Understanding the origins of life has been one of the greatest dreams throughout history. It is now known that star-forming regions contain complex organic molecules, known as Polycyclic Aromatic Hydrocarbons (PAHs), each of which has particular infrared spectral characteristics. By understanding which PAH species are found in specific star-forming regions, we can better understand the biochemistry that takes place in interstellar clouds. Identifying and classifying PAHs is not an easy task: we can only observe a single superposition of PAH spectra at any given astrophysical site, with the PAH species perhaps numbering in the hundreds or even thousands. This is a challenging source separation problem since we have only one observation composed of numerous mixed sources. However, it is made easier with the help of a library of hundreds of PAH spectra. In order to separate PAH molecules from their mixture, we need to identify the specific species and their unique concentrations that would provide the given mixture. We develop a Bayesian approach for this problem where sources are separated from their mixture by Metropolis Hastings algorithm. Separated PAH concentrations are provided with their error bars, illustrating the uncertainties involved in the estimation process. The approach is demonstrated on synthetic spectral mixtures using spectral resolutions from the Infrared Space Observatory (ISO). Performance of the method is tested for different noise levels.