6950 0.7932 0.8972 1 0 0.1002 0.1990 0.3019 0.4027 0.5022 0.6054 0.6970 0.7992 0.9000 1a 0 0.0997 0.2019 0.2953 0.4033 0.4999 0.5645 0.6971 0.7909 0.8906 1 0 0.1061 0.1079 0.2054 0.2994 0.4032 0.4961 0.6006 0.6854 0.7986 1

1278.87 ± 0.02 1336.98 ± 0.06 1380.18 ± 0.07 1414.39 ± 0.00 1451.94 ± 0.02 1492.84 ± 0.03 1526.17 ± 0.08 1561.62 ± 0.02 1598.15 ± 0.02 1632.94 ± 0.01 984.66 ± 0.00 1017.42 ± 0.02 1059.49 ± 0.09 1109.80 ± 0.01 1164.45 ± 0.05 1223.69 ± 0.00 1292.94 ± 0.02 1358.88 ± 0.00 1442.15 ± 0.14 1533.22 ± 0.15

−3.9699 ± 0.0016 −3.8396 ± 0.0109 −3.6096 ± 0.0267 −3.5180 ± 0.0007 −3.4220 ± 0.0028 −3.3582 ± 0.0017 −3.3245 ± 0.0318 −3.2938 ± 0.0022 −3.2088 ± 0.0065 −3.2642 ± 0.0011 −3.3764 ± 0.0006 −3.1896 ± 0.0034 −3.0612 ± 0.0163 −3.0162 ± 0.0021 −2.9466 ± 0.0091 −3.0110 ± 0.0000 −2.9010 ± 0.0030 −3.1412 ± 0.0006 −3.0702 ± 0.0253 −3.1405 ± 0.0274

1278.58 ± 0.00 1311.57 ± 0.03 1345.37 ± 0.01 1375.02 ± 0.01 1407.58 ± 0.05 1434.40 ± 0.06 1450.84 ± 0.02 1483.76 ± 0.01 1503.36 ± 0.02 1524.81 ± 0.03 1544.64 ± 0.02 984.34 ± 0.01 1033.44 ± 0.18 1034.90 ± 0.01 1082.05 ± 0.03 1130.09 ± 0.03 1181.91 ± 0.05 1231.83 ± 0.02 1290.67 ± 0.01 1342.08 ± 0.03 1412.92 ± 0.01 1545.45 ± 0.02

−4.0343 ± 0.0006 −3.9383 ± 0.0107 −3.9363 ± 0.0011 −3.9175 ± 0.0012 −3.8872 ± 0.0201 −3.8688 ± 0.0240 −4.0232 ± 0.0080 −4.0157 ± 0.0043 −4.0324 ± 0.0087 −3.9382 ± 0.0120 −3.8696 ± 0.0021 −3.3379 ± 0.0012 −3.3542 ± 0.0323 −3.3242 ± 0.0025 −3.3302 ± 0.0062 −3.2016 ± 0.0048 −3.3109 ± 0.0083 −3.3249 ± 0.0040 −3.4373 ± 0.0014 −3.5540 ± 0.0049 −3.5667 ± 0.0021 −3.8605 ± 0.0027

C4H7NO (1) + CHCl3 (2)

C5H9NO (1) + C2H3N (2)

C5H9NO (1) + CHCl3 (2)

a

293−308

298−323

293−308

a2·103 3.009 ± 0.420 6.001 ± 2.650 1.437 ± 0.028

a3·105

−20.25 ± 6.96 2.64 ± 0.42

−5.357 ± 3.156 −2.085 ± 0.649 2.326 ± 0.042

13.82 ± 8.29 4.31 ± 0.33 8.00 ± 1.70

−5.630 ± 2.428 −1.589 ± 0.308 −5.959 ± 1.349 −1.000 ± 0.000 −7.863 ± 0.443 −3.730 ± 0.087 −4.453 ± 3.765 −3.026 ± 4.085 0.480 ± 0.022 −2.417 ± 1.067

−12.111 ± 1.998 −11.464 ± 2.389 −2.746 ± 0.791 −2.259 ± 0.424 −2.189 ± 0.862 −2.600 ± 1.192 −3.268 ± 0.176 −6.904 ± 4.812 1.300 ± 0.372 −4.532 ± 0.924

6.74 ± 2.80 2.43 ± 0.16 3.23 ± 0.19 30.16 ± 5.25 29.12 ± 6.27 11.72 ± 2.08 9.48 ± 1.11 7.80 ± 2.26 11.19 ± 3.13 6.65 ± 0.32

