We investigate the kinetic equation of electrons in a weakly-ionized plasma. We consider configurations that are characteristic of industrial atomic plasmas, such as those used for material processing for nanoelectronics (both for deposition and etching thin films) or electric propulsion. The starting point is the generalized Boltzmann equation, including the electrostatic force, electron-electron, electron-ion, and electron-gas elastic collisions, electron-gas inelastic collisions, and electron-gas reactive collisions. We perform a dimensional analysis of this equation and analyse the order of magnitude of the resulting non-dimensional numbers under the considered conditions. We propose a perturbative solution of the kinetic equation based on a Hilbert expansion, where we exploit the mass disparity of the electrons and the heavy-species (ions and atoms) to simplify the collision operators, as previously proposed by Graille et al. [1]. We analyze the resulting integro-differential equations at successive orders of approximation. We propose a moment model where the macroscopic variables are the scalar even velocity moments whereas the vectorial odd moments are computed as transport fluxes, as done in Alvarez Laguna et al. [2]. Different moment closures will be studied, including regularized-Grad’s models, quadrature moment models and entropy based closures. [1] Graille et al. Math. Models Methods Appl. Sci. 19, 527-599 (2009) [2] A. Alvarez Laguna, et al. Phys. Plasmas 29, 083507 (2022)