Continuous semihydrogenation of phenylacetylene over an amorphous Pd81Si19 catalyst in supercritical CO2 as a solvent has been studied. The amorphous alloy afforded high selectivity to styrene without catalyst modification, which is usually necessary for high selectivity in "Lindlar-type" hydrogenations. The application of the highly active glassy metal alloy combined with a supercritical solvent afforded efficient operation in a continuous fixed-bed reactor. A single-phase system was found to be an ideal reaction medium for such hydrogenation reactions. Highest conversions and good selectivities were achieved near the transition to a single-phase mixture, where mass transport is enhanced by elimination of the gas-liquid interface. In order to reach complete miscibility of the reactants in CO2 at moderate pressure, both temperature and hydrogen excess had to be kept low. The phase behavior was monitored by online video imaging. Consideration of the phase behavior was found to be indispensable for assessing single-phase conditions. A binary fluid-phase diagram is shown to serve as a good guide to understanding the multicomponent behavior.