Answer:
the amounts and compositions of the overflow V1 and underflow L1 leaving the stage are 75kg and 125kg respectively.
Explanation:
Let state the given parameters;
Let A= solvent (hexane)
B= solid(inert soiid)
C= solvent(oil)
[tex]F_{solution}[/tex] = mass of solvent + mass of oil (i.e A+C)
Feed Phase:
Total feed (i.e slurry of flakes soybeans)= 100kg
B= mass of solid =75 kg
F= mass of solvent + mass of oil (i.e A+C)
= 25kg
Mass ratio of oil to solution [tex]Y_{F}[/tex] =[tex]\frac{Mass C}{Mass (A+C)}[/tex]
mass of oil (C) =25 × 0.1 wt = 2.5kg
mass of hexane in feed = 25 × 0.9 =22.5kg + 2.5 =25kg
therefore [tex]Y_{F}[/tex] = [tex]\frac{2.5}{25}[/tex]
= 0.1
mass ratio of solid to solution [tex]Y_{A}[/tex] = [tex]\frac{Mass A}{Mass (A+C)}
=[tex]\frac{75}{25}[/tex]
=3
Solvent Phase:
C= Mass of oil= 0(kg)
A= Mass of hexane = 100kg
mass of solutions = A+C = 0+100kg
solvent= 100kg
Underflow:
underflow = L₁ = (unknown) ???
L₁ = E₁ + B
the value of N for the outlet and underflow is 1.5 kg
i.e N₁ = [tex]\frac{mass B}{mass(A+C)}[/tex]
solution in underflow E₁ = Mass (A+C)
Overflow:
Overflow = V₁ = (unknown) ???
solution in overflow V₁ = Mass (A+C)
This is because, B = 0 in overflow
Solid Balance: (since the solid is inert, then is said to be same in feed & underflow).
solid in feed = solid in underflow = 75
75= E₁ × N₁
75 = E₁ × 1.5
E₁ = 50kg
Underflow L₁ = E₁ × B
= 50 + 75
=125kg
The Overall Balance: Feed + Solvent = underflow + overflow
100 + 100 = 125 + V₁
V₁ = 75kg
