Four variants of the two-step Ping Pong mechanism for the reversible hydration of carbon dioxide to bicarbonate catalyzed by free human carbonic anhydrase II (HCA II) in solutions were derived and their goodness-of-lit to match measured initial hydration rates tested. The pseudo (i.e., no central complex) random Quad Quad Is Ping Pong mechanism with one transitory complex was retained which implied a possible competitive intermolecular proton transfer step by the CO2/HCO3- pair with respect to external buffer. The model suggests this role could he emphasized in product inhibition conditions at high bicarbonate/buffer concentration ratios. A 4-parameter kinetic model was derived to complement the existing single- (intra- or intermolecular) limiting-step models for HCA II catalyzed hydration of CO2 in which were accounted for altogether the enzyme isomerization and CO2/HCO3- proton transfer via a [CO2]center dot[HCO3-] coupling, the CO2/HCO3- proton transfer via [HCO3-](2) and [CO2]center dot[HCO3-](2) couplings, and an enzyme-substrate transitory complex via [CO2]center dot[HCO3-]center dot[Buffer] coupling. This model may prove helpful for analysis of CO2 capture reactor models subject to mixed (intra- or intermolecular) proton-transfer control, intermolecular proton transfer competition by the CO2/HCO3- pair, and large CO2 conversions.