δ 0.03 0.06 0.07 0.00 0.02 0.04 0.08 0.02 0.02 0.01 0.01 0.04 0.12 0.02 0.07 0.00 0.02 0.00 0.19 0.20 0.00 0.03 0.01 0.01 0.05 0.06 0.02 0.01 0.02 0.03 0.02 0.01 0.24 0.02 0.05 0.05 0.06 0.04 0.02 0.04 0.02 0.03

The same coefficients as for the system with C2H3N.

for proper representation of the excess molar thermal expansion as given by eq 9, or, if EEp,m(x1, T) was correctly approximated, the VEm(x1,T) function showed unphysical curvatures typical of polynomials of too high degree. To overcome this difficulty, we took into account the two functions VEm and EEp,m simultaneously and defined a new loss function for the fitting procedure: n

δ2 =

e=

n

(10)

where n is the number of experimental points, m is the number of fitted coefficients, and v and e are the relative excess volumes and expansions: v=

VmE x1x 2 max|VmE|

x1x 2 max|EpE,m|

(12)

In eq 10, the symbols with a caret stand for the values calculated from the model. Since the volume and expansion are expressed in different units, the loss function had to be defined in terms of relative deviations rather than absolute ones. Following this assumption, the maximum absolute values of the experimental excesses, max|VEm| and max|EEp,m|, were applied to provide similar “weights” of the volume and expansion excesses. Clearly, the statistical characteristics of the fit calculated in the above way would be incompatible with those obtained in the conventional least-squares fit. The fitting coefficients are reported in Table 8, and the excess functions are plotted in Figures 2−13. The number of significant digits reported in the former was adjusted in a way

∑k = 1 (vi − vî)2 + ∑k = 1 (ei − eî )2 2n − m

EpE,m

(11) I



Article

Table 8. Coefficients of the Modified Redlich−Kister Polynomials (eq 8) and Characteristics of the Fits: Correlation Coefficients (r), Standard Errors of the Fits (δ), and Numbers of Experimental Points (n) C4H7NO + C2H3N

C4H7NO + CHCl3

C5H9NO + C2H3N

C5H9NO + CHCl3

−1.590 −0.135 −0.087 −0.251 −0.601

−2.410 −0.379 −0.133 −2.312 −1.124 −0.123 −0.782 0.457 −0.152 0.593 −0.564 0.920

VEm a00 a01·10 a02·103 a10 a11·102 a12·103 a20 a21·102 a22·103 a30 a31·102 a32·104 a40 a41·102 a42·103 r δ n a00 a01·10 a02·103 a10 a11·10 a12·103 a20 a21·10 a22·103 a30 a31·10 a32 a40 a41·10 a42 r δ n a

−2.095 −0.211 −0.113 −0.426 −0.909 −0.253 −0.394 −0.078

0.171 0.000 0.9968 0.033 54 −1.878 −0.336 −0.340 −0.512

−2.617 −0.376 −0.137 −1.009 −0.980 −0.174 0.192 0.035 −0.301 −0.538 −0.509 0.767 −1.144 −0.596 0.356 0.9990 0.038 44 KES,m −1.844 −0.434 −0.323 −0.148 −0.121

0.078

0.156

−0.710 −0.379

0.190

0.9998 0.005 56

−a −a 36

−1.259 −0.211 −0.175 −0.361 −0.124 −0.178 −0.167

−1.282 −0.354 −0.665 −0.109 −0.407

0.132 −0.231 0.374

0.445

−0.229 −0.265 −0.263

0.143 −0.045

0.9970 0.037 49

0.9986 0.017 36

0.9996 0.012 48

0.9940 0.044 36

Combined least-squares fitting of VEm and EEp,m, incompatible characteristics of the fit.

Figure 2. Excess molar volume of the system N-methyl-2-pyrrolidone (1) + acetonitrile (2). Points are experimental results: ■, T = 293.15 K; □, T = 298.15 K; ▲, T = 303.15 K; △, T = 308.15 K; ●, T = 313.15 K; ○, T = 318.15 K; ▼, T = 323.15 K. Lines are graphical illustrations of eq 8.

