New-generation spectroscopic surveys of the Milky Way plane have been revealing the structure of the interstellar medium, allowing the simultaneous study of dense structures from single star-forming objects or systems to entire spiral arms. We present the catalogue of molecular clouds extracted from the $^{13}$CO(1-0) data cubes of the Forgotten Quadrant Survey, which mapped the Galactic plane in the range 220deg<l<240deg, and -2.5deg<b<0deg in $^{12}$CO(1-0) and $^{13}$CO(1-0).The catalogue contains 87 molecular clouds for which the main physical parameters such as area, mass, distance, velocity dispersion, and virial parameter were derived. These structures are overall less extended and less massive than the molecular clouds identified in the $^{12}$CO(1-0) data-set because they trace the brightest and densest part of the $^{12}$CO(1-0) clouds. Conversely, the distribution of aspect ratio, equivalent spherical radius, velocity dispersion, and virial parameter in the two catalogues are similar. The mean value of the mass surface density of molecular clouds is 87$pm$55 M$_{odot}$ pc$^{-2}$ and is almost constant across the galactocentric radius, indicating that this parameter, which is a proxy of star formation, is mostly affected by local conditions.In data of the Forgotten Quadrant Survey, we find a good agreement between the total mass and velocity dispersion of the clouds derived from $^{12}$CO(1-0) and $^{13}$CO(1-0). This is likely because in the surveyed portion of the Galactic plane, the H$_2$ column density is not particularly high, leading to a CO emission with a not very high optical depth. This mitigates the effects of the different line opacities between the two tracers on the derived physical parameters. This is a common feature in the outer Galaxy, but our result cannot be readily generalised to the entire Milky Way.
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