The individual mass transfer co-efficients (moles/m² . s) for absorption of a solute from a gas mixture into a liquid solvent are, K_L = 4.5 and K_G = 1.5. The slope of the equilibrium line is 3. Which of the following resistance (s) is (are) controlling ?

ANS:B - gas side

To determine which resistance(s) are controlling the mass transfer process in this case, we can use the concept of overall mass transfer coefficient (𝐾𝑜𝑣𝑒𝑟𝑎𝑙𝑙Koverall​) and the slope of the equilibrium line (𝑚m). The overall mass transfer coefficient can be calculated using the formula: 1𝐾𝑜𝑣𝑒𝑟𝑎𝑙𝑙=1𝐾𝐿+1𝐾𝐺Koverall​1​=KL​1​+KG​1​ Given:

• 𝐾𝐿=4.5KL​=4.5 moles/m²·s (liquid phase mass transfer coefficient)
• 𝐾𝐺=1.5KG​=1.5 moles/m²·s (gas phase mass transfer coefficient)

Using the given values: 1𝐾𝑜𝑣𝑒𝑟𝑎𝑙𝑙=14.5+11.5=13+23=1Koverall​1​=4.51​+1.51​=31​+32​=1 Therefore, 𝐾𝑜𝑣𝑒𝑟𝑎𝑙𝑙=1Koverall​=1 moles/m²·s. The slope of the equilibrium line (𝑚m) is given as 3. Now, the slope of the operating line (𝑚′m′) is related to the overall mass transfer coefficient (𝐾𝑜𝑣𝑒𝑟𝑎𝑙𝑙Koverall​) by the equation: 𝑚′=𝐾𝐿𝐾𝐺=𝑚1−𝑚m′=KG​KL​​=1−mm​ Given that 𝑚=3m=3, we can solve for 𝑚′m′: 𝑚′=31−3=−1m′=1−33​=−1 The negative slope of the operating line indicates that the liquid side resistance is controlling the mass transfer process. So, in this case, the controlling resistance is liquid side.