One hundred fifty k mol of an aqueous phosphoric acid solution contains 5.00 mole% H3PO4. The solution is concentrated by adding pure phosphoric acid at a rate of 20.0 L/min.

(a) Write a differential mole balance on phosphoric acid and provide an initial condition. [Start by defining np (k mol) to be the total quantity of phosphoric acid in the tank at any time.]

(b) Solve the balance to obtain an expression for np (t). Use the result to derive an expression for x(t), the mole fraction of phosphoric acid in the solution.

(c) How long will it take to concentrate the solution to 15% H3PO4?