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

##### 1 Answer

#### 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, **must be present** in the target solution.

A **for every**

#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

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

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)|)))#