Steady-state dissolution of benzoic acid (described by a single ODE). Water is initially passed through a tube constructed of solid benzoic acid. Because benzoic acid is slightly soluble in water with...

Steady-state dissolution of benzoic acid (described by a single ODE). Water is initially passed through a tube constructed of solid benzoic acid. Because benzoic acid is slightly soluble in water with a maximum (i.e., saturation) solubility, Csat moles acid/L solution at the given temperature. The inner walls of the tube will dissolve very slowly. By weighing the dried tube before and after exposure, it is possible to calculate the rate of mass transfer. Take a quasi-steady state material balance for plug velocity profiles and show that the ODE obtained is:Where D denotes the inner tube diameter (assuming that it barely changes with dissolution process, hence constant), uo is liquid velocity, and kc is the mass transfer coefficient