J. Chem. Eng. Data 2010, 55, 3793–3802
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The (p, G, T) Properties and Apparent Molar Volumes VO of LiBr + C2H5OH J. Safarov,*,†,‡ H. Israfilov,‡ A. Shahverdiyev,‡ and E. Hassel† Lehrstuhl fu¨r Technische Thermodynamik, Universita¨t Rostock, Albert-Einstein-Str. 2, 18059 Rostock, Germany, and Department: “Heat and Refrigeration Techniques”, Azerbaijan Technical University, H. Javid Avn. 25, AZ1073 Baku, Azerbaijan
The (p, F, T) properties and apparent molar volumes (Vφ) of LiBr in ethanol at T) (273.15 to 398.15) K and pressures up to p ) 100 MPa are reported. An empirical correlation for the density of (LiBr + C2H5OH) with pressure, temperature, and molality has been derived. The experiments were carried out at molalities m ) (0.23351, 0.59717, 0.94988, 1.46165, 2.27186, 2.83298, and 3.36783) mol · kg-1 using lithium bromide.
Introduction Absorption heat pumps perform heating of buildings or industrial installations by taking heat from a heat reservoir at low temperatures (e.g., environmental air or water) and “pumping” it via a cyclic process, with the help of an additional energy stream (often the electric power going into a fluid pump) and some additional heat flow, to a higher temperature level, where it is used as heating source. The simplest thermochemical compressor system consists of an absorber, a desorber, a solution pump, two heat exchangers, and two throttle valves. The efficiency of an absorption heat-transfer cycle is largely dependent on the physical and chemical properties of the heattransfer fluids. Similar systems with the same principal parts are used as absorption refrigerators (e.g., in hotel rooms) because they work very quietly. The most serious problems with using conventional aqueous solutions of electrolytes have been discussed in our previous publications on investigations of methanol and ethanol as nonaqueous solvents.1-4 This work is a continuation of our investigations of nonaqueous solutions for the absorption heat-transfer cycle. Applications of nonaqueous solvents as heat-transfer fluids in absorption heat transformer systems reduce these problems and can replace aqueous solutions at temperatures below the freezing point of water. Ethanol also has a freezing point below that of methanol, and this can help to increase the range over which these cycles can be used. The pressure-density-temperature (p, F, T) properties and apparent molar volumes (Vφ) of LiBr in ethanol at T ) (273.15 to 398.15) K and pressures up to p ) 100 MPa are reported. An empirical correlation for the density of LiBr + C2H5OH with pressure, temperature, and molality has been derived. In the literature analysis, we found only four studies5-8 of the thermodynamic properties of LiBr in ethanol solutions at ambient pressure: In 1975, Uemura5 investigated the specific gravity of LiBr + C2H5OH over the temperature range (278.15 to 333.15) K for mass fractions 100 w ) 5 to 40. In 1982, Glugla et al.6 studied the partial molar volume of monovalent salts and polar molecules in organic solvents. Highvolume injection and flow dilatometers were used during the experiments. The apparent molar volumes of LiBr in ethanol were measured at T ) (298.15 and 323.15) K and m ) (0.00167 * Corresponding author. Phone: +49 381 498 9415. Fax: +49 381 498 9402. E-mail:
[email protected]. † Universita¨t Rostock. ‡ Azerbaijan Technical University.
to 2.8287) mol · kg-1. The temperature bath used with this apparatus controlled the temperature fluctuations to within 0.001 K. The volume change was always less than 0.0001 mL and frequently less than 0.00005 mL. The partial molar volumes measured in solvents using this apparatus were accurate to better than ( 2 %. In 2007, Zafarani-Moattar and Shekaari7 measured the density of LiBr + ethanol solutions at T ) 298.15 K with m ) (0.0789 to 1.2642) mol · kg-1. Measurements were carried out using a commercial density measurement apparatus (Anton Paar DSA 5000 densitometer). The uncertainty of the density measurement was reported to be ( 0.003 kg · m-3. In 2004, Marcus and Hefter8 proposed values of the apparent molar volume at infinite dilution using various experimental data at ambient pressure. The apparent molar volume of LiBr in ethanol at infinite dilution at T ) 298.15 K was analyzed, and Vφ0 ) -5.2 cm3 · mol-1 was selected as the reference value. The (p, F, T) properties of these solutions are not available in the literature.
