Onsager's model of the dielectric constant is used to provide a molecular-level picture of how the dielectric constant affects mass and charge transport in organic liquids and organic liquid electrolytes. Specifically, the molecular and system parameters governing transport are the molecular dipole moment mu and the solvent dipole density N. The compensated Arrhenius formalism (CAF) writes the temperature-dependent ionic conductivity or diffusion coefficient as an Arrhenius-like expression that also includes a static dielectric constant (epsilon(s)) dependence in the exponential prefactor. The temperature dependence of epsilon(s) and therefore the temperature dependence of the exponential prefactor is due to the quantity NIT, where T is the temperature. Using the procedure described in the CAF, values of the activation energy can be obtained by scaling out the NIT dependence instead of the epsilon(s) dependence. It has been previously shown that a plot of the prefactors versus epsilon(s) results in a master curve, and here it is shown that a master curve also results by plotting the prefactors against N/T. Therefore, the CAF can be applied by using temperature dependent density data instead of temperature dependent dielectric constant data This application is demonstrated for diffusion data of n-nitriles, n-thiols, n-acetates, and 2-ketones, as well as conductivity data for dilute tetrabutylammonium triflate-nitrile electrolytes.