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Non-ideal gas - Van der Waal's Equation and Constants

The ideal gas law treats the molecules of a gas as point particles with perfectly elastic collisions. This works well for dilute gases in many experimental circumstances.

However,  gas molecules are not point masses, and there are many cases gases need to be treated as non-ideal .  Johannes D. van der Waals suggested a modification to take into account molecular size and molecular interaction forces. It is usually referred to as the van der Waals equation of state :

[P + a (n/V)2] (V/n - b ) = RT

The constants a and b are called van der Waals constants. They have positive values and are characteristic of the individual gas. If a gas behaves ideally, both a and b are zero, and van der Waals equations approaches the ideal gas law PV=nRT.

The constant a provides a correction for the intermolecular forces .
Constant b adjusts for the volume occupied by the gas particles . It is a correction for finite molecular size and its value is the volume of one mole of the atoms or molecules.

See also the Gas Compressibility Factor, z-factor for air, dependent on pressure and temperature and used to account for deviation from the ideal situation.
How to calculate total pressure and partial pressures from Ideal gas law

* To convert a into atm L2/mol2multiply by 0.986 atm/bar.    To convert a into kPa L2/mol2multiply by 100.0 kPa/bar

Non-ideal gas - Van der Waal's Constants
Name Molecular Formula a*
bar L2/mol2
b
L/mol
Aluminum trichloride AlCl3 42.63 0.245
Ammonia NH3 4.225 0.03713
Ammonium chloride NH 4 Cl 2.38 0.00734
Argon Ar 1.355 0.03201
Boron trichloride BCl3 15.6 0.1222
Boron trifluoride BF3 3.98 0.05443
Diborane B2H6 6.048 0.07437
Bromine Br 2 9.75 0.0591
Perchloryl fluoride ClFO 2 7.371 0.0713
Chlorine pentafluoride ClF5 9.58 0.08204
Phosphonium chloride ClH 4 P 4.111 0.04545
Chlorine Cl 2 6.343 0.05422
Trichlorofluorosilane Cl3 FSi 15.67 0.1273
Fluorine F 2 1.171 0.02896
Germanium tetrachloride GeCl 4 23.12 0.1489
Nitrogen trifluoride F3 N 3.58 0.05453
Phosphorus trifluoride F3 P 4.954 0.0651
Tetrafluorohydrazine F 4 N 2 7.426 0.08564
Germane GeH 4 5.743 0.06555
Helium He 0.0346 0.0238
Hydrogen bromide HBr 4.5 0.04415
Hydrogen chloride HCl 3.7 0.04061
Hydrogen cyanide HCN 11.29 0.08806
Hydrogen fluoride HF 9.565 0.0739
Hydrogen iodide HI 6.309 0.05303
Hydrogen H 2 0.2453 0.02651
Water H2O 5.537 0.03049
Hydrogen sulphide H2S 4.544 0.04339
Hydrogen selenide H2Se 5.523 0.0479
Krypton Kr 2.325 0.0396
Silane SiH 4 4.38 0.0579
Silicon tetrachloride SiCl 4 20.96 0.147
Silicon tetrafluoride SiF 4 5.259 0.07236
Titanium(IV) chloride TiCl 4 25.47 0.1423
Mercury Hg 5.193 0.01057
Nitric oxide NO 1.46 0.0289
Nitrogen dioxide NO 2 5.36 0.0443
Nitrogen N 2 1.37 0.0387
Nitrous oxide N2O 3.852 0.04435
Hydrazine N2H 4 8.46 0.0462
Neon Ne 0.208 0.01672
Oxygen O 2 1.382 0.03186
Ozone O3 3.57 0.0487
Phosphorus P 53.6 0.157
Phosphine PH3 4.696 0.05157
Radon Rn 6.601 0.06239
Stannic chloride SnCl 4 27.25 0.1641
Sulphur S 24.3 0.066
Sulphur dioxide SO 2 6.865 0.05679
Sulphur hexafluoride SF6 7.857 0.08786
Selenium Se 33.4 0.0675
