# Question 88214

Oct 21, 2017

${\text{4.0 g dm}}^{- 3}$

#### Explanation:

The idea here is that you need to convert the concentration of sodium hydroxide from moles per cubic decimeter to grams per cubic decimeter.

In order to to that, you need to use the molar mass of sodium hydroxide, which is equal to ${\text{39.997 g mol}}^{- 1}$. This tells you that in order to have $1$ mole of sodium hydroxide, you need to have $\text{39.997 g}$ of sodium hydroxide.

So, if you take a sample of this solution that has a volume of ${\text{1 dm}}^{3}$, you can say that it will contain $0.10$ moles of sodium hydroxide $\to$ this is what a ${\text{0.10 mol dm}}^{- 3}$ concentration actually means.

Use the molar mass of sodium hydroxide to convert the number of moles to grams

0.10 color(red)(cancel(color(black)("moles NaOH"))) * "39.997 g"/(1color(red)(cancel(color(black)("mole NaOH")))) = "3.9997 g"#

Since this represents the number of grams of sodium hydroxide present in ${\text{1 dm}}^{3}$ of this solution, you can say that the concentration of the solution in grams per cubic decimeter will be equal to

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{{\text{concentration NaOH = 4.0 g dm}}^{- 3}}}}$

The answer must be rounded to two sig figs, the number of sig figs you have for the concentration of the solution in moles per cubic decimeter.