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An alternate thermodynamic formalism is developed to correlate the solubility of a non-volatile solute in a supercritical fluid (SCF) as a function of the density of the fluid phase. We show that this solubility varies approximately in a linear fashion with the solvent density when examined in either log-log or log-linear coordinates, depending on the system in consideration. The slope of this plot is related to the solvent isothermal compressibility and the partial molar volume of the solute present at infinite dilution in the SCF phase. From literature solubility data, we obtain estimates for the partial molar volumes for some infinitely dilute mixtures of solutes in SCF which are in agreement with independently measured experimental values.