Uranium(VI) fluoride UF6 16.01 0.1128
Tungsten(VI) fluoride WF6 13.25 0.1063
Xenon Xe 4.192 0.05156
Xenon difluoride XeF 2 12.46 0.07037
Xenon tetrafluoride XeF 4 15.52 0.09035
Chlorotrifluoromethane CClF3 6.873 0.0811
Trichlorofluoromethane CCl3 F 14.68 0.1111
Tetrachloromethane CCl 4 20.01 0.1281
Tetrafluoromethane CF 4 4.04 0.06325
Carbon monoxide CO 1.472 0.03948
Carbon oxysulphide COS 6.975 0.06628
Carbon dioxide CO 2 3.658 0.04286
Carbon disulphide CS 2 11.25 0.07262
Trichloromethane CHCl3 15.34 0.1019
Trifluoromethane CHF3 5.378 0.06403
Dichloromethane CH2Cl 2 12.44 0.08689
Difluoromethane CH2F 2 6.184 0.06268
Chloromethane CH3 Cl 7.566 0.06477
Fluoromethane CH3F 5.009 0.05617
Nitromethane NH3 NO 2 17.18 0.1041
Methane CH 4 2.3 0.04301
Methanol CH3 OH 9.472 0.06584
Methanethiol CH3 SH 8.911 0.06756
Methylamine CH3 NH 2 7.106 0.05879
1,1,2-Trichlorotrifluoroethane C2Cl2F3 20.25 0.1481
Tetrafluoroethylene C2F 4 6.954 0.08085
Cyanogen C2N 2 7.803 0.6952
Acetylene C2H 2 4.516 0.0522
1,1-Difluoroethylene C2H2F 2 6 0.07058
1,1,1-Trichloroethane C2H3 Cl3 20.15 0.1317
Fluroethylene C2H3 F 5.984 0.06504
1,1,1-Trifluoroethane C2H3 F3 9.302 0.09572
Acetonitrile C2H3 N 17.89 0.1169
Ethylene C2H 4 4.612 0.05821
1,1-Dichloroethane C2H 4 Cl 2 15.73 0.1072
1,2-Dichloroethane C2H 4 Cl 2 17 0.108
Ethylene oxide C2H 4 O 8.922 0.06779
Acetic acid CH3 COOH 17.71 0.1065
Methyl formate C2H 4 O 2 11.54 0.08442
Bromoethane C2H5 Br 11.89 0.08406
Chloroethane C2H5 Cl 11.7 0.09
Fluoroethane C2H5 F 8.17 0.07758
Ethane C2H6 5.57 0.06499
Dimethyl ether C2H6 O 8.69 0.07742
Ethanol C2H5 OH 12.56 0.0871
Dimethyl sulphide C2H5 SH 13.34 0.09453
Ethanethiol C2H5 SH 13.23 0.09447
Dimethylamine C2H 7 N 10.44 0.0851
Ethylamine C2H 7 N 10.79 0.08433
Perfluoropropane C3 F 8 12.96 0.1338
Propanenitrile C3 H5 N 21.57 0.1369
Propene C3 H6 8.438 0.08242
Cyclopropane C3 H6 8.293 0.0742
Acetone C3 H6 O 16.02 0.1124
Propanal C3 H6 O 14.08 0.09947
Ethyl formate C3 H6 O 2 15.91 0.1115
Methyl acetate C3 H6 O 2 15.75 0.1108
Propanoic acid C3 H6 O 2 23.49 0.1386
1-Chloropropane C3 H 7 Cl 16.11 0.1141`
Propane C3 H 8 9.385 0.09044
1-Propanol C3 H 8 O 16.26 0.108
2-Propanol C3 H 8 O 15.82 0.1109
Ethyl methyl ether C3 H 8 O 12.7 0.1034
Ethyl methyl sulphide C3 H 8 S 19.45 0.13
Propylamine C3 H 9 N 15.26 0.1094
Trimethylamine C3 H 9 N 13.37 0.1101
Furan C 4 H 4 O 12.74 0.0926
Thiophene C 4 H 4 S 17.21 0.1058
Pyrrole C 4 H 4 N 18.82 0.1049
1,3-Butadiene C 4 H6 12.17 0.102
Acetic anhydride C 4 H6 O3 26.8 0.157
Butanenitrile C 4 H 7 N 25.76 0.1568
1-Butene C 4 H 8 12.76 0.1084
Cyclobutane C 4 H 8 12.39 0.096
2-Butanone C 4 H 8 O 19.97 0.1326
Tetrahydrofuran C 4 H 8 O 16.39 0.1082
1,4-Dioxane C 4 H 8 O 2 19.29 0.1171
Ethyl acetate C 4 H 8 O 2 20.57 0.1401
Methyl propanoate C 4 H 8 O 2 20.51 0.1377
Propyl formate C 4 H 8 O 2 20.79 0.1377
Butanoic acid C 4 H 8 O 2 28.18 0.1609
Pyrrolidine C 4 H 9 N 16.84 0.1056
Butane C 4 H 10 13.93 0.1168
Isobutane C 4 H 10 13.36 0.1168
1-Butanol C 4 H 10 O 20.9 0.1323
2-Methyl-2-propanol C 4 H 10 O 18.81 0.1324
2-Methyl-1-propanol C 4 H 10 O 20.35 0.1324
Diethyl ether C 4 H 10 O 17.46 0.1333
Diethyl sulphide C 4 H 10 S 22.85 0.1462
