A new model is presented for the gas dynamics within a bubble at conditions that lead to the phenomenon of sonoluminescence. The spherically symmetric Navier--Stokes equations with variable properties are solved together with momentum and energy equations in the liquid. Calculations are presented for bubbles of argon, helium, and xenon in liquid water. The first main result is that, in contrast to recent models of air bubbles in water, there are no sharp shocks focusing at the origin of the bubble. An alternative mechanism for energy focusing in noble gas bubbles is proposed that is consistent with a smooth onset of sonoluminescence with increasing acoustic forcing, as observed in experiments. The second main result concerns an observed correlation between sonoluminescence intensity and the thermal conductivity of the gas, which suggests that heat transfer plays a dominant role in the focusing of acoustic energy. It is shown instead, that mechanical effects associated with the molecular mass of the gas figure prominently in determining the peak temperatures and pressures in strongly forced bubbles. Finally, mass transfer into and out of the bubble is examined using a special nonlinear form of Henry's law.