Figure 3. Excess molar volume of the system N-methyl-2-pyrrolidone (1) + chloroform (2). Points are experimental results: ■, T = 293.15 K; □, T = 298.15 K; ▲, T = 303.15 K; △, T = 308.15 K. Lines are graphical illustrations of eq 8. J



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Figure 4. Excess molar volume of the system 2-pyrrolidone (1) + acetonitrile (2). Points are experimental results: □, T = 298.15 K; ▲, T = 303.15 K; △, T = 308.15 K; ●, T = 313.15 K; ○, T = 318.15 K; ▼, T = 323.15 K. Lines are graphical illustrations of eq 8.

Figure 7. Excess molar thermal expansion of the system N-methyl-2pyrrolidone (1) + chloroform (2). Points are experimental results: ■, T = 293.15 K; □, T = 298.15 K; ▲, T = 303.15 K; △, T = 308.15 K. Lines are temperature derivatives of VEm given by eq 9.

Figure 5. Excess molar volume of the system 2-pyrrolidone (1) + chloroform (2). Points are experimental results: ■, T = 293.15 K; □, T = 298.15 K; ▲, T = 303.15 K; △, T = 308.15 K. Lines are graphical illustrations of eq 8.

Figure 8. Excess molar thermal expansion of the system 2-pyrrolidone (1) + acetonitrile (2). Points are experimental results: □, T = 298.15 K; ▲, T = 303.15 K; △, T = 308.15 K; ●, T = 313.15 K; ○, T = 318.15 K; ▼, T = 323.15 K. Lines are temperature derivatives of VEm given by eq 9.

Figure 6. Excess molar thermal expansion of the system N-methyl-2pyrrolidone (1) + acetonitrile (2). Points are experimental results: ■, T = 293.15 K; □, T = 298.15 K; ▲, T = 303.15 K; △, T = 308.15 K; ●, T = 313.15 K; ○, T = 318.15 K; ▼, T = 323.15 K. Lines are temperature derivatives of VEm given by eq 9.

Figure 9. Excess molar thermal expansion of the system 2-pyrrolidone (1) + chloroform (2). Points are experimental results: ■, T = 293.15 K; □, T = 298.15 K; ▲, T = 303.15 K; △, T = 308.15 K. Lines are temperature derivatives of VEm given by eq 9. K



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Figure 10. Excess molar isentropic compression of the system N-methyl2-pyrrolidone (1) + acetonitrile (2). Points are experimental results: □, T = 298.15 K; ▲, T = 303.15 K; △, T = 308.15 K; ●, T = 313.15 K; ○, T = 318.15 K; ▼, T = 323.15 K. Lines are fits to eq 8.

Figure 13. Excess molar isentropic compression of the system 2-pyrrolidone (1) + chloroform (2). Points are experimental results: ■, T = 293.15 K; □, T = 298.15 K; ▲, T = 303.15 K; △, T = 308.15 K. Lines are fits to eq 8.

Figure 11. Excess molar isentropic compression of the system N-methyl2-pyrrolidone (1) + chloroform (2). Points are experimental results: ■, T = 293.15 K; □, T = 298.15 K; ▲, T = 303.15 K; △, T = 308.15 K. Lines are fits to eq 8.

Figure 14. Excess molar volume of the system 2-pyrrolidone (1) + acetonitrile (2) at T = 303.15 K. Points and solid line: this work. Dashed line: Mehta and Sharma.17

Figure 12. Excess molar isentropic compression of the system 2-pyrrolidone (1) + acetonitrile (2). Points are experimental results: □, T = 298.15 K; ▲, T = 303.15 K; △, T = 308.15 K; ●, T = 313.15 K; ○, T = 318.15 K; ▼, T = 323.15 K. Lines are fits to eq 8.

Figure 15. Excess molar isentropic compression of the system 2-pyrrolidone (1) + acetonitrile (2) at T = 303.15 K. Points and solid line: this work. Dashed line: Mehta and Sharma.17 L



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Table 9. Dissociation of Hydrogen-Bonded Self-Associates and Formation of Cross-Associates in Binary Mixtures of 2-Pyrrolidone or N-Methyl-2-pyrrolidone with Acetonitrile or Chloroform and Their Effects on the System Volume (ΔV)

