388
J. Chem. Eng. Data 2008, 53, 388–397
Investigations of the (p, G, T) Properties and Apparent Molar Volumes VO of the LiCl + C2H5OH Solutions H. Israfilov,† J. Safarov,*,†,‡ A. Shahverdiyev,† and E. Hassel‡ Department: “Heat and Refrigeration Techniques”, Azerbaijan Technical University, H. Javid Avn. 25, AZ1073 Baku, Azerbaijan, and Lehrstuhl für Technische Thermodynamik, Universität Rostock, Albert-Einstein-Str. 2, 18059, Rostock, Germany
The (p, F, T) properties and apparent molar volumes Vφ of LiCl in ethanol at T ) (298.15 to 398.15) K and pressures up to p ) 40 MPa are reported. An empirical correlation for the density of (LiCl + C2H5OH) with pressure, temperature, and molality has been derived. The experiments were carried out at molalities of m ) (0.10487, 0.30229, 0.58732, 1.22211, 2.02242, and 2.87989) mol · kg-1 using lithium chloride.
Introduction An absorption heat transfer performs cooling and/or heating by using outside air as a radiation source and an absorption source. It is similar to a vapor-compression device except that compression is accomplished in the absorption heat pump through the use of a thermochemical compressor. The simple thermochemical compressor consists of an absorber, a solution pump, a heat exchanger, and a desorber. The efficiency of an absorption heat transfer cycle is largely dependent on the physical and chemical properties of the heat transfer fluids. The most serious problems by using the conventional aqueous solutions of electrolytes were discussed in our previous publications on the investigation of methanol solutions of electrolytes.1,2 In the present work, we begin to analyze the thermal properties of ethanol solutions of electrolytes for their future application as heat transfer fluids in absorption heat transfer systems, where they can replace aqueous solutions at temperatures below the freezing point of water. Ethanol has a lower freezing point than methanol, and this effect can help the optimal circulation of the heat transfer agent in the closed system. In the present work, the (p, F, T) properties and apparent molar volumes Vφ of LiCl in ethanol at T ) (298.15 to 398.15) K and pressures up to p ) 40 MPa are reported. An empirical correlation for the density of (LiCl + C2H5OH) with pressure, temperature, and molality has been derived. Few works 3–8 with density measurements and apparent molar volumes of LiCl in ethanol solutions are available in the literature. (p, F, T) properties of these solutions were not available in the literature. Butler and Less3 studied the refractive index, density, and partial molar volume of these solutions at T ) 291.15 K, m ) (0 to 1.2339) mol · kg-1, and p ) 0.1 MPa. Density results were measured by a silika pycnometer with 15 c.c. capacity. Vosburgh et al.4 investigated the density and apparent molar volume of LiCl in ethanol at T ) 298.05 K, m ) (0.276 to 0.87708) mol · kg-1, and p ) 0.1 MPa. Temperature was measured with a thermometer calibrated by the N.P.L. with ( 0.01 °C. Density was measured by a pycnometer with 33 c.c. capacity. Millero5 in 1971 fully analyzed the apparent molar * Corresponding author. Tel: +49 381 4989415. Fax: +49 381 4989402. E-mail:
[email protected]. † Azerbaijan Technical University. ‡ Universität Rostock.
Figure 1. Plot of experimental density F of ethanol solutions of LiCl versus pressure p at m ) 0.58732 mol · kg-1: (, 298.15 K; 9, 323.15 K; 2, 348.15 K; b, 373.15 K; 0, 398.15 K; ___ calculated by eqs 5 to 8.
volumes of electrolytes in various substances. Using the available previous research works, he found the apparent molar volume of LiCl in ethanol at infinite dilution. Kawaizumi and Zana6 studied the partial molal volumes of ions in organic solvents from ultrasonic vibration potentials and density measurements. The apparent molar volume of LiCl in ethanol at infinite dilution was determined and compared with the results from ref 3. Glugla et al.7 investigated the partial molar volume of monovalent salts and polar molecules in organic solvents. High-volume injection and flow dilatometers were used during the experiments. The apparent molar volumes of LiCl in ethanol were measured at T ) 298.15 K, m ) (0.00196 to 2.2998) mol · kg-1, and p ) 0.1 MPa. The temperature bath used with this apparatus controlled temperature fluctuation to within 0.001 °C. The volume change was always less than 0.0001 mL and frequently less than 0.00005 mL. The partial molar volumes measured in aprotic solvents with this apparatus were precise to better than ( 2 %. In 2004, Marcus and Hefter8 carried out a full literature analysis of investigations of thermodynamic
10.1021/je700438d CCC: $40.75 2008 American Chemical Society Published on Web 02/14/2008
Journal of Chemical & Engineering Data, Vol. 53, No. 2, 2008 389
Figure 2. Plot of experimental density F of ethanol solutions of LiCl versus pressure p at T ) 298.15 K: 0, m ) 0 (from refs 14 to 16); (, m ) 0.10487 mol · kg-1; 9, m ) 0.30229 mol · kg-1; 2, m ) 0.58732 mol · kg-1; b, m ) 1.22211 mol · kg-1; ], m ) 2.02242 mol · kg-1; ∆, m ) 2.87989 mol · kg-1; __ calculated by eqs 5 to 8.
Figure 4. Plot of isothermal compressibility k · 106/MPa-1 of ethanol solutions of LiCl versus pressure p at m ) 0.30229 mol · kg-1: (, 298.15 K; 9, 323.15 K; 2, 348.15 K; b, 373.15 K; 0, 398.15 K.
