Ionization cooling is a critical building block for the realization of a muon collider. To suppress breakdown in the presence of the external magnetic field, an idea of using an RF cavity filled with high pressure hydrogen gas is being considered for the cooling channel design. One possible problem expected in the high pressure RF cavity is, however, the dissipation of significant RF power through the beam-induced electrons accumulated inside the cavity. To characterize this detrimental loading effect, we develop a simplified model that relates the electron density evolution and the observed pickup voltage signal in the cavity, with consideration of several key molecular processes such as the formation of the polyatomic molecules, recombination and attachment. This model is expected to be compared with the actual beam test of the cavity in the MuCool Test Area (MTA) of Fermilab.