3. (50 points) A 20L batch of hard water is treated to remove with a strong acid cation ion-exchange resins (made of polystyrene with 8% DVB crosslinking). The hard water initially contains 0.1 M Nat and 0.1 M Mg2+. The capacity of the resins is 1.5 eq/L and the resins are initially charged with Nat. (a) What is the volume of the resins that is needed to remove 90% Mg2+ in the solution? (b) After the ion- exchange process is completed, regeneration of the resin is achieved by transferring the resins into a 10L highly concentrated 1 M sodium chloride solution. Calculate the final concentrations of Mg2+ and Nat in the solution, and the concentrations of MgR2 and NaR in the resin