# The density of ethanol is 0.789 g/cm^3 at 20°C. What volume of ethanol has a mass of 15.5 grams?

Jun 11, 2017

Well, by definition, $\text{density"="mass"/"volume}$

#### Explanation:

And given the quotient, if I have $\text{density}$ and $\text{mass}$, I can work out the $\text{volume}$ fairly easily:

$\frac{\text{volume"="mass}}{\rho} = \frac{15.5 \cdot \cancel{g}}{0.789 \cdot \cancel{g} \cdot c {m}^{-} 3} \cong 20 \cdot c {m}^{3}$

Note that this is dimensionally consistent. We wanted an answer with units of volume, i.e. $m L \equiv c {m}^{3}$; we got an answer with units of $\frac{1}{c {m}^{-} 3} = \frac{1}{\frac{1}{c {m}^{3}}} = c {m}^{3}$, i.e. units of volume as required.......

Note that in terms of units...$1 \cdot c {m}^{3} \equiv {\left(1 \times {10}^{-} 2 \cdot m\right)}^{3} = 1 \times {10}^{-} 6 \cdot {m}^{3}$...that is $\text{one millionth of a cubic metre}$, just as $1 \cdot L \equiv 1 \cdot {\mathrm{dm}}^{3} \equiv {\left(1 \times {10}^{-} 1 \cdot m\right)}^{3}$, that is $\text{one thousandth of a cubic metre}$. Capisce?