. A gas that contains CO2 is contacted with liquid water in an agitated batch absorber

QUESTION:

. A gas that contains CO2 is contacted with liquid water in an agitated batch absorber. The equilibrium solubility of CO2 in water is given by Henrys law (Section 6.4b) CA pA/HA where CAmol/cm3 concentration of CO2 in solution, pAatm partial pressure of CO2 in the gas phase, and HAatm/mol/cm3 Henrys law constant. The rate of absorption of CO2 (i.e., the rate of transfer of CO2 from the gas to the liquid per unit area of gasliquid interface) is given by the expression rA mol/cm2 s k C* A CA where CA actual concentration of CO2 in the liquid, C* A concentration of CO2 in the liquid that would be in equilibrium with the CO2 in the gas phase, and kcm/s a mass transf er coef f icient. The gas phase is at a total pressure P(atm) and contains yAmol CO2/mol gas, and the liquid phase initially consists of Vcm3 of pure water. The agitation of the liquid phase is sufficient for the composition to be considered spatially uniform, and the amount of CO2 absorbed is low enough for P, V, and yA to be considered constant throughout the process. (a) Derive an expression for dCA/dt and provide an initial condition. Without doing any calculations, sketch a plot of CA versus t, labeling the value of CA at t 0 and the asymptotic value at t ! 1. Give a physical explanation for the asymptotic value of the concentration. (b) Prove that CAt pA HA 1 expkSt/V where Scm2 is the effective contact area between the gas and liquid phases. (c) Suppose the system pressure is 20.0 atm, the liquid volume is 5.00 liters, the tank diameter is 10.0 cm, the gas contains 30.0 mole% CO2, the Henrys law constant is 9230 atm/(mole/cm3 ), and the mass transfer coefficient is 0.020 cm/s. Calculate the time required for CA to reach 0.620 mol/L if the gas-phase properties remain essentially constant. (d) If A were not CO2 but instead a gas with a moderately high solubility in water, the expression for CA given in Part (b) would be incorrect. Explain where the derivation that led to it would break down.