Figure 5. Plot of thermal expansibilities R · 106/K-1 of ethanol solutions of LiCl versus pressure p at m ) 1.22211 mol · kg-1: (, 298.15 K; 9, 323.15 K; 2, 348.15 K; b, 373.15 K; 0, 398.15 K. Figure 3. Plot of deviations of experimental density Fexp from density calculated Fcal by eqs 5 to 8 versus pressure p: ∆, m ) 0.10487 mol · kg-1; 0, m ) 0.30229 mol · kg-1; b, m ) 0.58732 mol · kg-1; 2, m ) 1.22211 mol · kg-1; (, m ) 2.02242 mol · kg-1; 9, m ) 2.87989 mol · kg-1.
properties of LiCl + ethanol solutions from previous years. The apparent molar volumes at infinite dilution at T ) 298.15 K were analyzed, and Vφ0 ) -4.9 cm3 · mol-1 was selected as the reference value.
Experimental Section The (p, F, T) properties were investigated using a modified high-pressure-high-temperature Anton-Paar vibrating-tube densimeter (model DMA 5000).9 This instrument is very suitable
for fast and precise measurements of the density of liquids in wide temperature and pressure ranges. The principle of a vibrating tube densimeter is in the phenomena in which the vibrating period of the unilaterally fixed U-tube changes with the density of the sample fluid. In this method, the vibration period τ of the U-shape tube completely filled with the sample liquid is measured, and then the densities F of the sample liquid are computed by applying a principle of a fixed relation between τ and F. The liquid sample is a part of the vibrating system affecting directly its mass and thus also its resonant frequency. Due to the complexity of the geometry of the vibrating tube, it requires calibration with a reference fluid of well-known density. This method is suited to precisely measure the difference between the density of the liquid and reference fluid. The precision of the density measurements with the instrument is
390 Journal of Chemical & Engineering Data, Vol. 53, No. 2, 2008 Table 1. Experimental (p, G, T) Results of (LiCl + C2H5OH) m ) 0.10487 mol · kg-1 p/MPa
F/(kg · m-3)
p/MPa
T ) 298.15 K 0.21 5.12 10.03 15.24 20.06 25.41 30.06 35.71 39.98
p/MPa
T ) 348.15 K 789.29 793.51 797.57 801.71 805.39 809.29 812.53 816.28 818.97
0.14 5.08 10.06 15.41 20.06 25.84 30.71 35.24 39.93
767.47 772.47 777.11 781.93 786.01 790.15 794.13 798.15 801.15
0.29 5.14 10.08 15.42 20.08 25.41 30.26 35.84 39.91
T ) 323.15 K 0.12 5.14 10.02 15.32 20.04 25.06 30.15 35.61 39.94
F/(kg · m-3)
F/(kg · m-3) T ) 398.15 K
743.86 749.63 755.18 760.81 765.44 770.86 775.12 778.84 782.45
0.74 5.01 10.45 15.42 20.09 25.84 30.15 35.86 39.86
688.68 695.99 704.75 712.20 718.73 726.13 731.22 737.37 741.26
p/MPa
F/(kg · m-3)
T ) 373.15 K 717.74 724.52 731.05 737.69 743.13 748.94 753.85 759.05 762.54
m ) 0.30229 mol · kg-1 p/MPa
F/(kg · m-3)
p/MPa
T ) 298.15 K 0.18 5.04 10.24 15.62 20.05 25.84 30.56 35.84 39.91
T ) 348.15 K 795.82 799.96 804.22 808.44 811.77 815.92 819.15 822.58 825.10
0.17 5.06 10.07 15.12 20.09 25.86 30.06 35.84 39.94
774.35 779.31 784.00 788.31 792.88 796.57 800.40 803.97 807.32
0.31 5.06 10.07 15.02 20.31 25.41 30.06 35.16 39.96
T ) 323.15 K 0.14 5.21 10.23 15.06 20.45 25.04 30.06 35.02 39.98
F/(kg · m-3)
T ) 398.15 K 751.06 756.68 762.15 767.36 772.20 777.45 781.03 785.62 788.64
0.68 5.07 10.06 15.09 20.14 25.23 30.07 35.24 39.97
696.61 704.02 711.93 719.36 726.27 732.68 738.24 743.62 748.04
p/MPa
F/(kg · m-3)
T ) 373.15 K 725.29 731.82 738.32 744.36 750.38 755.77 760.33 764.94 768.90
m ) 0.58732 mol · kg-1 p/MPa
F/(kg · m-3)
p/MPa
T ) 298.15 K 0.25 5.52 10.44 15.17 19.25 25.64 30.11 35.56 39.82
T ) 348.15 K 804.88 809.31 813.28 816.95 819.98 824.52 827.53 831.01 833.60
0.74 5.06 10.53 15.29 20.48 25.32 30.61 35.84 39.86
783.81 788.42 793.02 797.87 801.87 805.52 809.15 812.74 815.82
0.96 5.42 10.09 15.85 20.09 25.84 30.15 35.98 39.97
