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ABSTRACT Our ability to trace the star-forming molecular gas is important to our understanding of the Universe. We can trace this gas using CO emission, converting the observed CO intensity into the H$$_2$$ gas mass of the region using the CO-to-H$$_2$$ conversion factor ($$X_{\rm{{\small CO}}}$$). In this paper, we use simulations to study the conversion factor and the molecular gas within galaxies. We analysed a suite of simulations of isolated disc galaxies, ranging from dwarfs to Milky Way-mass galaxies, that were run using the fire-2 subgrid models coupled to the chimes non-equilibrium chemistry solver. We use the non-equilibrium abundances from the simulations, and we also compare to results using abundances assuming equilibrium, which we calculate from the simulation in post-processing. Our non-equilibrium simulations are able to reproduce the relation between CO and H$$_2$$ column densities, and the relation between $$X_{\rm{{\small CO}}}$$ and metallicity, seen within observations of the Milky Way. We also compare to the xCOLD GASS survey, and find agreement with their data to our predicted CO luminosities at fixed star formation rate. We also find the multivariate function used by xCOLD GASS overpredicts the H$$_2$$ mass for our simulations, motivating us to suggest an alternative multivariate function of our fitting, though we caution that this fitting is uncertain due to the limited range of galaxy conditions covered by our simulations. We also find that the non-equilibrium chemistry has little effect on the conversion factor (<5 per cent) for our high-mass galaxies, though still affects the H$$_2$$ mass and $$L_{\rm{{\small CO}}}$$ by $$\approx$$25  per cent.