Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

This is an AMP page - Open full page! for all features.

• the most efficient way to navigate the Engineering ToolBox!

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 L 2 /mol 2 multiply by 0.986 atm/bar.    To convert a into kPa L 2 /mol 2 multiply by 100.0 kPa/bar

Non-ideal gas - Van der Waal's Constants
Name Molecular Formula a*
bar L 2 /mol 2
b
L/mol
Aluminum trichloride AlCl 3 42.63 0.245
Ammonia NH 3 4.225 0.03713
Ammonium chloride NH 4 Cl 2.38 0.00734
Argon Ar 1.355 0.03201
Boron trichloride BCl 3 15.6 0.1222
Boron trifluoride BF 3 3.98 0.05443
Diborane B 2 H 6 6.048 0.07437
Bromine Br 2 9.75 0.0591
Perchloryl fluoride ClFO 2 7.371 0.0713
Chlorine pentafluoride ClF 5 9.58 0.08204
Phosphonium chloride ClH 4 P 4.111 0.04545
Chlorine Cl 2 6.343 0.05422
Trichlorofluorosilane Cl 3 FSi 15.67 0.1273
Fluorine F 2 1.171 0.02896
Germanium tetrachloride GeCl 4 23.12 0.1489
Nitrogen trifluoride F 3 N 3.58 0.05453
Phosphorus trifluoride F 3 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 H 2 O 5.537 0.03049
Hydrogen sulphide H 2 S 4.544 0.04339
Hydrogen selenide H 2 Se 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 N 2 O 3.852 0.04435
Hydrazine N 2 H 4 8.46 0.0462
Neon Ne 0.208 0.01672
Oxygen O 2 1.382 0.03186
Ozone O 3 3.57 0.0487
Phosphorus P 53.6 0.157
Phosphine PH 3 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 SF 6 7.857 0.08786
Selenium Se 33.4 0.0675
Uranium(VI) fluoride UF 6 16.01 0.1128
Tungsten(VI) fluoride WF 6 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 CClF 3 6.873 0.0811
Trichlorofluoromethane CCl 3 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 CHCl 3 15.34 0.1019
Trifluoromethane CHF 3 5.378 0.06403
Dichloromethane CH 2 Cl 2 12.44 0.08689
Difluoromethane CH 2 F 2 6.184 0.06268
Chloromethane CH 3 Cl 7.566 0.06477
Fluoromethane CH3F 5.009 0.05617
Nitromethane NH 3 NO 2 17.18 0.1041
Methane CH 4 2.3 0.04301
Methanol CH 3 OH 9.472 0.06584
Methanethiol CH 3 SH 8.911 0.06756
Methylamine CH 3 NH 2 7.106 0.05879
1,1,2-Trichlorotrifluoroethane C 2 Cl 2 F 3 20.25 0.1481
Tetrafluoroethylene C 2 F 4 6.954 0.08085
Cyanogen C 2 N 2 7.803 0.6952
Acetylene C 2 H 2 4.516 0.0522
1,1-Difluoroethylene C 2 H 2 F 2 6 0.07058
1,1,1-Trichloroethane C 2 H 3 Cl 3 20.15 0.1317
Fluroethylene C 2 H 3 F 5.984 0.06504
1,1,1-Trifluoroethane C 2 H 3 F 3 9.302 0.09572
Acetonitrile C 2 H 3 N 17.89 0.1169
Ethylene C 2 H 4 4.612 0.05821
1,1-Dichloroethane C 2 H 4 Cl 2 15.73 0.1072
1,2-Dichloroethane C 2 H 4 Cl 2 17 0.108
Ethylene oxide C 2 H 4 O 8.922 0.06779
Acetic acid CH 3 COOH 17.71 0.1065
Methyl formate C 2 H 4 O 2 11.54 0.08442
Bromoethane C 2 H 5 Br 11.89 0.08406
Chloroethane C 2 H 5 Cl 11.7 0.09
Fluoroethane C 2 H 5 F 8.17 0.07758
Ethane C 2 H 6 5.57 0.06499
Dimethyl ether C 2 H 6 O 8.69 0.07742
Ethanol C 2 H 5 OH 12.56 0.0871
Dimethyl sulphide C 2 H 5 SH 13.34 0.09453
Ethanethiol C 2 H 5 SH 13.23 0.09447
Dimethylamine C 2 H 7 N 10.44 0.0851
Ethylamine C 2 H 7 N 10.79 0.08433
Perfluoropropane C 3 F 8 12.96 0.1338
Propanenitrile C 3 H 5 N 21.57 0.1369
Propene C 3 H 6 8.438 0.08242
Cyclopropane C 3 H 6 8.293 0.0742
Acetone C 3 H 6 O 16.02 0.1124
Propanal C 3 H 6 O 14.08 0.09947
Ethyl formate C 3 H 6 O 2 15.91 0.1115
Methyl acetate C 3 H 6 O 2 15.75 0.1108
Propanoic acid C 3 H 6 O 2 23.49 0.1386
1-Chloropropane C 3 H 7 Cl 16.11 0.1141`
Propane C 3 H 8 9.385 0.09044
1-Propanol C 3 H 8 O 16.26 0.108
2-Propanol C 3 H 8 O 15.82 0.1109
Ethyl methyl ether C 3 H 8 O 12.7 0.1034
Ethyl methyl sulphide C 3 H 8 S 19.45 0.13
Propylamine C 3 H 9 N 15.26 0.1094
Trimethylamine C 3 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 H 6 12.17 0.102
Acetic anhydride C 4 H 6 O 3 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 C 5 H 4 O 2 22.23 0.1182
Pyridine C 5 H 5 N 19.77 0.1137
Cyclopentene C 5 H 8 15.61 0.1097
1-Pentene C 5 H 10 17.86 0.137
2-Methyl-1-butene C 5 H 10 16.9 0.129
2-Methyl-2-butene C 5 H 10 17.26 0.1279
Cyclopentane C 5 H 10 16.94 0.118
Tetrahydropyran C 5 H 10 O 20.02 0.1247
Isobutyl formate C 5 H 10 O 2 22.82 0.1476
Propyl acetate C 5 H 10 O 2 26.23 0.17
Ethyl propanoate C 5 H 10 O 2 25.86 0.1688
Methyl butanoate C 5 H 10 O 2 25.83 0.1661
Methyl isobutanoate C 5 H 10 O 2 24.87 0.1639
Piperidine C 5 H 11 N 20.84 0.125
Pentane C 5 H 12 19.13 0.1451
Isopentane C 5 H 12 18.29 0.1415
Neopentane C 5 H 12 17.17 0.141
1-Pentanol C 5 H 12 O 25.81 0.1564
Bromobenzene C 6 H 5 Br 28.96 0.1541
Chlorobenzene C 6 H 5 Cl 25.8 0.1454
Fluorobenzene C 6 H 5 F 20.1 0.1279
Iodobenzene C 6 H 5 I 33.54 0.1658
Benzene C 6 H 6 18.82 0.1193
Phenol C 6 H 5 OH 22.93 0.1177
Aniline C 6 H 5 NH 2 29.14 0.1486
Cyclohexanone C 6 H 10 O 31.1 0.17
Hexanenitrile C 6 H 11 N 35.5 0.1996
Cyclohexane C 6 H 12 21.95 0.1413
Cyclohexanol C 6 H 11 OH 28.93 0.1586
Pentyl formate C 6 H 12 O 2 27.97 0.173
Isobutyl acetate C 6 H 12 O 2 29.05 0.1845
Ethyl butanoate C 6 H 12 O 2 30.53 0.1922
Ethyl 2-methylpropanoate C 6 H 12 O 2 29.05 0.1872
Methyl pentanoate C 6 H 12 O 2 29.39 0.1847
Hexane C 6 H 14 24.97 0.1753
2,3-Dimethylbutane C 6 H 14 23.29 0.166
1-Hexanol C 6 H 14 O 31.35 0.1829
Triethylamine C 6 H 15 N 27.59 0.1836
Dipropylamine C 6 H 15 N 24.82 0.1591
Benzonitrile C 7 H 5 N 33.89 0.1727
Benzaldehyde C 7 H 6 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