T ) 323.15 K 0.24 5.03 10.05 15.62 20.47 25.14 30.06 35.22 39.97
F/(kg · m-3)
T ) 398.15 K 761.48 766.32 772.13 776.89 781.78 786.04 790.37 794.33 797.14
T ) 373.15 K 736.55 742.51 748.41 755.19 759.84 765.68 769.70 774.65 777.73
1.02 5.74 10.06 15.96 20.35 25.42 30.05 34.95 39.92
708.33 716.08 722.74 731.15 736.90 742.99 748.05 752.88 757.22
Journal of Chemical & Engineering Data, Vol. 53, No. 2, 2008 391 Table 1. (Continued) m ) 1.22211 mol · kg-1 p/MPa
F/(kg · m-3)
p/MPa
T ) 298.15 K 0.21 5.47 9.82 14.99 19.04 25.46 30.19 35.87 40.07
p/MPa
T ) 348.15 K 823.50 827.84 831.28 835.20 838.14 842.57 845.65 849.13 851.57
0.42 5.06 10.21 15.28 20.14 25.07 30.41 35.42 39.97
802.86 807.19 811.76 816.02 819.88 823.57 827.32 830.59 833.36
0.84 5.06 10.06 15.74 20.34 25.08 30.41 35.84 39.82
T ) 323.15 K 0.41 5.07 10.20 15.29 20.15 25.06 30.42 35.41 39.96
F/(kg · m-3)
F/(kg · m-3) T ) 398.15 K
780.84 785.85 791.09 795.92 800.25 804.33 808.41 811.91 814.81
0.96 4.86 9.68 15.06 20.47 25.62 30.41 35.95 39.94
731.58 737.73 744.82 752.07 758.65 764.26 768.90 773.57 776.48
p/MPa
F/(kg · m-3)
T ) 373.15 K 757.56 762.98 769.02 775.35 780.06 784.55 789.12 793.28 796.01
m ) 2.02242 mol · kg-1 p/MPa
F/(kg · m-3)
p/MPa
T ) 298.15 K 0.41 5.23 10.05 15.03 20.12 25.61 30.08 35.41 39.94
T ) 348.15 K 845.20 849.07 852.76 856.40 859.94 863.54 866.32 869.43 871.92
0.15 4.96 10.03 14.96 20.03 25.42 30.16 35.61 39.96
824.57 829.25 833.25 837.42 841.36 844.84 847.97 851.30 853.89
0.32 5.86 10.09 15.72 20.31 25.05 30.06 35.41 39.97
T ) 323.15 K 0.23 5.41 10.08 15.23 20.41 25.31 30.01 35.42 39.97
F/(kg · m-3)
T ) 398.15 K 803.25 808.25 813.19 817.67 821.94 826.11 829.46 832.94 835.44
0.74 5.03 10.42 15.06 20.74 25.61 30.09 35.81 39.94
758.72 765.06 772.34 778.00 784.18 788.80 792.51 796.49 798.83
p/MPa
F/(kg · m-3)
T ) 373.15 K 781.71 788.43 793.18 799.00 803.31 807.37 811.20 814.80 817.45
m ) 2.87989 mol · kg-1 p/MPa
F/(kg · m-3)
p/MPa
T ) 298.15 K 0.12 5.04 10.32 15.64 20.61 25.08 30.41 35.09 39.98
T ) 348.15 K 865.97 869.78 873.67 877.37 880.65 883.43 886.56 889.13 891.64
0.54 5.14 10.08 15.06 20.07 25.64 30.84 35.19 39.86
845.88 850.34 854.11 858.04 861.48 864.98 867.94 870.90 873.36
0.98 5.14 9.98 14.62 21.42 24.94 30.15 35.74 39.98
T ) 323.15 K 0.18 5.41 10.08 15.24 20.06 25.30 30.07 35.21 39.86
F/(kg · m-3)
T ) 398.15 K 825.55 829.96 834.46 838.73 842.77 846.96 850.58 853.39 856.19
T ) 373.15 K 805.91 810.39 815.52 819.69 825.53 828.37 832.41 836.30 839.22
1.01 5.07 10.14 15.28 20.01 25.32 30.07 34.98 39.98
785.44 790.37 796.07 801.31 805.83 810.70 814.57 818.00 821.90
392 Journal of Chemical & Engineering Data, Vol. 53, No. 2, 2008 Table 2. Values of the Coefficients aij , bij, and cij in Equations 5 to 8 aij ) ) ) ) ) ) ) ) ) )
a10 a11 a12 a13 a14 a20 a21 a22 a23 a24
bij
-1.360094 -0.0510372 0.15135715 -0.06578586 0.0118697 0.002760349 0.16961 · 10-5 -0.145706 · 10-3 0.250216 · 10-4 -0.614345 · 10-5
b00 b01 b02 b03 b04 b10 b11 b12 b13 b14
) ) ) ) ) ) ) ) ) )
cij
-1419.63206381 587.21071 275.65116767 -271.34232 44.5829 5.730492 -2.19719472 -1.428243344 1.249180504 -0.21176755
c00 c01 c02 c03 c04 c10 c11 c12 c13 c14
) ) ) ) ) ) ) ) ) )
1724.38987323 -1357.667957 -532.3577943 605.31548324 -108.611242 -2.293768 3.3961916 2.633988 -2.45685 0.4390121444
Table 3. Standard, Absolute, and Average Deviations of Equations 5 to 8 standard absolute maximum absolute average percent molality, m/(mol · kg-1) deviationa deviationa deviation deviationa 0.10487 0.30229 0.58732 1.22211 2.02242 2.87989 a
0.03095 0.02407 0.02308 0.03768 0.06915 0.02900
0.14165 0.12001 0.12157 0.18973 0.34834 0.16087
0.46 0.40 0.38 0.54 0.63 0.45
Figure 6. Plot of deviations of extrapolated density Fext of this work from the literature values of ref 4 vs molality m at T ) 298.05 K.
