How to convert ppm to g/m3?
I am trying to understand ppm, too. As far as I have understood there are different kinds of ppm, which is basically a ratio: it can be a ratio of amount of substance, masses, or volumes.
Assuming your ppm is a molar ratio I did this reasoning:
Indicating with $n$ the amount of substance, with $M$ the molar mass and with $V$ the volume, the concentration of your gas is:
$$c = \frac{n_\mathrm{gas} \cdot M}{V},$$
and defining the $\mathrm{ppm}$ as:
$$\mathrm{ppm} =\frac{n_\mathrm{gas}}{n_\mathrm{total}}\cdot 10^6.$$
Using the gas law:
$$n_\mathrm{tot} = \frac{p\cdot V}{R \cdot T}, $$
where $T$ is the temperature in kelvin and $p$ the pressure in pascal, and substituting, you get:
$$c = \frac{\mathrm{ppm} \cdot M \cdot p}{R\cdot T}\left[\frac{\mu \pu{g}}{\pu{m^3}}\right].$$