Experimental Section The (p, F, T) properties of LiBr + C2H5OH were studied using a high-pressure-high-temperature vibrating tube densiometer (DMA HPM).9-11 Density measurements were based on the dependence of the oscillation frequency of a unilaterally fixed U-tube on its mass. The vibration U-tube material (Hastelloy C-276, nickel-molybdenum-chromium-tungsten alloy) was selected with the requirements that it show good corrosion resistance and be easily fabricated. The behavior of the vibrating tube can be described by a simple mathematical-physical mass-spring-damper model,12 where the mass of the vibration tube (m) is equal to the sum of the mass of the tube in vacuum and the mass of liquid contained in it. The frequency of oscillation (f, in s-1) is given by
f(T, p) )
ω0 1 ) 2π 2π
k m0 + F(T, p)V(T, p)
(1)
where ω0 is the angular frequency (rad · s-1); k is the force constant (or spring constant) of the tube material (N · m-1), which depends on the size and shape of the tube and is proportional to the Young’s modulus of the tube material; m0 is the mass of
10.1021/je1003065 2010 American Chemical Society Published on Web 07/20/2010
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Journal of Chemical & Engineering Data, Vol. 55, No. 9, 2010
the evacuated vibration tube (kg); V(T, p) is the volume of the vibration tube (m3); and F(T, p) is the density of the liquid inside the vibration tube (kg · m-3). For a given force constant k, the sensitivity increases with increasing ratio of the mass of fluid to that of the tube, FV/m0. Measurement of the density of the liquid inside of the vibration tube can be achieved by measuring the period of vibration of the tube (τ ) 1/f), which from eq 1 is given by:
τ(T, p) ) 2π
m0 + F(T, p)V(T, p) k
(2)
The period depends on the elasticity and length of the tube. From eq 2 it is seen that the frequency of the harmonic oscillation of the vibration tube can be directly related to the density of the fluid:
F(T, p) ) A1(T, p) - B1(T, p)τ2(T, p)
(3)
where A1(T, p) ) -m0/V(T, p) and B1(T, p) ) -k/[4π2V(T, p)]. The parameters A1(T, p) and B1(T, p) do not depend on the properties of the fluid to be measured. Thus, the instrument may be calibrated by measuring the period of oscillation for at least two substances of known density as calibration samples. To check the apparatus and procedures of the measurements and the accuracy of calibration before the apparatus was used in measurements on solutions, the densities of water (distillate),13 methanol,14-16 ethanol,17-19 and NaCl(aq)20,21 at various molalities were used as reference substances for the calibration of the installation. Measurements of the frequency of the evacuated oscillating tube as a function of temperature were performed after creation of a minimal pressure of (3 to 5) Pa within the tube. Unfortunately, the parameters A1(T, p) and B1(T, p) depend strongly on temperature and pressure. Therefore, the parameters must be determined for each temperature and pressure separately, and the classical eq 3 must be extended to include additional temperature- and pressure-dependent terms. The following calibration equations containing 14 adjustable parameters were employed:22
10 mK and measured using the (ITS-90) Pt100 thermometer (type 2141) with an experimental error of ( 15 mK. Pressure was generated using a pressure intensifier (model 37-6-30, HIP, USA) and measured using a pressure transmitter (model P-10, up to 100 MPa, WIKA Alexander Wiegand GmbH & Co., Germany) with an experimental uncertainty of 0.1 % of the full scale. LiBr (w > 0.998) was obtained from Merck (Germany) and used without further purification. Before each experiment, the salt was dried for about 48 h in a special cell by heating it to 413.15 K under reduced pressure (3 to 5 Pa). Ethanol (w > 0.998) was obtained from Merck (Germany) and 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). In order to prevent subsequent absorption of water, the preparation of the salt solutions was performed in a glovebox. For the preparation of samples, flasks with LiBr and ethanol were connected to a vacuum pump using a glass adapter. Before the valves of the flasks were opened, the air in the glass adapter was evacuated. Ethanol in the top flask streamed to the bottom flask containing LiBr under vacuum. The samples were obtained by successive dilutions of the concentrated solutions. The solutions were prepared by mass weighing using an electronic scale (ED224S, Sartorius, Germany) with a resolution of 0.0001 g.
Results and Discussion In this work, the (p, F, T) properties and Vφ values of LiBr in ethanol for T ) (273.15 to 398.15) K at pressures up to p ) 100 MPa are reported. The experiments were carried out at m ) (0.23351, 0.59717, 0.94988, 1.46165, 2.27186, 2.83298, and 3.36783) mol · kg-1 LiBr. The obtained (p, F, T) results are listed in Table 1. The measured densities as a function of pressure and temperature were fitted to the following equation of state1 from ref 23:
p/MPa ) A(10-3F/kg · m-3)2 + B(10-3F/kg · m-3)8 + C(10-3F/kg · m-3)12
in which the coefficients A, B, and C are functions of temperature and molalities m: 3
3
A1(T, p) )
∑ di(T/K)
i
i)0
A)
2
+
∑ ej(p/MPa)
j
+ f(T/K)(p/MPa)
j)1
(4)
B1(T, p) )
3
2
i)0
j)1
∑ hi(T/K)i + ∑ lj(p/MPa)j + n(T/K)(p/MPa) (5)
where d0, d1, d2, d3, e1, e2, f, h0, h1, h2, h3, l1, l2, and n are parameters to be determined. The temperature in the measuring cell was controlled using a thermostat (F32-ME, Julabo, Germany) with an error of (
(6)
B)
C)
3
∑ T ∑ aijmj i
i)1
j)0
2
3
i)0
j)0
2
3
i)0
j)0
∑ Ti ∑ bijmj
(7)
∑ Ti ∑ cijmj
The values of the parameters aij, bij, and cij in eqs 6 and 7 are given in Table 2. Equations 6 and 7 describe the experimental results as well as values extrapolated to m ) 0 and interpolated between the m ) (0.23351 to 3.36783) mol · kg-1 results with an average percent deviation of ( 0.023 %, a standard deviation of 0.261 kg · m-3, and an average absolute deviation of 0.198 kg · m-3.