0.01910 0.01602 0.01583 0.02417 0.04323 0.01916
The equations of deviations are available in ref 1.
about 0.01 kg · m-3, although for glass tubes at low pressures the uncertainty in density measurements is about 0.001 kg · m-3. The precision of the method is limited by the calibration procedure. The behavior of the vibrating tube can be described by the simple mathematical-physical model of the undamped spring-mass system.10 The tube is filled with a sample of interest and vibrates perpendicular to its plane in an electromagnetic field. The frequency of the harmonic oscillation of the tube can be directly related to the density of the fluid contained in the tube. The characteristic period of the vibrator, τ (µs), is oscillating at its resonance frequency in the fundamental harmonic mode11
(
τ ) 2π
mt + FVt C
)
1⁄2
(1)
where τ is the period of oscillation of the vibration tube (µs); mt is the mass of the empty vibrating tube (kg); Vt is the volume of the vibrating tube (m3); F is the sample density (kg · m-3); and C is the spring constant (N · m-1), which depends on the size and shape of the tube and is proportional to Yong’s modulus of the tube material. From written explicitly as eq 1, the density can be
F ) A - Bτ2
Figure 7. Plot of Vφ of LiCl in ethanol versus m at T ) 298.15 K: (, p ) 0.1 MPa; 9, p ) 5 MPa; 2, p ) 10 MPa; b, p ) 15 MPa; ], p ) 20 MPa; 0, p ) 25 MPa; ∆, p ) 30 MPa; O, p ) 35 MPa; *, p ) 40 MPa; +, T ) 298.05 K and p ) 0.1 MPa [ref 3]; x, p ) 0.1 MPa [ref 7]; the calculated points are connected with solid lines only for the visual comparios.
expanded with temperature- and pressure-dependent terms. For measurements at T ) (298.15 to 398.15) K and up to p ) 40 MPa, an extended calibration equation with 14 significant parameters is employed12
A)
∑ ai(T ⁄ K)i+∑ bj(p ⁄ MPa)j+c(T ⁄ K)(p ⁄ MPa)
(3)
∑ di(T ⁄ K)i+∑ ej(p ⁄ MPa)j+f(T ⁄ K)(p ⁄ MPa)
(4)
i
(2)
where
B)
i
B(T, P) ) -
C(T, P) 4π2VT(T, P)
and
A(T, P) ) -
mt VT(T, P)
The parameters A and B can be determined by substance calibration measuring the period of oscillation of at least two substances of known density (in this work, water and methanol). Unfortunately, the parameters A and B are highly temperature dependent and also pressure dependent. Therefore, the parameters must be determined for each temperature and pressure separately, or like in this work, the classical equation must be
j
j
where a0, a1, a2, a3, b1, b2, c, d0, d1, d2, d3, e1, e2, and f are parameters of the extended vibrating tube equations. The observed reproducibility and estimated maximum uncertainty of the density measurements between T ) (298.15 and 398.15) K and up to p ) 40 MPa is within F ) ( 0.05 kg · m-3 and F ) ( 0.2 kg · m-3, respectively. This leads to maximum relative uncertainties of ( 0.03 % for the performed measurements for the solutions. For the pressure measurement, a pressure transducer (S-10, WIKA Alexander Wiegand GmbH & Co., Germany) was used. The precision after calibration with a dead weight pressure gauge was estimated to be better than ( 5 kPa. The calibrated (ITS-90) Pt100 temperature sensors installed show a resolution of ( 3 mK and a precision of ( 30 mK, while the thermostat has a stability of ( 20 mK.
Journal of Chemical & Engineering Data, Vol. 53, No. 2, 2008 393 Table 4. Isothermal Compressibilities k · 106/MPa-1 of (LiCl + C2H5OH) m ) 0.10487 mol · kg-1
m ) 0.30229 mol · kg-1
p/MPa
k · 106/MPa-1
R · 106/K-1
p/MPa
0.21 5.12 10.03 15.24 20.06 25.41 30.06 35.71 39.98
1186 1108 1039 974 919 866 824 779 748
1056 1020 988 956 930 903 881 858 841
0.18 5.04 10.24 15.62 20.05 25.84 30.56 35.84 39.91
0.12 5.14 10.02 15.32 20.04 25.06 30.15 35.61 39.94
1423 1314 1222 1135 1066 1002 944 889 851
1177 1130 1088 1047 1015 984 955 927 907
0.14 5.08 10.06 15.41 20.06 25.84 30.71 35.24 39.93
1741 1590 1459 1339 1249 1152 1083 1026 973
0.29 5.14 10.08 15.42 20.08 25.41 30.26 35.84 39.91 0.74 5.01 10.45 15.42 20.09 25.84 30.15 35.86 39.86
R · 106/K-1
p/MPa
k · 106/MPa-1
R · 106/K-1
T ) 298.15 K 1155 1081 1010 945 898 842 802 762 733
1043 1010 977 947 924 897 876 855 841
0.25 5.52 10.44 15.17 19.25 25.64 30.11 35.56 39.82
1117 1041 977 923 880 821 784 744 716
1030 997 969 944 924 896 878 858 844
0.14 5.21 10.23 15.06 20.45 25.04 30.06 35.02 39.98
T ) 323.15 K 1373 1269 1180 1104 1029 974 919 872 830
1152 1107 1066 1032 997 970 943 919 898
0.24 5.03 10.05 15.62 20.47 25.14 30.06 35.22 39.97
1313 1220 1135 1053 991 937 887 841 804
