Membrane osmometry is used to measure osmotic pressures of dilute solutions containing quasispherical CdSe nanocrystals covered with polymer brushes in toluene in the range 31-45 degreesC. Osmotic-pressure data, as a function of nanocrystal concentration, yield the molecular weight and the osmotic second virial coefficient of the nanocrystals; the latter is related to the potential of mean force between two nanocrystal particles in dilute solution. Coupled with molecular-weight data, extinction coefficients and oscillator strengths are also obtained for nanocrystals of various sizes in toluene, CdSe nanocrystal sizes were obtained either from transmission electron microscopy or from correlations between the wavelength of the absorbing peak and nanocrystal size.Osmotic-pressure data are reduced with a simple perturbed-hard-sphere equation of state; the perturbation is due to long-range (London dispersion) attraction and a short-range interaction potential. The only adjustable parameter, the strength of this short-range potential, shows two-body repulsion or attraction, depending on the sample and on solution conditions.