Journal of Chemical & Engineering Data, Vol. 55, No. 9, 2010 3795 Table 1. Experimental Values of Pressure (p), Density (G), and Temperature (T) for LiBr + C2H5OH p
F
T
p
F
T
p
F
T
MPa
kg · m-3
K
MPa
kg · m-3
K
MPa
kg · m-3
K
1.023 5.012 10.002 20.031 30.024 39.945 49.923 59.985 70.003 80.014 90.023 99.945 1.003 5.014 10.003 20.003 30.014 39.956 49.985 59.924 69.784 79.926 89.954 99.986 1.204 5.002 10.064 20.004 29.124 39.784 49.956 59.942 69.784 79.924 89.921 99.468 2.012 5.028 10.023 19.956
821.76 824.80 828.53 835.19 841.53 847.51 853.22 858.67 863.78 868.58 873.07 877.21 805.64 809.13 812.89 820.16 827.08 833.59 839.79 845.57 850.96 856.13 860.88 865.27 801.78 805.08 808.99 816.39 822.86 830.01 836.44 842.36 847.83 853.09 857.88 862.11 789.90 792.77 796.94 804.92
273.15 273.14 273.15 273.15 273.13 273.15 273.15 273.16 273.15 273.14 273.15 273.15 293.15 293.14 293.15 293.15 293.13 293.15 293.14 293.15 293.16 293.15 293.15 293.15 298.15 298.15 298.15 298.14 298.15 298.16 298.15 298.17 298.15 298.14 298.15 298.15 313.15 313.15 313.16 313.14
29.924 40.032 50.014 60.002 70.035 80.042 89.924 99.985 2.012 5.012 10.001 20.023 29.921 39.926 49.912 59.926 70.004 79.924 89.956 99.965 1.023 5.021 10.026 19.985 29.945 39.784 50.021 60.012 69.985 79.924 89.965 99.958 1.024 5.002 10.032 19.985 29.954 39.947 49.923 59.947
m/mol · kg-1 ) 0.23351 812.49 819.73 826.45 832.74 838.62 844.05 848.99 853.58 781.53 784.23 788.63 797.12 805.03 812.55 819.58 825.76 831.80 837.48 843.04 847.91 771.66 775.49 780.15 789.05 797.44 805.21 812.76 819.01 825.32 831.20 837.01 842.17 757.55 761.71 766.83 776.82 785.62 794.15 802.07 809.42
313.15 313.16 313.14 313.15 313.16 313.15 313.15 313.15 323.15 323.13 323.14 323.15 323.16 323.15 323.14 323.15 323.16 323.15 323.15 323.15 333.14 333.16 333.15 333.14 333.16 333.17 333.15 333.15 333.15 333.13 333.15 333.15 348.15 348.15 348.14 348.15 348.13 348.15 348.16 348.15
69.845 80.004 89.926 99.957 1.023 5.002 10.021 19.985 29.974 39.986 50.031 60.014 70.025 80.004 89.945 99.987 1.235 5.004 10.024 19.985 29.954 40.001 50.023 59.987 69.957 80.004 89.956 99.874 2.451 5.024 10.023 19.974 29.928 39.941 49.931 59.978 69.953 80.014 89.921 99.624
816.09 822.02 827.80 833.35 752.56 756.87 762.65 772.17 781.57 790.37 798.55 805.45 812.93 818.76 824.73 829.93 732.64 737.23 743.18 754.93 764.93 774.75 783.79 791.31 799.09 806.27 812.23 817.91 705.58 709.80 717.61 731.71 744.10 754.26 764.05 773.47 781.36 788.79 795.82 802.67
348.17 348.15 348.15 348.15 353.15 353.15 353.15 353.14 353.15 353.15 353.16 353.15 353.17 353.15 353.13 353.15 373.15 373.15 373.14 373.15 373.16 373.15 373.17 373.15 373.13 373.14 373.15 373.15 398.15 398.15 398.15 398.16 398.14 398.15 398.15 398.17 398.15 398.16 398.15 398.15
1.306 4.686 9.917 19.964 29.993 39.918 49.994 59.884 69.990 80.091 89.993 100.098 1.504 4.938 10.061 19.905 29.993 39.912 49.993 59.817 69.979 79.675 89.926 99.971 1.141 5.221 9.947 20.192 29.993 39.830 49.963 59.998 69.931 80.151 89.963 99.874
845.06 847.38 850.91 857.46 863.70 869.58 875.26 880.54 885.63 890.43 894.84 899.04 829.09 831.68 835.46 842.47 849.31 855.69 861.83 867.48 872.97 877.88 882.72 887.12 824.73 827.89 831.46 838.95 845.75 852.23 858.53 864.41 869.87 875.11 879.79 884.17
273.18 273.18 273.18 273.17 273.17 273.17 273.16 273.16 273.16 273.17 273.17 273.18 293.17 293.17 293.15 293.16 293.15 293.15 293.15 293.14 293.14 293.14 293.15 293.16 298.09 298.15 298.18 298.16 298.15 298.15 298.15 298.13 298.15 298.15 298.15 298.15
29.958 39.844 49.963 59.831 69.997 79.828 89.993 99.841 1.026 5.021 10.023 19.945 29.978 39.926 50.001 59.974 69.923 79.954 90.021 99.745 2.100 5.223 10.112 20.295 29.996 40.191 49.994 60.159 69.994 80.063 89.993 100.035 1.002 5.412 10.035 19.902
m/mol · kg-1 ) 0.59717 834.89 841.83 848.54 854.67 860.59 865.90 870.99 875.52 803.74 807.24 811.53 819.71 827.54 834.87 841.84 848.31 854.32 859.95 865.14 869.74 796.01 798.91 803.35 812.23 820.22 828.11 835.21 841.68 847.73 854.04 859.28 864.08 781.38 785.83 790.37 799.98
313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 323.15 323.15 323.15 323.16 323.15 323.17 323.15 323.18 323.15 323.13 323.15 323.15 333.15 333.15 333.13 333.16 333.16 333.17 333.16 333.15 333.16 333.16 333.16 333.16 348.15 348.15 348.14 348.16
70.013 80.021 89.957 99.985 2.037 5.143 10.149 20.259 29.993 40.152 49.993 60.225 69.979 80.139 89.993 100.098 2.757 5.125 10.201 20.555 29.993 40.172 49.979 59.801 69.994 79.738 89.934 99.866 2.804 5.071 9.730 19.941 29.996 40.001 49.993 59.907
