We have obtained 12CO and 13CO J=1-0 observations of the nearby spiral galaxy M33 to try to resolve the long-standing discrepancy between 12CO/13CO line ratios measured in Galactic giant molecular clouds and external galaxies. Interferometer maps of the molecular cloud MC20 give a 12CO/13CO line ratio of 7.5+/-2.1, which agrees reasonably well with the line ratio measured in Galactic giant molecular clouds. In contrast, the 12CO/13CO line ratio obtained from single dish data is 10.0+/-0.9, significantly higher than Galactic values but in good agreement with line ratios measured in other galaxies. The interferometer map of MC20 reveals that the cloud has similar spatial and velocity extents in the two lines, and thus the high single dish line ratio cannot be due to different filling factors in the two lines. In addition, the single dish data show no evidence for significant variations in the line ratio with metallicity, which eliminates abundance changes as the explanation for the high single dish line ratio. We conclude that the high 12CO/13CO line ratio s observed in M33, and in the disks of spiral galaxies in general, are due to the presence of a population of diffuse molecular clouds. The lower limit to the fraction of the total 12CO emission from M33 that originates in the diffuse clouds is 30+/-30%, while the upper limit is ~60%.

16 pages + 9 figures, uuencoded compressed postscript file