H₂S is being absorbed in a gas absorber unit. The height of the transfer unit based on the overall mass transfer coefficient on the gas side is 0.4 m. The equilibrium data is given by, y = 1.5 x. The bulk concentration of H₂S has to be reduced from 0.05 to 0.001 mole fraction in the gas side. The height of the tower (in metres) corresponding to an operating line given by, y = 5x + 0.001 is

ANS:A - 2.0

To find the height of the tower corresponding to the given operating line equation, we first need to determine the point of intersection between the operating line and the equilibrium line. The operating line equation is 𝑦=5𝑥+0.001y=5x+0.001. The equilibrium line equation is given as 𝑦=1.5𝑥y=1.5x. To find the point of intersection, we set these two equations equal to each other: 5𝑥+0.001=1.5𝑥5x+0.001=1.5x 3.5𝑥=0.0013.5x=0.001 𝑥=0.0013.5x=3.50.001​ 𝑥≈0.000286x≈0.000286 Now, we can find the corresponding value of 𝑦y using the equilibrium line equation: 𝑦=1.5×0.000286y=1.5×0.000286 𝑦≈0.000429y≈0.000429 The point of intersection is approximately (0.000286, 0.000429). Now, we can calculate the height of the tower using the difference in mole fractions: Δ𝑦=0.05−0.001=0.049Δy=0.05−0.001=0.049 Since the height of the transfer unit (H.T.U.) based on the overall mass transfer coefficient on the gas side is given as 0.4 m, we can calculate the height of the tower using the formula: Height of tower=Δ𝑦H.T.U.Height of tower=H.T.U.Δy​ Height of tower=0.0490.4Height of tower=0.40.049​ Height of tower=0.1225 mHeight of tower=0.1225m So, the height of the tower corresponding to the given operating line equation is approximately 0.1225 m0.1225m.