838.69 844.82 850.38 855.43 777.89 781.10 786.15 796.52 804.77 813.43 821.26 828.81 835.44 841.77 847.35 852.48 759.44 762.20 767.99 780.15 788.87 798.56 807.22 815.22 822.13 829.02 835.63 840.98 733.32 736.75 743.51 757.12 769.06 779.67 789.19 797.77
348.16 348.15 348.14 348.15 353.16 353.13 353.17 353.14 353.14 353.15 353.15 353.15 353.15 353.15 353.16 353.18 373.14 373.16 373.14 373.13 373.14 373.16 373.16 373.17 373.15 373.14 373.15 373.15 398.15 398.17 398.17 398.16 398.15 398.14 398.15 398.17
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Table 1 Continued p
F
T
p
F
T
p
F
T
MPa
kg · m-3
K
MPa
kg · m-3
K
MPa
kg · m-3
K
1.459 4.759 9.792 19.554
812.65 815.39 819.49 827.15
313.19 313.09 313.11 313.13
29.914 39.945 50.012 59.956
809.07 816.93 824.77 831.96
348.14 348.15 348.14 348.15
69.979 79.787 89.994 99.863
805.77 813.07 820.32 827.19
398.15 398.15 398.15 398.14
1.024 5.021 10.002 20.031 30.045 40.015 50.027 60.029 70.002 79.954 89.935 99.986 1.034 5.029 10.041 19.924 29.895 40.003 50.002 60.032 70.102 79.956 89.245 99.965 1.045 5.004 10.024 19.956 29.945 39.784 50.012 60.024 69.784 79.215 89.926 99.975 1.045 5.003 9.985 19.924
866.06 868.77 872.07 878.51 884.65 890.49 896.06 901.35 906.34 911.03 915.46 919.63 850.27 853.20 856.81 863.69 870.31 876.70 882.70 888.39 893.78 898.74 903.13 907.85 845.75 848.93 852.82 860.13 866.97 873.28 879.42 885.07 890.31 895.14 900.43 905.24 833.87 837.08 841.04 848.66
273.15 273.15 273.15 273.15 273.15 273.15 273.15 273.15 273.15 273.15 273.15 273.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 293.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 313.15 313.15 313.15 313.15
29.935 40.021 50.035 60.047 69.784 79.935 89.986 99.954 1.203 5.451 10.026 19.957 29.928 39.784 49.928 60.024 69.794 79.935 89.925 99.969 1.305 5.214 1.267 19.923 29.942 40.014 50.078 59.924 69.794 79.935 89.984 99.986 1.304 5.004 10.064 19.985 29.942 39.784 49.927 60.002
m/mol · kg-1 ) 0.94988 855.96 862.92 869.45 875.60 881.21 886.68 891.71 896.31 825.48 829.11 832.95 840.97 848.61 855.75 862.68 869.15 875.00 880.66 885.81 890.57 816.80 820.56 816.76 833.66 841.73 849.24 856.20 862.57 868.58 874.45 880.02 885.41 803.97 807.60 812.44 821.56 830.19 838.22 845.97 853.14
313.15 313.15 313.15 313.15 313.15 313.15 313.15 313.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 323.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 333.15 348.15 348.15 348.15 348.15 348.15 348.15 348.15 348.15
69.784 79.325 89.935 99.935 1.405 5.074 9.985 19.924 29.784 39.784 49.925 59.926 69.845 79.924 90.021 99.925 1.026 5.412 10.068 19.935 29.974 39.236 50.023 59.926 69.895 79.936 89.945 99.968 1.425 5.025 9.986 19.923 29.784 39.926 50.024 59.926 69.784 79.935 89.936 99.021
859.60 865.42 871.34 876.39 799.45 803.32 808.32 817.86 826.60 834.79 842.49 849.56 856.11 862.38 868.33 873.94 780.35 785.62 790.99 801.67 811.66 820.14 829.23 836.92 844.11 850.88 857.23 863.30 756.04 761.36 768.11 780.63 791.83 802.25 811.67 820.12 827.92 835.45 842.54 848.81
348.15 348.15 348.15 348.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 353.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 398.15 398.15 398.15 398.15 398.15 398.15 398.15 398.15 398.15 398.15 398.15 398.15
2.048 5.195 9.742 20.115 29.966 39.973 49.922 60.091 69.993 80.129 89.963 99.708 1.999 5.005 9.790 19.962 29.997 40.468 49.901 60.137 69.979 79.914 89.963 99.824 1.341 5.308 9.947 20.358 29.993 39.801 49.922 60.144
896.66 898.75 901.73 908.30 914.27 920.07 925.55 930.87 935.78 940.52 944.86 948.89 881.23 883.38 886.75 893.68 900.21 906.69 912.25 917.97 923.18 928.13 932.84 937.16 876.32 879.29 882.69 890.05 896.53 902.81 908.93 914.77
273.15 273.16 273.17 273.18 273.18 273.19 273.18 273.18 273.18 273.18 273.18 273.20 293.13 293.13 293.12 293.13 293.13 293.13 293.13 293.14 293.14 293.15 293.15 293.15 298.16 298.13 298.17 298.19 298.15 298.12 298.12 298.11
29.979 39.715 49.925 59.623 69.928 79.877 89.926 99.649 1.035 5.106 10.065 20.003 29.975 39.954 49.926 59.957 70.002 79.923 89.956 99.957 2.291 5.163 9.932 20.223 29.979 39.966 49.993 59.791 69.993 79.815 89.925 100.027
m/mol · kg-1 ) 1.46165 885.66 892.26 898.82 904.69 910.56 915.87 920.86 925.34 855.48 859.08 863.30 871.29 878.73 885.66 892.13 898.25 904.07 909.56 914.93 920.17 848.63 851.27 855.51 864.16 871.75 878.97 885.74 891.94 898.03 903.61 909.13 914.48
313.15 313.16 313.15 313.15 313.15 313.15 313.15 313.16 323.15 323.15 323.15 323.16 323.15 323.14 323.15 323.15 323.14 323.15 323.16 323.15 333.11 333.12 333.11 333.10 333.11 333.12 333.12 333.12 333.12 333.12 333.12 333.12
