# A flask was weighed dry and then filled with water. If the masses of the empty flask and filled flask were 56.12 g and 87.39 g, respectively, and the density of water is 0.9976 g/cm^3, how would you calculate the volume of the flask in cm^3?

Jul 22, 2016

${\text{31.45 cm}}^{3}$

#### Explanation:

The idea here is that you can sue the mass of the empty flask and the mass of the filled flask to find the mass of water that can be pouted into the flask.

Once you know this, you can use the density of water to find the volume of water, which is of course equivalent to the volume of the flask.

So, you know that you make two measurements and find

$\text{56.12 g } \to$ the mass of the empty flask

$\text{87.39 g } \to$ the mass of the filled flask

The difference between these two values will be the mass of the added water

${m}_{\text{water" = "87.39 g" - "56.12 g" = "31.27 g}}$

Now, the density of the water is equal to ${\text{0.9976 g cm}}^{- 3}$, which implies that every cubic centimeter of water at the temperature you're performing the experiment has a mass of $\text{0.9976 g}$.

You can thus use the density of water as a conversion factor to find the volume of $\text{31.27 g}$ of water

31.27 color(red)(cancel(color(black)("g"))) * overbrace("1 cm"^3/(0.9976color(red)(cancel(color(black)("g")))))^(color(blue)("the given density")) = color(green)(|bar(ul(color(white)(a/a)color(black)("31.45 cm"^(3))color(white)(a/a)|)))

The answer is rounded to four sig figs.

So, your flask can hold a volume of ${\text{31.45 cm}}^{3}$, which means that it has a volume of ${\text{31.45 cm}}^{3}$.