Water vapour is added to the ALICE TPC gas to enhance its stability. These polar molecules create large protonated water clusters around a H+ core. In this context, the reactions H3O+ (H2O)(n-1) + H2O -> H-3 O+(H2O)(n) (n=1-9) were studied in the gas phase. Structures for these clusters are suggested and the most stable structures for each cluster size are shown. The thermodynamic parameters Delta H-n-1,n(0), Delta G(n-1,n)(0), Delta S-n-1,n(0) and equilibrium constants K-n-1,K-n for the reaction were calculated to determine the size of the water clusters. The results are close to experimental data found in the literature. Protonated water clusters at stp have a size of 6-9 which corresponds to a mass of 127.1-181.2 g/mole. (C) 2015 Elsevier B.V. All rights reserved.