# Universal and Individual Gas Constants

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

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, R_{u} (given in several units below), and the gas molecular weight, M_{gas}:

R = R_{u}/M_{gas} [1]

In the imperial system the most common units for the individual gas constant are *ft lb/slug ^{o}R*. 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:

For full table -** rotate the screen!**

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 lb_{f}/lb °R] | [ft lb_{f}/slug °R] |

Acetylene | C_{2}H_{2} | 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 | NH_{3} | 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 | C_{4}H_{10} | 58.122 | 143.05 | 0.1431 | 0.03974 | 0.03417 | 0.0279 | 26.588 | 855 |

Butene | C_{4}H_{8} | 56.106 | 148.19 | 0.1482 | 0.04116 | 0.03539 | 0.0289 | 27.543 | 886 |

Carbon Dioxide | CO_{2} | 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 | H_{2}CO_{3} | 62.025 | 134.05 | 0.1341 | 0.03724 | 0.03202 | 0.0261 | 24.915 | 802 |

Chlorine | Cl_{2} | 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 | C_{2}H_{6} | 30.069 | 276.51 | 0.2765 | 0.07681 | 0.06604 | 0.0539 | 51.393 | 1654 |

Ethene | C_{2}H_{4} | 28.053 | 296.38 | 0.2964 | 0.08233 | 0.07079 | 0.0578 | 55.086 | 1772 |

Fluorine | F_{2} | 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 | H_{2} | 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) | CH_{4} | 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 | N_{2} | 28.013 | 296.80 | 0.2968 | 0.08245 | 0.07089 | 0.0579 | 55.165 | 1775 |

Nitrogen dioxide | NO_{2} | 46.006 | 180.73 | 0.1807 | 0.05020 | 0.04317 | 0.0352 | 33.590 | 1081 |

Nitrogen trifluoride | NF_{3} | 71.002 | 117.10 | 0.1171 | 0.03253 | 0.02797 | 0.0228 | 21.765 | 700 |

Nitrous oxide | N_{2}O | 44.012 | 188.91 | 0.1889 | 0.05248 | 0.04512 | 0.0368 | 35.112 | 1130 |

Oxygen | O_{2} | 31.999 | 259.84 | 0.2598 | 0.07218 | 0.06206 | 0.0507 | 48.294 | 1554 |

Propane | C_{3}H_{8} | 44.096 | 188.56 | 0.1886 | 0.05238 | 0.04504 | 0.0368 | 35.045 | 1128 |

Propene | C_{3}H_{6} | 42.080 | 197.59 | 0.1976 | 0.05489 | 0.04719 | 0.0385 | 36.724 | 1182 |

Sulfur dioxide | SO_{2} | 64.064 | 129.78 | 0.1298 | 0.03605 | 0.03100 | 0.0253 | 24.122 | 776 |

Sulfur hexafluoride | SF_{6} | 146.055 | 56.93 | 0.0569 | 0.01581 | 0.01360 | 0.0111 | 10.581 | 340 |

Sulfur trioxide | SO_{3} | 80.063 | 103.85 | 0.1038 | 0.02885 | 0.02480 | 0.0203 | 19.302 | 621 |

Water vapor | H_{2}O | 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 - *R*_{u}

_{u}

The **Universal Gas Constant** - ** R_{u}** - 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*-

*M*- for the gas, and is

_{gas}**the same for all ideal or perfect gases**:

R

_{u}= M_{gas}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:

R

_{u}= k N_{A}[3]where

k = Boltzmann's constant = 1.381 x 10^{-23}[J/K]

N_{A}= Avogadro Number = 6.022 x 10^{23}[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:

M

_{mixture}= Σx_{i}*M_{i}= (x_{1}*M_{1}+ ......+ x_{n}*M_{n}) [4]where

x

_{i }= mole fractions of each gas

M_{i}= the molar mass of each gas

### The Universal Gas Constant - *R*_{u} - in alternative Units

_{u}-

*atm.cm*^{3}/(mol.K) : 82.057338*atm.ft*^{3}/(lbmol.K) : 1.31443*atm.ft*^{3}/(lbmol.^{o}R) : 0.73024*atm.l/(mol.K) : 0.0820**57338**bar.cm*^{3}/(mol.K) : 83.144598*bar.l/(mol.K) : 0.083144**598**Btu/(lbmol.*^{o}R) : 1.9872036*cal/(mol.K) : 1.9859**erg/(mol.K) : 83144**598**hp.h/(lbmol.*^{o}R) : 0.0007805*inHg.ft*^{3}/(lbmol.^{o}R) : 21.85**J/(mol.K) : 8.3144598****kJ/(kmol.K) : 8.3144598***J/(kmol.K) : 8314.472**(kgf/cm*^{2}).l/(mol.K) : 0.084784*kPa.cm*^{3}/(mol.K) : 8314.4*598**kWh/(lbmol.*^{o}R) : 0.000582**lbf.ft/(lbmol.**^{o}**R) : 1545.349***mmHg.ft*^{3}/(lbmol.K) : 999*mmHg.ft*^{3}/(lbmol.^{o}R) : 555*mmHg.l/(mol.K) : 62.363577**Pa.m*^{3}/(mol.K) : 8.3144*598**psf.ft*^{3}/(lbmol.^{o}R) : 1545.3465*psi.ft*^{3}/(lbmol.^{o}R) : 10.73*Torr.cm*^{3}/(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