The Heat of Dissociation of Non-Polar Molecules

Abstract

Heat of dissociation from band spectra data.---The limiting amount of vibrational energy which a diatomic molecule can possess is given by ${E}_{n}=h\ensuremath{\int}{o}^{{n}_{o}}{\ensuremath{\omega}}^{n}\mathrm{dn},$ where ${\ensuremath{\omega}}^{n}$ is the frequency of vibration, as a function of the vibrational quantum number $n$, and ${n}_{o}$ is the value of $n$ for ${\ensuremath{\omega}}^{n}=0$. For non-polar molecules ${n}_{o}$ is finite, for polar molecules it is infinite. The ${\ensuremath{\omega}}^{n}:n$ curve for the normal state of each of the molecules here discussed is strictly linear, over the known range, and its linear extrapolation to ${\ensuremath{\omega}}^{n}=0$, for essentially non-polar molecules, seems to give the true value of ${E}_{n}$ to within half a volt. Since increasing the vibrational energy until the two nuclei dissociate, results in the formation of two normal atoms, ${E}_{n}=D$, the heat of dissociation. When a molecule dissociates, while excited by ${E}_{e}$ units of electronic energy, the products of dissociation seem in some cases to include at least one excited atom. The total energy required for the dissociation thus exceeds the true heat of dissociation by the amount of the resulting atomic excitation. The ${\ensuremath{\omega}}^{n}:n$ curves, and the correlated sets of energy levels are shown for all known band systems of ${\mathrm{O}}_{2}$, ${\mathrm{O}}_{2}^{+}$, ${\mathrm{N}}_{2}$, ${\mathrm{N}}_{2}^{+}$, CO, C${\mathrm{O}}^{+}$, and NO.Oxygen. The ${\ensuremath{\omega}}^{n}:n$ curve of one excited state can be followed almost to ${\ensuremath{\omega}}^{n}=0$, and the resulting limiting energy is 7.05\ifmmode\pm\else\textpm\fi{}0.01 volts. The situation is similar to that found in iodine. From the known structure of the oxygen atom, the products of dissociation are either two normal atoms, or one or two atoms excited with 0.02 or 0.03 volts energy. Hence $D=7.02\ifmmode\pm\else\textpm\fi{}0.05$ volts. The linear ${\ensuremath{\omega}}^{n}:n$ curve of the normal state gives 6.65 volts. For ${\mathrm{O}}_{2}^{+}$ the normal state curve gives 6.46 volts, and the only known excited state curve, 6.49 volts. Knowing the heat of dissociation of an ionized molecule (${D}^{\ensuremath{'}}$) and of a neutral molecule ($D$), and the ionization potential of the constituent atom (${I}_{a}$), one can calculate the ionization potential of the molecule (${I}_{m}$), since from conservation of energy, ${I}_{m}+{D}^{\ensuremath{'}}=D+I$. For oxygen this gives ${I}_{m}=14.1$ volts. ${D}^{\ensuremath{'}}=6.5$ volts is however probably too low, and ${I}_{m}=14.1$ volts too high, according to recent work on the spectrum of ${\mathrm{O}}_{2}^{+}$.Nitrogen. From the energy of active nitrogen, $D$ for ${\mathrm{N}}_{2}$ is 11.4 volts. This value can be checked approximately, but not accurately, from band spectra data. The normal state of the nitrogen molecule is not known. ${D}^{\ensuremath{'}}$ is found to be about 9.1 volts, and ${I}_{m}$ is 16.5 volts, giving ${I}_{a}=14.2$ volts, compared to Hopfield's observed value of 14.5 volts. These results for oxygen and nitrogen are in satisfactory agreement with the positive ray work of Hogness and Lunn.Carbon monoxide. $D=11.2$ volts, from the ${\ensuremath{\omega}}^{n}:n$ curve of the normal state. Assuming our value of $D$ for ${\mathrm{O}}_{2}$ and certain chemical data, $D$ for CO can be calculated as 10.8 volts. ${D}^{\ensuremath{'}}=9.8$ volts, from the spectral data. ${I}_{m}$ is known to be closely 14.2 volts, and if C${\mathrm{O}}^{+}$ dissociates into C+${\mathrm{O}}^{+}$, ${I}_{a}=13.56$ volts. The equation ${I}_{m}+{D}^{\ensuremath{'}}=D+{I}_{a}$ checks to 0.3 volts.Nitric oxide. $D=7.9$ volts, from the normal state curve. Assuming our value of $D$ for ${\mathrm{O}}_{2}$ and for ${\mathrm{N}}_{2}$, and certain chemical data, $D$ for NO is 8.3 volts. From one of the excited state curves, the total limiting energy is 17.2 volts, indicating dissociation into one normal nitrogen atom and one 9.1 volt ("resoanance" state) excited oxygen atom.General considerations. The possibility of the dissociation of a molecule adiabatically, by means of light absorption, is discussed and a tentative explanation given of the difference in behavior found in the positive ray analysis for oxygen and nitrogen. The various possible processes resulting in dissociation from excited molecular states are considered in the light of the evidence presented by the known sets of vibrational energy levels.