Recent measurements of the resonance frequency of a copper disk covered with carbon nanotube bundles have shown characteristic resonance shifts during exposure with various gas molecules. The shifts were interpreted as the change of the dielectric permittivity of the system forming the sensor due to the electric properties of the adsorbed molecules. Starting from a simplified sensor model formed by one single wall nanotube, we develop a self-consistent approach to describe the variation of the linear dielectric susceptibility of the tube at the atomic scale when molecules are adsorbed at its external surface. The sensitivity of this model sensor is tested as a function of the apolar or polar nature of the admolecules, their adsorption geometry, their concentration, and the characteristics of the tube (length, diameter,...). The comparison with data on dielectric constant changes vs adsorption, coming from measurements of the resonance frequency shifts, displays striking agreement for most of the molecular species considered.