1224
J. Chem. Eng. Data 2005, 50, 1224-1233
Compressed Liquid Densities and Excess Volumes for the Binary System CO2 + N,N-Dimethylformamide (DMF) from (313 to 363) K and Pressures up to 25 MPa Abel Zu ´n ˜ iga-Moreno and Luis A. Galicia-Luna* Instituto Polite´cnico Nacional, ESIQIE, Laboratorio de Termodina´mica, Edif. Z, Secc. 6, 1er piso, UPALM Zacatenco, 07738, Lindavista, Me´xico, D.F., Me´xico
Compressed liquid densities for DMF and for CO2 (1) + DMF (2) binary mixtures are reported from (313 to 363) K and up to 25 MPa. Densities were measured for binary mixtures at nine different compositions, x1) 0.2618, 0.2876, 0.4068, 0.4268, 0.4461, 0.4502, 0.6235, 0.8091, and 0.9311. There are no experimental density data concerning CO2 + DMF mixtures reported in the literature. The estimated uncertainty is (0.20 kg‚m-3 for the experimental compressed liquid densities. Densities of DMF were correlated with the Benedict-Webb-Rubin-Starling equation of state (BWRS EoS) and the Tait equation. A fiveparameter equation was used to correlate the experimental densities of DMF and CO2 + DMF mixtures. Excess molar volumes were determined using DMF densities calculated from the BWRS EoS and CO2 densities calculated from the Span-Wagner EoS.
Introduction New applications for particle formation, materials processing, polymerizations, and these separations using supercritical fluids (SCF) have brought renewed interest to the use of this type of fluid.1 Phase equilibria and volumetric behavior of mixtures are of great importance to the development of these processes. Supercritical fluid technology strongly depends on the temperature and pressure conditions; consequently, accurate experimental phase equilibria and volumetric properties of SCF + cosolvent binary mixtures are required.2,3 The addition of a SCF to a polar liquid leads to an enhancement in the fluid properties such as the viscosity, diffusion coefficient, and density,3 and this effect is important in the antisolvent crystallization process using SCF.1 DMF has been used in materials processing in SCF media.4-6 It is used in the synthesis of pharmaceuticals, in agricultural chemistry, and as a solvent for polymers.7 DMF is a dipolar aprotic and unassociated solvent.8,9 It is miscible with almost all common polar and nonpolar solvents.9 Phase equilibria and densities of CO2 + DMF are limited in the literature. Duran-Valencia et al.10 measured vaporliquid equilibria for this system. Chang et al.11 measured solubilities of CO2 in DMF. Experimental density data were not found in the literature for this binary system. In this paper, experimental compressed liquid densities are reported for DMF and CO2 + DMF mixtures from (313 to 363) K at pressures up to 25 MPa using a vibrating tube densimeter. Densities of DMF were correlated using the BWRS EoS12 and the Tait equation.13 A simple five-parameter empirical equation14 was used to correlate the densities of DMF and CO2 + DMF mixtures at fixed compositions. Experimental Section Materials. CO2 and nitrogen were supplied by Infra Air Products Me´xico with a certified mol fraction purity of 99.995%. Aldrich supplied HPLC-grade water with a specified mol fraction purity of 99.95%. Merck supplied spec* To whom correspondence should be addressed: E-mail: lgalicial@ ipn.mx. Phone: +52 55-5729-6000, ext 55133. Fax: +52 55-5586-2728.
Figure 1. Flow diagram of the apparatus: AB, air bath; CA, cathetometer; DMA 60, period meter; DPI 145, digital indicator of pressure; EC, equilibrium cell; GC, gas compressor; LB, liquid bath; MC, measurement cell; MR, magnetic rod; PI, Isco pump; PT, pressure transducer; PTPi, platinum probe i; TD, digital indicator of temperature F250; Vi, shut-off valve i; VSE, variablespeed engine; VP, vacuum pump; VTD, vibrating tube densimeter, FV feeding valve, ST, sapphire tube, B cylindrical support, C cap, O window.
troscopy-grade DMF with a specified mol fraction purity of 99.9%. All compounds were used as received, and no further purification was performed except for a careful degassing under vacuum of water and DMF. Apparatus and Procedure. An Anton Paar DMA 60/ 512P vibrating tube densimeter (VTD) was used to determine the density. The full scale in temperature is from (263.15 to 423.15) K and in pressure is from (0 to 70) MPa. The manufacturer specifications of the resolution, repeatability, and uncertainty of the density are 1 × 10-6, 1 × 10-5, and 1 × 10-4 g‚cm-3. The VTD requires the building
10.1021/je050050p CCC: $30.25 © 2005 American Chemical Society Published on Web 05/12/2005
Journal of Chemical and Engineering Data, Vol. 50, No. 4, 2005 1225
Figure 2. Relative deviations between experimental data and those calculated with eq 5 and the BWRS EoS, with parameters fitted to data reported in this work for DMF at the following temperatures: b, 313.12 K; 1, 323.06 K; 9, 333.00 K; [, 342.86; 2, 352.80 K; b, 362.67 K. Closed and open symbols are for eq 5 and the BWRS EoS, respectively.
determinations and of the apparatus has been demonstrated in previous papers.15-17 The experimental apparatus is presented in Figure 1. The measurement circuit consists of the vibrating tube (Hastelloy C-276 U-tube) containing a sample of approximately 1 cm3. It is connected to a sapphire tube cell, which is used to feed the fluids to the VTD. The experimental procedure is detailed by Zu´n˜iga-Moreno and Galicia-Luna.16 Temperature calibrations are made using a calibration system (Automatic Systems F300S) using a 25-Ω reference probe (Rosemount, England, model 162CE; (0.005 K certified accuracy on the ITS-90 scale) and a water triplepoint cell. The uncertainty in the temperature measurements made with a platinum probe Pt 100 is estimated to be (0.03 K. The pressure measurements are made directly in the equilibrium cell by means of a 25-MPa Sedeme pressure transducer, and their estimated uncertainty is (0.008 MPa. It was calibrated at temperatures from (313 to 363) K against a dead weight balance (Desgranges & Huot, France, model 5304; accuracy (0.005% full scale). Water and nitrogen were used as the reference fluids as described in the classical method.18 The equations of state proposed by Wagner and Pruss19 and Span et al.20 were used to calculate the densities of water and of nitrogen, respectively. Calibrating procedures of the platinum temperature probes, the pressure transducer, and the VTD are described in previous papers.15,21 The estimated uncertainty of the experimental liquid densities presented in this work is (0.20 kg‚m-3. The calculation of the uncertainty of the experimental densities was made according to the next procedure. The vibration period, τ, for nitrogen, water, and DMF is recorded under the same conditions of pressure and temperature within experimental uncertainty, which means that the temperature is fixed and the vibration period is determined at each pressure for all fluids. For a VTD, the density of the studied fluid FF is given by18 2 FF ) FH2O + K(τ2F - τH ) 2O
Figure 3. Excess molar volumes of the CO2 (1) + DMF (2) binary mixtures at ∼313.15 K reported in this work: b, 10 MPa; O, 11 MPa; 9, 12 MPa; 0, 13 MPa; 2, 14 MPa; 4, 15 MPa; -, trend.