Related Topics

• Air Psychrometrics

Moist and humid air - psychrometric charts, Mollier diagrams, air-condition temperatures and absolute and relative humidity and moisture content.

• Basics

The SI-system, unit converters, physical constants, drawing scales and more.

• Fluid Mechanics

The study of fluids - liquids and gases. Involving velocity, pressure, density and temperature as functions of space and time.

• Gases and Compressed Air

Air, LNG, LPG and other common gas properties, pipeline capacities, sizing of relief valves.

Related Documents

Air - Molecular Weight and Composition

Dry air is a mixture of gases where the average molecular weight (or molar mass) can be calculated by adding the weight of each component.

Air - SCFM versus ACFM and ICFM

Actual air compressor capacity (ACFM) vs. standard air capacity (SCFM) and inlet air capacity (ICFM).

Charles' Law

Volume of an ideal gas vs. temperature.

Compression and Expansion of Gases

Isothermal and isentropic gas compression and expansion processes.

Critical Temperatures and Pressures for some Common Substances

Critical temperatures and pressures for some common substances like air, alcohol, ether, oxygen and more.

Gas Mixtures - Properties

Gas mixtures and the ideal gas law, mass calculations, the individual gas constant and density.

Gases - Dynamic Viscosities

Absolute (dynamic) viscosities of some common gases.

Gases - Ratios of Specific Heat

Ratios of specific heat for gases with constant pressure and volume processes.

Gases - Specific Heats and Individual Gas Constants

Specific heat at constant volume, specific heat at constant pressure, specific heat ratio and individual gas constant - R - common gases as argon, air, ether, nitrogen and many more.

Helium - Thermophysical Properties

Chemical, Physical and Thermal Properties of Helium - He.

Humid Air vs. the Ideal Gas Law

Pressure, temperature and volume in a perfect ideal gas like moist air (air with water vapor).

Temperature

Introduction to temperature - including Celsius, Fahrenheit, Kelvin and Rankine definitions - and an online temperature converter.

The Ideal Gas Law

The relationship between volume, pressure, temperature and quantity of a gas, including definition of gas density.

Total and Partial Pressure - Dalton's Law of Partial Pressures

How to calculate total pressure and partial pressures for gas mixtures from Ideal Gas Law.

Universal and Individual Gas Constants

The Universal and Individual Gas Constants in fluid mechanics and thermodynamics. Individual gas constants for the most common gases.

Vapor and Steam

An introduction to vapor and steam.

Search Engineering ToolBox

• the most efficient way to navigate the Engineering ToolBox!

SketchUp Extension - Online 3D modeling!

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp from the Sketchup Extension Warehouse!