Known theoretical relations provide constraints on variations of the partial molar volume of an infinitely diluted solute at: (1) low solvent densities (as follows from the truncated virial EoS), (2) at the critical point of the solvent (as follows from the near-critical theory of dilute mixtures); and (3) at conditions where repulsive interactions dominate, i.e. at rho(c1) > 1.5 close to and above the Boyle temperature of a solvent, and rho(c1) > 3 close to the melting temperature of a solvent (as follows from the theory of mixtures of hard spheres). These constraints are discussed for the case of aqueous solutions at various temperatures and water densities. The constraints provide rigorous checks of the quality of models proposed to correlate or predict V-2(infinity) values, and, if applied properly, can significantly improve the reliability of predictions of both V-2(infinity) and the fugacity coefficients phi(infinity)(2). (C) 2014 Elsevier B.V. All rights reserved.