It is simply to convert mg/m3 to ppm for gaseous molecule if knowing its molecular weight. But for the soot particle, I could not find a relationship between these two units.
We had a rather similar question before:
https://www.researchgate.net/post/How_to_calculate_particulate_matter_in_g_s_from_ppm_concentration
And on the general problems of using [ppm] units, there is an interesting article on Wikipedia:
https://en.wikipedia.org/wiki/Parts-per_notation
Devide it by the density of the exhaust gas in kg/m3. This gives you the concentration in ppm by weight.
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