Reactions of ${\mathrm{H}}^{+}$ in ${\mathrm{H}}_2$ and ${\mathrm{D}}^{+}$ in ${\mathrm{D}}_2$; Mobilities of Hydrogen and Alkali Ions in ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ Gases

Measurements of transport parameters of low-energy mass-identified ions in ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ gases have been made in a drift-tube mass spectrometer at room temperatures. In addition, the variable drift distance of this apparatus has been used to vary the residence time of the ions in the gases to determine ion-molecule reaction rates. The zero-field reduced mobilities of ${\mathrm{H}}^{+}$ and $\mathrm{H}_3^{}{}_{}{}^{+}$ in ${\mathrm{H}}_2$ were found to be 15.7 ± 0.6 and 11.1 ± 0.5 ${\mathrm{cm}}^2$/V sec, respectively. Those for ${\mathrm{D}}^{+}$ and $\mathrm{D}_3^{}{}_{}{}^{+}$ in ${\mathrm{D}}_2$ were found to be 11.2 ± 0.5 and 8.0 ± 0.3 ${\mathrm{cm}}^2$/V sec, respectively. The zero-field reduced mobilities for ${\mathrm{Li}}^{+}$, ${\mathrm{Na}}^{+}$, and ${\mathrm{K}}^{+}$ ions in ${\mathrm{H}}_2$ were measured to be 12.3 ± 0.6, 12.2 ± 0.6, and 12.8 ± 0.6 ${\mathrm{cm}}^2$/V sec. The zero-field reduced mobilities for these same alkali ions in ${\mathrm{D}}_2$ were measured to be 9.6 ± 0.5, 8.9 ± 0.4, and 9.4 ± 0.5 ${\mathrm{cm}}^2$/V sec, respectively. The mobilities of ${\mathrm{H}}^{+}$, $\mathrm{H}_3^{}{}_{}{}^{+}$, ${\mathrm{Li}}^{+}$, ${\mathrm{Na}}^{+}$, and ${\mathrm{K}}^{+}$ in ${\mathrm{H}}_2$ were found to be related to the mobilities of ${\mathrm{D}}^{+}$, $\mathrm{D}_3^{}{}_{}{}^{+}$, ${\mathrm{Li}}^{+}$, ${\mathrm{Na}}^{+}$, and ${\mathrm{K}}^{+}$ in ${\mathrm{D}}_2$, respectively, by the appropriate ratios of the square roots of the reduced masses in each case, as predicted by Langevin's theory. However, the mobilities within either set of ions in a given gas did not follow the ${M_r}^{\frac{-1\mathrm{}}{2}}$ reduced mass dependence. The three-body reaction rate coefficients for the reactions ${\mathrm{H}}^{+}$ + 2${\mathrm{H}}_2$ → $\mathrm{H}_3^{}{}_{}{}^{+}$ + ${\mathrm{H}}_2$ and ${\mathrm{D}}^{+}$ + 2${\mathrm{D}}_2$ → $\mathrm{D}_3^{}{}_{}{}^{+}$ + ${\mathrm{D}}_2$ were found to be (3.2 ± 0.3) and (3.0 ± 0.4) × ${10}^{-29\mathrm{}}$ ${\mathrm{cm}}^6$/sec, respectively, and were observed to be independent of $\frac{E}{N}$ in the thermal range ($\frac{E}{N}<28\mathrm{}\times {10}^{-17\mathrm{}}$ V ${\mathrm{cm}}^2$) and independent of the gas pressure from 0.1 to 0.6 Torr. A classical calculation shows that the assumption of Langevin-type spiraling collisions between the ions and gas molecules does not yield collision times long enough to account for the large three-body rate coefficients measured. Finally, a few measurements of the radial diffusion coefficient for $\mathrm{H}_3^{}{}_{}{}^{+}$ ions in ${\mathrm{H}}_2$ have been made, and they agree with those reported by Dutton et al., within the scatter in the data, but not with those reported by Skullerud.