The 10% sodium bicarbonate solution is made in the plant by adding two 50-lb_m bags of NaHCO₃ powder to a batch dissolving tank filled to roughly 80% of its capacity. From the dissolving tank, the solution is sent to a feed drum from which solution is pumped continuously to the resin neutralizer. It takes an operator four hours to make a batch of solution, pump the solution to the feed drum, and rinse the dissolving tank to prepare it for the next batch. The feed drum can hold a 2.5-day supply of solution. The addition of each new batch of solution brings the feed drum contents up to a 2-day (48- hour) supply, so that the plant can continue to run for at least 40 hours if the bicarbonate powder inventory runs low or the dissolver is shut down for maintenance.

(a) Calculate the feed drum volume (liters), the volume of solution made in each batch (liters), and the probable volume of the dissolving tank (liters).

(b) What is the minimum dissolving tank volume needed to meet the requirements of the process, assuming that roughly four hours would be required to prepare a batch of any size and the tank is always filled to 80% of its capacity? What are the benefits of using a larger tank?

(c) Suppose the dissolver agitator breaks down just after an operator finishes transferring a batch of solution to the feed drum and it takes 32 hours to repair the agitator. How quickly can the operators replenish the 48-hour supply of solution in the feed drum once the agitator has been repaired? What would have happened if the minimum tank volume calculated in part (b) had been used?

(d) The feed drum is outdoors. Neglecting dissociation of NaHCO₃ in solution, estimate the outside temperature (°C) at which freezing of the tank contents would become a concern. (Use Equation 6.5-5.) The calculated temperature would be a conservative estimate, since dissociation of the salt would lower the freezing point of water even more.