I wonder if the question ppmV versus μmol/mol for atmospheric CO2 might do better in Chemistry or Physics SE. The science behind the answer probably will need the correction to the ideal gas law as expressed in van der Waals equation or van der Waals Equation of State as applied to mixtures of non-ideal gasses.
But the simplest answer could be just a conversion factor close to 1.0 which would be close enough for me for now.
edit: I've just won a "Tumbleweed" with this question! :) I've also added a
+50 bounty on the original question. If still no luck, I'll either ask for migration, or just delete and repost.