(1)
where the constant K is expressed in terms of the two reference fluids by
K)
FH2O - FN2 2 2 τH - τN 2O 2
(2)
On the basis of the propagation of uncertainties, the standard uncertainty in the density σFF is defined by N
σF2F )
Figure 4. Excess molar volumes of the CO2 (1) + DMF (2) binary mixtures at ∼20 MPa reported in this work: b, 313.15 K; O, 323.09 K; 9, 332.99 K; 0, 342.92 K; 2, 352.85 K; 4, 362.74 K; -, trend.
and setup of special peripherals. In our case, it was built to determine densities from (313 to 363 K) and pressures up to 25 MPa. Details of the apparatus and experimental procedure used in this work have been described previously.15-18 The reliability of the experimental density
( ) ∂FF
∑ ∂X i)1
2
σX2 i
(3)
i
where the Xi’s are referred to as sensitivity coefficients and σXi is the standard uncertainty associated with each Xi. Because the density is determined at a fixed temperature and pressure, it is a function only of the water density (FH2O), nitrogen density (FN2), water period (τH2O), nitrogen period (τN2), and studied fluid period (τF). Therefore, the standard uncertainty for the experimental densities is expressed by
σF2F )
( )
( )
( ) ( ) ( )
∂FF 2 2 ∂FF 2 2 ∂FF 2 2 σFH2O + σFN2 + σ + ∂FH2O ∂FN2 ∂τH2O τH2O ∂FF 2 2 ∂FF 2 2 στN2 + σ (4) ∂τN2 ∂τF τF
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Journal of Chemical and Engineering Data, Vol. 50, No. 4, 2005
Table 1. Experimental Densities of DMF at Six Temperatures T/K ) 313.12 P/MPa
F/kg‚m-3
1.008 2.010 3.012 4.008 5.004 6.002 7.002 8.004 9.000 10.004 11.004 12.004 13.005 14.007 15.002 16.012 17.009 18.015 19.010 20.013 21.009 22.011 23.019 24.013 25.011
930.41 931.09 931.73 932.38 933.04 933.68 934.32 934.97 935.62 936.27 936.89 937.51 938.14 938.78 939.37 940.00 940.59 941.19 941.79 942.42 942.99 943.58 944.17 944.75 945.35
T/K ) 323.06
T/K ) 333.00
P/MPa
F/kg‚m-3
1.014 2.007 3.026 4.006 5.016 6.010 7.006 8.010 9.012 10.014 11.011 12.013 13.007 14.011 15.008 16.014 17.004 18.006 19.006 20.005 21.002 22.013 23.015 24.008 25.012
920.89 921.59 922.27 922.95 923.62 924.30 924.99 925.64 926.32 926.99 927.65 928.31 928.97 929.62 930.29 930.92 931.54 932.19 932.82 933.44 934.07 934.70 935.31 935.92 936.53
P/MPa
F/kg‚m-3
1.008 2.018 3.006 4.005 5.005 6.008 7.003 8.009 9.010 10.008 11.008 12.008 13.013 14.006 15.007 16.011 17.019 18.010 19.004 20.012 21.005 22.005 23.014 24.009 25.009
911.34 912.08 912.78 913.51 914.23 914.97 915.68 916.39 917.11 917.81 918.51 919.20 919.90 920.57 921.24 921.92 922.59 923.27 923.91 924.58 925.24 925.88 926.52 927.19 927.83
Table 2. BWRS EOS Adjusted Parameters for DMF BWRS parameters
DMF
Tmin/K Tmax/K Pmin/MPa Pmax/MPa B0/cm3‚mol-1 A0/bar‚cm6‚mol-2 C0/bar‚K2‚cm6‚mol-2 D0/bar‚K3‚cm6‚mol-2 E0/bar‚K4‚cm6‚mol-2 b/cm6‚mol-2 a/bar‚cm9‚mol-3 d/bar‚K‚cm9‚mol-3 c/bar‚K2‚cm9‚mol-3 R/cm9‚mol-3 u/cm6‚mol-2 AAD/% bias/% SDV/% RMS/%
313.12 362.67 1.008 25.056 479.78 3.7073 × 107 -3.0291 × 1011 1.710386 × 1014 1.573066 × 1016 18 645.374 6.90669 × 107 3.38876 × 109 -1.05572 × 1014 1.13193 × 107 1571.8772 0.0075 -0.0004 0.0097 0.0090
2 2 2 τ2F - τH ∂FF 2O 2 σ ) - 2 σF2N2 2 ∂FN2 FN2 τH2O - τN 2
(6)
2 FH2O - FN2 ∂FF στ2N2 ) (2τN2)2 2 2 ∂τN2 τH2O - τN 2
()
[
2 τ2F - τN 2
2 τH 2O
2
-
2 τN 2
2 τ2F - τH 2O
2 2 τH - τN 2O 2
]
FH2O - FN2 2 ∂FF 2 2 στF ) (2τF)2 2 στ2F 2 ∂τF τH2O - τN 2
901.52 902.30 903.09 903.84 904.63 905.39 906.13 906.89 907.66 908.38 909.14 909.83 910.60 911.32 912.03 912.71 913.47 914.16 914.85 915.55 916.22 916.90 917.63 918.25 918.93
P/MPa
F/kg‚m-3
1.040 2.009 3.011 4.020 5.050 6.060 6.996 8.008 9.034 10.019 11.043 11.998 13.028 14.015 15.028 16.000 17.011 17.999 19.044 20.050 21.038 21.955 23.009 23.996 25.056
891.76 892.57 893.41 894.22 895.06 895.78 896.53 897.34 898.16 898.93 899.73 900.45 901.24 901.99 902.74 903.48 904.23 904.96 905.73 906.43 907.16 907.80 908.57 909.27 910.04
1.058 2.038 3.044 4.027 5.068 6.036 7.025 8.027 9.045 10.021 11.024 11.996 13.061 14.027 15.025 15.987 17.050 18.009 19.041 20.032 21.035 22.014 23.018 24.007 25.016
882.04 882.89 883.77 884.62 885.54 886.37 887.22 888.03 888.90 889.71 890.55 891.30 892.19 892.95 893.73 894.49 895.32 896.08 896.85 897.62 898.36 899.10 899.87 900.58 901.35
313.12 362.67 1.008 25.056 -1.03931 × 106 -2.49997 × 109 3.00581 × 108 100 1.69494 3.68341 × 10-2 1.43644 × 103 3.80646 × 10-1 0.0488 -0.0135 0.0209 0.0690
Table 4. Experimental8 and Calculated Densities of DMF 100(Fexptl - Fcalcd)
N2
2
1.028 2.020 3.015 4.002 5.035 6.026 7.013 8.017 9.024 10.012 11.048 11.999 13.018 14.029 15.007 15.994 17.041 18.012 19.006 20.042 21.025 22.008 23.079 24.008 25.017
P/MPa
DMF
(5)
2 FH2O -FN2 ∂FF στ2H2O )(-2τH2O)2 2 2 ∂τH2O τH2O -τN 2
P/MPa
T/K ) 362.67
F/kg‚m-3
Tmin/K Tmax/K Pmin/MPa Pmax/MPa C b0/MPa b1/MPa E/K AR/kg‚m-3 BR CR/K DR AAD/% bias/% SDV/% RMS/%
2 2 2 τ2F - τH ∂FF 2O σF2H2O ) 1 + 2 σF2H2O ∂FH2O τ - τ2 H2O
