How much water should be evaporated from 20 L of a 20% salt solution to increase it to a 25% salt solution?

Oct 31, 2016

$\text{4 L}$

Explanation:

The idea here is that you're dealing with a 20% mass by volume solution, presumably, which means that you get $\text{20 g}$ of salt for every $\text{100 mL}$ of solution.

In this particular case, your solution will contain a total of

20 color(red)(cancel(color(black)("L solution"))) * (10^3color(red)(cancel(color(black)("mL"))))/(1color(red)(cancel(color(black)("L solution")))) * "20 g salt"/(100color(red)(cancel(color(black)("mL solution"))))

$= \text{ 4,000 g salt}$

Now, you can increase the concentration of this solution by removing some of the solvent, i.e. by evaporating some of the water.

The amount of salt present in the solution does not change, which means that you can use the target concentration to figure out what is the final volume of the solution

"4,000" color(red)(cancel(color(black)("kg salt"))) * (100 color(red)(cancel(color(black)("mL solution"))))/(25 color(red)(cancel(color(black)("g salt")))) * "1 L"/(10^3color(red)(cancel(color(black)("mL"))))

$= \text{ 16 L solution}$

Therefore, you can make this target solution by evaporating a total of

$\textcolor{g r e e n}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{V}_{\text{evaporated" = "20 L" - "16 L" = "4 L}}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$