Question

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

Answer 1

`barV = M/D`

`D` in `"g/L"`
`M` in `"g/mol"`

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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 `"g"/"L"`, you're almost there already. A molar volume is known to have typical units of `"L"/"mol"`. So, take the reciprocal to get:

`=> "L"/"g"`

Now, since you want to cancel out `"g"` and have `"mol"^(-1)` remaining, simply multiply by the molar mass.

`"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 `"g"/"L"` and a molar mass in `"g"/"mol"`, the molar volume `barV` is:

`color(blue)(barV = M/D)`