69.784 79.956 89.932 99.845 1.217 5.043 9.980 19.703 29.947 39.836 49.993 60.279 69.928 80.053 89.979 99.915 2.369 5.019 9.909 20.097 29.993 40.176 49.993 59.977 69.979 79.993 89.924 99.791 2.214 5.252 10.085 19.859
888.55 894.65 900.39 905.92 830.74 834.64 839.50 848.50 857.25 865.06 872.50 879.53 885.72 891.89 897.68 903.29 814.46 817.48 822.87 833.45 842.95 851.97 860.02 867.61 874.66 881.25 887.37 893.10 790.21 795.21 801.33 812.89
348.16 348.15 348.15 348.15 353.13 353.11 353.10 353.10 353.10 353.10 353.10 353.10 353.10 353.09 353.10 353.10 373.14 373.15 373.16 373.17 373.17 373.19 373.17 373.15 373.15 373.16 373.16 373.17 398.15 398.13 398.12 398.15
Journal of Chemical & Engineering Data, Vol. 55, No. 9, 2010 3797 Table 1 Continued p
F
T
p
F
T
p
F
T
MPa
kg · m-3
K
MPa
kg · m-3
K
MPa
kg · m-3
K
69.993 80.053 89.994 99.739 2.109 5.147 9.909 19.994
920.05 925.10 929.76 933.99 864.85 867.25 870.96 878.53
298.15 298.17 298.16 298.15 313.11 313.13 313.15 313.15
2.021 5.002 10.034 20.024 30.021 40.002 50.201 59.986
835.77 838.72 843.52 852.51 860.82 868.51 875.81 882.36
348.15 348.15 348.16 348.15 348.14 348.15 348.17 348.15
29.946 39.959 49.925 60.031 69.947 80.059 89.928 99.816
823.95 834.18 843.34 851.51 859.16 866.49 872.71 879.34
398.15 398.14 398.15 398.16 398.16 398.18 398.16 398.15
1.948 4.590 10.177 20.349 29.947 40.359 49.964 59.570 69.980 79.857 89.925 100.090 1.430 4.902 10.030 19.789 29.946 40.161 49.963 60.025 69.979 79.838 89.964 99.958 2.166 5.165 9.642 20.184 29.950 39.933 49.993 60.039 69.983 79.970 89.925 99.589 1.319 4.863 9.982 20.135
941.72 943.92 947.50 953.97 959.72 965.49 970.63 975.51 980.49 985.04 989.55 994.02 926.33 928.89 932.58 939.24 945.75 951.90 957.45 962.80 967.88 972.67 977.54 982.14 922.88 925.09 928.25 935.31 941.76 947.93 953.69 959.15 964.25 969.11 973.93 978.52 910.08 912.94 916.81 924.35
273.17 273.09 273.15 273.17 273.17 273.19 273.17 273.15 273.15 273.15 273.15 273.16 293.17 293.17 293.17 293.17 293.17 293.17 293.17 293.18 293.18 293.19 293.17 293.17 298.19 298.18 298.18 298.20 298.15 298.12 298.12 298.12 298.13 298.15 298.13 298.10 313.11 313.11 313.14 313.14
29.993 40.450 49.925 59.995 69.943 80.160 89.963 100.029 1.032 5.024 10.002 19.956 29.986 39.945 49.921 60.002 69.794 79.953 89.926 99.985 2.335 5.177 10.272 20.737 29.993 40.158 49.954 60.271 69.979 79.359 89.994 99.907 1.003 5.004 10.021 19.956 29.784 39.925 49.921 59.932
m/mol · kg-1 ) 2.27186 931.18 937.95 943.67 949.40 954.83 960.11 965.03 969.91 901.60 905.02 909.13 916.87 924.09 930.75 937.00 942.94 948.43 953.90 959.13 964.32 895.03 897.13 902.05 910.39 917.22 924.19 930.45 936.65 942.19 947.33 952.98 958.17 881.25 885.02 890.16 898.47 906.12 913.47 920.25 926.65
313.14 313.14 313.15 313.16 313.16 313.17 313.17 313.18 323.15 323.15 323.15 323.16 323.15 323.14 323.15 323.16 323.15 323.15 323.15 323.15 333.13 333.15 333.09 333.18 333.18 333.18 333.18 333.18 333.18 333.18 333.17 333.15 348.15 348.15 348.16 348.14 348.16 348.14 348.15 348.16
69.784 79.624 89.931 99.945 1.827 5.076 10.028 20.124 29.947 39.486 49.994 60.014 69.979 80.071 89.993 99.992 1.353 4.985 9.782 19.637 29.927 39.864 49.979 59.597 69.993 79.585 89.994 99.892 1.833 4.702 9.704 20.117 29.993 39.724 49.958 59.977 69.928 79.836 89.963 99.619
932.62 938.32 944.08 949.54 878.19 881.19 886.04 895.23 902.89 909.80 916.93 924.01 929.91 936.01 941.40 946.74 860.50 864.78 870.51 879.78 888.82 896.99 904.77 911.69 918.69 924.75 930.92 936.43 839.10 842.75 848.87 860.65 870.74 879.80 888.51 896.37 903.66 910.54 917.33 923.71
348.15 348.14 348.15 348.15 353.16 353.16 353.13 353.13 353.13 353.14 353.14 353.14 353.14 353.14 353.14 353.13 373.17 373.18 373.18 373.19 373.19 373.19 373.15 373.12 373.12 373.11 373.14 373.16 398.18 398.22 398.14 398.14 398.13 398.12 398.12 398.12 398.12 398.11 398.15 398.19
1.024 5.002 10.032 19.956 29.954 39.974 49.926 60.021 70.035 80.061 89.956 99.986 1.024 5.201 10.032 19.953 29.938 39.985 49.968 60.001 70.032 79.956 89.958 99.965 1.023 5.004 9.986 19.935
971.83 974.56 977.92 984.22 990.17 995.79 1001.06 1006.15 1010.98 1015.64 1020.12 1024.57 956.08 959.11 962.50 969.14 975.41 981.35 986.92 992.24 997.31 1002.13 1006.83 1011.42 951.93 954.84 958.39 965.15
273.15 273.15 273.16 273.15 273.14 273.15 273.14 273.15 273.15 273.16 273.15 273.15 293.15 293.15 293.15 293.14 293.16 293.15 293.14 293.15 293.15 293.15 293.15 293.15 298.15 298.14 298.16 298.15
