Published isopiestic molalities for aqueous HReO4 solutions at T = 298.15 K are completed. Binary data (variation of the osmotic coefficient and activity coefficient of the electrolyte in solution in the water) at T = 298.15 K for perrhenic acid HReO4 are determined by direct water activity and osmolality measurements. The variation of the osmotic coefficient of this acid in water is represented mathematically according to a model recommended by the National Institute of Standards and Technology and according to the specific interaction theory. The data are also used to evaluate the parameters of the standard three-parameters of Pitzer’s ion-interaction model, along with the parameters of Archer’s four-parameter extended ion-interaction model, to higher molalities than previously advised. Experimental thermodynamic data are well represented by these models. Density variations at T = 298.15 K are also established and used to express the activity coefficient values on both the molar and molal concentration scales.