A gas that contains CO2 is contacted at time = 0 with initially pure liquid water in an agitated batch absorber. With CA(mol/cm3) as the concentration of CO2 in the liquid, PA(atm) as the partial pressure of CO2 in the gas phase, and HA (atm/(mol/cm3)) as the Henry’s Law constant, Henry's Law relates the equilibrium concentration in the liquid phase (C*A) to the partial pressure via the equation C*A=PA/HA. The rate of absorption of CO2 from the gas to the liquid per unit liquid-to-gas interfacial area is given by the expression RA=k(C*A−CA), where k(cm/s) is the mass transfer coefficient. The interfacial area is S (cm2). You may assume k and S are constant. The gas phase is at a total pressure P (atm) and contains YA(mol CO2/mol gas), and the liquid phase initially consists of V(cm3) of pure water. The agitation of the liquid phase is sufficient for the liquid composition to be considered spatially uniform, and the amount of CO2 absorbed is low enough for YA, V, and P to be considered constant throughout the process. Starting with the general balance equation (in - out + gen = acc), use a mole balance on A (=CO2) in the liquid phase to derive an expression for dCA/dt and provide the initial condition. Show that your equation is dimensionally consistent. Without doing any calculations, sketch a plot of CA versus t and include axis limits (value of CA at t= 0 and what CA approaches at long time). Integrate the equation to get an expression for CA(t). Type the final form of CA(t) here. Final form should not include C*A.
A gas that contains CO2 is contacted at time = 0 with initially pure liquid water in an agitated batch absorber. With CA(mol/cm3) as the concentration of CO2 in the liquid, PA(atm) as the partial pressure of CO2 in the gas phase, and HA (atm/(mol/cm3)) as the Henry’s Law constant, Henry's Law relates the equilibrium concentration in the liquid phase (C*A) to the partial pressure via the equation C*A=PA/HA. The rate of absorption of CO2 from the gas to the liquid per unit liquid-to-gas interfacial area is given by the expression RA=k(C*A−CA), where k(cm/s) is the
The gas phase is at a total pressure P (atm) and contains YA(mol CO2/mol gas), and the liquid phase initially consists of V(cm3) of pure water. The agitation of the liquid phase is sufficient for the liquid composition to be considered spatially uniform, and the amount of CO2 absorbed is low enough for YA, V, and P to be considered constant throughout the process.
Starting with the general balance equation (in - out + gen = acc), use a mole balance on A (=CO2) in the liquid phase to derive an expression for dCA/dt and provide the initial condition. Show that your equation is dimensionally consistent. Without doing any calculations, sketch a plot of CA versus t and include axis limits (value of CA at t= 0 and what CA approaches at long time). Integrate the equation to get an expression for CA(t). Type the final form of CA(t) here. Final form should not include C*A.
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