Theoretical and observational investigations have indicated that the abundance of carbon monoxide (CO) is very sensitive to intrinsic properties of the gaseous medium, such as density, metallicity and the background radiation field. CO observations are often employed to study the properties of molecular clouds (MCs), such as mass, morphology and kinematics. It is thus important to understand how well CO traces the total mass, which in MCs is predominantly due to molecular hydrogen (H2). Recent hydrodynamic simulations by Glover & Mac Low have explicitly followed the formation and destruction of molecules in model MCs under varying conditions. These models have confirmed that CO formation strongly depends on the cloud properties. Conversely, the formation of H2 is primarily determined by the amount of time available for its formation. We apply radiative transfer calculations to these MC models in order to investigate the properties of CO line emission. We focus on integrated CO (J= 1–0) intensities emerging from individual clouds, including its relationship to the total, H2 and CO column densities, as well as the ‘X factor,’ the ratio of H2 column density to CO intensity. Models with high CO abundances have a threshold CO intensity of ≈65 K km s−1 at sufficiently large extinctions (or column densities). Clouds with low CO abundances show no such intensity thresholds. The distributions of total and H2 column densities are well described as lognormal functions, though the distributions of CO intensities and column densities are usually not lognormal. In general, the probability distribution functions of the integrated intensity do not follow the distribution functions of CO column densities. In the model with Milky Way-like conditions, the X factor is in agreement with the near-constant value determined from observations. In clouds with lower metallicity, lower density or a higher background UV radiation field, the CO abundances are in general lower, and hence the X factor can vary appreciably – sometimes by up to 4 orders of magnitude. In models with high densities, the CO line is fully saturated, so that the X factor is directly proportional to the molecular column density.