Question $4.$ Consider that an elementary chemical reaction $A2B$ is taking place in a perfectly mixed vessel shown in Figure $3.$ The influent to the vessel has volumetric rate $F_f(\frac{m^3}{s}),$ density ${}_f(k\frac{g}{m^3}),$ and mole fraction $y_f.$ Product comes out of the reactor with volumetric rate $F_o,$ density ${}_o,$ and mole fraction $y_o.$ The temperature and volume inside the vessel are constant. The reactor effluent passes through control valve which regulate the gas pressure at constant pressure $P_g.$ Write down the continuity equations for the given system.