# Question #ffbb0

Apr 15, 2017

The solution is $\text{0.94 % (m/v)"color(white)(l) "NaCl}$.

#### Explanation:

The density of $\text{NaCl}$ is ${\text{2.16 g/cm}}^{3}$, so I presume you are referring to a solution of $\text{NaCl}$ with a density of ${\text{1.8 g/cm}}^{3}$.

An $\text{NaCl}$ solution with a density of 1.8 g/mL contains 24 g $\text{NaCl}$ in 100 g of solution.

∴ For 20 g of your solution,

$\text{Mass of NaCl" = 20 color(red)(cancel(color(black)("g solution"))) × "24 g NaCl"/(100 color(red)(cancel(color(black)("g solution")))) = "4.8 g NaCl}$

$\text{Volume" = 20 color(red)(cancel(color(black)("g solution"))) × "1 mL solution"/(1.8 color(red)(cancel(color(black)("g solution")))) = "11.1 mL}$

When you add this solution to 500 mL of water, you will have 4.8 g $\text{NaCl}$ in 511.1 mL of solution.

$\text{Percent (m/v)" = "4.8 g"/"511.1 mL" × 100 % = "0.94 % NaCl}$