Heats of Linkage of C-H and N-H Bonds from Vibration Spectra

The visible and near infra-red absorption data for several representative molecules are taken from a previous paper and fitted to the formula of an anharmonic vibrator, ${\nu }^n={\omega }^{0}n-b{n}^2$. The mechanical frequencies, ${\omega }^n={\omega }^0-2\mathrm{bn}$, are evaluated and plotted. Assuming that these frequencies originate in oscillations between a hydrogen atom and the remainder of the molecule, the restoring force residing in the C-H and N-H bonds, the heats of linkage of these bonds are calculated. The method originated by Birge and Sponer for the determination of the heats of dissociation of non-polar, diatomic, gaseous molecules is used. The heats of linkage for a hexane C-H bond is calculated to be 97,000 cal/mol in fair agreement with the 92,500 cal/mol value obtained thermochemically for its homologue, methane. The values for the heat of linkage vary among the different types of molecules, having the relatively high value of 117,000 cal/mol for benzene C-H bonds. The value for the N-H heat of linkage is calculated for one substance, aniline. It evaluates as 113,000 cal/mol and is believed to agree with the 101,000 cal/mol obtained thermochemically for an ammonia N-H bond within the limits of determination of the former value. A possible explanation of the doubleness of the absorption bands observed in the spectra of several substances, notably hexane and cyclohexane, is sought in two types of carbon valence. This doubleness indicates a slight inequivalence in the energy content of two types of C-H bond.