Experimental Determination and Correlation of Liquid Density Data of

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Ind. Eng. Chem. Res. 2003, 42, 2022-2029

Experimental Determination and Correlation of Liquid Density Data of Electrolyte Mixtures Containing Water or Methanol Jo1 rn Kiepe,† Anne Karine de Arau ´ jo Rodrigues,† Sven Horstmann,‡ and Ju 1 rgen Gmehling*,† Department of Industrial Chemistry, University of Oldenburg, P.O. Box 2503, D-26111 Oldenburg, Germany, and Laboratory for Thermophysical Properties (LTP GmbH), Institute at the University of Oldenburg, P.O. Box 2503, D-26111 Oldenburg, Germany

Liquid densities of several binary aqueous electrolyte mixtures and mixtures containing methanol and electrolytes were measured over a large range of concentrations and temperatures from 283 to 353 K using an oscillating-tube densitometer. From these values, molar volumes were calculated for all experimental data. A new empirical correlation method was introduced to determine densities and molar volumes using only two additional parameters, which were fitted for all ionic species investigated in this work. The experimental and calculated results are presented in comparison to results of other authors. 1. Introduction For a large number of industrial applications, e.g., in petroleum refining, the gas processing industry, coal gasification, environmental protection, gas antisolvent salt crystallization, petroleum and natural gas exploitation, formation of gas hydrates and various absorption processes, the influence of electrolytes on the phase equilibrium behavior has to be considered. A new model to predict gas solubility data in solvents containing electrolytes was proposed by Li et al.1 linking the predictive Soave-Redlich-Kwong (PSRK) group contribution equation of state (EoS)2,3 with the LIFAC method.4 In the PSRK model, the advantages of EoS are combined with the local composition concept and the group contribution approach UNIFAC. The influence of strong electrolytes on the activity coefficients of the nonelectrolytes is considered using the LIFAC model in the PSRK mixing rule. In this approach, published group interaction parameters of the PSRK and LIFAC models can be used directly, and only the gas-ion interaction parameters have to be fitted to the experimental data. In contrast to nonelectrolyte systems, only a few gas solubility data of systems containing electrolyte compounds are available in the literature. Therefore, experimental investigations were carried out with the static synthetic method.5 Because only temperature, pressure, total loadings, and total volumes are measured using this technique, the compositions of the coexisting phases have to be determined by evaluation of the raw data.6 For the evaluation procedure, reliable knowledge of the conditions in the equilibrium cell, the liquid-phase volume, and the volume of the vapor phase are required. Because of the great importance of the correct determination of the liquid volume of the electrolyte solution in the cell, liquid densities have been measured over a large concentration and temperature range (283-353 K) for several electrolyte systems. To be able to calculate the precise density for a mixture at a desired temper* To whom correspondence should be addressed. Phone: +49-(0)441-798-3831. Fax: +49-(0)441-798-3330. E-mail: [email protected]. † University of Oldenburg. ‡ Institute at the University of Oldenburg.

ature and salt concentration, a method to correlate the required density data is introduced. In this paper, experimental and calculated liquid densities and the derived molar volumes for aqueous mixtures containing LiCl, LiBr, LiNO3, NaCl, NaBr, NaNO3, Na2SO4, KCl, KBr, KNO3, and CaCl2 as well as mixtures containing methanol and LiCl, LiBr, and LiNO3 are presented and compared to the data available from other authors. 2. Experimental Section 2.1. Chemicals. Desalinated water was distilled twice. Methanol was dried over molecular sieves and then distilled. All salts used for the experiments have an indicated purity greater than 99% and were finally dried in a vacuum oven at 80 °C for 48 h. 2.2. Apparatus and Procedure. The electrolyte mixtures were prepared gravimetrically using a Sartorius analytical balance with a standard uncertainty of 0.0001 g. To ensure homogeneity, the mixtures were stirred for a sufficient time. To avoid the occurrence of disturbing bubbles in the mixture at higher temperatures and disruptive crystallization processes of the high concentrated mixtures, the mixtures were kept in a closed vessel at a higher temperature than the measurement conditions and finally injected directly in the tube via a preheated syringe. The densities of the prepared samples were measured using a vibrating-tube densitometer (model DMA 4500; Anton Paar; estimated uncertainty of 0.0001 g‚cm-3) with internal temperature control (uncertainty of 0.01 K). The densitometer was calibrated with pure water and dry air prior to experimentation. 3. Correlation In eq 1, an empirical approach is shown, which allows one to describe the temperature dependence of liquid density data at saturation conditions or at ambient pressure (for temperatures below the normal boiling point of the component) for pure substances up to the critical point using four parameters:

