Calculate the quantities of lime and soda ash for excess-lime softening, and the carbon dioxide reacted for neutralization by two-stage recarbonation. Assume that the practical limits of hardness removal for calcium are 30 mg/l as and for magnesium are 10 mg/l as and that three-quarters of the final alkalinity is converted to bicarbonate. Calculate the finished hardness and sketch the bar graphs for the raw and finished waters.