The Universal Gas Constant and Molecular Weights

It is convenient to introduce the concepts of molecular weight and the universal gas constant at this point. We shall introduce these concepts by making use of Boyle s law and the absolute temperature scale. 

We shall now demonstrate that the arbitrary mass unit m-, for gas i can be chosen in such a way that R has the same value for all gases. The mass units M,-, which yield a universal gas constant R, are, respectively, the molecular weights of the gases /. We first choose an arbitrary mass unit for oxygen gas in order to determine the value of R. The mass unit for oxygen, A/qj, is arbitrarily set equal to 32 g. By definition, 

In order to establish experimental values for the mass units A/ it is sufficient to measure the limit, as the pressure tends to zero, of the ratio of the density of gas /, p, to the pressure p at any temperature. The molecular weight Mi can then be determined from the relation 

This argument, then, introduces the molecular weights A/,- and the universal gas constant R into thermodynamics. 

---