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Mass Transfer - Engineering

Q1:

Compound A is extracted from a solution of A + B into a pure solvent S. A Co-current unit is used for the liquid-liquid extraction. The inlet rate of the solution containing A is 200 moles of B/hr.m2 and the solvent flow, rate is 400 moles of S/m2. hr. The equilibrium data is represented by Y = 3X2 , where Y is in moles of a A/moles of B and X is in moles A/moles of S. The maximum percentage extraction achieved in the unit is

A 25%

B 50%

C 70%

D 90%

ANS:B - 50%

To find the maximum percentage extraction achieved in the unit, we need to determine the outlet concentration of A in the solvent phase. Given:

  • Inlet rate of solution containing A (B component) = 200 moles of B/hr.m²
  • Solvent flow rate = 400 moles of S/hr.m²
  • Equilibrium relationship: 𝑌=3𝑋2Y=3X2, where Y is moles of A/moles of B and X is moles of A/moles of S
We can find the outlet concentration of A (B component) using the equilibrium relationship and the overall material balance equation: Material balance equation: Inlet flow rate of A = Outlet flow rate of A 200×(1−𝑋)=400×𝑋200×(1−X)=400×X Solving for X: 200−200𝑋=400𝑋200−200X=400X 600𝑋=200600X=200 𝑋=13X=31​ Using this value of X in the equilibrium relationship: 𝑌=3×(13)2=3×19=13Y=3×(31​)2=3×91​=31​ So, the maximum percentage extraction achieved in the unit is 13×100%=33.33%31​×100%=33.33%. Therefore, none of the given options match the correct value.