Dependence of the rate of formation of nitrate ions in water on the intensity and frequency of ultrasound waves

The dependence of the rate of the sonochemical formation of nitrate ions in water saturated with air on the intensity (within 0–2.5 W/cm²) and frequency (20–1600 kHz) of ultrasound waves was studied. The acoustic power was measured by the comparative calorimetric method. The reaction was conducted in the kinetic region, where the reaction rate was independent of the rate of mass transfer processes, such as the degasification and stirring of the solution and the depletion of the reactants, being determined only by the formation of radicals in cavitation bubbles. It was demonstrated that, within the indicated range of ultrasound frequencies, the dependence of the reaction rate on the ultrasound intensity behaved as follows: at intensities below 0.1–0.2 W/cm², the w(I) dependence is nonlinear and can be roughly approximated by a quadratic function; at I > 0.2 W/cm², w(I) becomes linear. This behavior can be explained in the following way: at I < 0.2 W/cm², with increasing I, both the fraction of acoustic power absorbed by the cavitation cloud and the reaction rate in the cavitation cloud increase; as I increases still further, nearly the entire acoustic power is absorbed by the cavitation cloud, and the w(I) dependence becomes linear. To make it possible to compare the sonochemical effects of ultrasound waves at different frequencies, a criterion K was introduced, which was defined as the slope of the w(I) plot within its linear portion (at I > 0.2 W/cm²). The K(f) dependences passes through a maximum at a frequency of f ∼ 100 kHz; at frequencies of f > 500 kHz, K ∼ f ⁻¹.