The chemical constant of hydrogen vapour and the entropy of crystalline hydrogen

Abstract

In a paper called "The Chemical constant of Hydrogen Vapour and the failure of Nernst's Heat Theorem," R. H. Fowler has investigated the vapour pressure of hydrogen crystals at low temperature; taking account of the existence of two sorts of hydrogen molecules, namely, ortho-hydrogen with even rotational quantum numbers and para-hydrogen with odd rotational quantum numbers, which retain their individuality over long periods at very low temperatures. By the use of the classical statistics, he was able to show that at very low temperatures hydrogen, as obtained by cooling hydrogen gas from ordinary temperatures, ought to have very nearly the experimentally observed chemical constant. Since the theory of the specific heat of hydrogen yielded correct values at low temperatures, it followed that at ordinary temperatures also his theory would yield a correct value for the chemical constant. Finally from the form of the partition function for hydrogen gas, Fowler attempted to obtain inferences concerning the validity of Nernst's heat theorem. By the use of the classical statistics fairly accurate results were obtained. But we shall find that when we make use of the Einstein-Bose statistics-the correct statistics for an assembly of hydrogen moleclues-a result will be obtained for the vapour pressure of hydrogen crystals at low temperatures which will furnish a value for the chemical constant of hydrogen in even closer agreement with experiment than Fowler's result.