1119 1079 1042 1005 976 951 928 905 887
1337 1272 1214 1160 1119 1073 1039 1011 984
0.17 5.06 10.07 15.12 20.09 25.86 30.06 35.84 39.94
T ) 348.15 K 1671 1529 1405 1298 1206 1116 1058 990 947
1300 1240 1185 1137 1094 1052 1024 990 969
0.74 5.06 10.53 15.29 20.48 25.32 30.61 35.84 39.86
1573 1457 1331 1237 1148 1077 1010 953 915
1246 1196 1141 1099 1059 1025 993 966 947
2199 1976 1787 1616 1491 1369 1275 1183 1126
1558 1465 1384 1309 1252 1196 1151 1107 1078
0.31 5.06 10.07 15.02 20.31 25.41 30.06 35.16 39.96
T ) 373.15 K 2103 1897 1716 1566 1431 1322 1237 1157 1093
1512 1425 1347 1280 1219 1168 1127 1089 1057
0.96 5.42 10.09 15.85 20.09 25.84 30.15 35.98 39.97
1962 1785 1628 1467 1367 1253 1181 1099 1051
1438 1362 1294 1222 1177 1124 1090 1050 1026
2884 2569 2245 2006 1821 1636 1520 1394 1320
1878 1750 1614 1511 1429 1345 1291 1231 1195
0.68 5.07 10.06 15.09 20.14 25.23 30.07 35.24 39.97
T ) 398.15 K 2753 2448 2165 1935 1746 1589 1467 1358 1276
1821 1695 1575 1475 1390 1318 1261 1208 1168
1.02 5.74 10.06 15.96 20.35 25.42 30.05 34.95 39.92
2568 2269 2044 1797 1648 1506 1398 1304 1225
1733 1607 1510 1400 1332 1266 1215 1169 1131
m ) 1.22211 mol · kg-1
k · 106/MPa-1
m ) 0.58732 mol · kg-1
m ) 2.02242 mol · kg-1
p/MPa
k · 106/MPa-1
R · 106/K-1
p/MPa
0.21 5.47 9.82 14.99 19.04 25.46 30.19 35.87 40.07
1052 981 929 873 834 779 743 705 680
1015 987 966 943 926 903 887 870 859
0.41 5.23 10.05 15.03 20.12 25.61 30.08 35.41 39.94
0.42 5.06 10.21 15.28 20.14 25.07
1211 1130 1050 982 925 874
1060 1027 995 967 942 920
0.23 5.41 10.08 15.23 20.41 25.31
k · 106/MPa-1
m ) 2.87989 mol · kg-1
R · 106/K-1
p/MPa
k · 106/MPa-1
R · 106/K-1
T ) 298.15 K 974 916 864 816 772 731 700 668 644
989 967 946 927 910 893 880 866 856
0.12 5.04 10.32 15.64 20.61 25.08 30.41 35.09 39.98
901 847 796 750 713 683 651 626 602
959 936 913 893 875 861 846 833 822
T ) 323.15 K 1110 1030 966 905 852 808
1000 970 946 922 900 882
0.18 5.41 10.08 15.24 20.06 25.30
1024 954 899 845 801 759
958 931 908 886 868 850
394 Journal of Chemical & Engineering Data, Vol. 53, No. 2, 2008 Table 4. (Continued) m ) 1.22211 mol · kg-1
m ) 2.02242 mol · kg-1
m ) 2.87989 mol · kg-1
p/MPa
k · 106/MPa-1
R · 106/K-1
p/MPa
k · 106/MPa-1
R · 106/K-1
p/MPa
k · 106/MPa-1
R · 106/K-1
30.41 35.42 39.97
826 786 754
899 881 867
30.01 35.42 39.97
770 732 704
867 851 839
30.07 35.21 39.86
726 694 669
835 821 810
0.41 5.07 10.20 15.29 20.15 25.06 30.42 35.41 39.96
1441 1329 1222 1133 1059 995 935 887 849
1154 1108 1063 1025 993 965 938 916 899
0.15 4.96 10.03 14.96 20.03 25.42 30.16 35.61 39.96
T ) 348.15 K 1298 1198 1107 1032 966 906 861 817 787
1054 1015 980 950 923 899 880 861 848
0.54 5.14 10.08 15.06 20.07 25.64 30.84 35.19 39.86
1179 1099 1024 958 901 845 800 767 736
979 950 922 896 874 851 833 819 806
0.84 5.06 10.06 15.74 20.34 25.08 30.41 35.84 39.82
1763 1614 1465 1326 1232 1150 1073 1007 967
1305 1242 1179 1118 1077 1040 1004 974 955
0.32 5.86 10.09 15.72 20.31 25.05 30.06 35.41 39.97
T ) 373.15 K 1542 1382 1282 1169 1094 1028 969 918 882
1147 1085 1045 999 968 940 916 893 878
0.98 5.14 9.98 14.62 21.42 24.94 30.15 35.74 39.98
1350 1257 1161 1089 996 954 899 848 813
1016 983 948 921 886 870 848 828 813
0.96 4.86 9.68 15.06 20.47 25.62 30.41 35.95 39.94
2262 2044 1822 1624 1466 1345 1254 1169 1119
1549 1457 1361 1274 1202 1146 1103 1063 1039
0.74 5.03 10.42 15.06 20.74 25.61 30.09 35.81 39.94
T ) 398.15 K 1889 1702 1514 1385 1258 1172 1107 1043 1007
1300 1226 1150 1096 1042 1005 977 949 932
1.01 5.07 10.14 15.28 20.01 25.32 30.07 34.98 39.98
1575 1457 1333 1230 1149 1068 1009 959 906
1080 1040 996 959 929 898 875 856 835
LiCl (w > 0.998) was supplied from Merck, Germany, and was used without further purification. Before the experiment, the salt was dried in a special cell by prolonged heating at T ) 413.15 K and the vacuum being renewed by pumping at frequent intervals for 24 h prior to use. To prevent absorption of water, preparation of salt solutions was performed in a glovebox. The
samples were obtained by successive dilutions of the concentrated solutions. Ethanol (w > 0.998) was supplied from Carl Roth, Germany, and was degassed by vacuum distillation using a Vigreux column with a height of 90 cm. The final purity of the ethanol was checked by gas chromatography (w > 0.999) and Karl Fischer titration (water content < 50 ppm). The solutions were prepared by mass using an electronic scale with a resolution of 0.0001 g.
