We investigate the mobility of supercooled liquid toluene, ethylbenzene, and benzene near their respective glass transition temperatures (T-g). The permeation rate of Ar, Kr, and Xe through the supercooled liquid created when initially amorphous overlayers are heated above their glass transition temperature is used to determine the diffusivity. Amorphous benzene crystallizes at temperatures well below its T-g, and as a result, the inert gas underlayer remains trapped until the onset of benzene desorption. In contrast, for toluene and ethylbenzene the onset of inert gas permeation is observed at temperatues near T-g. The inert gas desorption peak temperature as a function of the heating rate and overlayer thickness is used to quantify the diffusivity of supercooled liquid toluene and ethylbenzene from 115 to 135 K. In this temperature range, diffusivities are found to vary across 5 orders of magnitude (similar to 10(-14) to 10(-9) cm(2)/s). The diffusivity data are compared to viscosity measurements and reveal a breakdown in the Stokes-Einstein relationship at low temperatures. However, the data are well fit by the fractional Stokes-Einstein equation with an exponent of 0.66. Efforts to determine the diffusivity of a mixture of benzene and ethylbenzene are detailed, and the effect of mixing these materials on benzene crystallization is explored using infrared spectroscopy.