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

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Answer 1 · 2015-08-24T20:19:58

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!