Results and Discussion In this work, the (p, F, T) properties and apparent molar volumes Vφ of LiCl in ethanol at T ) (298.15 to 398.15) K, at
Figure 8. Plot of apparent molar volumes Vφ of LiCl in ethanol versus temperature T at m ) 1.22211 mol · kg-1: (, p ) (0.101, 0.24, and 0.52) MPa; 9, p ) 5 MPa; 2, p ) 10 MPa; b, p ) 15 MPa, ], p ) 20 MPa; 0, p ) 25 MPa; ∆, p ) 30 MPa; O, p ) 35 MPa; *, p ) 40 MPa; the calculated points are connected with solid lines only for the visual showing.
Figure 9. Plot of deviations of calculated results of apparent molar volume Vφcalcd of LiCl in ethanol from the literature values Vφlit versus molality m: ∆, ref 4 at T ) 298.05 K; and 9, ref 7 at T ) 298.15 K.
Journal of Chemical & Engineering Data, Vol. 53, No. 2, 2008 395 Table 5. Apparent Molar Volumes VO/(cm3 · mol-1) of LiCl in C2H5OH m/(mol · kg-1) p/MPa
0.10487
0.30229
0.101 5 10 15 20 25 30 35 40
-2.550 -2.090 -1.509 -1.020 -0.230 0.680 1.530 2.430 3.340
-0.680 -0.340 0.110 0.570 1.200 2.040 2.782 3.570 4.400
0.101 5 10 15 20 25 30 35 40
-5.670 -5.040 -4.350 -3.600 -2.650 -1.460 -0.260 1.250 2.660
0.101 5 10 15 20 25 30 35 40
0.58732
1.22211
2.02242
2.87989
T ) 298.15 K 0.882 1.265 1.765 2.295 2.908 3.552 4.228 4.937 5.654
3.359 3.854 4.382 4.902 5.427 5.947 6.463 6.977 7.502
5.649 6.168 6.670 7.153 7.627 8.078 8.516 8.942 9.364
7.715 8.220 8.705 9.167 9.605 10.024 10.421 10.808 11.180
-4.100 -3.350 -2.590 -1.840 -0.800 0.102 1.254 2.478 3.774
T ) 323.15 K -2.126 -1.354 -0.532 0.336 1.195 2.132 3.066 3.999 4.960
0.952 1.811 2.651 3.469 4.255 5.028 5.764 6.478 7.184
3.574 4.402 5.177 5.914 6.592 7.249 7.870 8.457 9.028
5.946 6.688 7.378 8.025 8.617 9.184 9.713 10.210 10.689
-11.002 -10.003 -8.910 -7.650 -6.240 -4.750 -2.923 -0.740 1.001
-9.150 -7.937 -6.822 -5.545 -4.101 -2.604 -0.996 0.617 2.238
T ) 348.15 K -7.118 -5.760 -4.410 -3.100 -1.760 -0.446 0.822 2.076 3.320
-3.592 -2.185 -0.856 0.358 1.534 2.625 3.650 4.643 5.592
-0.489 0.833 2.032 3.130 4.143 5.079 5.951 6.763 7.536
2.537 3.681 4.720 5.653 6.515 7.296 8.022 8.698 9.332
0.24 5 10 15 20 25 30 35 40
-19.601 -17.702 -16.001 -13.903 -11.304 -9.000 -6.694 -4.201 -1.801
-17.215 -15.374 -13.386 -11.281 -9.171 -6.982 -4.824 -2.687 -0.800
T ) 373.15 K -14.779 -12.571 -10.441 -8.405 -6.504 -4.661 -2.924 -1.252 0.391
-10.684 -8.504 -6.470 -4.632 -2.958 -1.415 0.024 1.367 2.637
-7.032 -4.974 -3.108 -1.440 0.039 1.379 2.608 3.735 4.791
-3.107 -1.323 0.284 1.706 2.962 4.090 5.116 6.054 6.921
0.52 5 10 15 20 25 30 35 40
-32.002 -28.402 -25.003 -22.301 -19.101 -16.004 -13.005 -9.701 -7.202
-28.643 -25.100 -22.002 -18.926 -15.897 -12.850 -10.300 -7.700 -5.500
T ) 398.15 K -25.277 -21.874 -18.517 -15.538 -12.846 -10.306 -7.955 -5.772 -3.709
-20.742 -17.430 -14.284 -11.572 -9.176 -7.015 -5.064 -3.258 -1.599
-16.802 -13.605 -10.620 -8.088 -5.906 -3.968 -2.242 -0.677 0.741
-11.887 -9.077 -6.462 -4.262 -2.373 -0.705 0.766 2.086 3.284
pressures up to p ) 40 MPa, are reported. The experiments were carried out at m ) (0.10487, 0.30229, 0.58732, 1.22211, 2.02242, and 2.87989) mol · kg-1 of LiCl. The obtained (p, F, T) results are listed in Table 1. Using a program for standard thermodynamic analysis to describe the (p, F, T) properties of ethanol solutions of LiCl, the equation of state (1) from ref 13 was used
p ) AF2 + BF8 + CF12
(5)
where the coefficients of eq 5, A, B, and C are functions of temperature and molalities m 2
A) B)
4
∑ ∑ aijmj Ti
i)1
j)0
1
4
i)0
j)0
∑ Ti∑ bijmj
(6)
(7)
1
C)
4
∑ T ∑ cijmj i
i)0
(8)
j)0
aij, bij, and cij are the coefficients of the polynomials, and they are given in Table 2. Equations 5 to 8 describe the experimental and interpolated results between the m ) (0 and 2.87989) mol · kg-1 molality interval with ( 0.03 % average deviation. During the molality m dependence analysis of experimental results, the (p, F, T) properties of ethanol from refs 14 to 16 were used for m ) 0. The standard, absolute, and average deviations of fitting by eqs 5 to 8 are presented in Table 3. Figures 1 to 3 show the plot of pressure of (LiCl + C2H5OH) versus density at m ) 0.58732 mol · kg-1, pressure versus density at T ) 298.15 K, and deviations of experimental density from calculated density versus pressure. The graphical analysis of the temperature dependence of the coefficients of eq 5 revealed that, at TfTc, Af0. Such behavior