F0 ) A/B1+[1-(T/C)]

D

(1)

where F0 represents the salt-free liquid density. The form of the equation is similar to a modified Racket

10.1021/ie020936b CCC: $25.00 © 2003 American Chemical Society Published on Web 04/04/2003

Ind. Eng. Chem. Res., Vol. 42, No. 9, 2003 2023 Table 1. Experimental and Calculated Densities and Molar Volumes for Water T/K 283.16 298.14 313.14 323.15 333.12 343.15 353.15 mean standard deviation

Table 4. Experimental and Calculated Densities and Molar Volumes for Methanol + LiCl Mixtures

F(exp)/ g‚cm-3

F(calc)/ g‚cm-3

v(exp)/ cm3‚mol-1

v(calc)/ cm3‚mol-1

0.999 72 0.997 06 0.992 23 0.988 04 0.983 04 0.977 72 0.971 81

1.002 06 0.997 30 0.991 93 0.987 93 0.983 52 0.978 55 0.972 90 0.000 78

18.020 18.068 18.156 18.233 18.326 18.426 18.538

17.978 18.064 18.161 18.235 18.317 18.410 18.517

Table 2. Experimental and Calculated Densities and Molar Volumes for Methanol T/K 283.15 298.15 313.15 323.15 333.13 mean standard deviation

F(exp)/ g‚cm-3

F(calc)/ g‚cm-3

v(exp)/ cm3‚mol-1

v(calc)/ cm3‚mol-1

0.800 70 0.786 62 0.772 40 0.763 13 0.752 94

0.801 41 0.787 73 0.773 52 0.763 73 0.753 67 0.001 10

40.018 40.734 41.484 41.988 42.556

39.982 40.676 41.423 41.955 42.515

283.16 298.15 313.14 333.14 343.13 283.16 298.16 313.14 333.14 343.15 298.16 313.14 333.14 343.14 298.16 313.14 333.14 343.14 298.17 313.15 333.14 343.14 mean standard deviation

283.16 298.15 313.15 333.14 283.16 298.15 313.15 333.15 283.16 298.15 313.15 333.15 298.16 313.15 333.14 mean standard deviation

m/mol‚(kg of F(exp)/ solvent)-1 g‚cm-3 1.019 1.019 1.019 1.019 1.019 2.653 2.653 2.653 2.653 2.653 4.973 4.973 4.973 4.973 7.480 7.480 7.480 7.480 9.887 9.887 9.887 9.887

1.023 97 1.020 71 1.015 97 1.007 14 1.002 18 1.058 41 1.054 80 1.049 92 1.041 68 1.037 03 1.097 18 1.092 44 1.084 88 1.080 71 1.136 97 1.132 23 1.125 07 1.121 12 1.172 84 1.167 82 1.160 85 1.156 83

F(calc)/ v(exp)/ v(calc)/ g‚cm-3 cm3‚mol-1 cm3‚mol-1 1.025 95 1.021 08 1.015 59 1.006 97 1.001 89 1.060 56 1.055 51 1.049 84 1.040 93 1.035 67 1.098 71 1.092 81 1.083 52 1.078 06 1.139 99 1.133 87 1.124 24 1.118 57 1.175 79 1.169 47 1.159 54 1.153 69 0.001 29

18.023 18.080 18.164 18.324 18.414 18.071 18.133 18.218 18.362 18.444 18.246 18.326 18.453 18.525 18.391 18.468 18.586 18.651 18.503 18.582 18.694 18.759

17.988 18.074 18.171 18.327 18.420 18.035 18.121 18.219 18.375 18.468 18.221 18.320 18.476 18.570 18.342 18.441 18.599 18.694 18.456 18.556 18.715 18.810

equation,7 but in this approach all parameters (A, B, C, and D) are adjustable parameters that were fitted to a large number of experimental density data stored in the Dortmund Data Bank (DDB 2002). To extend this correlation method to mixtures containing electrolytes, the following approach is proposed in this work:

F(m) )