29.451 40.021 49.968 59.926 69.784 80.024 89.925 99.985 1.023 5.021 9.995 19.956 29.784 39.928 50.021 59.986 69.926 79.956 89.958 99.678 1.032 5.026 9.985 19.968 29.965 40.021 49.925 59.945
m/mol · kg-1 ) 2.83298 960.70 967.43 973.38 978.99 984.26 989.48 994.32 999.09 931.78 935.15 939.18 946.78 953.72 960.39 966.58 972.34 977.81 983.13 988.29 993.25 924.49 927.90 931.98 939.71 946.88 953.59 959.77 965.67
313.15 313.17 313.15 313.14 313.15 313.16 313.15 313.15 323.15 323.15 323.15 323.14 323.15 323.16 323.15 323.15 323.14 323.15 323.15 323.15 333.15 333.14 333.15 333.16 333.15 333.14 333.15 333.16
70.024 79.926 89.954 99.968 1.302 5.015 9.986 19.927 30.024 39.945 49.965 60.014 69.784 79.968 89.925 99.895 1.415 5.002 10.004 19.957 29.956 39.984 50.002 59.924 69.784 80.021 89.926 99.845
962.07 967.67 973.13 978.42 908.32 911.75 916.20 924.60 932.51 939.73 946.54 952.95 958.82 964.64 970.10 975.38 892.25 895.82 900.66 909.82 918.40 926.44 933.93 940.87 947.33 953.61 959.33 964.74
348.15 348.16 348.15 348.15 353.15 353.15 353.14 353.15 353.16 353.15 353.14 353.15 353.16 353.15 353.14 353.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15 373.15
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Journal of Chemical & Engineering Data, Vol. 55, No. 9, 2010
Table 1 Continued p
F
T
p
F
T
p
F
T
MPa
kg · m-3
K
MPa
kg · m-3
K
MPa
kg · m-3
K
30.021 39.845 49.924 59.968 70.023 80.014 89.927 99.968 1.021 5.102 9.978 19.926
971.59 977.51 983.25 988.68 993.85 998.77 1003.47 1008.08 940.06 943.28 947.00 954.23
298.14 298.15 298.16 298.15 298.14 298.15 298.15 298.15 313.15 313.14 313.15 313.16
69.784 80.002 89.956 99.967 1.035 5.012 9.989 19.957 30.024 39.957 49.926 59.964
971.18 976.70 981.93 987.14 912.41 915.98 920.29 928.46 936.13 943.19 949.82 956.11
333.15 333.14 333.15 333.15 348.15 348.15 348.14 348.15 348.16 348.15 348.15 348.13
1.326 5.002 9.986 19.925 29.947 40.021 49.956 59.926 69.784 80.002 89.925 99.985
868.98 873.54 879.45 890.37 900.32 909.38 917.53 925.07 932.03 938.86 945.26 951.65
398.15 398.15 398.14 398.15 398.16 398.15 398.14 398.15 398.16 398.15 398.14 398.15
1.537 4.965 10.114 20.027 29.980 39.977 49.974 60.277 69.994 79.725 89.924 99.951 1.250 5.015 10.097 20.038 29.978 39.654 49.936 59.950 69.946 80.104 89.989 99.895 2.703 5.041 9.735 19.511 29.936 40.157 49.943 59.916 69.994 80.661 89.985 99.737 1.995 5.344 10.286 19.807
1000.06 1002.30 1005.60 1011.76 1017.69 1023.39 1028.82 1034.14 1038.90 1043.43 1047.90 1052.03 983.60 986.33 989.90 996.51 1002.69 1008.34 1014.01 1019.25 1024.25 1029.17 1033.84 1038.46 980.82 982.47 985.72 992.17 998.66 1004.65 1010.11 1015.42 1020.58 1025.85 1030.35 1034.98 968.15 970.84 974.66 981.61
273.15 273.18 273.17 273.16 273.16 273.16 273.17 273.18 273.18 273.18 273.17 273.17 293.16 293.15 293.14 293.15 293.15 293.16 293.15 293.13 293.14 293.15 293.15 293.15 298.18 298.18 298.18 298.18 298.18 298.18 298.18 298.20 298.17 298.13 298.13 298.12 313.17 313.17 313.17 313.17
29.957 40.159 49.914 59.836 69.925 79.843 89.986 99.603 1.032 5.014 10.058 19.957 29.926 39.984 49.957 59.924 70.002 79.926 89.924 99.956 1.618 5.051 9.894 19.918 29.946 39.652 49.993 59.593 69.927 79.861 89.946 99.575 1.002 5.024 10.032 19.956 29.985 39.978 49.952 60.024
m/mol · kg-1 ) 3.36783 988.47 994.86 1000.58 1006.06 1011.36 1016.39 1021.40 1026.10 959.14 962.48 966.55 974.07 981.06 987.61 993.67 999.37 1004.85 1010.05 1015.15 1020.21 952.85 955.66 959.51 967.06 974.09 980.47 986.85 992.46 998.21 1003.51 1008.74 1013.64 940.13 943.65 947.88 955.83 963.31 970.26 976.77 982.97
313.17 313.17 313.17 313.18 313.18 313.20 313.18 313.17 323.15 323.15 323.16 323.15 323.14 323.15 323.16 323.15 323.14 323.15 323.15 323.15 333.14 333.19 333.19 333.18 333.18 333.18 333.18 333.18 333.18 333.18 333.18 333.17 348.15 348.15 348.16 348.14 348.15 348.15 348.16 348.15
69.957 79.924 89.923 99.934 1.063 4.909 10.311 19.643 30.003 40.073 49.925 59.786 69.928 79.893 89.986 99.526 2.208 5.044 10.014 19.844 29.963 39.934 49.924 60.080 69.925 80.063 89.993 99.876 2.012 5.023 9.911 19.987 29.993 39.727 49.926 60.122 69.957 79.919 89.993 100.000
988.75 994.30 999.65 1004.87 935.92 939.35 944.02 951.68 959.64 966.87 973.50 979.72 985.74 991.32 996.68 1001.50 920.02 922.80 927.55 936.43 944.93 952.72 960.01 966.95 973.28 979.45 985.20 990.71 896.84 900.37 905.89 916.46 926.00 934.47 942.62 950.15 956.94 963.47 969.83 976.03
348.14 348.15 348.15 348.15 353.21 353.21 353.21 353.22 353.21 353.21 353.21 353.21 353.21 353.20 353.20 353.20 373.12 373.12 373.13 373.12 373.14 373.14 373.14 373.14 373.14 373.14 373.14 373.14 398.15 398.16 398.15 398.14 398.14 398.13 398.15 398.16 398.16 398.16 398.16 398.15
