A wide range of analytes adsorb irreversibly to the surfaces of single walled carbon nanotube electronic networks typically used as sensors or thin-film transistors, although the mechanism remains poorly understood. Using thionyl chloride as a model electron-withdrawing adsorbate, we show that reversible adsorption sites can be created on the nanotube array via functionalization with amine-terminated molecules of pK_a < 8.5. The reversible response enables extraction of the characteristic free energy of adsorption for each type of amine. A nanotube network comprised of single, largely unbundled nanotubes, near the electronic percolation threshold is required for the effective conversion to a reversibly binding array. In-situ Raman spectroscopy confirms that adsorption takes place on the amine coating and does not distinguish between SWNT by electronic type. By screening 11 types of amine-functionalization, we show that analyte adsorption is largely affected by the basicity of surface groups. A mechanism of reduced binding energy by surface chemistry is proposed based upon XPS and molecular potential calculations. Parts-per-trillion level sensitivity is demonstrated by creating a higher adsorption site density with a polymer amine, such as polyethyleneimine (PEI). The ability to systematically tune molecular adsorption to maximize both analyte sensitivity and reversible response has applications to the detection of trace analytes in real time from a micro-fluidic chromatographic column. We demonstrate, for the first time, that a pulse as small as ~10⁹ molecules of dimethyl methylphosphonate (DMPP), a nerve agent simulant, is reversibly detected at the end of a micro-fabricated gas chromatographic (µGC) column coupled to the functionalized SWNT array.