Derive the design equation for a CSTR.

From steady-state mole balance on reactant A: (molar flow in) - (molar flow out) + (generation by reaction) = 0. FA0 - FA + rA*V = 0, where FA0 = CA0*v0, FA = CA*v0 = CA0*(1-X)*v0, and rA is negative for reactant consumption. Rearranging: V/FA0 = -X/rA or tau = CA0*X/(-rA). Since CSTR is uniform, rA is evaluated at exit conditions. This shows larger volumes needed for low concentrations (high conversion) where rate is low.