The reaction rate in some important catalytic systems is governed by kinetics of dissociative adsorption of reactants on a catalyst surface. This, for instance, is the case of ammonia synthesis. Since the beginning of the previous century, the expressions based on the theory of activated adsorption/desorption (TAAD) approach have commonly been attempted to analyze the pressure and coverage dependence of the observed kinetics. However, neither the simple classical TAAD approach nor its further modifications attempted during the last few decades could explain the kinetics observed in many important systems. In particular, it concerned the kinetics of dissociative adsorption in chemisorption systems. For instance, no successful attempt was published to describe quantitatively the pressure and coverage dependence of the kinetics of the dissociative dinitrogen adsorption on iron surfaces, studied for a large part of the previous century, in relation to ammonia synthesis. Here we propose the first successful description of that dissociative adsorption kinetics based on the new statistical rate theory approach, linking the rate of the dissociative kinetics to the chemical potentials in the bulk and the adsorbed phases. The developed theoretical expressions are able to describe quantitatively the kinetic isotherms of dinitrogen dissociative adsorption, recorded experimentally at the pressures ranging from 10(-6) to 10(2) Torr and the temperatures ranging from 140 to 485 K. These expressions also explain some unusual features of this dissociative kinetics, such as small negative apparent activation energy for the dissociative adsorption and the pressure invariance of the kinetics at high dinitrogen pressures, when considered as a function of exposure.