# Given density in "g/L", how to calculate molar volume?

Aug 29, 2017

$\overline{V} = \frac{M}{D}$

$D$ in $\text{g/L}$
$M$ in $\text{g/mol}$

You can do that with a unit conversion. In principle, if you can convert from the density to the molar volume, you can convert from the molar volume to the density, so I will show the former case.

Given a density in $\text{g"/"L}$, you're almost there already. A molar volume is known to have typical units of $\text{L"/"mol}$. So, take the reciprocal to get:

$\implies \text{L"/"g}$

Now, since you want to cancel out $\text{g}$ and have ${\text{mol}}^{- 1}$ remaining, simply multiply by the molar mass.

$\text{L"/cancel"g" xx cancel"g"/"mol" = "L"/"mol}$ color(blue)(sqrt"")

What we've just done can be written in variables.

Given a density $D$ ALREADY in $\text{g"/"L}$ and a molar mass in $\text{g"/"mol}$, the molar volume $\overline{V}$ is:

$\textcolor{b l u e}{\overline{V} = \frac{M}{D}}$