The short empirical equation given by eq 8 can be used for the technical calculation of the (p, F, T) properties of ethanol solutions of LiBr:
p/MPa ) [d0T + (d1 + d2m)T2 + d3T3]F2 + eT2F8 + [f0m + f1m3 + (f2 + f3m3)T + (f4m + f5m2 + f6m3)T2]F12 (8) Equation 8 describes the experimental results as well as values extrapolated to m ) 0 and interpolated between the m ) (0.23351 to 3.36783) mol · kg-1 results with an average percent deviation of ( 0.225 %, a standard deviation of 0.095 kg · m-3, and an average absolute deviation of 1.993 kg · m-3. The values of the coefficients in eq 8 are given in Table 3. For the molality-dependence analysis of the experimental results, the (p, F, T) properties of ethanol from refs 17-19 were used. Figures 1 to 3, respectively, show plots of the pressure of
Table 2. Values of the Coefficients aij, bij, and cij in Equations 6 and 7 aij a10 a11 a12 a13 a20 a21 a22 a23 a30 a31 a32 a33
) ) ) ) ) ) ) ) ) ) ) )
-2.90589 0.109313 -0.373513 · 10-2 0.844221 · 10-2 0.88116 · 10-2 -0.334263 · 10-3 0.328985 · 10-3 -0.145379 · 10-3 -0.603842 · 10-5 -0.931409 · 10-7 -0.474398 · 10-6 0.226398 · 10-6
bij b00 b01 b02 b03 b10 b11 b12 b13 b20 b21 b22 b23
) ) ) ) ) ) ) ) ) ) ) )
-854.902 -725.491 550.368 -85.1256 7.71683 3.53617 -3.1252 0.487376 -0.427719 · 10-2 -0.0102272 0.568101 · 10-2 -0.7499 · 10-3
cij c00 c01 c02 c03 c10 c11 c12 c13 c20 c21 c22 c23
) ) ) ) ) ) ) ) ) ) ) )
220.842 1345.81 -821.217 119.774 2.77871 -11.3066 5.7741 -0.786006 -0.0127063 0.0248023 -0.0108598 0.13516 · 10-2
LiBr + C2H5OH vs density at m ) 1.46165 mol · kg-1 for various temperatures, the pressure vs density at T ) 298.15 K for various molalities, and the deviation of the experimental density (Fexp) from the calculated density (Fcal) vs pressure for different temperatures and molalities,.
Journal of Chemical & Engineering Data, Vol. 55, No. 9, 2010 3799 Table 3. Values of the Coefficients di, e, and fi in Equation 8 di d0 d1 d2 d3
) ) ) )
e e ) 0.25848 · 10-2
-2.3101169 0.82076 · 10-2 -0.2343753 · 10-3 -0.703232 · 10-5
fi f0 f1 f2 f3 f4 f5 f6
) ) ) ) ) ) )
-178.144 12.0626135 3.503227 -0.04860244 -0.813238 · 10-2 0.33885335 · 10-2 -0.387565655 · 10-3
The (p, F, T) properties of these solutions were used to derive various thermal and caloric properties. The isothermal compressibility κT can be calculated from the experimental (p, F, T) results for ethanol solutions of LiBr obtained using eqs 6 and 7 as follows:
κT )
1 2AF + 8BF8 + 12CF12 2
(9)
Calculated κT values for ethanol solutions of LiBr are given in the Supporting Information, and the values for m ) 2.27186 mol · kg-1 are also shown in Figure 4. Another thermal coefficient that can be calculated from the experimental (p, F, T) results for ethanol solutions of LiBr obtained using eqs 6 and 7 is the isobaric thermal expansibility (Rp):
Rp )
A' + B'F6 + C'F10 2A + 8BF6 + 12CF10
Figure 2. Plots of experimental pressure (p) of ethanol solutions of LiBr vs density (F) at T ) 298.15 K: 0, m ) 0 (from refs 17-19); [, m ) 0.23351 mol · kg-1; 9, m ) 0.59717 mol · kg-1; 2, m ) 0.94988 mol · kg-1; b, m ) 1.46165 mol · kg-1; ], m ) 2.27186 mol · kg-1; 4, m ) 2.83298 mol · kg-1; O, m ) 3.36783 mol · kg-1. Lines were calculated using eqs 6 and 7. 3
(10)
A' )
∑
3
iTi-1
i)1
j)0
2
where A′, B′, and C′ are the temperature derivatives of A, B, and C, which are given by:
B' )
∑
3
iTi-1
i)1
∑
∑ bijmj
(11)
j)0
2
C' )
∑ aijmj
3
iTi-1
i)1
∑ cijmj j)0
Calculated values of Rp for ethanol solutions of LiBr are given in the Supporting Information, and the values for m ) 0.59717 mol · kg-1 are also shown in Figure 5. The next important parameter for the investigation is the difference in specific heat capacities, cp - cV. Measuring the heat capacity at constant volume can be prohibitively difficult for liquids. That is, small temperature changes typically require large pressures to maintain a liquid at constant volume, so the containing vessel must be nearly rigid or at least very strong. Instead, it is easier to measure the heat capacity at constant pressure. Solving for the heat capacity at constant pressure using mathematical relationships derived from basic thermodynamic laws gives:
cp ) cV + T
Figure 1. Plots of experimental at m ) 1.46165 mol · kg-1: [, 273.18 K; 9, 293.14 K; 2, 298.15; b, 313.15 K; ], 323.15 K; 0, 333.12 K; 4, 348.15 K; O; 353.10 K; *, 373.16 K; +, 398.15 K. Solid lines were calculated using eqs 6 and 7.
