Brown dwarf spectra are rich in information revealing of the chemical and physical processes operating in their atmospheres. We apply a recently developed atmospheric retrieval tool to an ensemble of late T-dwarf (600-800K) near infrared spectra. With these spectra we are able to place direct constraints the molecular abundances of H$_2$O, CH$_4$, CO, CO$_2$, NH$_3$, H$_2$S, and Na+K, gravity, thermal structure (and effective temperature), photometric radius, and cloud optical depths. We find that ammonia, water, methane, and the alkali metals are present and well constrained in all 11 objects. From the abundance constraints we find no significant trend in the water, methane, or ammonia abundances with temperature, but find a very strong ($>$25$\sigma$) increasing trend in the alkali metal abundances with effective temperature, indicative of alkali rainout. We also find little evidence for optically thick clouds. With the methane and water abundances, we derive the intrinsic atmospheric metallicity and carbon-to-oxygen ratios. We find in our sample, that metallicities are typically sub solar and carbon-to-oxygen ratios are somewhat super solar, different than expectations from the local stellar population. We also find that the retrieved vertical thermal profiles are consistent with radiative equilibrium over the photospheric regions. Finally, we find that our retrieved effective temperatures are lower than previous inferences for some objects and that our radii are larger than expectations from evolutionary models, possibly indicative of un-resolved binaries. This investigation and methodology represents a paradigm in linking spectra to the determination of the fundamental chemical and physical processes governing cool brown dwarf atmospheres.