Question cb299

Mar 5, 2017

$\text{2 kg NaCl}$

Explanation:

Don't forget that a solution's percent concentration by mass tells you the amount of solute present for every $\text{100 g}$ 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 $\text{100 g}$ 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 $\text{40 kg}$ of sodium chloride for every $\text{100 kg}$ of solution.

$\text{40 kg NaCl " stackrel(color(white)(acolor(red)("for every")aaa))(->) "100 kg NaCl" + "H"_2"O}$

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

You know that $x$ $\text{kg}$ of sodium chloride in

$\left(3 + x\right) \textcolor{w h i t e}{.} \text{kg solution}$

will be equivalent to $\text{40 kg}$ of sodium chloride in $\text{100 kg}$ of solution, so set up the proportion as

$\left(x \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{kg NaCl"))))/((3 + x) color(red)(cancel(color(black)("kg solution"))) ) = (40 color(red)(cancel(color(black)("kg NaCl"))))/(100color(red)(cancel(color(black)("kg solution}}}}\right)$

This means that you will have

$x = \frac{40}{100} \left(3 + x\right)$

$100 x = 120 + 40 x$

$60 x = 120 \implies x = \frac{120}{60} = 2$

Therefore, you need to add $\text{2 kg}$ of sodium chloride, the equivalent of $\text{2000 g}$, to $\text{3 kg}$ of water in order to make a 40%# by mass sodium chloride solution.