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Question 11.1.2: Prediction of the Solubility of a Gas in a Liquid Using an E...

Prediction of the Solubility of a Gas in a Liquid Using an EOS

Predict the solubility of carbon dioxide in toluene at 25°C and 1.013 bar carbon dioxide partial pressure using the Peng-Robinson equation of state.

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The critical properties for both carbon dioxide and toluene are given in Table 6.6-1. The binary interaction parameter for the CO _{2}-toluene mixture is not given in Table 9.4-1. However, as the value for CO _{2}-benzene is 0.077 and that for CO _{2}–n-heptane is 0.10, we estimate that the CO _{2}-toluene interaction parameter will be 0.09. Using this value and the bubble point pressure calculation in either the programs or the MATHCAD worksheet for the Peng-Robinson equation of state for mixtures (described in Appendix B and on the website this book), the following values were obtained:

 

x _{ CO _{2}} P_{\text {tot }}(\text { bar }) y_{ CO _{2}} P_{ CO _{2}}(\text { bar })=y_{ CO _{2}} P_{\text {tot }}
0.001 0.11 0.6579 0.072
0.002 0.20 0.7915 0.158
0.004 0.36 0.8834 0.318
0.006 0.51 0.9189 0.469
0.008 0.67 0.9378 0.628
0.010 0.83 0.9495 0.788
0.0125 1.03 0.9590 0.988
0.013 1.07 0.9605 1.028
0.015 1.23 0.9655 1.188

 

Therefore, using the Peng-Robinson equation of state, we estimate that at a partial pressure of 1.013 bar, carbon dioxide will be soluble in liquid toluene to the extent of 0.0128 mole fraction. This value differs from the value of 0.0077 computed in the last illustration using the Prausnitz- Shair correlation and regular solution theory. However, given the inaccuracy of both methods, this difference is not unreasonable.

Comment

Had we assumed that the CO _{2}-toluene binary interaction parameter was zero, the predicted CO _{2} solubility in toluene at 1.013 bar CO _{2} partial pressure would be 0.0221 mole fraction (Problem 11.1-6).

In order to compare the results with those of the previous illustration, we can also compute the solubility of carbon dioxide in carbon disulfide. There is no binary interaction parameter reported for the CO _{2}- CS _{2} mixture, or for any similar mixtures. If we assume the binary interaction parameter is zero, we find that the CO _{2} \text { solubility in } CS _{2} \text { at } 1.013 \text { bar } CO _{2} partial pressure is 0.0159 mole fraction, which is greater than the measured value by a factor of 5 (Problem 11.1-7). However, if we set k_{ CO _{2}- CS _{2}}=0.2 \text {, we obtain a } CO _{2} \text { solubility of } 3.4 \times 10^{-3}, which is in excellent agreement with experiment.

 