T/K ) 352.80
F/kg‚m-3
Table 3. Tait and Rackett Equations: Adjusted Parameters for DMF
where each term is obtained by differentiation of eq 1, resulting in the following expressions
( ) [ ] ( ) [ ] ( ) ( )[ ] ( ) ( )[ ]
T/K ) 342.86
2
στ2H2O (7) 2
στ2N2 (8)
(9)
T/K
Fexptl/kg‚m-3
Fcalcd/kg‚m-3
Fexptl
278.15 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 373.15
961.49 956.98 952.36 948.05 942.92 938.88 933.96 929.55 925.02
962.7 958.3 953.8 949.2 944.6 939.9 935.1 930.4 925.6 920.7 915.9 911.0 906.1 901.2 896.3 891.4 886.5 881.6 871.8
-0.13 -0.14 -0.15 -0.12 -0.18 -0.11 -0.12 -0.09 -0.06
Journal of Chemical and Engineering Data, Vol. 50, No. 4, 2005 1227 Table 5. Experimental Densities and Excess Molar Volumes for the CO2 (1) + DMF (2) Mixture P/MPa
3.057 4.042 4.997 5.993 7.023 8.024 8.999 10.030 11.014 12.053 12.988 14.015 15.002 16.013 16.992 18.031 19.040 19.999 21.010 22.014 23.013 24.023 25.025
F/kg‚m-3 T/K ) 313.16 946.31 947.22 948.10 948.97 949.87 950.72 951.54 952.40 953.24 954.09 954.86 955.71 956.51 957.33 958.09 958.92 959.71 960.46 961.25 962.01 962.76 963.52 964.27
VE/cm3‚mol-1
-180.10 -124.52 -90.80 -66.15 -46.62 -29.91 -12.62 -7.15 -5.75 -4.95 -4.46 -4.06 -3.75 -3.50 -3.29 -3.10 -2.94 -2.80 -2.67 -2.56 -2.45 -2.35 -2.27
P/MPa
3.091 4.015 4.980 5.955 7.001 7.997 9.038 10.044 11.007 12.038 13.004 14.021 14.999 16.028 16.993 18.010 19.004 20.020 21.005 22.035 23.013 24.055 25.019
F/kg‚m-3
VE/cm3‚mol-1
x1 ) 0.2618 T/K ) 323.10 934.49 935.38 936.31 937.21 938.19 939.10 940.05 940.96 941.80 942.72 943.54 944.43 945.30 946.18 947.00 947.83 948.68 949.52 950.32 951.15 951.94 952.80 953.55
-187.08 -133.87 -98.95 -74.65 -55.48 -41.14 -28.55 -18.14 -11.48 -8.27 -6.78 -5.82 -5.19 -4.70 -4.33 -4.01 -3.75 -3.53 -3.33 -3.16 -3.01 -2.87 -2.75
P/MPa
F/kg‚m-3
VE/cm3‚mol-1
T/K ) 333.00 923.54 924.48 925.50 926.45 927.45 928.39 929.41 930.36 931.36 932.20 933.12 934.06 934.97 935.86 936.77 937.63 938.54 939.38 940.26 941.11 941.95 942.83
-139.74 -104.54 -79.66 -62.56 -48.11 -37.08 -27.74 -20.32 -14.47 -11.13 -8.92 -7.49 -6.52 -5.83 -5.27 -4.86 -4.48 -4.20 -3.93 -3.71 -3.52 -3.34
F/kg‚m-3
VE/cm3‚mol-1
4.056 5.026 6.035 6.980 8.017 9.008 10.028 11.020 12.076 13.005 13.999 15.008 16.020 17.005 18.041 18.979 20.048 20.998 22.045 23.012 23.999 25.038
Table 6. Experimental Densities and Excess Molar Volumes for the CO2 (1) + DMF (2) Mixture P/MPa
F/kg‚m-3
VE/cm3‚mol-1
P/MPa
F/kg‚m-3
VE/cm3‚mol-1
P/MPa
x1 ) 0.2876 T/K ) 323.09
4.032 5.041 6.004 6.967 8.002 9.005 10.000 11.017 12.024 13.007 14.004 15.006 15.999 17.005 18.009 19.021 20.001 21.004 22.022 23.016 23.989 25.004
T/K ) 313.15 948.43 949.39 950.24 951.12 952.05 952.94 953.81 954.68 955.56 956.41 957.26 958.10 958.91 959.75 960.57 961.39 962.21 963.00 963.82 964.58 965.35 966.15
-137.19 -98.27 -72.36 -52.23 -33.21 -13.73 -7.89 -6.28 -5.42 -4.86 -4.43 -4.09 -3.82 -3.58 -3.38 -3.20 -3.05 -2.91 -2.79 -2.67 -2.57 -2.47
5.022 6.019 7.007 8.008 9.023 10.001 11.006 12.003 13.004 14.005 14.999 15.994 17.022 17.996 19.004 20.021 21.018 22.030 23.007 24.019 25.012
937.32 938.29 939.23 940.16 941.14 942.04 942.98 943.90 944.81 945.73 946.61 947.48 948.41 949.25 950.13 950.99 951.84 952.68 953.51 954.35 955.16
7.012 7.999 9.007 10.005 11.003 12.011 13.016 14.012 15.013 16.000 17.024 18.001 19.036 20.015 21.009 22.027 23.002 24.027 25.009
T/K ) 342.93 914.85 915.95 917.04 918.13 919.16 920.23 921.27 922.31 923.35 924.33 925.34 926.31 927.32 928.27 929.23 930.22 931.10 932.06 932.97
-74.56 -59.52 -47.40 -37.72 -29.78 -23.28 -18.22 -14.52 -11.89 -10.05 -8.68 -7.70 -6.90 -6.30 -5.80 -5.37 -5.02 -4.70 -4.43
7.031 8.016 9.024 10.027 11.011 12.022 13.022 14.004 15.013 16.013 17.044 18.012 19.015 20.024 21.004 22.030 23.027 24.021 25.022
T/K ) 352.87 902.49 903.63 904.79 905.96 907.05 908.20 909.31 910.39 911.48 912.56 913.64 914.66 915.70 916.74 917.74 918.79 919.77 920.77 921.74
where the corresponding standard deviations for the densities of reference fluids and periods are σFH2O ) 0.003%,19
T/K ) 332.99 -107.28 -80.47 -60.79 -44.98 -31.50 -20.31 -12.58 -9.13 -7.42 -6.38 -5.67 -5.14 -4.71 -4.38 -4.10 -3.85 -3.64 -3.45 -3.28 -3.13 -3.00 -80.05 -64.96 -52.85 -43.20 -35.46 -28.92 -23.65 -19.49 -16.13 -13.58 -11.58 -10.15 -8.99 -8.07 -7.34 -6.71 -6.20 -5.77 -5.39
6.007 6.998 7.991 9.021 10.024 11.006 12.020 13.024 14.028 15.010 16.010 17.003 18.005 19.008 20.007 21.004 21.990 23.037 24.000 24.996
926.13 927.15 928.18 929.22 930.23 931.19 932.19 933.16 934.12 935.07 936.01 936.96 937.87 938.78 939.69 940.60 941.48 942.42 943.28 944.13
-88.06 -68.34 -53.15 -40.53 -30.45 -22.37 -16.12 -12.12 -9.70 -8.19 -7.13 -6.37 -5.77 -5.29 -4.90 -4.58 -4.30 -4.04 -3.84 -3.64
T/K ) 362.75 8.032 9.018 9.986 10.994 12.000 13.037 14.023 15.039 16.011 17.019 18.012 19.006 20.035 20.994 22.029 23.004 24.034 25.002
