Question

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

Answer 1

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 " kg of water"` to get a 50 % solution.

Then

`40/(100-x) = 50/100`

`40×100 = 50(100-x)`

`4000= 5000-50x`

`50x = 1000`

`x=20`

You would have to evaporate 20 kg of water.

Check:

`40/(100-20) = 50/100`

`40/80 = 50/100`

`1/2 = 1/2`

It checks!