Table 6.6-1 The Critical and Other Constants for Selected Fluids
Substance Symbol Molecular Weight \left( g mol ^{-1}\right) T_{c}( K ) P_{c}( MPa ) V_{c}\left( m ^{3} / kmol \right) Z_{c} ω T_{\text {boil }}( K )
Acetylene C _{2} H _{2} 26.038 308.3 6.14 0.113 0.271 0.184 189.2
Ammonia NH _{3} 17.031 405.6 11.28 0.0724 0.242 0.25 239.7
Argon Ar 39.948 150.8 4.874 0.0749 0.291 -0.004 87.3
Benzene C _{6} H _{6} 78.114 562.1 4.894 0.259 0.271 0.212 353.3
n-Butane C _{4} H _{10} 58.124 425.2 3.8 0.255 0.274 0.193 272.7
Isobutane C _{4} H _{10} 58.124 408.1 3.648 0.263 0.283 0.176 261.3
1-Butene C _{4} H _{8} 56.108 419.6 4.023 0.24 0.277 0.187 266.9
Carbon dioxide CO _{2} 44.01 304.2 7.376 0.094 0.274 0.225 194.7
Carbon monoxide CO 28.01 132.9 3.496 0.0931 0.295 0.049 81.7
Carbon tetrachloride CCl _{4} 153.823 556.4 4.56 0.276 0.272 0.194 349.7
n-Decane C _{10} H _{22} 142.286 617.6 2.108 0.603 0.247 0.49 447.3
n-Dodecane C _{12} H _{26} 170.34 658.3 1.824 0.713 0.24 0.562 489.5
Ethane C _{2} H _{6} 30.07 305.4 4.884 0.148 0.285 0.098 184.5
Ethyl ether C _{4} H _{10} O 74.123 466.7 3.638 0.28 0.262 0.281 307.7
Ethylene C _{2} H _{4} 28.054 282.4 5.036 0.129 0.276 0.085 169.4
Helium He 4.003 5.19 0.227 0.0573 0.301 -0.387 4.21
n-Heptane C _{7} H _{16} 100.205 540.2 2.736 0.304 0.263 0.351 371.6
n-Hexane C _{6} H _{14} 86.178 507.4 2.969 0.37 0.26 0.296 341.9
Hydrogen H _{2} 2.016 33.2 1.297 0.065 0.305 -0.22 20.4
Hydrogen fluoride HF 20.006 461 6.488 0.069 0.12 0.372 292.7
Hydrogen sulfide H _{2} S 34.08 373.2 8.942 0.0985 0.284 0.1 212.8
Methane CH _{4} 16.043 190.6 4.6 0.099 0.288 0.008 111.7
Naphthalene C _{10} H _{8} 128.174 748.4 4.05 0.41 0.267 0.302 491.1
Neon Ne 20.183 44.4 2.756 0.0417 0.311 0 27
Nitric oxide NO 30.006 180 6.485 0.058 0.25 0.607 121.4
Nitrogen N _{2} 28.013 126.2 3.394 0.0895 0.29 0.04 77.4
n-Octane C _{8} H _{18} 114.232 568.8 2.482 0.492 0.259 0.394 398.8
Oxygen O _{2} 31.999 154.6 5.046 0.0732 0.288 0.021 90.2
n-Pentane C _{5} H _{12} 72.151 469.6 3.374 0.304 0.262 0.251 309.2
Isopentane C _{5} H _{12} 72.151 460.4 3.384 0.306 0.271 0.227 301
Propane C _{3} H _{8} 44.097 369.8 4.246 0.203 0.281 0.152 231.1
Propylene C _{3} H _{6} 42.081 365 4.62 0.181 0.275 0.148 225.4
Refrigerant R12 CCl _{2} F _{2} 120.914 385 4.124 0.217 0.28 0.176 243.4
Refrigerant HFC-134a CH _{2} FCF _{3} 102.03 374.23 4.06 0.198 0.258 0.332 247.1
Sulfur dioxide SO _{2} 64.063 430.8 7.883 0.122 0.268 0.251 263
Toluene C _{7} H _{8} 92.141 591.7 4.113 0.316 0.264 0.257 383.8
Water H _{2} O 18.015 647.3 22.048 0.056 0.229 0.344 373.2
Xenon Xe 131.3 289.7 5.836 0.118 0.286 0.002 165
Source: Adapted from R. C. Reid, J. M. Prausnitz, and B. E. Poling, The Properties of Gases and Liquids, 4th ed.,McGraw-Hill, New York, 1986, Appendix A and other sources.

 

Table 9.4-1 Binary Interaction Parameters k_{12} for the Peng-Robinson Equation of State*
C _{2} H _{4} C _{2} H _{6} C _{3} H _{6} C _{3} H _{8} i- C _{4} H _{10} n- C _{4} H _{10} i- C _{5} H _{12} n- C _{6} H _{14} C _{6} H _{6} c- C _{6} H _{12} n- C _{7} H _{16} n- C _{8} H _{18} n- C _{10} H _{22} N _{2} CO CO _{2} SO _{2} H _{2} S
CH _{4} 0.022 -0.003 0.033 0.016 0.026 0.019 0.026 0.04 0.055 0.039 0.035 0.05 0.049 0.03 0.03 0.09 0.136 0.08
C _{2} H _{4} 0.01 0.092 0.031 0.014 0.025 0.086 -0.022 0.056
C _{2} H _{6} 0.089 0.001 -0.007 0.01 0.008 -0.04 0.042 0.018 0.007 0.019 0.014 0.044 0.026 0.13 0.086
C _{3} H _{6} 0.007 -0.014 0.09 0.026 0.093 0.08
C _{3} H _{8} -0.007 0.003 0.027 0.001 0.023 0.006 0 0 0.078 0.03 0.12 0.08
i- C _{4} H _{10} 0 0.1 0.04 0.13 0.047
n- C _{4} H _{10} 0.017 -0.006 0.003 0.007 0.008 0.087 0.04 0.135 0.07
i- C _{5} H _{12} 0.06 0.018 0.004 0.092 0.04 0.121 0.06
n- C _{5} H _{12} 0.01 -0.004 0.007 0 0.1 0.04 0.125 0.063
n- C _{6} H _{14} 0.013 -0.008 0.15 0.04 0.11 0.06
C _{6} H _{6} 0.001 0.003 0.1 0.164 0.11 0.077 0.015
c- C _{6} H _{12} 0.14 0.1 0.105
n- C _{7} H _{16} 0 0.1 0.04 0.1 0.06
n- C _{8} H _{18} 0.1 0.04 0.12 0.06
n- C _{10} H _{22} 0.11 0.04 0.114 0.033
N _{2} 0.012 -0.02 0.08 0.17
CO 0.03 0.054
CO _{2} 0.136 0.097
SO _{2}
H _{2} S
*Obtained from data in “Vapor-Liquid Equilibria for Mixtures of Low-Boiling Substances,” by H. Knapp, R. D¨oring, L. Oellrich, U. Pl¨ocker, and J. M. Prausnitz, DECHEMA Chemistry Data Series, Vol. VI, Frankfurt/Main, 1982, and other sources. Blanks indicate no data are available from which the k12 could be evaluated. In such case use estimates from mixtures of similar compounds.

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