# How many kilograms of water must be evaporated from 40 kg of a 10% salt solution to produce a 25% solution?

Apr 11, 2016

$\text{24 kg}$

#### Explanation:

The idea here is that you can increase the solution's percent concentration by decreasing the mass of solvent while keeping the mass of solute constant.

You are told that water is being evaporated from the initial solution, which confirms the fact that the mass of salt remains unchanged.

Use the concentration of the initial solution to figure out how many kilograms of solute, which in your case is salt, or sodium chloride, $\text{NaCl}$, must be present in the target solution.

A $\text{10% w/w}$ salt solution will contain $\text{10 kg}$ of salt for every $\text{100 kg}$ of solution, which means that your $\text{40-kg}$ sample will contain

40 color(red)(cancel(color(black)("kg solution"))) * "10 kg NaCl"/(100color(red)(cancel(color(black)("kg solution")))) = "4 kg NaCl"

This is exactly how much solute must be present in the target solution. This time, however, this amount of solute makes for a $\text{25% w/w}$ solution.

This means that the total mass of the target solution will be

4color(red)(cancel(color(black)("kg NaCl"))) * "100 kg solution"/(25color(red)(cancel(color(black)("kg solution")))) = "16 kg solution"

This tells you that the mass of the solution decreased from $\text{40 kg}$ to $\text{16 kg}$.

Since the mass of salt remained constant, it follows that this change is accounted for by the evaporation of the water. Therefore, the mass of water evaporated from the initial solution will be

"mass of water" = "40 kg" - "16 kg" = color(green)(|bar(ul(color(white)(a/a)"24 kg"color(white)(a/a)|)))