I wonder if the question [ppmV versus μmol/mol for atmospheric CO2][1] 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][2] or [van der Waals Equation of State][3] 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.

Any thoughts?

[1]: https://earthscience.stackexchange.com/q/10157/6031
[2]: https://en.wikipedia.org/wiki/Van_der_Waals_equation
[3]: http://hyperphysics.phy-astr.gsu.edu/hbase/Kinetic/waal.html#c1