Butylamine C 4 H 11 N 19.41 0.1301
Diethylamine C 4 H 11 N 19.4 0.1383
Tetramethylsilane C 4 H 12 Si 20.81 0.1653
Furfural C5 H 4 O 2 22.23 0.1182
Pyridine C5 H5 N 19.77 0.1137
Cyclopentene C5 H 8 15.61 0.1097
1-Pentene C5 H 10 17.86 0.137
2-Methyl-1-butene C5 H 10 16.9 0.129
2-Methyl-2-butene C5 H 10 17.26 0.1279
Cyclopentane C5 H 10 16.94 0.118
Tetrahydropyran C5 H 10 O 20.02 0.1247
Isobutyl formate C5 H 10 O 2 22.82 0.1476
Propyl acetate C5 H 10 O 2 26.23 0.17
Ethyl propanoate C5 H 10 O 2 25.86 0.1688
Methyl butanoate C5 H 10 O 2 25.83 0.1661
Methyl isobutanoate C5 H 10 O 2 24.87 0.1639
Piperidine C5 H 11 N 20.84 0.125
Pentane C5 H 12 19.13 0.1451
Isopentane C5 H 12 18.29 0.1415
Neopentane C5 H 12 17.17 0.141
1-Pentanol C5 H 12 O 25.81 0.1564
Bromobenzene C6 H5 Br 28.96 0.1541
Chlorobenzene C6 H5 Cl 25.8 0.1454
Fluorobenzene C6 H5 F 20.1 0.1279
Iodobenzene C6 H5 I 33.54 0.1658
Benzene C6 H6 18.82 0.1193
Phenol C6 H5 OH 22.93 0.1177
Aniline C6 H5 NH 2 29.14 0.1486
Cyclohexanone C6 H 10 O 31.1 0.17
Hexanenitrile C6 H 11 N 35.5 0.1996
Cyclohexane C6 H 12 21.95 0.1413
Cyclohexanol C6 H 11 OH 28.93 0.1586
Pentyl formate C6 H 12 O 2 27.97 0.173
Isobutyl acetate C6 H 12 O 2 29.05 0.1845
Ethyl butanoate C6 H 12 O 2 30.53 0.1922
Ethyl 2-methylpropanoate C6 H 12 O 2 29.05 0.1872
Methyl pentanoate C6 H 12 O 2 29.39 0.1847
Hexane C6 H 14 24.97 0.1753
2,3-Dimethylbutane C6 H 14 23.29 0.166
1-Hexanol C6 H 14 O 31.35 0.1829
Triethylamine C6 H 15 N 27.59 0.1836
Dipropylamine C6 H 15 N 24.82 0.1591
Benzonitrile C 7 H5 N 33.89 0.1727
Benzaldehyde C 7 H6 O 30.3 0.1553
Toluene C 7 H 8 24.89 0.1499
o-Cresol C 7 H 8 O 28.33 0.1447
m-Cresol C 7 H 8 O 31.86 0.1609
p-Cresol C 7 H 8 O 28.11 0.1422
Benzyl alcohol C 7 H 8 O 34.7 0.173
Anisole C 7 H 8 O 28.6 0.1579
Heptane C 7 H 16 30.89 0.2038
Heptanol C 7 H 15 OH 37.22 0.2097
Ethylbenzene C 8 H 10 30.86 0.1782
o-Xylene C 8 H 10 31.06 0.1756
m-Xylene C 8 H 10 31.41 0.1814
p-Xylene C 8 H 10 31.54 0.1824
Phenetole C 8 H 10 O 35.7 0.1966
N,N-Dimethylaniline C 8 H 11 N 37.92 0.1967
Octane C 8 H 18 37.86 0.2372
2,5-Dimethylhexane C 8 H 18 35.49 0.2299
1-Octanol C 8 H 18 O 43.42 0.2371
Quinoline C 9 H 7 N 36.7 0.1672
Cumene C 9 H 12 36.2 0.2044
Propylbenzene C 9 H 12 37.14 0.2073
1,2,4-Trimethylbenzene C 9 H 12 38.03 0.2088
Mesitylene C 9 H 12 37.87 0.2118
Nonane C 9 H 20 45.11 0.2702
1-Nonanol C 9 H 20 O 50 0.2654
Naphthalene C 10 H 8 40.32 0.192
Butylbenzene C 10 H 14 44.07 0.2378
Isobutylbenzene C 10 H 14 40.4 0.2215
o-Cymene C 10 H 14 42.7 0.234
p-Cymene C 10 H 14 45.27 0.2478
p-Diethylbenzene C 10 H 14 45.03 0.2439
1,2,4,5-Tetramethylbenzene C 10 H 14 45.8 0.24
Decane C 10 H 22 52.88 0.3051
1-Decanol C 10 H 22 O 57.45 0.2971
Undecane C 11 H 24 60.88 0.3396
Biphenyl C 12 H 10 47.16 0.213
Dodecane C 12 H 26 69.14 0.3741
1-Dodecanol C 12 H 26 O 72.69 0.3598
Diphenylmethane C 13 H 12 60.46 0.2798
Tridecane C 13 H 28 77.94 0.4109
1-Tridecanol C 13 H 28 O 81.2 0.3942
1-Tetradecanol C 14 H 30 O 89.91 0.4289
Pentadecane C 15 H 32 96.5 0.4857

* To convert a into atm L2/mol2 multiply by 0.986 atm/bar

* To convert a into kPa L2/mol2 multiply by 100.0 kPa/bar

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