Adsorption kinetics on energetically heterogeneous surfaces under isothermal conditions is analyzed using the uniform energy distribution model. Considering the quasi-equilibrium of surface diffusion between the adsorption sites with different energy, the kinetic equations d Theta/dt = (k(a)P - A(d)K(diff))(1 - Theta) for first-order adsorption and d Theta/dt = k(a)P(1 - Theta)(2) - A(d)K(diff)Theta(1 - Theta) for dissociative adsorption are obtained, where K-diff is a coefficient describing the surface diffusion equilibrium, which depends on the coverage and the energy distribution. Under isochoric conditions with p decreasing due to adsorption, surface diffusion accelerates the rate towards equilibrium significantly, as observed in static calorimetric adsorption experiments. An approximate solution in Lagergren form is derived for this condition. (c) 2007 Elsevier B.V. All rights reserved.