891.20 892.47 893.65 894.89 896.09 897.35 898.48 899.66 900.77 901.92 903.04 904.14 905.27 906.30 907.43 908.45 909.57 910.55
-69.82 -57.84 -48.40 -40.37 -33.77 -28.18 -23.78 -20.08 -17.20 -14.80 -12.90 -11.38 -10.12 -9.15 -8.30 -7.62 -7.02 -6.53
σFN2 ) 0.02%,20 στH2O ) 5 × 10-6, στN2 ) 5 × 10-6, and στF ) 5 × 10-6. The uncertainties for the densities of water and
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Journal of Chemical and Engineering Data, Vol. 50, No. 4, 2005
Table 7. Experimental Densities and Excess Molar Volumes for the CO2 (1) + DMF (2) Mixture P/MPa F/kg‚m-3 VE/cm3‚mol-1 P/MPa F/kg‚m-3 VE/cm3‚mol-1 P/MPa F/kg‚m-3 VE/cm3‚mol-1 P/MPa F/kg‚m-3 VE/cm3‚mol-1
6.028 7.010 8.028 9.005 10.041 10.994 11.990 12.989 14.027 14.992 15.994 16.994 18.006 18.978 20.043 21.020 22.002 23.059 24.032 25.024
T/K ) 313.16 955.07 -101.34 956.12 -72.49 957.19 -46.09 958.24 -19.22 959.33 -10.80 960.30 -8.69 961.32 -7.48 962.33 -6.67 963.34 -6.04 964.31 -5.58 965.30 -5.19 966.27 -4.86 967.25 -4.58 968.19 -4.34 969.19 -4.11 970.10 -3.92 970.98 -3.74 971.98 -3.58 972.87 -3.44 973.76 -3.30
T/K ) 323.10 7.058 8.007 9.034 10.001 11.013 12.000 12.998 13.979 15.004 16.001 16.989 18.017 18.998 20.005 20.986 22.021 22.998 23.987 25.057
942.59 943.65 944.82 945.91 947.04 948.11 949.23 950.27 951.37 952.41 953.45 954.51 955.51 956.52 957.50 958.56 959.49 960.47 961.50
x1 ) 0.4068
-84.48 -63.41 -44.11 -28.48 -17.51 -12.67 -10.26 -8.82 -7.78 -7.04 -6.45 -5.96 -5.57 -5.22 -4.93 -4.66 -4.43 -4.23 -4.02
T/K ) 333.00
8.029 9.016 10.008 11.025 12.006 13.019 14.010 15.002 16.010 16.998 18.013 19.008 20.008 20.981 22.001 22.996 24.013 25.001
930.01 931.23 932.42 933.65 934.81 936.04 937.15 938.28 939.41 940.54 941.67 942.75 943.81 944.88 945.96 947.02 948.07 949.09
T/K ) 342.94
-74.16 -57.14 -43.01 -31.18 -22.63 -16.90 -13.50 -11.34 -9.84 -8.76 -7.91 -7.24 -6.69 -6.24 -5.84 -5.50 -5.19 -4.93
9.055 9.984 11.061 11.996 13.050 14.076 15.011 16.021 17.029 18.001 19.026 20.073 21.008 22.005 22.992 24.049 25.062
917.41 918.63 920.01 921.23 922.57 923.82 925.00 926.20 927.42 928.58 929.79 931.01 932.09 933.21 934.31 935.49 936.61
-66.03 -53.31 -41.24 -32.76 -25.28 -19.97 -16.54 -13.89 -12.00 -10.63 -9.51 -8.61 -7.95 -7.35 -6.85 -6.39 -6.01
Table 8. Experimental Densities and Excess Molar Volumes for the CO2 (1) + DMF (2) Mixture P/MPa
F/kg‚m-3
VE/cm3‚mol-1
6.005 7.013 8.008 9.014 10.006 11.017 12.006 13.004 13.997 15.003 16.007 17.000 17.994 19.017 19.994 20.983 22.024 23.020 24.016 24.996
T/K ) 313.15 955.61 956.75 957.90 958.99 960.05 961.14 962.22 963.25 964.28 965.36 966.35 967.35 968.36 969.38 970.35 971.33 972.32 973.26 974.20 975.14
-107.06 -75.92 -48.84 -19.92 -11.41 -9.04 -7.79 -6.94 -6.32 -5.82 -5.41 -5.07 -4.77 -4.51 -4.29 -4.09 -3.90 -3.73 -3.58 -3.45
9.047 10.045 11.042 12.037 13.020 13.997 14.981 15.991 17.002 18.025 19.044 19.999 20.984 22.002 23.042 23.981 25.047
T/K ) 342.92 916.56 917.97 919.28 920.66 921.93 923.27 924.53 925.79 927.11 928.36 929.60 930.83 931.96 933.20 934.44 935.53 936.75
-69.28 -55.03 -43.35 -33.91 -26.60 -21.22 -17.35 -14.55 -12.54 -11.03 -9.87 -9.01 -8.27 -7.64 -7.10 -6.67 -6.25
P/MPa
F/kg‚m-3
VE/cm3‚mol-1
P/MPa
x1 ) 0.4268 T/K ) 323.09 7.005 8.007 9.005 9.996 11.020 12.000 13.035 14.007 15.007 15.987 16.984 17.998 19.040 20.050 21.048 22.041 23.037 24.061 25.036
8.015 9.023 9.996 11.004 12.004 13.005 14.003 15.006 16.024 17.036 18.017 19.025 20.004 21.001 21.993 23.015 24.114 25.061
T/K ) 352.87 10.008 11.005 12.055 13.027 13.995 15.002 16.029 17.030 18.010 19.003 20.032 21.047 22.005 23.001 24.014 25.024
903.63 905.13 906.66 908.06 909.43 910.84 912.27 913.63 914.96 916.29 917.62 918.93 920.15 921.41 922.68 923.93
nitrogen correspond for the interval of temperature and pressure reported here. For example, for the density of DMF at 313.12 K and at 1.008 MPa, the vibration periods for water, nitrogen, and DMF are 0.819483, 0.778266, and 0.816933, respectively, whereas the densities of water and nitrogen obtained from the EoS19,20 are 992.62 and 10.85 kg‚m-3, respectively. With these values and using eqs 4 to 9, a standard uncertainty of (0.17 kg‚m-3 is calculated for
VE/cm3‚mol-1
T/K ) 332.98 -89.91 -66.44 -46.74 -29.89 -18.24 -13.23 -10.64 -9.16 -8.11 -7.34 -6.73 -6.22 -5.78 -5.42 -5.12 -4.84 -4.60 -4.38 -4.19
942.62 943.86 944.97 946.20 947.43 948.52 949.74 950.83 951.95 952.99 954.11 955.17 956.31 957.38 958.44 959.46 960.49 961.52 962.52
F/kg‚m-3
929.54 930.86 932.09 933.37 934.65 935.88 937.07 938.28 939.46 940.67 941.85 943.00 944.10 945.19 946.33 947.45 948.62 949.68
-77.99 -59.74 -45.18 -32.85 -23.67 -17.71 -14.10 -11.81 -10.22 -9.08 -8.23 -7.52 -6.96 -6.48 -6.07 -5.70 -5.36 -5.10
T/K ) 362.75 -63.89 -52.23 -42.19 -34.62 -28.54 -23.57 -19.69 -16.83 -14.68 -12.98 -11.59 -10.48 -9.62 -8.87 -8.22 -7.67
