We derive the physical properties of 580 molecular clouds based on their ^12^CO and ^13^CO line emission detected in the University of Massachusetts-Stony Brook (UMSB) and Galactic Ring surveys (GRS). We provide a range of values of the physical properties of molecular clouds, and find a power-law correlation between their radii and masses, suggesting that the fractal dimension of the interstellar medium is around 2.36. This relation, M=(228+/-18)R^2.36+/-0.04^, allows us to derive masses for an additional 170 Galactic Ring Survey (GRS) molecular clouds not covered by the UMSB survey. We derive the Galactic surface mass density of molecular gas and examine its spatial variations throughout the Galaxy. We find that the azimuthally averaged Galactic surface density of molecular gas peaks between Galactocentric radii of 4 and 5kpc. Although the Perseus arm is not detected in molecular gas, the Galactic surface density of molecular gas is enhanced along the positions of the Scutum-Crux and Sagittarius arms.