(∂p/∂T)F2 F2(∂p/∂F)T
(12)
where cp and cV are the heat capacities at constant pressure and volume, respectively. Using mathematical relationships for the isothermal compressibility κT and isobaric thermal expansibility Rp, we can find the following relationship:
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Journal of Chemical & Engineering Data, Vol. 55, No. 9, 2010
Figure 3. Plots of the relative deviation of the experimental density (Fexp) from the density calculated using eqs 6 and 7 (Fcal) vs pressure (p) at different temperatures and molalities.
Figure 5. Plots of thermal expansibility (Rp) of ethanol solutions of LiBr vs pressure (p) at m ) 0.59717 mol · kg-1: [, 273.16 K; 9, 293.17 K; 2, 298.15 K; b, 313.15 K; ], 323.15 K; 0, 333.16 K; 4, 348.15 K; O, 353.14 K; *, 373.16 K; ×, 398.15 K.
γ)
Rp κT
(14)
Calculated values of γ for ethanol solutions of LiBr are given in the Supporting Information. The internal pressure (pint) is related to the thermal pressure coefficient γ and defined by the following relationship:
pint ≡
( ∂U ∂V )
T
( ∂T∂p )
)T
V
- p ) Tγ - p )
TRp -p κT (15)
Calculated values of pint for LiBr + C2H5OH are given in the Supporting Information. The apparent molar volume (Vφ) is the volume that would be attributed to the LiBr in the LiBr + C2H5OH solution if one assumes that the ethanol contributes the same volume it has in its pure state. The apparent molar volume is given by Figure 4. Plots of isothermal compressibility (κT) of ethanol solutions of LiBr vs pressure (p) at m ) 2.27186 mol · kg-1: [, 273.16 K; 9, 293.17 K; 2, 298.15 K; b, 313.15 K; ], 323.15 K; 0, 333.16 K; 4, 348.15 K; O, 353.14 K; *, 373.16 K; ×, 398.15 K.
V - n1V01 Vφ ) n2
Rp2T cp - cV ) FκT
where n1 and n2 are the numbers of moles of pure ethanol and LiBr, respectively, and V10 is the molar volume of pure ethanol. In terms of the densities of LiBr + C2H5OH and pure ethanol at high temperatures and pressures, the apparent molar volume Vφ of LiBr in ethanol can be expressed as:
(13)
Calculated values of cp - cV for ethanol solutions of LiBr are given in the Supporting Information. The thermal pressure coefficient γ is calculated as the ratio of the isobaric thermal expansibility Rp to the isothermal compressibility κT at the same state parameters T and p:
Vφ )
Fe - Fs M + mFsFe Fs
(16)
(17)
where Fe and Fs are the densities of ethanol and the solution, respectively, m is the molality of the LiBr + C2H5OH solution,
Journal of Chemical & Engineering Data, Vol. 55, No. 9, 2010 3801
398.15) K and pressures up to p ) 100 MPa are reported. An empirical correlation of the density of the investigated solutions with composition, pressure, and temperature has been derived. The measured volumetric results are useful for absorption refrigeration machines and absorption heat pumps. Supporting Information Available: Calculated values of isothermal compressibility (κT), isobaric thermal expansibility (Rp), difference in isobaric and isochoric heat capacities (cp - cV), thermal pressure coefficient (γ), and internal pressure (pint) for ethanol solutions of LiBr. This material is available free of charge via the Internet at http://pubs.acs.org.
Literature Cited
Figure 6. Plots of apparent molar volume (Vφ) of LiBr in ethanol vs molality (m) at T ) 298.15 K: [, p ) 0.1 MPa; ], p ) 5 MPa; 9, p ) 10 MPa; 0, p ) 20 MPa, 2, p ) 30 MPa; 4, p ) 40 MPa; 1, p ) 50 MPa; 3, p ) 60 MPa; f, p ) 70 MPa; dotted diamonds, p ) 80 MPa; ~, p ) 90 MPa; +, p ) 100 MPa; g, p ) 0.1 MPa6, ×, p ) 0.1 MPa7.
and M is the molar mass of the dissolved LiBr. The calculations were carried out using the density results for ethanol and LiBr + C2H5OH at the same temperatures and pressures. The maximum relative uncertainty24 (δVφ) in the Vφ determination for the investigated concentrations was δVφ ) 0.94 %. Figure 6 shows plots of Vφ for LiBr in ethanol versus m at T ) 298.15 K for various pressures. The 18 density values of Zafarani-Moattar and Shekaari7 for LiBr + ethanol solutions at T ) 298.15 K and p ) 0.1 MPa with m ) (0.0789 to 1.2642) mol · kg-1 were compared with our results, and an average relative deviation of ∆F/F ) ( 0.0418 % between the two sets of values was obtained. Our results are higher than those of Zafarani-Moattar and Shekaari.7 The calculated apparent molar volume results were compared with the available literature values. Only one point from the 11 determined results of Glugla et al.6 for LiBr + ethanol solutions at T ) 298.15 K and p ) 0.1 MPa with m ) (0.00285 to 2.82870) mol · kg-1 has the molality in the range of our measured molalities (m ) 2.8287 mol · kg-1), and it has a deviation of ∆Vφ ) ( 0.282 cm3 · mol-1 from our result at the same molality. There are 12 apparent molar volume results of ZafaraniMoattar and Shekaari7 for LiBr + ethanol solutions at T ) 298.15 K and p ) 0.1 MPa with m ) (0.00285 to 2.82870) mol · kg-1 whose molalities fall in our measured molality interval [m ) (0.2348 to 1.2146) mol · kg-1], and they have an average deviation of ∆Vφ ) ( 0.267 cm3 · mol-1 with our results. Our results are higher than the results of Zafarani-Moattar and Shekaari.7 The apparent molar volume results from refs 6 and 7 at T ) 298.15 K have been added to Figure 6 along with our results to provide a visual comparison.
Conclusion For the first time, the (p, F, T) properties and apparent molar volumes Vφ of LiBr in ethanol for T ) (273.15 to
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Received for review March 29, 2010. Accepted July 1, 2010.
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