11.002 12.008 13.010 14.000 15.027 16.015 17.017 18.013 19.024 20.028 21.039 22.014 23.027
890.57 892.17 893.74 895.32 896.84 898.33 899.81 901.24 902.72 904.14 905.51 906.89 908.24
-59.30 -49.54 -41.51 -34.95 -29.38 -25.05 -21.51 -18.70 -16.42 -14.60 -13.11 -11.92 -10.89
the density of DMF. Similar results are obtained for all of the densities reported in this work. Loading of the Measurement Cell. The loading procedure for pure fluid and mixtures is based in that described in previous papers.15,18 The samples at fixed compositions are prepared by successive loadings18 of the pure compounds in the sapphire feeding cell with a maximum volume of 12 cm3. The amounts of the com-
Journal of Chemical and Engineering Data, Vol. 50, No. 4, 2005 1229 Table 9. Experimental Densities and Excess Molar Volumes for the CO2 (1) + DMF (2) Mixture P/MPa
6.022 6.991 8.024 9.006 9.998 10.989 12.025 13.003 13.999 14.993 16.006 17.007 17.985 19.015 20.007 20.996 22.022 22.993 23.996 24.992
F/kg‚m-3
VE/cm3‚mol-1
T/K ) 313.15 956.18 957.31 958.53 959.66 960.80 961.90 963.02 964.12 965.20 966.26 967.34 968.38 969.42 970.46 971.48 972.47 973.50 974.47 975.45 976.41
F/kg‚m-3
P/MPa
VE/cm3‚mol-1
F/Fkg‚m-3
P/MPa
x1 ) 0.4461 T/K ) 323.09
-111.22 -79.93 -50.53 -20.92 -11.91 -9.46 -8.08 -7.22 -6.56 -6.05 -5.62 -5.26 -4.96 -4.68 -4.45 -4.24 -4.05 -3.88 -3.72 -3.58
7.062 7.958 9.022 9.998 11.005 12.039 13.002 14.007 14.996 16.001 17.004 18.000 18.994 20.031 21.020 22.029 23.008 24.019 25.007
T/K ) 332.99 -92.38 -70.49 -48.47 -31.16 -19.14 -13.65 -11.14 -9.54 -8.45 -7.62 -6.98 -6.46 -6.03 -5.64 -5.32 -5.03 -4.79 -4.56 -4.36
942.94 944.11 945.39 946.60 947.83 949.09 950.23 951.42 952.54 953.67 954.83 955.98 957.05 958.19 959.24 960.34 961.38 962.44 963.48
VE/cm3‚mol-1
9.011 9.993 11.013 12.003 13.012 13.991 15.009 16.010 17.001 17.994 18.988 20.001 20.995 21.998 23.023 23.982 25.021
930.78 931.95 933.65 934.90 936.18 937.43 938.71 939.93 941.16 942.35 943.52 944.69 945.88 947.03 948.19 949.27 950.44
-62.57 -47.20 -34.19 -24.71 -18.43 -14.74 -12.30 -10.67 -9.49 -8.58 -7.85 -7.24 -6.75 -6.31 -5.93 -5.62 -5.31
Table 10. Experimental Densities and Excess Molar Volumes for the CO2 (1) + DMF (2) Mixture P/MPa F/kg‚m-3 VE/cm3‚mol-1 P/MPa F/kg‚m-3 VE/cm3‚mol-1 P/MPa F/kg‚m-3 VE/cm3‚mol-1 P/MPa F/kg‚m-3 VE/cm3‚mol-1
5.026 5.988 7.004 7.999 9.031 10.012 11.036 12.022 13.014 14.015 15.005 16.019 17.003 17.999 19.033 19.978 21.007 22.023 23.040 24.007 24.995
T/K ) 313.16 955.28 -154.22 956.32 -113.50 957.42 -80.30 958.57 -51.73 959.69 -20.61 960.79 -11.96 961.92 -9.45 963.01 -8.15 964.13 -7.26 965.19 -6.60 966.24 -6.08 967.32 -5.65 968.34 -5.29 969.40 -4.98 970.43 -4.70 971.41 -4.48 972.47 -4.26 973.48 -4.06 974.49 -3.89 975.45 -3.73 976.42 -3.59
T/K ) 323.10 7.005 8.009 9.003 10.005 11.002 12.012 13.022 14.010 15.007 16.010 17.008 18.013 19.001 19.996 21.010 22.004 22.997 23.995 25.019
x1 ) 0.4502
-94.78 -69.99 -49.29 -31.33 -19.34 -13.87 -11.19 -9.60 -8.50 -7.67 -7.02 -6.49 -6.06 -5.68 -5.35 -5.07 -4.81 -4.59 -4.37
942.87 944.10 945.32 946.57 947.78 948.99 950.22 951.35 952.52 953.67 954.76 955.90 956.99 958.07 959.20 960.27 961.32 962.39 963.43
pounds are determined with a Sartorius comparator balance (MCA1200) by mass measurements within (10-7 kg accuracy. It was periodically calibrated with a standard mass of 1 kg class E1. The estimated uncertainty for the mole fraction of the mixtures is less than (10-4. Theory. The experimental densities of DMF were correlated using three EoS’s, the 11-parameter BWRS EoS,12 2
3
(bRT - a - d/T) V3
+
R(a + d/T)
V3T2
-105.94 -82.50 -63.07 -47.37 -34.57 -24.92 -18.54 -14.77 -12.41 -10.74 -9.55 -8.62 -7.89 -7.28 -6.78 -6.33 -5.96 -5.63 -5.34
7.029 8.013 9.011 9.999 11.025 12.004 13.007 13.993 15.025 16.028 17.002 18.035 19.023 20.023 21.013 22.036 23.032 24.003 25.041
913.19 914.64 916.09 917.51 918.98 920.36 921.76 923.08 924.49 925.84 927.13 928.51 929.75 931.00 932.27 933.51 934.76 935.89 937.14
-115.71 -92.34 -73.61 -58.61 -45.86 -36.01 -28.10 -22.35 -18.09 -15.20 -13.17 -11.57 -10.38 -9.43 -8.65 -7.99 -7.44 -6.97 -6.54
equation,13 which is expressed as follows
F)
F0 (BT + P) 1 - C ln (BT + P0)
(11)
where F0 is given as a modified Rackett equation13
AR [1+(1 - T/CR)DR]
(12)
BR
P0 is a reference pressure equal to 0.1 MPa, and BT in the Tait equation is expressed as13
+
V6 c(1 + u/V2) exp(-u/V2)
928.11 929.45 930.81 932.14 933.42 934.74 936.04 937.31 938.54 939.78 941.01 942.21 943.40 944.58 945.74 946.90 948.04 949.18 950.28
T/K ) 342.94
F0 )
4
RT (B0RT - A0 - C0/T + D0/T - E0/T ) P) + V V2 +
7.019 8.001 9.015 10.013 11.006 12.004 13.021 14.019 15.001 16.014 17.013 18.021 19.006 20.021 21.001 22.027 23.019 24.013 25.015
T/K ) 333.00
(10)
where V is the molar volume and the units for the corresponding constants are shown in Table 2, and the Tait
T BT ) b0 + b1 E
(13)
