  We derive the physical properties of 580 molecular clouds based on their 12CO
and 13CO line emission detected in the University of Massachusetts-Stony Brook
(UMSB) and Galactic Ring surveys. 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 ISM is around
2.36. This relation, M = (228 +/- 18) R^{2.36+/-0.04}, allows us to derive
masses for an additional 170 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 5 kpc. 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. This may indicate
that molecular clouds form in spiral arms and are disrupted in the inter-arm
space. Last, we find that the CO excitation temperature of molecular clouds
decreases away from the Galactic center, suggesting a possible decline in the
star formation rate with Galactocentric radius. There is a marginally
significant enhancement in the CO excitation temperature of molecular clouds at
a Galactocentric radius of about 6 kpc, which in the longitude range of the GRS
corresponds to the Sagittarius arm. This temperature increase could be
associated with massive star formation in the Sagittarius spiral arm.
