Self-assembly of nanoparticles involves manipulating particle interactions such that attractions are on the order of the average thermal energy in the system. If the self-assembly is to result in an ordered packing, an understanding of their phase behavior is necessary. Here we test the ability of simple pair potentials to characterize the interactions and phase behavior of silico tungstic acid (STA), a 1.2 nm particle. The strength of interaction is controlled by dispersing STA in different background salt concentrations. The experimental variables used in characterizing the interactions are the osmotic compressibility (d Pi/d rho), the second virial coefficient (B-2), relative solution viscosity (eta/eta(c)), and the solubility (rho sigma(3))(sat). Various techniques are then developed to extract the parameters of square well, the adhesive hard sphere (AHS), and the Yukawa pair potentials that best describe the experimental data. The AHS model describes the solution thermodynamic behavior only where the system is weakly attractive but, as would be expected, fails when long range repulsions or nonmonotonic pair potentials become important. Model free representations are presented which offer the opportunity to extract pair potential parameters.