Sodium bicarbonate is synthesized by reacting sodium carbonate with carbon dioxide and water at 70°C and 2.0 atm gauge: Na₂CO₃ + CO₂ + H₂0 → 2 NaHCO₃ an aqueous solution containing 7.00 wt% sodium carbonate and a gas stream containing 70.0 mole% CO₂ and 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 un-reacted 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 no dissolved CO₂ leaves the reactor and is pumped to a filter. The wet filter cake contains 86 wt% sodium bicarbonate crystals and the balance saturated solution, and the filtrate is also 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 flow 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 flow rate (m3lmin) of the gas stream leaving the reactor.

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

(c) Calculate the flow rate (kWh) of the liquid feed to the process. What more would you need to know to calculate the volumetric flow rate of this stream?

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

(e) The reactor pressure of 2 atm gauge was arrived at in an optimization study. What benefit do you suppose would result from increasing the pressure? What penalty would be associated with this increase? The term “Henrys law” should appear in your explanation.