Box models are widely used in air pollution modeling. They allow the use of simple computational tools instead of the simulation of 3D Eulerian grid models, given by a large set of partial differential equations. We investigate the theoretical justification of such box models. The key point is the comparison with the underlying Eulerian model describing the dispersion of pollutants in the atmosphere. We restrict the study to a vertical monodimensional case for more clarity. The main result is that the nonlinearity of the chemical kinetics, which is a characteristic feature of chemistry, induces the loss of accuracy