Most acidities and basicities of chemical compounds are measured in aqueous solution since this solvent is most important for biochemical and environmental applications, but the acidities of compounds in the gas phase and in other solvents can also be of interest. As a polar, aprotic solvent, dimethyl sulfoxide (DMSO) presents a unique environment for acid dissociation, and this solvent offers informative comparisons with both the vacuum and aqueous environments. Here, quantum chemical approaches previously used for the estimation of aqueous pKa values are applied to the estimation of DMSO, aqueous, and gas-phase acidities for two representative series of compounds: alcohols/phenols and azoles. Calculations were performed using both the semiempirical RM1 method and density functional theory (B3LYP/6-31+G**). The effectiveness of the SM5.4 and SM8 solvent models in estimating the solution-phase acidities was also examined. © 2012 Wiley Periodicals, Inc.