where E is a constant taken to be equal to 100 as reported by Ihmels and Gmehling.13 Densities for DMF at atmospheric pressure reported in the literature8,9,22-26 were correlated to obtain constants AR, BR, CR, and DR of eq 12.
1230
Journal of Chemical and Engineering Data, Vol. 50, No. 4, 2005
Because excellent results were obtained for liquid densities of decane and CO2 + decane mixtures in a previous paper,14 a five-parameter empirical equation was used to correlate the densities of DMF and CO2 + DMF mixtures. This equation is a modification of eq 12 from the paper by Toscani and Szwarc27 and is expressed as follows
V)
c1 + c2P
(14)
c3 - (c4/T + c5/T1/3) + P
where different sets of c1, c2, c3, c4, and c5 were obtained by fitting experimental data for the different compositions of the mixtures and DMF reported in this work. The different statistical values used to evaluate the correlations are defined by the following equations:
%∆V ) 100 ADD ) bias )
SDV )
x
1
(
)
Vexptl - Vcalcd Vexptl
1 n 1 n
(15)
n
∑|%∆V |
(16)
i
i)1 n
∑(%∆V )
(17)
i
i)1 n
∑(%∆V - bias) n-1
RMS )
2
i
(18)
(%∆Vi)2
(19)
i)1
x∑ 1
n
n
i)1
The values for the different correlations are reported in Tables 2, 3, 14, and 15. Results and Discussion Compressed liquid densities of DMF at six different temperatures from (313 to 363) K and pressures up to 25 MPa are reported in Table 1. The BWRS EoS,12 the Tait equation,13 and eq 14 were used to correlate the experimental densities using the same procedure detailed in a previous paper.15 The parameters fitted to experimental densities of DMF reported in this work for the three equations and their statistical values are given in Tables 2, 3, and 14. Relative deviations 100(Vexptl - Vcalcd)/Vexptl for DMF using eq 14 and the BWRS EoS are plotted in Figure 2. Equation 14 gave similar deviations to those obtained with the multiparametric BWRS EoS. For the Tait equation, the maximum relative deviations are +0.26% and -0.12%. The deviations are larger for this equation because the correlation for the racket term was done for the interval (298.15 to 318.15) K and this introduces deviations into the extrapolation at higher temperatures in the calculation of the experimental densities. Equation 14 is extrapolated to lower temperatures to calculate the densities of DMF reported by Scherlin et al.8 The values calculated by eq 14 were compared to experimental data reported by Scherlin et al.,8 and a maximum relative deviation of -0.18 kg‚m-3 was found in density at temperatures from (283.15 to 318.15) K. These results are shown in Table 4. Densities of DMF from (323.15 to 373.15) K at atmospheric pressure calculated with eq 14 are also reported in Table 4. Because of the absence of data for making comparisons under these conditions, and consider-
Table 11. Experimental Densities and Excess Molar Volumes for the CO2 (1) + DMF (2) Mixture P/MPa
F/kg‚m-3
VE/cm3‚mol-1
8.014 9.041 10.057 10.998 11.991 12.985 14.000 14.996 16.016 16.993 18.006 18.988 20.033 21.061 22.021 22.996 24.001 25.034
T/K ) 313.13 949.79 952.04 954.25 956.28 958.34 960.34 962.36 964.28 966.23 968.02 969.86 971.70 973.47 975.25 976.88 978.52 980.14 981.79
-69.68 -26.92 -15.14 -12.04 -10.24 -9.05 -8.15 -7.47 -6.90 -6.45 -6.05 -5.72 -5.40 -5.13 -4.90 -4.70 -4.50 -4.32
10.992 12.012 13.020 14.010 15.018 16.005 17.023 18.015 19.032 20.044 21.008 21.997 23.022 24.005 25.050
T/K ) 342.89 886.15 889.74 893.05 896.16 899.25 902.14 905.02 907.74 910.42 913.05 915.46 917.87 920.31 922.57 924.92
-61.42 -47.30 -36.44 -28.59 -22.96 -19.10 -16.26 -14.21 -12.60 -11.34 -10.36 -9.53 -8.81 -8.21 -7.67
P/MPa
F/kg‚m-3
VE/cm3‚mol-1
P/MPa
x1 ) 0.6235 T/K ) 323.07 9.001 10.031 11.013 12.042 13.033 13.992 14.972 15.993 16.998 18.015 18.988 20.012 21.005 22.029 23.012 24.020 24.979
928.72 931.44 933.93 936.47 938.86 941.10 943.31 945.57 947.71 949.84 951.84 953.89 955.83 957.78 959.63 961.47 963.24
863.79 868.11 871.85 875.54 878.85 882.12 885.31 888.42 891.37 894.02 897.02 899.54 902.21 904.90
VE/cm3‚mol-1
T/K ) 332.96 -66.58 -41.17 -25.09 -17.58 -14.07 -12.00 -10.54 -9.42 -8.56 -7.87 -7.32 -6.83 -6.42 -6.05 -5.74 -5.45 -5.21
10.005 10.991 12.056 13.000 14.042 15.010 15.997 17.030 18.038 19.028 20.027 21.009 22.009 23.042 24.041 25.008
T/K ) 352.81 11.994 13.017 14.003 15.051 16.021 17.011 18.025 19.034 20.027 20.969 22.044 22.987 24.010 25.062
F/kg‚m-3
907.82 910.93 913.98 916.59 919.37 921.91 924.40 926.91 929.31 931.63 933.85 936.05 938.17 940.35 942.44 944.38
-63.63 -46.10 -32.02 -23.99 -18.63 -15.51 -13.33 -11.69 -10.47 -9.53 -8.75 -8.11 -7.56 -7.07 -6.66 -6.31
T/K ) 362.68 -59.08 -47.55 -38.65 -31.29 -26.10 -22.07 -18.94 -16.54 -14.69 -13.26 -11.95 -10.99 -10.11 -9.34
13.997 15.019 16.021 16.992 18.022 19.000 20.047 21.057 22.005 22.981 24.005 24.998
842.98 847.62 851.83 855.82 859.78 863.40 867.10 870.49 873.58 876.69 879.78 882.71
