The Vapor Pressure Constant of Methane

\textsection{}1. It can be shown by statistical quantum mechanics that the vapor pressure constant of a molecule whose principal moments of inertia are all equal to $A$ is $i=log (\frac{64{\ensuremath{\pi}}^{5}{k}^{4}{m}^{\frac{3}{2}}{A}^{\frac{3}{2}}}{{h}^{6}})+{\ensuremath{\Sigma}}_{r}{D}_{r}log (\frac{{G}_{r}}{_{r}\ensuremath{\omega}_{0}})$ at ordinary temperatures; where $m$ is the mass, $k$ is Boltzmann's constant, $h$ is Planck's constant, the ${D}_{r}'\mathrm{s}$ are the gram molecular fractions of the two varieties, and where the ${\mathrm{G}}_{r}'\mathrm{s}$ and $_{r}\ensuremath{\omega}_{0}'\mathrm{s}$ are constants.\textsection{}2. It is found that ${G}_{1}$ for methane is $\frac{5}{12}$, ${G}_{2}$ is $\frac{9}{12}$ and ${G}_{3}$ is $\frac{2}{12}$.\textsection{}3 and \textsection{}4. It is shown by quantum mechanics that $_{1}\ensuremath{\omega}_{0}$ for methane is 5, $_{2}\ensuremath{\omega}_{0}$ is 9, and $_{3}\ensuremath{\omega}_{0}$ is 2; if the spins of the hydrogen nuclei are taken into consideration but the spin of the carbon nucleus neglected, which is permissible.\textsection{}5. With the value $A=5.17\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}40}$ c.g.s. units, it is found that the vapor pressure constant in atmospheres and common logarithms of methane at ordinary temperatures should be -1.94. The experimental result given by Eucken, -1.97\ifmmode\pm\else\textpm\fi{}0.05, agrees with this.