# Universal and Individual Gas Constants

## The Universal and Individual Gas Constants in fluid mechanics and thermodynamics

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.

In the imperial system the units for the individual gas constant are ft lb/slug oR. In the SI system the units are J/kg K.

The Individual Gas Constant for some gases:

GasIndividual Gas Constant - R
Imperial Units
[ft lb/slug oR]
SI Units
[J/kg K]
Molecular Weight
[kg/kmol]
Argon, Ar 208 39.94
Acetylene 319 26
Ammonia 488 17
Carbon Dioxide, CO2 1130 188.9 44.01
Carbon Monoxide, CO 297 28.01
Carbonic acid 189 44
Helium, He 12420 2077 4.003
Hydrogen, H2 24660 4124 2.016
Methane - natural gas, CH4 3099 518.3 16.04
Nitrogen, N2 1775 296.8 28.02
Oxygen, O2 1554 259.8 32
Propane, C3H8 189 44.09
Sulfur dioxide, SO2 (sulfuric acid) 130 64.07
Air 1716 286.9 28.97
Water vapor 2760 461.5 18.02

### 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                               (1)

where

Ru = universal gas constant

Mgas = molecular weight of the ideal gas or mixture of gases

### 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 = (x1*M1 + ......+ xn*Mn)                                        (2)

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) : 82.0575
• atm.ft3/(lbmol.K) : 1.31443
• atm.ft3/(lbmol.oR) : 0.73024
• atm.l/(mol.K) : 0.08206
• bar.cm3/(mol.K) : 83.14472
• bar.l/(mol.K) : 0.08314472
• Btu/(lbmol.oR) : 1.9859
• cal/(mol.K) : 1.9859
• erg/(mol.K) : 83144720
• 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) : 8314.472
• 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) : 62.364
• Pa.m3/(mol.K) : 8.314472
• psf.ft3/(lbmol.oR) : 1545.349
• psi.ft3/(lbmol.oR) : 10.73
• Torr.cm3/(mol.K) : 62364
• 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.

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

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

Ru = k NA                                 (2)

where

k = Boltzmann's constant = 1.381 x 10-23 (J/K)

NA = Avogadro Number = 6.022 x 1023 (1/mol)

## Related Topics

• Fluid Mechanics - The study of fluids - liquids and gases. Involves 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

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