ppmV versus μmol/mol for atmospheric CO2 - how to convert?
According to the US Carbon Dioxide Information Analysis Center :
Though in their data table they use the term &quot;ppmv&quot;, they explain:

The CO2 mixing ratios are reported as micromoles per mole (µmol/mol = ppmv) of dry air in the World Meteorological Organization (WMO) X85 mole fraction scale, traceable to primary standards at the Scripps Institution of Oceanography (SIO)

This is further explained in The WMO Mole Fraction Scales for CO2 and other greenhouse gases, and uncertainty of the atmospheric measurements:

Abbreviations can be ppm, ppb, etc., whereas widely used abbreviations such as ppmv (the v is for volume) are wrong and should be abandoned. When reviewing papers, or when we are co-authors, we should convince first authors to abandon the ppmv notation. Volume has nothing to do with mole fraction.

Supposing you know the mole fraction, if you literally wanted to calculate the parts per million by volume, first you need to define what that would mean.  Are you interested in the ratio of the volume of CO2 separately isolated relative to the whole volume? Or are you interested in the volume of CO2 separately isolated, relative to the sum of all the gases separately isolated? For either of these methods, you would need to choose a temperature and pressure, such as the actual temperature and pressure of a sample, or standard temperature and pressure.
Then you need an equation of state at least for the CO2, that is more real than the ideal gas law, such as van der Waals.