Predictions from gas phase nucleation models are highly sensitive to the thermodynamics of the initial stages of particle growth, where free energies calculated using classical nucleation theory are expected to be the least accurate. There is strong evidence that H2SO4 and H2O are directly involved in atmospheric nucleation. These species are also principal components of atmospheric ions, suggesting that they may play important roles in ion-induced nucleation mechanisms. In part I of this work, we measured equilibrium constants for the reactions of H2O with the cluster ions, H+(H2SO4)(s)(H2O)(w) s less than or equal to 4 and w less than or equal to 15, over a range of temperatures using an ion flow reactor. H2O bond enthalpies and entropies were derived from van't Hoff analyses, and results for the H+(H2O), system are in agreement with literature values. Thermodynamics of H2SO4 binding in the H+(H2SO4)(s)(H2O)(w) cluster ions were also estimated based on comparisons with the HSO4-(H2SO4), system, whose bond enthalpies were measured previously. As clusters grow in size, some thermodynamic trends begin to reflect those for bulk H2SO4/H2O solutions. A stable population of the H+(H2O)(w) cluster ions is present in the atmosphere, but for typical concentrations, incorporation of the first H2SO4 molecule to form H+(H2SO4)(H2O)(w) is thermodynamically unfavorable at 270 K. As a result, significant growth and subsequent nucleation of the H+ (H2SO4)(s)(HO)(w) system is not anticipated in the middle or lower troposphere.