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 Henry's law (Section 6.4b) CA = pA/HA where CA (mol/cm3) = concentration of CO2 in solution PA (atm) = partial pressure of CO2 in the gas phase HA [atm/ (mol/cm3)] = Henry's law constant
(a) Write a differential balance on CO2 in the liquid phase and integrate it to derive the relation CA (t) = C*A [1 - exp (- kSt/V)] where S (cm2) is the effective contact area between the gas and liquid phases.
(b) 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 Henry's 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.