Question

Question #cb299

Answer 1

`"2 kg NaCl"`

Explanation:

Don't forget that a solution's percent concentration by mass tells you the amount of solute present for every `"100 g"` of solution.

In other words, the solution's percent concentration by mass is a measure of the number of grams of solute present for every `"100 g"` of solute and solvent.

You can replace grams with kilograms if you want and say that a `40%` by mass sodium chloride solution will contain `"40 kg"` of sodium chloride for every `"100 kg"` of solution.

`"40 kg NaCl " stackrel(color(white)(acolor(red)("for every")aaa))(->) "100 kg NaCl" + "H"_2"O"`

You already know that you have `"3 kg"` of water available. Let's assume that `x` represents the number of kilograms of sodium chloride that must be added to `"3 kg"` of water in order to make a `40%` sodium chloride solution.

You know that `x` `"kg"` of sodium chloride in

`(3 + x)color(white)(.)"kg solution"`

will be equivalent to `"40 kg"` of sodium chloride in `"100 kg"` of solution, so set up the proportion as

`(xcolor(red)(cancel(color(black)("kg NaCl"))))/((3 + x) color(red)(cancel(color(black)("kg solution"))) ) = (40 color(red)(cancel(color(black)("kg NaCl"))))/(100color(red)(cancel(color(black)("kg solution"))))`

This means that you will have

`x = 40/100 (3 + x)`

`100x = 120 + 40x`

`60x = 120 implies x= 120/60 = 2`

Therefore, you need to add `"2 kg"` of sodium chloride, the equivalent of `"2000 g"`, to `"3 kg"` of water in order to make a `40%` by mass sodium chloride solution.