Reaction mechanisms of protonated water clusters [D3O+(D2O)(n), n = 4-30] with hydrogen bromide (HBr) and nitric acid (DNO3) were elucidated using a fast-flow reactor operated at thermal conditions over a temperature range of 143-173 K. The dissolution of these acid species is found to occur at critical cluster sizes as reported herein. Rate coefficients of the thermal energy reactions of DNO3 and D3O+(D2O)(n) (n = 6-22) were investigated and found to display a dependence on cluster size. We also report findings on the minimum cluster size necessary for, the first uptake of nitric acid and hydrogen chloride by hydrated sodium and potassium cluster ions and compare the values with those for protonated water clusters. The present work is considered along with previous literature results obtained using surface sensitive and mass spectrometric techniques, with the objective of providing complementary information about the uptake of acid molecules on ice/aqueous surfaces.