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Individual & Universal Gas Constants: Definitions, Values, and Applications

The Universal and Individual Gas Constants are known from the Ideal Gas Law.

The Individual Gas Constant - R

The Individual Gas Constant depends on the particular gas and is related to the molecular weight of the gas. The value is independent of temperature. The induvidual gas constant, R, for a gas can be calculated from the universal gas constant, Ru ( given in several units below),  and the gas molecular weight, Mgas :

R = Ru / Mgas                     (1)

In the imperial system the most common units for the individual gas constant are ft lb/slugoR. In the SI system the most common units are J/kg K.

Unit conversion: 1 J/kg K = 5.97994 ft lb/slug °R, and 1 ft lb/slug °R = 0.167226 J/kg K.

The Individual Gas Constant for gases:

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Individual Gas Constants
Gas Molecular
Weight 		Individual Gas Constant - R
Name Formula (g/mol),
(kg/kmol) 		(J/kg K) (kJ/kg K) (Wh/(kg K)) (kcal/(kg K)),
(Btu(IT)/lb °F) 		(kcal/(lb °F)) (ft lbf/lb °R) (ft lbf/slug °R)
Acetylene C2H2 26.038 319.32 0.3193 0.08870 0.07627 0.0623 59.350 1910
Air A mixture 28.9647 287.05 0.2871 0.07974 0.06856 0.0560 53.353 1717
Ammonia NH3 17.031 488.21 0.4882 0.13561 0.11661 0.0952 90.740 2919
Argon Ar 39.948 208.13 0.2081 0.05781 0.04971 0.0406 38.684 1245
Butane C4 H10 58.122 143.05 0.1431 0.03974 0.03417 0.0279 26.588 855
Butene C4 H8 56.106 148.19 0.1482 0.04116 0.03539 0.0289 27.543 886
Carbon Dioxide CO2 44.010 188.92 0.1889 0.05248 0.04512 0.0368 35.114 1130
Carbon Monoxide CO 28.010 296.84 0.2968 0.08246 0.07090 0.0579 55.171 1775
Carbonic acid H2CO3 62.025 134.05 0.1341 0.03724 0.03202 0.0261 24.915 802
Chlorine Cl2 70.906 117.26 0.1173 0.03257 0.02801 0.0229 21.794 701
Chloromethane CH3Cl 50.488 164.68 0.1647 0.04575 0.03933 0.0321 30.608 985
Dichlorofluorumethane CHCl2F 102.923 80.78 0.0808 0.02244 0.01929 0.0158 15.015 483
Ethane C2H6 30.069 276.51 0.2765 0.07681 0.06604 0.0539 51.393 1654
Ethene C2H4 28.053 296.38 0.2964 0.08233 0.07079 0.0578 55.086 1772
Fluorine F2 37.997 218.82 0.2188 0.06078 0.05226 0.0427 40.670 1309
Helium He 4.003 2077.1 2.0771 0.57696 0.49610 0.4050 386.047 12421
Hydrogen H2 2.016 4124.2 4.1242 1.14563 0.98506 0.8043 766.541 24663
Hydrogen bromide HBr 80.912 102.76 0.1028 0.02854 0.02454 0.0200 19.099 614
Hydrogen chloride HCl 36.461 228.04 0.2280 0.06334 0.05447 0.0445 42.384 1364
Hydrogen sulfide H2S 34.081 243.96 0.2440 0.06777 0.05827 0.0476 45.344 1459
Krypton Kr 83.798 99.22 0.0992 0.02756 0.02370 0.0193 18.441 593
Methane (natural gas) CH4 16.042 518.28 0.5183 0.14397 0.12379 0.1011 96.329 3099
Neon Ne 20.180 412.02 0.4120 0.11445 0.09841 0.0803 76.579 2464
Nitrogen N2 28.013 296.80 0.2968 0.08245 0.07089 0.0579 55.165 1775
Nitrogen dioxide NO2 46.006 180.73 0.1807 0.05020 0.04317 0.0352 33.590 1081
Nitrogen trifluoride NF3 71.002 117.10 0.1171 0.03253 0.02797 0.0228 21.765 700
Nitrous oxide N2O 44.012 188.91 0.1889 0.05248 0.04512 0.0368 35.112 1130
Oxygen O2 31.999 259.84 0.2598 0.07218 0.06206 0.0507 48.294 1554
Propane C3 H8 44.096 188.56 0.1886 0.05238 0.04504 0.0368 35.045 1128
Propene C3 H6 42.080 197.59 0.1976 0.05489 0.04719 0.0385 36.724 1182
Sulfur dioxide SO2 64.064 129.78 0.1298 0.03605 0.03100 0.0253 24.122 776
Sulfur hexafluoride SF6 146.055 56.93 0.0569 0.01581 0.01360 0.0111 10.581 340
Sulfur trioxide SO3 80.063 103.85 0.1038 0.02885 0.02480 0.0203 19.302 621
Water vapor H2O 18.015 461.52 0.4615 0.12820 0.11023 0.0900 85.780 2760
Xenon Xe 131.293 63.33 0.0633 0.01759 0.01513 0.0123 11.770 379

