The Rosseland mean opacity was determined for an ensemble of dust grain species though to have been present in the early solar nebula, as well as in the primordial nebulae that helped to form the outer planets. In performing these calculations, we have derived and used more general equation for the Rosseland opacity that allows for anisotropic scattering. The identity of the major particle species and their relative abundances were found from thermodynamic equilibrium and solar elemental abundances. The optical constants of these materials were defined at wavelengths ranging from near-UV to the radio domain. Calculations were performed for a very wide range of particle size distributions, including a nominal one based on that of interstellar dust grains. In addition, asymptotic expressions for the Rosseland opacity are derived in the limits of very small and very large sized particles. Results are presented for nebular temperatures varying from 10 to 2500°K and for nebular gas densities varying from 10 -14 to 1 g/cm 3. The values of the Rosseland mean opacity do not depend sensitively on the choice of the particle size distribution function, provided that there are few particles having sizes in excess of several tens of microns. At low temperatures that lie within the stability field of condensed water (⪅200°K), this opacity varies approximately as the square of the temperature for the nominal size distribution and for all distributions having few particles larger than several tens of microns. However, the Rosseland opacity has a much weaker temperature dependence at higher temperatures for this class of size distributions and at all temperatures for size distributions containing numerous particles larger than several tens of microns. As a result, thermal convection in primordial nebulae occurs over broader ranges of altitudes at low temperatures and for size distributions for which extensive aggregation has not yet occurred.