We study Giant Molecular Cloud (GMC) environments surrounding 10 Infrared Dark Clouds (IRDCs), using $^{13}$CO(1-0) emission from the Galactic Ring Survey. We measure physical properties of these IRDCs/GMCs on a range of scales extending to radii, R, of 30 pc. By comparing different methods for defining cloud boundaries and for deriving mass surface densities and velocity dispersions, we settle on a preferred CE,$tau$,G method of Connected Extraction in position-velocity space plus Gaussian fitting to opacity-corrected line profiles for velocity dispersion and mass estimation. We examine how cloud definition affects measurements of the magnitude and direction of line-of-sight velocity gradients and velocity dispersions, including associated dependencies on size scale. CE,$tau$,G-defined GMCs show velocity dispersion versus size relations $sigmapropto{s}^{1/2}$, which are consistent with the large-scale gradients being caused by turbulence. However, IRDCs have velocity dispersions that are moderately enhanced above those predicted by this scaling relation. We examine the dynamical state of the clouds finding mean virial parameters $bar{alpha}_{rm{vir}}simeq 1.0$ for GMCs and 1.6 for IRDCs, broadly consistent with models of magnetized virialized pressure-confined polytropic clouds, but potentially indicating that IRDCs have more disturbed kinematics. CE,$tau$,G-defined clouds exhibit a tight correlation of $sigma/R^{1/2}proptoSigma^n$, with $nsimeq0.7$ for GMCs and 1.3 for IRDCs (c.f., a value of 0.5 expected for a population of virialized clouds). We conclude that while GMCs show evidence for virialization over a range of scales, IRDCs may be moderately super virial. Alternatively, IRDCs could be virialized but have systematically different $^{13}$CO gas phase abundances, i.e., due to freeze-out, affecting mass estimations.
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