396 Journal of Chemical & Engineering Data, Vol. 53, No. 2, 2008
of A ) f(T) may be explained by the fact that, according to Putilov,17 the first term on the right-hand side of eq 5, AF2, is the attractive force (attractor pressure) and the second and third terms are the repulsive force (repulsive pressure). As the temperature rises, the spacing between molecules increases, which contributes to a decrease in the attractive force. As the attractive force tends to zero (Af0), molecules under the effect of the repulsive force are capable of displacement. The extent of their displacement is defined only by the density of the substance, i.e., external pressure. As a result, the aggregate state changes. Note that the form of eq 5 was derived from Putilov’s molecular-kinetic theory. The (p, F, T) properties of these solutions can be used to derive the isothermal compressibilities k · 106/MPa-1 and thermal expansibilities R · 106/K-1. These properties were calculated from eqs 5 to 8
k ) (1/F)( ∂ p/ ∂ F)T-1
(9)
R ) (1/F)( ∂ p/ ∂ T)( ∂ p/ ∂ F)T-1
(10)
k ) 1 ⁄ (2AF2 + 8BF8 + 12CF12)
(11)
R ) (A′ + B′F + C′F )/(2A + 8BF + 12CF ) 6
10
6
10
(12)
where A′, B′, and C′ are the derivatives of A, B, and C in the following form 2
A′ )
∑ i)1
4
iTi-1
∑ j)0
4
aijmj,
B′ )
∑
4
b1jmj ,
C′ )
j)0
∑ c1jmj
Conclusion For the first time, the (p, F, T) properties and apparent molar volumes Vφ of LiCl in ethanol at T ) (298.15 to 398.15) K and pressures up to p ) 40 MPa are reported. An empirical correlation for the density of the investigated solutions with composition, pressure, and temperature has been derived. The thermal expansivity, isothermal compressibility of solutions, and apparent molar volume of LiCl in ethanol were calculated from the (p, F, T) properties at the above-mentioned state parameter intervals in the first time. The experimental (p, F, T) properties and calculated apparent molar volumes Vφ of LiCl in ethanol were compared with the few literature results, and good agreement was found. The measured volumetric results are useful for absorption refrigeration machines and heat pumps.
j)0
(13) The calculated values of the isothermal compressibilities k · 10 / MPa-1 and thermal expansibilities R · 106/K-1 are given in Table 4 and shown in Figures 4 and 5. There are two publications3,4 presenting the density results of these solutions. The experimental density results of Butler and Lees3 were measured at T ) 291.15 K, and this temperature point is outside of our temperature interval. In this case, our results were not compared with the results from ref 3. The experimental investigations of thermal properties of LiCl + C2H5OH solutions at T ) 298.04 K were carried out by Vosburgh et al.4 using a pycnometer method. The comparison of our extrapolated results to T ) 298.05 K results with the results from ref 4 showed ( 0.037 % average deviation (Figure 6). Our values are mainly higher than the results of ref 4. The apparent molar volumes Vφ of LiCl in ethanol were defined by eq 14 and are listed in Table 5 6
Vφ ) (Fe - Fs) ⁄ (mFsFe) + M ⁄ Fs
298.05 K, and ∆Vφ ) ( (0.89 cm3 · mol-1) absolute deviation was found. The five values of apparent molar volume from ref 7 were compared with our calculated values at T ) 298.15 K, and ∆Vφ ) ( 0.65 (cm3 · mol-1) absolute deviation was found. The apparent molar volume results of ref 4 at T ) 298.05 K and ref 7 at T ) 298.15 K were added to Figure 7 for visual comparison, and deviation of calculated results from refs 4 and 7 are shown in Figure 9. The nonavailability of dielectric permittivity data of ethanol in the literature at the experimental pressures and temperature intervals in this work has made it impossible to calculate the apparent molar volume of these solutions in infinite dilution and compare them with the literature results (refs 5, 6, and 8).
