# If the density of a sample is 14 g/mL, and its mass is 56 grams, what would its volume be?

Apr 13, 2016

$\text{4.0 mL}$

#### Explanation:

The idea here is that the density of a substance can be thought of as being a conversion factor between the mass of a sample of this substance and the volume it occupies.

In your case, the sample is said to have a density of ${\text{14 g mL}}^{- 1}$. This means that $\text{1 mL}$ of this substance will have a mass of $\text{14 g}$.

In other words, for every milliliter of that substance that you have in your sample, you get a mass of $\text{14 g}$.

The problem tells you that the mass of the sample is equal to $\text{56 g}$. Since this is more than the mass of $\text{1 mL}$, you can say for a fact that this sample will occupy more than $\text{1 mL}$.

How much more?

Use the given density to find out!

$56 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{g"))) * overbrace("1 mL"/(14color(red)(cancel(color(black)("g")))))^(color(purple)("density as a conversion factor")) = color(green)(|bar(ul(color(white)(a/a)"4.0 mL} \textcolor{w h i t e}{\frac{a}{a}} |}}}$