-47.09 -39.21 -32.98 -28.15 -24.07 -21.00 -18.37 -16.33 -14.76 -13.42 -12.23 -11.26
Journal of Chemical and Engineering Data, Vol. 50, No. 4, 2005 1231 Table 12. Experimental Densities and Excess Molar Volumes for the CO2 (1) + DMF (2) Mixture P/MPa
F/kg‚m-3
VE/cm3‚mol-1
9.015 9.992 11.003 12.022 13.011 14.003 15.006 16.000 16.988 18.019 18.996 20.032 21.035 21.995 23.033 24.015 25.006
T/K ) 313.14 920.03 923.92 927.79 931.54 934.99 938.37 941.63 944.75 947.80 950.82 953.63 956.51 959.25 961.81 964.52 966.98 969.42
-33.74 -17.94 -13.55 -11.24 -9.77 -8.69 -7.85 -7.18 -6.63 -6.14 -5.74 -5.37 -5.06 -4.80 -4.54 -4.32 -4.12
15.061 15.988 17.027 18.016 19.028 20.057 21.012 21.992 22.999 24.029 25.020
T/K ) 342.92 832.64 839.54 845.55 851.10 856.53 861.77 866.52 871.08 875.54 879.90 883.99
-25.50 -21.08 -17.48 -14.99 -13.06 -11.54 -10.42 -9.46 -8.64 -7.93 -7.35
P/MPa
F/kg‚m-3
VE/cm3‚mol-1
P/MPa
x1 ) 0.8091 T/K ) 323.08 11.047 12.004 13.042 14.006 15.005 16.016 16.989 18.023 18.997 20.018 21.002 22.041 22.980 23.989 25.049
13.046 14.016 15.002 16.027 17.017 18.042 19.003 20.021 21.029 22.019 23.004 24.041 24.998
T/K ) 352.86 16.031 17.002 18.047 19.050 20.005 21.045 22.052 23.029 24.015 25.051
858.28 863.75 869.06 874.28 879.06 883.74 887.97 892.23 896.31 900.16 903.83 907.60 910.97
-27.18 -20.90 -16.88 -14.10 -12.18 -10.68 -9.59 -8.65 -7.89 -7.26 -6.73 -6.25 -5.86
T/K ) 362.79 -28.94 -24.09 -20.18 -17.34 -15.24 -13.40 -11.99 -10.86 -9.90 -9.05
799.40 806.61 814.20 820.88 827.13 833.27 839.08 844.25 849.31 854.32
VE/cm3‚mol-1
T/K ) 332.97 -29.27 -20.32 -15.60 -12.99 -11.15 -9.79 -8.78 -7.92 -7.26 -6.67 -6.19 -5.75 -5.41 -5.08 -4.77
888.99 893.47 898.20 902.33 906.31 910.13 913.66 917.28 920.57 923.89 927.01 930.23 933.13 936.00 939.12
F/kg‚m-3
18.033 19.005 20.003 21.014 22.017 23.043 24.052 25.083
777.33 784.90 792.49 799.75 806.50 813.10 819.28 825.05
-26.19 -22.51 -19.53 -17.11 -15.18 -13.56 -12.25 -11.12
Table 13. Experimental Densities and Excess Molar Volumes for the CO2 (1) + DMF (2) Mixture P/MPa
F/kg‚m-3
VE/cm3‚mol-1
10.006 11.013 12.041 13.017 14.036 15.031 16.006 17.030 17.988 19.037 20.022 21.000 22.002 23.016 24.006 25.020
T/K ) 313.14 835.47 846.13 855.75 864.01 871.87 878.95 885.43 891.82 897.48 903.28 908.47 913.41 918.23 922.92 927.35 931.70
-15.44 -10.89 -8.60 -7.23 -6.23 -5.50 -4.93 -4.46 -4.09 -3.75 -3.47 -3.24 -3.03 -2.84 -2.68 -2.53
15.034 16.002 17.015 18.024 19.002 20.000 21.034 22.002 23.014 24.017 25.008
T/K ) 342.92 711.76 729.81 745.62 759.30 770.95 781.74 791.87 800.53 809.02 816.82 824.06
-21.30 -16.99 -13.83 -11.58 -9.95 -8.68 -7.64 -6.85 -6.18 -5.62 -5.16
P/MPa
F/kg‚m-3
VE/cm3‚mol-1
P/MPa
x1 ) 0.9311 T/K ) 323.09 12.017 13.010 14.016 15.005 16.036 17.025 18.021 19.034 20.010 21.029 22.009 23.050 23.995 25.056
13.019 14.011 15.009 16.030 17.017 18.002 19.031 20.025 21.030 21.994 22.998 24.024 25.011
T/K ) 352.86 17.024 18.005 19.028 20.001 21.006 22.024 23.012 23.999 25.019
684.50 702.67 718.94 732.41 744.94 756.39 766.47 775.83 784.81
ing the relative deviations obtained at lower temperatures between experimental and calculated densities, similar behavior can be expected at temperatures higher than 318.15 K; however, this statement must be probed in the future. Compressed liquid densities and excess molar volumes for the CO2 + DMF mixtures from (313 to 363) K and
VE/cm3‚mol-1
T/K ) 332.98 -17.58 -12.94 -10.27 -8.56 -7.31 -6.42 -5.72 -5.14 -4.69 -4.29 -3.97 -3.67 -3.44 -3.20
797.65 810.33 821.48 831.25 840.41 848.46 855.96 863.06 869.50 875.82 881.60 887.36 892.39 897.78
F/kg‚m-3
744.38 761.83 776.41 789.22 800.11 809.93 819.29 827.57 835.37 842.35 849.15 855.75 861.78
-24.22 -17.75 -13.81 -11.20 -9.45 -8.16 -7.14 -6.36 -5.72 -5.22 -4.77 -4.39 -4.07
T/K ) 362.73 -18.89 -15.79 -13.33 -11.51 -10.04 -8.85 -7.91 -7.14 -6.47
18.005 19.024 20.021 21.028 22.008 23.017 24.029 25.019
641.86 662.81 680.44 696.02 709.54 722.12 733.65 744.01
-19.62 -16.72 -14.42 -12.55 -11.06 -9.81 -8.77 -7.92
pressures up to 25 MPa are presented in Tables 5 to 13 for nine different compositions. The parameters obtained by correlating the densities of DMF and CO2 + DMF mixtures using eq 14 are reported in Tables 14 and 15. The error in the correlation of the densities increases as the composition of CO2 in the mixture is increased. This behavior is similar to previous results.14
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Journal of Chemical and Engineering Data, Vol. 50, No. 4, 2005
Table 14. Parameters for Equation 14 for Data Reported in This Work Tmin/K Tmax/K Pmin/MPa Pmax/MPa Fmin/kg‚m-3 Fmax/kg‚m-3 data points c1/MPa‚kg-1‚m3 c2/kg-1‚m3 c3/MPa c4/K‚MPa c5/MPa‚K1/3 AAD/% bias/% SDV/% RMS/%
DMF
x1 ) 0.2618
x1 ) 0.2876
x1 ) 0.4068
x1 ) 0.4268
313.12 362.67 1.008 25.056 882.04 945.35 150 0.221338 9.124 × 10-4 -346.628 55 160.410 -4947.3870 0.0060 -1.01 × 10-6 8.42 × 10-5 0.0072