F0 1 - Am ln(1 + Bmm)

m/mol‚(kg of F(exp)/ solvent)-1 g‚cm-3 0.635 0.635 0.635 0.635 1.127 1.127 1.127 1.127 2.457 2.457 2.457 2.457 5.131 5.131 5.131

0.820 07 0.806 81 0.793 47 0.775 29 0.833 99 0.821 21 0.808 37 0.790 99 0.869 70 0.857 94 0.846 45 0.830 61 0.925 55 0.915 16 0.897 00

F(calc)/ v(exp)/ v(calc)/ g‚cm-3 cm3‚mol-1 cm3‚mol-1 0.821 74 0.807 71 0.793 15 0.772 79 0.836 95 0.822 66 0.807 83 0.787 07 0.876 01 0.861 06 0.845 53 0.823 80 0.931 69 0.914 89 0.891 40 0.003 40

39.324 39.970 40.642 41.595 38.853 39.457 40.084 40.965 37.711 38.228 38.747 39.486 36.199 36.610 37.351

39.244 39.925 40.658 41.730 38.715 39.388 40.111 41.169 37.440 38.090 38.789 39.812 35.960 36.620 37.585

Table 5. Experimental and Calculated Densities and Molar Volumes for Water + LiBr Mixtures T/K

Table 3. Experimental and Calculated Densities and Molar Volumes for Water + LiCl Mixtures T/K

T/K

283.16 298.15 313.15 333.15 343.12 283.15 298.15 313.15 333.15 343.14 283.15 298.15 313.15 333.15 343.14 283.15 298.15 313.16 333.15 343.15 283.15 298.15 313.15 333.15 343.14 mean standard deviation

m/mol‚(kg of F(exp)/ solvent)-1 g‚cm-3 1.015 1.015 1.015 1.015 1.015 2.943 2.943 2.943 2.943 2.943 5.002 5.002 5.002 5.002 5.002 7.447 7.447 7.447 7.447 7.447 9.967 9.967 9.967 9.967 9.967

1.061 34 1.057 83 1.052 51 1.043 33 1.038 07 1.167 75 1.163 18 1.157 05 1.147 60 1.142 40 1.269 34 1.263 58 1.257 11 1.247 25 1.241 90 1.377 78 1.370 98 1.363 98 1.353 52 1.348 05 1.478 82 1.471 10 1.463 15 1.452 34 1.446 67

F(calc)/ v(exp)/ v(calc)/ g‚cm-3 cm3‚mol-1 cm3‚mol-1 1.064 84 1.059 77 1.054 07 1.045 12 1.039 87 1.169 72 1.164 15 1.157 89 1.148 06 1.142 27 1.269 01 1.262 98 1.256 18 1.245 51 1.239 23 1.376 81 1.370 26 1.362 88 1.351 31 1.344 50 1.480 75 1.473 71 1.465 78 1.453 33 1.446 01 0.001 25

18.138 18.198 18.290 18.451 18.545 18.395 18.467 18.565 18.718 18.803 18.675 18.760 18.857 19.006 19.088 18.985 19.079 19.177 19.325 19.404 19.267 19.368 19.473 19.618 19.695

18.078 18.165 18.263 18.419 18.513 18.364 18.452 18.552 18.711 18.805 18.680 18.769 18.871 19.032 19.129 18.998 19.089 19.193 19.357 19.455 19.242 19.334 19.439 19.605 19.704

pure solvent, whereas the salt effect is represented by two temperature-independent parameters in eq 2. With this method, liquid densities can be determined at any given state and, furthermore, it is also possible to extrapolate the density data beyond the covered experimental concentration range (near saturation), which cannot be established by any polynomial term. 4. Results and Discussion

(2)

where m is the salt molality in mol‚kg-1 solvent and Am and Bm are adjustable parameters representing the influence of the electrolyte species on the density of the solvent. These parameters were fitted to the experimental data obtained in this work. The exact liquid density of the pure solvent F0 can naturally be calculated by suitable equations other than eq 1. As can be seen, the temperature effect on the density of the mixture is only considered in eq 1 based on the

The experimental density data obtained in this work as well as the calculated results and molar volumes of pure water and methanol are listed in Tables 1 and 2, whereas the experimental and calculated liquid density data and molar volumes for all electrolyte mixtures are summarized in Tables 3-16. In Figure 1, a variety of experimental liquid density data of pure methanol at saturation conditions are plotted against the temperature. At temperatures above 250 K, the calculated results derived from eq 1 are in excellent agreement with the experiments. Even the typical progression of the density close to the critical

