How much water must be evaporated from 400 gallons of a 15% saline solution to get a 40% saline solution?

Question

Thanks =) Icky chemical mixture problems.. can someone please explain this for me? Percentiles are my worst.

Answer 1

I assume US gallons (at 8 pounds per gallon for pure water?)

A 15% solution (by weight) in perfect solution (the salt ions occupy no extra volume) means that you have 564.7 pounds of salt in 3200 pounds of water, for a total solution weight of 3764.7 pounds.

564.7 / 3764.7 = 0.15

You want to evaporate x pounds of water (salt quantity remains the same) so that the remaining quantity of water is 3200 - x, and
564 / (3764.7 - x) = 0.4

Once you have x in pounds, divide by 8 to find the number of gallons.

Answer 2

210 gals to be evaporated

You started with .15 x 400 or 60 gals of salt

Therefore

60/x = 40% or x = 150 gals.

Saline solutions = 150 gals. water and 60 gals. salt