Single-walled 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 and solubility. In this study, we propose two different approaches to quantitatively analyze the ATP partitioning of DNA/SWCNT hybrids. First, we present a model that extracts the 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 the solubility of various DNA/SWCNT hybrids.