Magnetohydrodynamic (MHD) is one of the most promising novel propulsion technologies with the advantages of no pollution, high specific impulse, and high acceleration efficiency. As the carrier of this technology, the MHD accelerator has enormous potential for applications in hypersonic wind tunnels, supersonic ramjet engines, and deep space propulsion. In this study, a three-dimensional numerical simulation of an ideal Faraday magnetohydrodynamic (MHD) accelerator is conducted to assess the effect on performance with respect to applied potential and magnetic field intensity. The study is performed by employing a low magnetic Reynolds number MHD model coupled with a 7-component chemical reaction model to simplify the impact of real gas effects. The chemical reaction exhibits an increasing trend with rising applied potential and a decreasing trend with diminishing magnetic field strength. This variation influences the gas conductivity, subsequently affecting the velocity and thrust of the system. Specifically, at a magnetic field intensity of 2.0 T and an applied potential of 600 V, the accelerator exhibits maximum velocity and thrust growth rates of 18.6% and 59.8%, respectively.