  The carbon monoxide (CO) rotational transition lines are the most common
tracers of molecular gas within giant molecular clouds (MCs). We study the
ratio ($R_{2-1/1-0}$) between CO's first two emission lines and examine what
information it provides about the physical properties of the cloud. To study
$R_{2-1/1-0}$ we perform smooth particle hydrodynamic simulations with time
dependent chemistry (using GADGET-2), along with post-process radiative
transfer calculations on an adaptive grid (using RADMC-3D) to create synthetic
emission maps of a MC. $R_{2-1/1-0}$ has a bimodal distribution that is a
consequence of the excitation properties of each line, given that $J=1$ reaches
local thermal equilibrium (LTE) while $J=2$ is still sub-thermally excited in
the considered clouds. The bimodality of $R_{2-1/1-0}$ serves as a tracer of
the physical properties of different regions of the cloud and it helps
constrain local temperatures, densities and opacities. Additionally this
bimodal structure shows an important portion of the CO emission comes from
diffuse regions of the cloud, suggesting that the commonly used conversion
factor of $R_{2-1/1-0}\sim 0.7$ between both lines may need to be studied
further.