hydrogen bonding. The fact that the minimum of the VEm(x1) function is located at a mole fraction of N-methyl-2-pyrrolidone close to 0.3 (Figure 3) suggests the 1:2 complex. Partial dissociation of the latter would account for the slight shift of the minimum toward higher concentrations with increasing temperature. Indirect support for the 1:2 complexes comes from the results of crystallographic studies of 2-pyrrolidone monohydrate, which revealed that the carbonyl group is hydrogen-bonded to two molecules of water.30 The monohydrate is rather stable, as it melts congruently at T ≈ 303 K.31 On the other hand, infrared spectra of N-methyl-2-pyrrolidone diluted in mixtures of hexane with CDCl3 showed only 1:1 complexes of different geometry and free N-methyl-2-pyrrolidone molecules, depending on the concentration.32 The maximum negative excess volume of the 2-pyrrolidone + chloroform system is slightly smaller than that of N-methyl-2pyrrolidone + chloroform (Figures 3 and 5), and it occurs at x1 ≈ 0.4 rather than at x1 ≈ 0.3. The positive volume effect of dissociation of 2-pyrrolidone aggregates probably partially compensates for the volume contraction due to the crossassociation, as shown in reactions a and c in Table 9. Again, there is no proof for 1:2 complexes. The fact that the VEm(x1) functions are more nearly symmetrical than those for N-methyl2-pyrrolidone + chloroform seem to suggest 1:1 complexes. However, one should be aware that self-association of 2-pyrrolidone may consist of much more complex aggregation than just in the formation of cyclic dimers. IR spectra suggested that such species as trimers, tetramers, or other more complex oligomers are present in pure liquid 2-pyrrolidone.2

that provided values of the calculated excess functions equal to the experimental ones within the limits of the standard errors of fitting in the seven out of the eight cases where the standard errors were calculated. For the excess molar volume of N-methyl-2pyrrolidone + chloroform, where simultaneous fitting of VEm and EEp,m was applied, the number of significant digits was assumed to be the same as for the other cases. The negative excess molar volume of 2-pyrrolidone + acetonitrile at 303.15 K is slightly bigger than that reported by Mehta and Sharma,17 while the relation is opposite for the excess molar isentropic compression (Figures 14 and 15).

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DISCUSSION AND CONCLUSIONS

All of the studied excess functions of the four systems are negative, which reflects changes in the arrangement of the molecules on mixing. The changes are due to the geometries of the molecules as well as changes in hydrogen bonding upon mixing: disintegration of self-associates and formation of crossassociates. Rough sketches of the latter reactions are shown in Table 9. In the simplest case, the N-methyl-2-pyrrolidone + acetonitrile system, the negative excess of volume results from the different sizes of the molecules, because the components are incapable of forming either self- or cross-associates. If acetonitrile is substituted by chloroform in the mixture, |VEm| becomes larger as a result of the formation of C−H···O hydrogen bonds (Table 9, reaction d). Obviously, the stoichiometry of the crossassociates cannot be concluded from the present results. Both C5H9NO·CHCl3 and C5H9NO·2CHCl3 are probable, as two lone electron pairs of the carbonyl group may participate in M



