The PVTx relationship of aqueous n-hexane solutions (0.0201, 0.082, and 0.8500 mole fraction of n-hexane) has been measured in the near-critical and supercritical regions with a constant-volume piezometer. Measurements were made on the critical isotherm of pure water 647.1 K with pressures ranging from 8 to 33 MPa. The total uncertainties of density, pressure, temperature, and composition measurements are estimated to be less than 0.16%, 0.05%, 15 mK, and 0.001 mole fraction, respectively. The Krichevskii parameter was estimated (124.4 +/- 20 MPa) from direct measurements of the P-x dependence along the critical isotherm-isochore of pure water. The measured PVTx data were used to calculate partial molar volumes at infinite dilution for n-hexane (V) over bar (infinity)(2) in near-critical water. The asymptotic behavior of the partial molar volume along the solvent's (pure water) critical isotherm-isobar was studied. The molar volume values for the dilute H2O + n-C6H14 mixture along the critical isotherm-isochore of pure water were also used to estimate the critical exponent of partial molar volume (V) over bar (infinity)(2) proportional to x-(epsilon) (epsilon = 0.795 +/- 0.001). Using our new PVTx data together with data obtained in other studies, we developed a crossover Helmholtz free-energy model (CREOS) for dilute aqueous n-hexane solutions in wide temperature and pressure ranges around the vapor-liquid critical points. The CREOS model requires only the critical focus as an input and represents all available experimental PVTx data for a dilute H2O + n-C6H14 mixture with an average absolute deviation (AAD) of about 0.50-0.65% in the temperature and density ranges 0.98T(c)(x) <= T <= 1.15T(c)(x) and 0.35 rho(c)(x) <= rho <= 1.65 rho(c)(x), respectively, and concentrations up to 0.05 mole fractions of n-hexane. The accuracy and predictive capability of the crossover model was confirmed by comprehensive comparison of present crossover EOS for the pure n-hexane with the available experimental data in the critical and supercritical regions.