A reliable estimate of the molecular gas content in galaxies plays a crucial role in determining their dynamical and star-forming properties. However, H₂, the dominant molecular species, is difficult to observe directly, particularly in the regions where most molecular gas is thought to reside. Its mass is therefore commonly inferred by assuming a direct proportionality with the integrated intensity of the ¹²CO(J = 1 -> 0) emission line, using a CO-to-H₂ conversion factor, X. Although a canonical value for X is used extensively in such estimates, there is increasing evidence, both theoretical and observational, that the conversion factor may vary by over an order of magnitude under conditions different from those of the local neighbourhood. In an effort to understand the influence of changing environmental conditions on the conversion factor, we derive theoretical estimates of X for a wide range of physical parameters using a photon-dominated region (PDR) time-dependent chemical model, benchmarking key results against those of an independent PDR code to ensure reliability. Based on these results, the sensitivity of the X factor to change in each physical parameter is interpreted in terms of the chemistry and physical processes within the cloud. In addition to confirming previous observationally derived trends, we find that the time-dependence of the chemistry, often neglected in such models, has a considerable influence on the value of the conversion factor.