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Ind. Eng. Chem. Res., Vol. 42, No. 9, 2003

Table 6. Experimental and Calculated Densities and Molar Volumes for Methanol + LiBr Mixtures T/K 283.15 298.15 313.15 333.15 283.16 298.15 313.15 333.15 283.15 298.14 313.14 333.14 283.15 298.14 313.13 333.13 mean standard deviation

m/mol‚(kg of F(exp)/ solvent)-1 g‚cm-3 0.546 0.546 0.546 0.546 1.075 1.075 1.075 1.075 2.488 2.488 2.488 2.488 4.496 4.496 4.496 4.496

0.835 94 0.822 36 0.808 62 0.790 40 0.867 80 0.854 47 0.840 41 0.822 47 0.945 99 0.933 31 0.920 62 0.896 12 1.044 00 1.025 22 1.004 58 0.982 00

F(calc)/ v(exp)/ v(calc)/ g‚cm-3 cm3‚mol-1 cm3‚mol-1 0.838 95 0.824 63 0.809 76 0.788 96 0.871 92 0.857 04 0.841 58 0.819 97 0.949 33 0.933 14 0.916 31 0.892 77 1.043 10 1.025 31 1.006 83 0.980 97 0.002 39

39.459 40.110 40.791 41.732 39.027 39.635 40.298 41.177 38.148 38.667 39.200 40.271 37.301 37.984 38.765 39.656

39.317 40.000 40.734 41.808 38.842 39.516 40.242 41.303 38.014 38.674 39.384 40.422 37.333 37.981 38.678 39.698

Table 7. Experimental and Calculated Densities and Molar Volumes for Water + LiNO3 Mixtures T/K 283.15 298.15 313.13 333.15 343.12 283.15 298.15 313.15 333.15 343.14 283.15 298.15 313.15 333.15 343.14 283.15 298.16 313.15 333.15 343.14 283.15 298.15 313.15 333.14 343.14 mean standard deviation


1.038 55 1.034 36 1.028 58 1.018 79 1.013 13 1.093 74 1.087 77 1.080 79 1.070 24 1.064 10 1.169 20 1.161 43 1.153 13 1.141 25 1.134 86 1.234 61 1.225 69 1.216 53 1.203 85 1.197 25 1.273 74 1.264 28 1.254 61 1.241 41 1.234 66


18.196 18.270 18.372 18.549 18.652 18.496 18.597 18.718 18.902 19.011 18.980 19.107 19.244 19.445 19.554 19.464 19.605 19.753 19.961 20.071 19.781 19.929 20.082 20.296 20.407

18.181 18.268 18.366 18.524 18.617 18.525 18.614 18.715 18.875 18.970 19.061 19.152 19.256 19.421 19.519 19.556 19.649 19.756 19.925 20.026 19.855 19.949 20.057 20.229 20.332

Table 8. Experimental and Calculated Densities and Molar Volumes for Methanol + LiNO3 Mixtures T/K 283.16 298.15 313.14 333.14 283.16 298.15 313.15 333.14 283.15 298.16 313.16 333.14 283.16 298.16 313.15 mean standard deviation

m/mol‚(kg of F(exp)/ solvent)-1 g‚cm-3 0.628 0.628 0.628 0.628 1.089 1.089 1.089 1.089 2.464 2.464 2.464 2.464 4.954 4.954 4.954

0.828 44 0.815 01 0.801 46 0.782 93 0.847 41 0.834 31 0.821 09 0.803 14 0.900 04 0.887 52 0.874 73 0.847 70 0.971 40 0.959 41 0.943 59

F(calc)/ v(exp)/ v(calc)/ g‚cm-3 cm3‚mol-1 cm3‚mol-1 0.830 52 0.816 34 0.801 63 0.781 04 0.849 93 0.835 42 0.820 36 0.799 29 0.900 75 0.885 37 0.869 39 0.847 08 0.976 12 0.959 46 0.942 16 0.002 22

39.556 40.208 40.887 41.855 39.280 39.897 40.539 41.445 38.600 39.145 39.717 40.984 38.190 38.667 39.316

39.457 40.142 40.879 41.956 39.164 39.844 40.575 41.645 38.570 39.240 39.961 41.014 38.005 38.665 39.375

point of methanol is described accurately. The parameters taken for the pure solvents can be found in Table 17, which had been fitted to the large database.

