Molecular diffusivities of H2 16O, HD16O, and H2 18O in gases

Abstract

Isotopic effects on the molecular diffusion coefficients of $H_2{\hspace{0.17em}}^{16}\mathrm{O},$ ${\mathrm{HD}}^{16}\mathrm{O},$ and ${\mathrm{H}}_2{\hspace{0.17em}}^{18}\mathrm{O}$ have been determined by two independent methods. In the first one, the evaporation of liquid water under controlled laminar flow conditions was investigated. In the second one, the transport of water vapor through a diffusion tube was measured. The molecular diffusion coefficient of natural water vapor in nitrogen was redetermined. At 21 °C and $\text{P=760\hspace{0.17em}}\mathrm{Hg}\hspace{0.17em}\mathrm{mm},$ $\text{D=0.244±0.004\hspace{0.17em}}{\mathrm{cm}}^2/\sec .$ For the isotopic molecules we have $D_{{\mathrm{HD}}^{16}\mathrm{O}}{\mathrm{/D}}_{H_2^{16}\mathrm{O}}\text{=0.9757±0.0009}$ and $D_{{\mathrm{H}}_2^{18}\mathrm{O}}{\mathrm{/D}}_{H_2^{16}\mathrm{O}}\text{=0.9727±0.0007.}$ Agreement between the data obtained in the pure gas phase experiment and the two‐phase experiment shows that the condensation coefficients of the isotopically substituted molecules are identical. Interpretation of the isotopic effects on molecule diffusivities indicates that the relative mass differences between $H_2{\hspace{0.17em}}^{16}\mathrm{O},$ ${\mathrm{HD}}^{16}\mathrm{O},$ and ${\mathrm{H}}_2{\hspace{0.17em}}^{18}\mathrm{O}$ alone cannot account for the experimental results. This is more important for the D–H substitution in which the asymetric molecule ${\mathrm{HD}}^{16}\mathrm{O}$ is formed. Qualitatively, the displacement of the center of gravity of the molecules $H_2{\hspace{0.17em}}^{16}\mathrm{O}$ and ${\mathrm{HD}}^{16}\mathrm{O}$ in this substitution can explain the observed effect. Interpretation of these isotopic effects in terms of simple kinetic theory of gases indicates that for rigid spherical molecule models with diameters Γ we have the relation ${\Gamma }_{{\mathrm{H}}_{2^{18}\mathrm{O}}}{\mathrm{<\Gamma }}_{{\mathrm{H}}_2^{16}\mathrm{O}}{\mathrm{<\Gamma }}_{{\mathrm{HD}}^{16}\mathrm{O}}.$ We calculate from the experimental data ratio of the coefficients of diffusion of the three isotopic molecules in air $D_{{\mathrm{HD}}^{16}\mathrm{O}}{\mathrm{/D}}_{{\mathrm{H}}_2^{16}\mathrm{O}}\text{=0.9757±0.0009}$ and $D_{{\mathrm{H}}_2^{18}\mathrm{O}}{\mathrm{/D}}_{H_2^{16}\mathrm{O}}\text{=0.9727±0.0007.}$