How and to what extent do molecular motions in a liquid depend upon the molecular mass? Since this fundamental problem could not yet be satisfactorily resolved by theoretical approaches, we present in this paper an experimental approach. In continuation of previous work from our laboratory, the effects of isotopic H-D substitution on viscosity and self-diffusion have been measured for twelve molecular liquids in a certain temperature range near room temperature. These liquids are the often used solvents : methanol, ethanol, formamide, N,N-dimethylformamide, dimethylsulfoxide, acetone, acetonitrile, pyridine, nitromethane, tetrahydrofuran, dioxane, and benzene; we have found comparatively high dynamic isotopic effects between 3% and 14%. Beside the NMR self-diffusion measurements we have, for the first time, performed measurements of the effect of mass change on the molecular rotational diffusion via O-17 and N-14 intramolecular quadrupole relaxation. In all the given molecular liquids, except benzene, the dynamic isotope effects on viscosity, translational, and rotational diffusion follow a square-root of the moment of inertia law, revealing strong translation-rotation coupling in these liquids. However, in the two further liquids n-octanol and n-dodecanol this coupling seems to be absent, since we find here for the dynamic isotopic effect on viscosity a square-root of mass law. We have also measured D*, the tracer-diffusion coefficients of light (protonated) molecules in the heavy (deuterated) liquids. Here, we find a very weak mass dependence of D*, which obviously follows a square-root of reduced mass law, as predicted from simple gas kinetic theory. A "negative" dynamic isotope effect for CHCl3/CDCl3 postulated in the literature could not be confirmed by our measurements. The NMR techniques used for this study turned out to be excellently suited for investigations of the mass effects on dynamic quantities in liquid systems.