Table 9. Experimental and Calculated Densities and Molar Volumes for Water + NaCl Mixtures T/K 283.15 298.13 313.15 333.15 353.15 283.15 298.14 313.16 333.15 353.15 283.15 298.15 313.16 333.15 353.15 283.15 298.15 313.15 333.15 353.15 283.15 298.15 313.15 333.15 353.15 mean standard deviation


1.020 61 1.017 11 1.010 65 1.001 89 0.990 04 1.040 53 1.036 31 1.030 44 1.020 58 1.008 72 1.069 63 1.064 44 1.056 54 1.047 61 1.033 59 1.094 80 1.089 19 1.082 37 1.071 94 1.059 77 1.178 40 1.171 02 1.163 09 1.151 81 1.139 65


18.005 18.067 18.183 18.342 18.561 18.003 18.076 18.179 18.355 18.571 17.997 18.085 18.220 18.376 18.625 18.047 18.140 18.254 18.432 18.643 18.122 18.237 18.361 18.541 18.739

17.991 18.077 18.175 18.330 18.530 18.007 18.093 18.191 18.347 18.547 18.036 18.122 18.220 18.376 18.577 18.067 18.154 18.252 18.408 18.609 18.170 18.257 18.355 18.513 18.715

Table 10. Experimental and Calculated Densities and Molar Volumes for Water + NaBr Mixtures T/K 283.16 298.14 313.13 333.14 343.06 283.15 298.14 313.14 333.13 343.04 283.15 298.13 313.11 333.13 343.07 283.15 298.15 313.13 333.14 343.14 283.17 298.14 313.11 333.00 343.13 283.15 298.13 313.14 333.14 343.04 mean standard deviation

m/mol‚(kg of F(exp)/ solvent)-1 g‚cm-3 0.501 0.501 0.501 0.501 0.501 1.000 1.000 1.000 1.000 1.000 1.751 1.751 1.751 1.751 1.751 2.496 2.496 2.496 2.496 2.496 4.993 4.993 4.993 4.993 4.993 7.993 7.993 7.993 7.993 7.993

1.040 10 1.036 40 1.030 90 1.021 30 1.015 80 1.077 93 1.073 30 1.067 20 1.057 00 1.051 27 1.132 20 1.126 40 1.119 40 1.108 40 1.102 30 1.183 50 1.176 60 1.168 80 1.157 10 1.150 80 1.337 50 1.328 10 1.318 30 1.304 60 1.297 50 1.498 30 1.486 90 1.475 23 1.459 60 1.451 60

F(calc)/ v(exp)/ v(calc)/ g‚cm-3 cm3‚mol-1 cm3‚mol-1 1.041 48 1.036 54 1.030 97 1.022 21 1.017 10 1.078 44 1.073 31 1.067 54 1.058 48 1.053 19 1.130 85 1.125 48 1.119 44 1.109 93 1.104 36 1.179 84 1.174 23 1.167 92 1.158 00 1.152 16 1.329 81 1.323 49 1.316 39 1.305 28 1.298 62 1.493 29 1.486 20 1.478 20 1.465 64 1.458 33 0.001 58

18.051 18.115 18.212 18.383 18.483 18.106 18.184 18.288 18.464 18.565 18.204 18.298 18.412 18.595 18.698 18.308 18.415 18.538 18.726 18.828 18.707 18.839 18.979 19.179 19.283 19.154 19.301 19.454 19.662 19.770

18.027 18.113 18.211 18.367 18.459 18.097 18.184 18.282 18.438 18.531 18.226 18.313 18.411 18.569 18.663 18.365 18.452 18.552 18.711 18.806 18.815 18.905 19.007 19.169 19.267 19.218 19.310 19.415 19.581 19.679

Figure 2a shows the influence of the temperature on the density of water and some aqueous lithium salt mixtures at m ) 5 mol‚kg-1. It can be seen that the calculated values for pure water are also in good agreement with the experimental results from the literature8 and this work. Whereas eq 1 is generally able to calculate accurate densities up to the critical point, the valid temperature range for water has to be limited in order to establish a consistent basis because of the specific density behavior of water. Moreover, near the