(14)
where Fe and Fs are densities of ethanol and the solutions, respectively; m is the molality of solution; and M is the molar mass of the dissolved LiCl. The calculations were carried out using the density results of ethanol and solution at the same temperatures and pressures. The maximum relative uncertainties18 δVφ in the Vφ determination by the investigated concentrations are δVφ ) (0.38, 0.13, 0.07, 0.03, 0.02, and 0.01) %, respectively. Figure 7 shows the plot of the apparent molar volumes Vφ of LiCl in ethanol versus m at T ) 298.15 K and various pressures together with literature results. Figure 8 gives the plot of the apparent molar volumes Vφ of LiCl in ethanol versus T at m ) 1.22211 mol · kg-1 and various pressures. The apparent molar volume results were compared with available literature values. The one value of ref 4 was compared with our extrapolated value of apparent molar volume at T )
Acknowledgment The authors thank Dipl.-Ing. Tristan Vincent for his work during the preparation of the manuscript.
Literature Cited (1) Ihmels, E. C.; Safarov, J.; Hassel, E.; Gmehling, J. (p, F, T) properties, and apparent molar volumes Vφ of ZnBr2 in methanol at T)(298.15 to 398.15) K and pressures up to p)40 MPa. J. Chem. Thermodyn. 2005, 37, 1318–1326. (2) Ihmels, E. C.; Safarov, J. (p, F, T) properties, and apparent molar volumes Vφ of ZnBr2 in CH3OH. J. Chem. Eng. Data 2006, 51, 1015– 1019. (3) Butler, J. A. V.; Lees, A. D. The Behaviour of Electrolytes in Mixed Solvents. Part III.- The Molecular Refractivities and Partial Molar Volumes of Lithium Chloride in Water-Ethyl Alcohol Solutions. Proc. Royal Soc. A 1931, 131, 382–390. (4) Vosburgh, W.; Connell, L. C.; Butler J. A. V. The Electrostriction produced by Salts in Some Aliphatic Alcohols. Part I. The Apparent Molar Volumes of Lithium Chloride in Some Aliphatic Alcohols. J. Chem. Soc. 1933, 933–942. (5) Millero, F. J. The Molal Volumes of Electrolytes. Chem. ReV. 1971, 71 (2), 147–176. (6) Kawaizumi, F.; Zana, R. Partial Molal Volumes of Ions in Organic Solvents from Ultrasonic Vibration Potentials and Density Measurements. II. Ethanol and Dimethylformamide. J. Phys. Chem. 1974, 78, 1099–1105. (7) Glugla, P. G.; Byon, J. H.; Eckert, Ch. A. Partial Molar Volume of Some Monovalent Salts and Polar Molecules in organic Solvents. J. Chem. Eng. Data 1982, 27, 393–398. (8) Marcus, Y.; Hefter, G. Standard Partial Molar Volume of Electrolytes and Ions in Nonaqueous Solvents. Chem. ReV. 2004, 104, 3406–3452. (9) Tekin, A.; Safarov, J.; Shahverdiyev, A.; Hassel, E. P. (p, F, T) properties of 1-Butyl-3-methylimidazolium tetrafluoroborate and 1-Butyl-3-methylimidazolium hexafluorophosphate at T)(298.15 to 398.15) K and pressures up to p ) 40 MPa. J. Mol. Liq. 2007, 136, 177–182. (10) Kratky, O.; Leopold, H.; Stabinger, H. H. Dichtemessungen an Flüssigkeiten und Gasen auf 10-6g/cm3 bei 0.6 cm3 Präparatvolumen. Z. Angew. Phys. 1969, 27, 273–277. (11) Majer, V.; Pádua, A. A. H. Measurement of the Thermodynamic Properties of Single Phases; Goodwin, A. R. H., Marsh, K.N., Wakeham, W.A., Eds.; Elsevier Science & Technology: NY, 2003; pp 149–168. (12) Ihmels, E. C.; Gmehling, J. Densities of Toluene, Carbon Dioxide, Carbonyl Sulfide, and Hydrogen Sulfide over a Wide Temperature
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(13)
(14) (15) (16)
and Pressure Range in the Sub- and Supercritical State. Ind. Eng. Chem. Res. 2001, 40, 4470–4477. Safarov, J. T. The investigation of the (p, F, T) and (ps, Fs, Ts) properties of {(1-x)CH3OH + xLiBr} for the application in absorption refrigeration machines and heat pumps. J. Chem. Thermodyn. 2003, 35, 1929– 1937. Dilon, H. E.; Penoncello, S. G. A Fundamental Equation for Calculation of the Thermodynamic Properties of ethanol. Int. J. Thermophys. 2004, 25 (2), 321–335. Takiguchi, Y.; Uematsu, M. PVT Measurements of Liquid Ethanol in the Temperature Range from 310 to 363 K at Pressures up to 200 MPa. Int. J. Thermophys. 1995, 16, 205–214. Takiguchi, Y.; Uematsu, M. Densities for liquid ethanol in the temperature range from 310 to 480 K at pressures up to 200 MPa. J. Chem. Thermodyn. 1996, 28, 7–16.
(17) Putilov, K. A. Thermodynamics of Simplest Liquids. IssledoVaniya po termodinamike (Thermodynamic Studies); Moscow: Nauka, 1973; p 105. (18) Safarov, J. T.; Najafov, G. N.; Shahverdiyev, A. N.; Hassel, E. (p, F, T) and (ps, Fs, Ts) properties, and apparent molar volumes Vφ of LiNO3 (aq) in the 298.15–398.15 K temperature range and pressures to p ) 60 MPa. J. Mol. Liq. 2005, 116, 157–163.
Received for review August 02, 2007. Accepted November 16, 2007. Dr. J.T. Safarov thanks the Alexander von Humboldt Foundation of Germany for the support of his research work at the Rostock University of Germany.
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