Single wall carbon nanotubes (SWCNTs) coated with single-stranded DNA can be effectively separated into various chiralities using an aqueous two phase (ATP) system. Partitioning is driven by small differences in the dissolution characteristics of the hybrid between the two phases. Thus, in addition to being a separation technique, the ATP system potentially also offers a way to quantify and rank the dissolution properties of the solute (here the DNA/SWCNT hybrids), such as the solvation free energy or solubility. In this study, we propose two different approaches to analyze quantitatively the ATP partitioning of DNA/SWCNT hybrids. First, we present a model that extracts relative solvation free energy of various DNA/SWCNT hybrids by using an expansion relative to a standard state. Second, we extract a solubility parameter by analyzing the partitioning of hybrids in the ATP system. The two approaches are found to be consistent, providing some confidence in each as a method of quantifying differences in solubility of various DNA/SWCNT hybrids.