Chapter 6, Problem 6.89P

Sodium bicarbonate is synthesized by reacting sodium carbonate with carbon dioxide and water at 70°C and 2.0 atm gauge pressure:

   ${\text{Na}}_{\text{2}}{\text{CO}}_{\text{3}}{\text{+CO}}_{\text{2}}{\text{+H}}_{\text{2}}\text{O}\to {\text{2NaHCO}}_{\text{3}}$

An aqueous solution containing 7.00 wt% sodium carbonate and a gas stream containing 70.0 mole% CO₂and the balance air are fed to the reactor. All of the sodium carbonate and some of the carbon dioxide in the feed react. The gas leaving the reactor, which contains the air and unreacted CO₂, is saturated with water vapor at the reactor conditions. A liquid—solid slurry of sodium bicarbonate crystals in a saturated aqueous solution containing 2.4 wt% dissolved sodium bicarbonate and a negligible amount of dissolved CO₂leaves the reactor and is pumped to a ?lter. The wet ?lter cake contains 86 wt% sodium bicarbonate crystals and the balance saturated solution, and the ?ltrate also is saturated solution. The production rate of solid crystals is 500 kg/h.

Suggestion: Although the problems to be given can be solved in terms of the product ?ow rate of 500 kg NaHCO₃(s)/h, it might be easier to assume a different basis and then scale the process to the desired production rate of crystals.

(a) Calculate the composition (component mole fractions) and volumetric ?ow rate (m³/min) of the gas stream leaving the reactor.

(b) Calculate the feed rate of gas to the process in standard cubic meters/min [m³(STP)/min].

(c) Calculate the ?ow rate (kg/h) of the liquid feed to the process. What more would you need to know to calculate the volumetric ?ow rate of this stream?

(d) The ?ltrate was assumed to leave the ?lter as a saturated solution at 70°C. What would be the effect on your calculations if the temperature of the ?ltrate actually dropped to 50°C as it passed through the ?lter?

(e) The reactor pressure of 2 atm gauge was arrived at in an optimization study. What bene?t do you suppose would result from increasing the pressure? What penalty would be associated with this increase? The term “Henry's law" should appear in your explanation. (Hint: The reaction occurs in the liquid phase and the CO₂enters the reactor as a gas. What step must precede the reaction?)