313.16 333.00 3.057 25.038 923.54 964.27 68 0.175480 8.863 × 10-4 -362.533 51 477.690 -4702.5200 0.0017 -5.90 × 10-7 6.16 × 10-6 0.0020
313.15 362.75 4.032 25.023 891.20 966.15 119 0.154355 8.979 × 10-4 -392.245 56 064.700 -4869.4760 0.0031 -4.75 × 10-7 3.56 × 10-5 0.0040
313.16 342.94 6.028 25.062 917.41 973.76 74 0.133045 8.874 × 10-4 -391.225 53 106.570 -4664.9520 0.0025 -6.57 × 10-7 1.86 × 10-5 0.0032
313.15 362.75 6.005 25.061 890.57 975.14 103 0.119142 8.951 × 10-4 -374.858 50 200.510 -4401.3990 0.0072 -1.65 × 10-6 1.28 × 10-4 0.0089
Table 15. Parameters for Equation 14 for Data Reported in This Work Tmin/K Tmax/K Pmin/MPa Pmax/MPa Fmin/kg‚m-3 Fmax/kg‚m-3 data points c1/MPa‚kg-1‚m3 c2/kg-1‚m3 c3/MPa c4/K‚MPa c5/MPa‚K1/3 AAD/% bias/% SDV/% RMS/%
x1 ) 0.4461
x1 ) 0.4502
x1 ) 0.6235
x1 ) 0.8091
x1 ) 0.9311
313.15 332.99 6.022 25.021 930.78 976.41 56 0.122905 8.842 × 10-4 -414.835 55 812.220 -4819.0100 0.0036 -5.83 × 10-7 1.01 × 10-4 0.0053
313.16 342.94 5.026 25.041 913.19 976.42 78 0.120817 8.874 × 10-4 -381.527 50 435.770 -4462.8840 0.0048 -8.50 × 10-7 1.18 × 10-4 0.0065
313.13 362.68 8.014 25.062 842.98 981.79 92 0.039001 9.318 × 10-4 -496.566 68 193.660 -5095.9140 0.0504 -8.51 × 10-5 8.73 × 10-3 0.0652
313.14 362.79 9.016 25.083 777.73 969.42 74 0.015331 9.601 × 10-4 -344.162 40 359.730 -3300.7560 0.1004 -2.66 × 10-4 1.97 × 10-2 0.1151
313.14 362.73 10.006 25.056 641.86 931.70 71 0.000841 1.003 × 10-3 -481.550 64 015.330 -4651.6070 0.1853 -1.21 × 10-3 1.17 × 10-1 0.2465
Because experimental measurement densities of DMF and its mixtures with CO2 were obtained, the excess volumes were calculated according to the relation
VE )
x 1W1 + x 2W2 Fmix
- (x1V1 + x2V2)
(20)
where VE is the excess molar volume, Fmix is the density of the mixture, V1 and V2 are the pure component molar volumes at the measured temperature and pressure of the mixture, W1 and W2 are the molecular weighs of CO2 and DMF, respectively, and x1 and x2 are the mole fractions of CO2 and DMF, respectively. V1 is calculated using the Span and Wagner EoS,28 and V2 is calculated using the BWRS EoS12 with the parameters given in Table 2. As shown in Figure 3, excess molar volumes become less negative as pressure increases at constant temperature. Besides, these volumes become more negative as temperature increases at constant pressure, as can be observed in Figure 4. In both cases, the minimum values of the excess volumes are found at higher CO2 concentrations, and these behaviors apply to all isobaric and isothermal data reported here. Conclusions New compressed liquid densities of DMF and CO2 + DMF binary mixtures at temperatures from (313 to 363) K and pressures up to 25 MPa at nine different compositions are reported. The BWRS EoS was used to correlate the experimental densities of DMF, giving a standard deviation equal to 0.0097%, whereas the Tait equation gave a standard deviation equal to 0.0209%. It was found that the Tait equation requires densities at atmospheric pres-
sure at the same interval of temperature of the highpressure densities in order to obtain the parameters of the Rackett term. A simple five-parameter equation was tested successfully to represent the densities of the systems reported in this work; this equation has the advantage of representing the compressed liquid region with half the number of parameters as the BWRS EoS with the same accuracy. Because eq 14 is explicit in volume, its implementation for industrial applications does not require great programming effort and computer time. This equation is also capable of extrapolating densities at atmospheric conditions and does not required data at some reference condition as the Tait equation does. The propagation of uncertainties was presented for the determination of densities using a VTD with the classical method of calibration. The calculated excess molar volumes have a negative trend for all of these systems under the reported experimental conditions. Acknowledgment Special thanks are given to Professor W. Wagner from Ruhr-Universitat Bochum, Germany, for providing us with his computer source code to calculate the densities of nitrogen and water. Note Added after ASAP Publication. This article was released ASAP on 5/12/05. Changes were made to eq 8, the text following eq 13, and ref 2. The article was reposted on 5/16/05. Literature Cited (1) Bungert, B.; Sadowski, G.; Arlt, W. Separations and Material Processing in Solutions with Dense Gases. Ind. Eng. Chem. Res. 1998, 37, 3208-3220.
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(17)
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Received for review January 29, 2005. Accepted April 11, 2005. We thank CONACYT and IPN for their financial support.
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