The Dispersion of Sound in Nitrogen Tetroxide and Its Interpretation in Terms of Dissociation Rate

Several types of dispersion of sound which may be manifest in a dissociating gas are discussed. Of these only the heat-capacity dispersion and the dissociation dispersion need be considered under suitable experimental conditions. The expression derived by Einstein for the velocity of sound in a dissociating gas has been modified to include heat-capacity dispersion. The experimental procedure indicated by this for obtaining significant dissociation rate constants is outlined. Measurements on the velocity of sound in nitrogen tetroxide which have been made with apparatus of special design, are reported. The range of temperature studied is 0°C to 30°C, the range of pressure 132 mm to 670 mm, and the range of frequency 9 kc to 451 kc. The velocity of sound has been thus defined with an estimated error of ±0.1 m·sec.—1. The maximum dispersion which has been observed is about 5 m·sec.—1. From these measurements it appears that the rate constant of the dissociation reaction is 4.8×104±0.5×104 at 25°C and 260 mm. The activation energy obtained for the dissociation reaction is 13.9±0.9 kg·cal. The rate constant appears to diminish slightly as the pressure is reduced. Since an upper limit for the heat capacity of nitrogen tetroxide is fixed by experiment, it is necessary to suppose that the effective molecular diameters for the activation process are at least three times those for ordinary kinetic collisions.