This work considers calculation of pK(a) for a series of related alcohols, carboxylic acids, and ammonium ions. spanning a wide range of acidities, using quantum mechanical treatment of solute electronic structure in conjunction with a dielectric continuum model for solvation of each bare solute. The electronic structure methods used are of sufficiently high quality to give very good agreement with experimental gas phase acidities. Dielectric continuum theory of solvation is used in a recently developed form that accurately takes account of solute charge density penetrating outside the solvent cavity that nominally encloses it. The cavity surface is defined by a single parameter characterizing an electronic isodensity contour, and contours are examined at and near the value 0.001 e/a(0)(3) that has previously led to a good account of solvation effects on properties of neutral solutes in various solvents. In water, the pK(a) values calculated for alcohols and carboxylic acids are generally much higher than experiment, while for ammonium ions they are comparable to experiment. Good results in water can be obtained from linear correlations that describe the effects of different substituents in solutes sharing the same acidic functional group, but different correlations apply for different acidic functional groups. For the polar nonprotic solvents DMSO and MeCN, pK(a) values close to experimental results are obtained, and very good linear correlations are found that simultaneously describe well all the solutes considered. It is argued this indicates that dielectric continuum theory properly accounts for long-range bulk solvent effects on pK(a) without the need for special parameterization of the cavity. To achieve good pK(a) results in water, further account must be taken of specific short-range effects such as hydrogen bonding. Rather than distort the cavity from the physical solute-solvent interface region in order to artificially force dielectric continuum theory to serve this purpose, as is commonly done through detailed parameterization schemes, it is recommended that other complementary approaches more appropriate for describing short-range interactions should be sought to complete the treatment of solvation effects in water.