Ind. Eng. Chem. Res., Vol. 42, No. 9, 2003 2025 Table 11. Experimental and Calculated Densities and Molar Volumes for Water + NaNO3 Mixtures T/K 283.16 298.13 313.13 333.13 343.14 283.16 298.14 313.14 333.14 343.14 283.16 298.13 313.13 333.14 343.14 283.15 298.14 313.13 333.14 343.14 283.15 298.14 313.14 333.13 343.14 283.16 298.14 313.14 333.14 343.14 283.16 298.14 313.14 333.14 343.14 mean standard deviation

m/mol‚(kg of F(exp)/ solvent)-1 g‚cm-3 0.499 0.499 0.499 0.499 0.499 0.999 0.999 0.999 0.999 0.999 1.749 1.749 1.749 1.749 1.749 2.500 2.500 2.500 2.500 2.500 4.997 4.997 4.997 4.997 4.997 7.994 7.994 7.994 7.994 7.994 9.948 9.948 9.948 9.948 9.948

1.028 29 1.024 30 1.018 54 1.008 73 1.005 94 1.055 39 1.050 28 1.043 73 1.033 21 1.030 90 1.093 30 1.086 90 1.079 36 1.067 81 1.064 47 1.128 68 1.121 25 1.112 91 1.100 54 1.095 89 1.223 18 1.220 59 1.210 48 1.199 27 1.192 10 1.324 12 1.317 25 1.306 04 1.290 59 1.282 68 1.382 00 1.370 65 1.359 02 1.347 12 1.341 00

F(calc)/ v(exp)/ v(calc)/ g‚cm-3 cm3‚mol-1 cm3‚mol-1 1.029 81 1.024 92 1.019 41 1.010 75 1.005 65 1.055 71 1.050 69 1.045 04 1.036 17 1.030 94 1.091 56 1.086 38 1.080 53 1.071 35 1.065 95 1.124 68 1.119 33 1.113 32 1.103 85 1.098 29 1.221 06 1.215 26 1.208 72 1.198 47 1.192 42 1.319 23 1.312 96 1.305 90 1.294 80 1.288 28 1.376 73 1.370 19 1.362 82 1.351 24 1.344 43 0.001 84

18.099 18.170 18.272 18.450 18.501 18.192 18.280 18.395 18.583 18.624 18.349 18.457 18.586 18.787 18.846 18.519 18.642 18.781 18.992 19.073 19.250 19.291 19.452 19.634 19.752 19.973 20.077 20.250 20.492 20.619 20.401 20.570 20.746 20.930 21.025

18.073 18.159 18.257 18.413 18.507 18.187 18.273 18.372 18.530 18.623 18.379 18.466 18.566 18.725 18.820 18.585 18.673 18.774 18.935 19.031 19.284 19.376 19.480 19.647 19.747 20.047 20.143 20.252 20.425 20.529 20.480 20.577 20.689 20.866 20.972

Table 12. Experimental and Calculated Densities and Molar Volumes for Water + NaSO4 Mixtures T/K 283.16 298.14 313.14 333.13 343.14 293.15 313.13 333.12 343.12 303.15 313.12 333.13 343.13 303.15 313.14 333.13 343.14 mean standard deviation

m/mol‚(kg of F(exp)/ solvent)-1 g‚cm-3 0.500 0.500 0.500 0.500 0.500 0.999 0.999 0.999 0.999 1.751 1.751 1.751 1.751 2.254 2.254 2.254 2.254

1.061 95 1.057 42 1.051 40 1.041 50 1.035 81 1.114 63 1.105 73 1.095 14 1.089 24 1.185 84 1.180 61 1.169 18 1.163 05 1.230 32 1.224 84 1.213 03 1.206 74

F(calc)/ v(exp)/ v(calc)/ g‚cm-3 cm3‚mol-1 cm3‚mol-1 1.061 95 1.056 90 1.051 21 1.042 29 1.037 03 1.112 82 1.105 01 1.095 64 1.090 11 1.183 37 1.179 04 1.169 03 1.163 13 1.229 76 1.225 25 1.214 86 1.208 72 0.000 81

17.814 17.890 17.992 18.163 18.263 17.765 17.908 18.081 18.179 17.797 17.876 18.050 18.146 17.848 17.927 18.102 18.196

17.814 17.899 17.996 18.150 18.242 17.794 17.920 18.073 18.165 17.834 17.899 18.053 18.144 17.856 17.921 18.075 18.166

density maximum (

Experimental Determination and Correlation of Liquid Density Data of

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