I am currently studying thermochemistry and specific heat capacity has been discussed. From observing a list in order of specific heat from highest to lowest and then comparing to a list of densities, it seems to me that the denser a substance is, the lower the specific heat. Is this true and if so is there an exact relationship?
Generally, sorta true. Specific relationship? No. What you've tripped over is "equipartition" of energy of a system among the degrees of freedom of the system. Translation: As far as chemists are concerned, heat capacities, or specific heats, can be interpreted as sums of translational, rotational, and vibrational degrees of freedom of molecules; translational and rotational degrees each contribute kT/2 (or, RT/2), and vibrational degrees kT to the total heat capacity. Notice, no mention of mass --- that means, roughly, that the heat capacity per mole of He is the same as that for Rn --- per unit mass, He is higher. Equipartion is approximate --- the vibrational degrees of freedom are not commonly fully excited, and, strictly speaking, you also have to include electronic states, nuclear states, and so on, but at temperatures at which molecules are stable (low energy excited states), you can pretty much ignore everything beyond translation, rotation, and vibration.