The Rate of Dissociation of Nitrogen Tetroxide

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Abstract
It has long been supposed that the rate of dissociation of nitrogen tetroxide could be calculated from observations of the dispersion of the sound in the gas. Einstein's equations gave the velocity constant in terms of the dispersion and the properties of the substances, regarded as ideal, acoustically transparent gases. Dispersion has been reported and rate constants calculated by several observers. On the other hand an equal number of negative results have been reported. Recently the theory has been examined critically by D. G. C. Luck and modified to take account of the absorption of sound and the deviations from the gas laws. Moreover dispersion has been observed for nondissociating gases, particularly carbon dioxide. In this gas, time lag in the equilibrium between vibrational and translational‐rotational degrees of freedom causes an increase of velocity exactly parallel with that caused by dissociation. Indeed any type of equilibrium in the system may be expected to produce a dispersion of sound in some frequency region related to its own frequency, and it is not possible to distinguish between the types of equilibrium by sound measurements. The use of very small measuring tubes also produces a dispersion of somewhat smaller magnitude. Under these circumstances it is difficult to see how any interpretation can be made or conclusions drawn. In a series of measurements made during the last five years, the author has found no measurable dispersion of sound in N2O4 up to 53.8 kc. The velocity of sound at this frequency agreed closely with that determined by Grüneisen and Goens at audible frequencies, although high absorption made observation difficult. At higher frequencies no evidence of transmission could be obtained although sound up to 860 kc was employed. This increasing absorption shows that we are entering a dispersive region but it is not possible to say whether dissociation, time lag, or a combination of both is responsible for the dispersion. This applies equally to the velocity increases found by Richards and Reid in the same frequency region. Hence it seems that the sonic method for measuring rates of dissociation is not likely to fulfill the hopes of its proponents, and further experimental work will not be fruitful.
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