The Universal Gas Constant - Ru

The Universal Gas Constant - Ru - appears in the ideal gas law and can be expressed as the product between the Individual Gas Constant - R - for the particular gas - and the Molecular Weight - Mgas - for the gas, and is the same for all ideal or perfect gases :

Ru = Mgas R                               (2)

The Universal Constant defined in Terms of the Boltzmann's Constant

The universal gas constant can be defined in terms of Boltzmann's constant k as:

Ru = k NA                             (3)

where
k = Boltzmann's constant = 1.381×10-23 (J/K)
NA = Avogadro Number = 6.022×1023 (1/mol)

The Molecular weight of a Gas Mixture

The average molecular weight of a gas mixture is equal to the sum of the mole fractions of each gas multiplied by the molecular weight of that particular gas:

Mmixture = Σ(xi Mi)

        = (x1 M1 + ......+ xn Mn )                                        (4)

where

xi = mole fractions of each gas

Mi = the molar mass of each gas

The Universal Gas Constant - Ru - in alternative Units

  • atm.cm3/(mol.K) : 82.057338
  • atm.ft3/(lbmol.K) : 1.31443
  • atm.ft3/(lbmol. oR) : 0.73024
  • atm.l/(mol.K) : 0.0820 57338
  • bar.cm3/(mol.K) : 83.144598
  • bar.l/(mol.K) : 0.083144 598
  • Btu/(lbmol.oR) : 1.9872036
  • cal/(mol.K) : 1.9872
  • erg/(mol.K) : 83144 598
  • hp.h/(lbmol.oR) : 0.0007805
  • inHg.ft3/(lbmol.oR) :  21.85
  • J/(mol.K) :  8.3144598
  • kJ/(kmol.K) :  8.3144598
  • J/(kmol.K) : 8314.472
  • (kgf/cm2).l/(mol.K) : 0.084784
  • kPa.cm3/(mol.K) : 8314.4 598
  • kWh/(lbmol.oR) : 0.000582
  • lbf.ft/(lbmol. oR) : 1545.349
  • mmHg.ft3/(lbmol.K) : 999
  • mmHg.ft3/(lbmol. oR) : 555
  • mmHg.l/(mol.K) : 62.363577
  • Pa.m3/(mol.K) : 8.3144 598
  • psf.ft3/(lbmol. oR) : 1545.3465
  • psi.ft3/(lbmol. oR) : 10.73
  • Torr.cm3/(mol.K) : 62364

See also:
- More material properties
- The Ideal Gas Law - Gases are highly compressible with changes in density directly related to changes in temperature and pressure.
- A Mixture of Gases - Properties of mixtures of gases.
- More about temperature