# If ethanol has a density of .785 g/mL, what is the volume of 83.3 g of ethanol?

Feb 20, 2016

$\text{106 mL}$

#### Explanation:

In order to be able to answer this question, you must understand what the density of a substance tells you.

The density of a substance is nothing more than the mass of that substance that occupies one unit of volume.

In your case, the density of ethanol is given in Grams per milliliter, which means that one unit of volume will be $\text{1 mL}$.

So, ethanol has a density of ${\text{0.785 g mL}}^{- 1}$, which is equivalent to saying that if you take exactly $\text{1 mL}$ of ethanol and weigh it, you will end up with a mass of $\text{0.785 g}$.

Now, you know that the volume you're using has a mass of $\text{83.3 g}$. Well, if you get $\text{0.785 g}$ for every $\text{1 mL}$ of ethanol, it follows that this much mass will correspond to a volume of

83.3color(red)(cancel(color(black)("g ethanol"))) * overbrace("1 mL"/(0.785color(red)(cancel(color(black)("g ethanol")))))^(color(purple)("ethanol's density")) = "106.11 mL"

Rounded to three sig figs, the answer will be

V_"ethanol" = color(green)("106 mL")