If the volume and temperature are kept constant, and nothing is added to the reaction mixture, what happens to the total pressure during the course of the reaction?

The ideal gas law is pV=nRT, where p = pressure, V = volumne, n = number of moles, R = gas constant, and T = temperature. If volume, temperature, and number of moles are kept constant, pressure will also be constant during the reaction since the gas constant is also unchanging.