# An unknown liquid occupies a volume of 5 ml and has a mass of 40 grams. How do you find the density?

Oct 30, 2016

${\text{8 g mL}}^{- 1}$

#### Explanation:

The thing to remember about density is that its purpose is to express the mass of one unit of volume of a given substance.

In other words, in order to find a substance's density, you must determine the exact mass of one unit of volume. In this case, the volume of the sample is said to be equal to $\text{5 mL}$.

This should automatically tell you that one unit of volume is equal to $\text{1 mL}$.

So, you essentially know the mass of five units of volume, since

$\text{5 mL" = 5 xx "1 mL}$

which means that all you have to do now is use the information given as a conversion factor to find the mass of $\text{1 mL}$

1 color(red)(cancel(color(black)("mL"))) * "40 g"/(5 color(red)(cancel(color(black)("mL")))) = "8 g"

You can thus say that the density of this liquid is equal to

$\textcolor{g r e e n}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{\text{8 g"/"1 mL" = "8 g/ mL" = "8 g mL}}^{- 1}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$