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Tuesday, February 6, 2024

Some comments on the ideal gas constant R

 The constant R in the ideal gas equation of state may have different values according to the unit system in use. For example


R Units
SI units
8.314 J\,K^{−1}\,mol^{−1}
8.314 m^3\,Pa\,K^{−1}\,mol^{−1}
8.314 kg\,m^2\,s^{-2}\,K^{−1}\,mol^{−1}
Other units
8314.462 L\,Pa\,K^{−1}\,mol^{−1}
8.314 L\,kPa\,K^{−1}\,mol^{−1}
8.314\times10^{-2} L\,bar\,K^{−1}\,mol^{−1}
8.314\times10^{7} erg\,K^{−1}\,mol^{−1}
7.302\times10^{-1} atm\,ft^3\,lb_{mol}^{−1}\,R^{−1}
10.731 psi\,ft^3\,lb_{mol}^{−1}\,R^{−1}
1.986 BTU\,lb_{mol}^{−1}\,R^{−1}
297.031 inH_2O\,ft^3\,lb_{mol}^{−1}\,R^{−1}
554.984 torr\,ft^3\,lb_{mol}^{−1}\,R^{−1}
8.206\times10^{-2} L\,atm\,K^{−1}\,mol^{−1}
62.363 L\,torr\,K^{−1}\,mol^{−1}
1.987 cal\,K^{−1}\,mol^{−1}
8.206\times10^{-5} m^3\,atm\,K^{−1}\,mol^{−1}


However, as you may imagine if a gas in question has an idealized behavior then the constant R may apply. A gas behaves as an ideal gas under certain conditions of pressure, P=0, and temperature so that the following equation of state applies

PV=nRT

One way to check for the constant R for any given gas is in a plot of PV/nT versus P which should be a straight line. Also, when this line cuts the vertical axis (PV/nT) at P=0 you should read any of the values of the table above (according to the units you were using).


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