The potential applications of dispersed and self-assembled nanoparticles depend critically on accurate control and prediction of their phase behavior. The chemical potential is essential in describing the equilibrium distribution of all components present in every phase of a system and is useful as a building block for constructing phase diagrams. Furthermore, the chemical potential is a sensitive indicator of the local environment of a molecule or particle and is defined in a mathematically rigorous manner in both classical and statistical thermodynamics. The goal of this research is to use simulations and experiments to understand how particle size and composition affect the particle chemical potential of attractive nanoparticle-polymer mixtures. The expanded ensemble Monte Carlo (EEMC) simulation method for the calculation of the particle chemical potential for a nanocolloid in a freely adsorbing polymer solution is extended to concentrated polymer mixtures. The dependence of the particle chemical potential and polymer adsorption on the polymer concentration and particle diameter are presented. The perturbed Lennard-Jones chain (PLJC) equation of state (EOS) for polymer chains1 is adapted to calculate the particle chemical potential of nanocolloid-polymer mixtures. The adapted PLJC equation is able to predict the EEMC simulation results of the particle chemical potential by introducing an additional parameter that reduces the effects of polymer adsorption and the effective size of the colloidal particle. Osmotic pressure measurements are used to calculate the chemical potential of nanocolloidal silica in an aqueous poly(ethylene oxide) (PEO) solution at different silica and PEO concentrations. The experimental data was compared with results calculated from Expanded Ensemble Monte Carlo (EEMC) simulations. The results agree qualitatively with the experimentally observed chemical potential trends and illustrate the experimentally-observed dependence of the chemical potential on the composition. Furthermore, as is the case with the EEMC simulations, polymer adsorption was found to play the most significant role in determining the chemical potential trends. The simulation and experimental results illustrate the relative importance of the particles size and composition as well as the polymer concentration on the particle chemical potential. Furthermore, a method for using osmometry to measure chemical potential of nanoparticles in a nanocolloid-mixture is presented that could be combined with simulation and theoretical efforts to develop accurate equations of state and phase behavior predictions. Finally, an equation of state originally developed for polymer liquid-liquid equilibria (LLE) was demonstrated to be effective in predicting nanoparticle chemical potential behavior observed in the EEMC simulations of particle-polymer mixtures.