We define a model of the composition and abundances of grains and gases in molecular cloud cores and accretion disks around young stars by employing a wide range of astronomical data and theory, the composition of primitive bodies in the solar system, and solar elemental abundances. In the coldest portions of these objects, we propose that the major grain species include olivine ([Fe, Mg]2SiO4), orthopyroxene ([Fe, Mg]SiO3), volatile and refractory organics, water ice, troilite (FeS), and metallic iron. This compositional model differs from almost all previous models of the interstellar medium (ISM) by having organics as the major condensed C species, rather than graphite; by including troilite as a major grain species; and by specifying the mineralogical composition of the condensed silicates. Using a combination of laboratory measurements of optical constants and asymptotic theory, we derive values of the real and imaginary indices of refraction of these grain species over a wavelength range that runs from the vacuum UV to the radio domain. The above information on grain properties is used to estimate the Rosseland mean opacity of the grains and their monochromatic opacity. We find that organics are the largest contributors to the Rosseland mean extinction coefficient at temperatures below their vaporization temperatures (similar or equal to 575 K in molecular cloud cores and 425 K in accretion disks), and that silicates and metallic iron jointly determine the Rosseland mean opacity at higher temperatures. At mid-infrared wavelengths, the computed monochromatic opacities are in approximate accord with the spectral characteristics of ''astronomical silicates.'' At low temperatures (<500 K), the position, strength, width, and contrast of the 10 and 20 mu m silicate vibrational fundamentals can be significantly affected by the opacities of organics and water ice. Strong silicate features are produced only when the average grain size is less than several tens of microns. The spectral index beta of the grain opacity at long wavelengths shows marked variation. In particular, we estimate that it has a value of about 2.5 between 100 and 650 mu m and a value of about 1.5 between 650 mu m and 2.7 mm for submicron- to millimeter-sized grains, in rough agreement with spectral flux measurements of the ISM and some disks around young stars. In the latter spectral region, grain opacity is dominated by silicates, with important contributions also coming from troilite and organics. However, the low values of beta (similar to 0) that appear to characterize a few disks around young stars in the 650 mu m to 2.7 mm region may be the result of significant grain growth that has occurred in these disks (sizes greater than or equal to 10 cm). In a similar vein, existing-far infrared spectral data for the older, Vega-like objects are consistent with grain sizes on the order of hundreds to thousands of microns. We also find that the grain absorption coefficient at 1 mm wavelength lies within a factor of 4 of 5 x 10(-3) cm(2) g-l (of gas and dust) for a wide variety of grain shapes and for grain sizes ranging from submicron to several millimeters. Thus, continuum flux values at 1 mm wavelength can lead to useful estimates of disk masses.
