The results of a theoretical study of the acid ionization to form first a contact ion pair and then a solvent-separated ion pair are presented for HF in water. The ionization reaction to produce the contact ion pair is found to involve adiabatic quantum proton transfer (PT) and has an activation barrier in a collective solvent reaction coordinate of 2.9 kcal/mol, with a positive reaction free energy estimated as 2.2 kcal/mol. This result identifies the weakness of HF acid in aqueous solution as arising from this intrinsic acid ionization step, rather than from the thermodynamic difficulty of separating the ions so produced. The calculated charge distributions for the first step are in support of the unconventional Mulliken picture for PT. The second step to produce a solvent-separated ion pair is found to be sequential in connection with the first step, rather than concerted, and is also a quantum adiabatic PT. This reaction step proceeds via a solvent reaction coordinate and is slightly activated. The two step sequence in reverse order is discussed in connection with the Eigen picture of acid-base recombination in aqueous solution.