# How many grams of water must be evaporated from 100 kilograms of a 40% salt solution to produce a 50% salt solution?

Aug 24, 2015

Mathematically, the answer is 20 000 g of water.

Practically speaking, this is impossible, because the maximum solubility of salt in water is 26 % by mass.

But let's do the mathematical exercise.

We will also assume that the density of the solution remains constant (even though the density changes with concentration!).

A 40 % concentration means

40 % = "40 kg salt"/"100 kg solution"

You want to remove $x \text{ kg of water}$ to get a 50 % solution.

Then

$\frac{40}{100 - x} = \frac{50}{100}$

40×100 = 50(100-x)

$4000 = 5000 - 50 x$

$50 x = 1000$

$x = 20$

You would have to evaporate 20 kg of water.

Check:

$\frac{40}{100 - 20} = \frac{50}{100}$

$\frac{40}{80} = \frac{50}{100}$

$\frac{1}{2} = \frac{1}{2}$

It checks!