Question

A 50.0-kg mixture of salt and water is 15.0% (by mass) salt. What is the mass of salt and water in the mixture?

Answer 1

Your solution contains `"7.50 kg"` of salt and `"42.5 kg"` of water.

Explanation:

You know that your mixture is `15.0%` salt by mass, so make sure that you understand what that means before moving forward.

For a component of a mixture, its percent concentration by mass is calculated by dividing the mass of that component by the total mass of the mixture, and multiplying the result by `100`.

`color(blue)("% component" = "mass of that component"/"total mass of the mixture" xx 100)`

In your case, the mixture is a solution of salt and water. You know that the total mass of the mixture is equal to `"50.0 kg"`, and that salt makes up `15.0%` of the total mass of the mixture.

That means that for every `"100 kg"` of this mixture, `"15.0 kg"` will be salt. This proportion between the mass of salt and the total mass of the mixture will help you find the mass of salt in any amount of solution.

In your case, you have

`50.0 color(red)(cancel(color(black)("kg solution"))) * overbrace("15.0 kg salt"/(100color(red)(cancel(color(black)("kg solution")))))^color(purple)("15.0% by mass") = color(green)("7.50 kg salt")`

Since the total mass of the solution can be written as

`m_"solution" = m_'water" + m_"salt"`

you can say that you solution will also contain

`m_"water" = "50.0 kg" - "7.50 kg" = color(green)("42.5 kg water")`