Xenon has nine stable isotopes. However, the relative populations of these isotopes vary between various sources across the Solar System. Of note, is the difference between the xenon composition of the solar wind and the xenon composition of the comets. This heterogeneity can be caused by variation in the nucleosynthesis of the xenon. Xenon is made from two nucleosynthetic routes: the r- and s-process. The s-process occurs when the rate of neutron addition is slower than the beta-decay. The r-process occurs when the rate of neutron addition is faster than the rate of beta-decay. The products of the s-process can be calculated and, thus, subtracted from the measured compositions. Once the s-process is removed, the remainder is considered to be from the r-process. By comparing the r-process compositions there is evidence of multiple r-processes contributing to the Solar System. Specifically, the xenon abundances are hard to reconcile with yields from a single uniform source of r-process elements. This paper considers neutron star mergers as the source of one of these r-processes. A model was used to consider the evolution of r-process matter in the Galaxy due to the neutron star mergers. In the model, the rotation of the Galaxy and the diffusion of matter through the interstellar matter was considered. Through this model, it was found that local conditions in only 1.3% of the Galaxy are consistent with the cometary and Solar xenon compositions. This suggests that the xenon composition of the Solar System is rare among solar systems that form in the Galaxy. Based on this, the effects of various simplifications and assumptions used to make the model were examined.