Materials with a high-degree of inter- and intra-molecular hydrogen bonding generally have limited solubility in conventional organic solvents. This presents a problem for the dissolution, manipulation and purification of these materials. Using a state-of-the-art density-functional-theory based quantum chemical solvation model we systematically evaluated solvents for a known hydrogen-bonded molecular crystal. This, coupled with direct solubility measurements, uncovered a class of ionic liquids involving fluoride anions that possess more than two orders of magnitude higher solvation power as compared with the best conventional solvents. The crystal structure of one such ionic liquid, determined by X-ray diffraction spectroscopy, indicates that F- ions are stabilized through H-bonded chains with water. The presence of coordinating water in such ionic liquids seems to facilitate the dissolution process by keeping the chemical activity of the F- ions in check.