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(6) Yekeler, H.; Guven, A.; Ozkan, R. Hydrogen bonding and dimeric self-association of 2-pyrrolidinone: An ab initio study. J. Comput.-Aided Mol. Des. 1999, 13, 589−596. (7) CRC Handbook of Data on Organic Compounds, 2nd ed.; Weast, R. C., Grasselli, J. G., Eds.; CRC Press, Boca Raton, FL, 1989 (cited in ref 8). (8) NIST Chemistry WebBook; Linstrom, P. J., Mallard, W. G., Eds.; NIST Standard Reference Database Number 69; National Institute of Standards and Technology: Gaithersburg MD; http://webbook.nist. gov (accessed June 2, 2015). (9) Handbook of Fine Chemicals; Aldrich Chemical Company: Milwaukee, WI, 1990 (cited in ref 8). (10) Steele, W. V.; Chirico, R. D.; Nguyen, A.; Hossenlopp, I. A.; Smith, N. K. Determination of ideal-gas enthalpies of formation for key compounds. AIChE Symp. Ser. 1990, 86, 138−154 (cited in ref 8). (11) Chyliński, K.; Fraś, Z.; Malanowski, S. K. Vapor-Liquid Equilibrium for Propylene Glycol + 2-(2-Hexyloxyethoxy)ethanol and 1-Methyl-2-pyrrolidone + 1-Methoxypropan-2-ol. J. Chem. Eng. Data 2004, 49, 18−23 (cited in ref 8). (12) Morgan, K. M.; Kopp, D. A. Solvent effects on the stability of simple secondary amides. J. Chem. Soc., Perkin Trans. 2 1998, 12, 2759− 2764 (cited in ref 8). (13) Mehta, S. K.; Chauhan, R. K.; Dewan, R. K. Excess volumes and isentropic compressibilities of pyrrolidin-2-one−alkanol (C1−C5) binary mixtures. J. Chem. Soc., Faraday Trans. 1996, 92, 1167−1173. (14) Mehta, S. K.; Chauhan, R. K.; Dewan, R. K. Partial molar volumes and isentropic compressibilities of mixtures of γ-butyrolactam (n = 5) with higher alkanols. J. Chem. Soc., Faraday Trans. 1996, 92, 4463−4469. (15) Papamatthaiakis, D.; Aroni, F.; Havredaki, V. Isentropic Compressibilities of (Amide + Water) Mixtures: A Comparative Study. J. Chem. Thermodyn. 2008, 40, 107−118. (16) George, J.; Sastry, N. V. Densities, Viscosities, Speeds of Sound, and Relative Permittivies for Water-Cyclic Amides (2-Pyrrolidinone, 1Methyl-2-pyrrolidinone and 1-Vinyl-2-pyrrolidinone) at Different Temperatures. J. Chem. Eng. Data 2004, 49, 235−242. (17) Mehta, S. K.; Sharma, A. K. Effect of − CN group on isentropic compressibility and volumetric parameters of mixtures of γbutyrolactam (n = 5) and nitriles. Fluid Phase Equilib. 2003, 205, 37−51. (18) Kimura, F.; Sugiura, T.; Ogawa, H. Solvation of N-Methyl-2pyrrolidone and N,N-Dimethylpropanamide in Cyclohexane, Heptane, n-Alkan-1-ols(C1−C4) and Water at 298.15 K. Thermochim. Acta 2013, 573, 206−212. (19) Blanco, A.; García-Abuín, A.; Gómez-Díaz, D.; Navaza, J. M. Density, Speed of Sound, Viscosity, Refractive Index, and Excess Volume of N-Methyl-2-pyrrolidone (NMP) + Water + Ethanol from T = (293.15 to 323.15) K. J. Chem. Eng. Data 2012, 57, 1009−1014. (20) Geppert-Rybczyńska, M.; Sitarek, M. Acoustic and Volumetric Properties of Binary Mixtures of Ionic Liquid 1-Butyl-3-methylimidazolium Bis(trifluoromethylsulfonyl)imide with Acetonitrile and Tetrahydrofuran. J. Chem. Eng. Data 2014, 59, 1213−1224. (21) González, E. J.; Domínguez, A.; Macedo, E. A. Excess Properties of Binary Mixtures Containing 1-Hexyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide Ionic Liquid and Polar Organic Compounds. J. Chem. Thermodyn. 2012, 47, 300−311. (22) Bhatia, S. C.; Bhatia, R.; Dubey, G. P. Ultrasonic Velocities, Isentropic Compressibilities and Excess Molar Volumes of Octan-1-ol with Chloroform, 1,2-Dichloroethane and 1,1,2,2-Tetrachloroethane at 298.15 and 308.15 K. Phys. Chem. Liq. 2010, 48, 199−230. (23) Varfolomeev, M. A.; Zaitseva, K. V.; Rakipov, I. T.; Solomonov, B. N.; Marczak, W. Speed of Sound, Density, and Related Thermodynamic Excess Properties of Binary Mixtures of Butan-2-one with C1−C4 nAlkanols and Chloroform. J. Chem. Eng. Data 2014, 59, 4118−4132. (24) Thamsen, J. Ultrasonic Velocity and Adiabatic Compressibility in Binary Mixtures of Chloroform and Diethyl Ether and of Chloroform and Acetone. Acta Acust. Acust. 1981, 49, 110−118. (25) Savaroglu, G.; Aral, E. Ultrasonic Velocity and Isentropic Compressibilities of the Ternary Mixture Benzene + Acetone + Chloroform and their Corresponding Binary Mixtres at 298.15 K. J. Mol. Liq. 2003, 105, 79−92.

