Question

Please help me out. :)

Coconut water can be concentrated to 20% solids by freeze concentration wherein water freezes and leaves most of the solid constituent in the liquid portion. Compound water normally contains 1.5% solids. How kg product (20% solids) can be obtained from 1000L of fresh coconut water if every kg of water frozen carries with it, 0.01 kg of liquid solution. Assume a density of 1 g/cm^3 for all liquids.

Answer 1

If I understand right, the picture is as above.

Original concentration = 1.5% = 15 kg/1000 L
total solid before freezing = 15 kg

Let x= volume of liquor (that is not frozen)
mass of solid in 20% liquor = 0.20x
mass of solid in 1% frozen portion = 0.01(1000-x)
total solid after freezing = 0.20x+10-0.01x = 0.19x + 10 kg

Equate solids before and after freezing
15 kg = 0.19x + 10
x=5/0.19 = 26.3 L = 26.3 kg (approx. if all liquids have density 1.0 g/mL)