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

##"106 mL"##

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

The 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 ##"1 mL"##.

So, ethanol has a density of ##"0.785 g mL"^(-1)##, which is equivalent to saying that if you take exactly ##"1 mL"## of ethanol and weigh it, you will end up with a mass of ##"0.785 g"##.

Now, you know that the volume you're using has a mass of ##"83.3 g"##. Well, if you get ##"0.785 g"## **for every** ##"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 , the answer will be

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

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