The bigger negative excess molar volume of the 2-pyrrolidone + acetonitrile system (Figure 4) in comparison with that of N-methyl-2-pyrrolidone + acetonitrile (Figure 2) shows that the net volume effect of breaking and forming the H-bonds according to reactions a and b in Table 9 is negative. The negative excess molar thermal expansions of the three hydrogen-bonded systems (Figures 7−9) are bigger than that of nonbonded N-methyl-2-pyrrolidone + acetonitrile (Figure 6). Hydrogen bonds between unlike molecules clearly make the volumes of the three systems less prone to changes caused by temperature. According to the thermodynamic relationship EpE = (∂V E/∂T )p = −(∂S E/∂p)T

(13)

a consequence of that is an increase in the excess entropy, SE, with increasing pressure. The negative excess compressions show that the mixture formation makes the liquid stiffer (Figures 10−13). This is probably mainly caused by filling in the gaps between the big lactam molecules by the smaller acetonitrile or chloroform molecules. The formation of the hydrogen-bonded cross-associates plays an additional role, as is evidenced by the fact that the maximum |KES,m| value is only 1.5 times bigger for the hydrogenbonded system 2-pyrrolidone + acetonitrile (Figure 12) than for the non-hydrogen-bonded N-methyl-2-pyrrolidone + acetonitrile system (Figure 10). For the binary mixtures with chloroform, the difference is even smaller (Figures 11 and 13).

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Funding

This work was supported by the Russian Government Program of Competitive Growth of Kazan Federal University. M.A.V. and I.T.R. gratefully acknowledge the financial support through Grant MK-7126.2015.3. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Mr. Rafał Flamholc from Anton Paar Poland sp. z o. o. for his competent and detailed answers to technical questions about the DSA 5000 instrument.

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REFERENCES

(1) Harreus, A. L.; Backes, R.; Eichler, J.-O.; Feuerhake, R.; Jäkel, C.; Mahn, U.; Pinkos, R.; Vogelsang, R. 2-Pyrrolidone. Ullmann’s Encyclopedia of Industrial Chemistry 2011, DOI: 10.1002/ 14356007.a22_457.pub2. (2) Tang, H.; Sun, S.; Wu, P. Thermally Induced Dissociation Nature of Pure 2-Pyrrolidinone via Near-Infrared Correlation Spectroscopy Analysis. Appl. Spectrosc. 2009, 63, 1174−1180. (3) Dávila, M. J.; Alcalde, R.; Aparicio, S. Pyrrolidone Derivatives in Water Solution: An Experimental and Theoretical Perspective. Ind. Eng. Chem. Res. 2009, 48, 1036−1050. (4) Yekeler, H. Solvent effects on dimeric self-association of 2pyrrolidinone: An ab initio study. J. Comput.-Aided Mol. Des. 2001, 15, 287−295. (5) Shchavlev, A. E.; Pankratov, A. N.; Borodulin, V. B.; Chaplygina, O. A. DFT Study of the Monomers and Dimers of 2-Pyrrolidone: Equilibrium Structures, Vibrational, Orbital, Topological, and NBO Analysis of Hydrogen-Bonded Interactions. J. Phys. Chem. A 2005, 109, 10982−10996. N



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(26) Steele, W. V.; Chirico, R. D.; Nguyen, A.; Hossenlopp, I. A.; Smith, N. K. Determination of some pure compound ideal-gas enthalpies of formation. AIChE Symp. Ser. 1989, 85, 140−162. (27) Vasilev, V. A.; Novikov, A. N. Thermochemical and volumetric properties of the system N-methylpyrrolidone - water at 288−323 K. Izv. Vyssh. Uchebn. Zaved. Khim. Khim. Tekhnol. 1989, 32, 53−56 (in Russian). (28) Kolker, A. M.; Kulikov, M. V.; Krestov, Al. G. Volumes and heat capacities of binary non-aqueous mixtures. Part 2. The systems acetonitrile-N,N-dimethylformamide and acetonitrile-hexamethylphosphoric triamide. Thermochim. Acta 1992, 211, 73−84. (29) Staveley, L. A. K.; Tupman, W. I.; Hart, K. R. Some thermodynamic properties of the systems benzene + ethylene dichloride, benzene + carbon tetrachloride, acetone + chloroform, and acetone + carbon disulphide. Trans. Faraday Soc. 1955, 51, 323−343. (30) Pirilä, P.; Mutikainen, I.; Pursiainen, J. Structure of the 2Pyrrolidinone Monohydrate. Z. Naturforsch., B: J. Chem. Sci. 1999, 54, 1598−1601. (31) Lohr, L. J. The System of 2-Pyrrolidone−Water. J. Phys. Chem. 1958, 62, 1150−1151. (32) Perjéssy, A.; Engberts, J. B. F. N. Infrared Study of Solvent-Solute Interactions of 1-Substituted 2-Pyrrolidones and Related Compounds. Monatsh. Chem. 1995, 126, 871−888.

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