The interaction of positronium (Ps) with molecular oxygen dissolved in liquids is experimentally investigated. Computer software has been developed for fitting the positron annihilation lifetime spectra in liquids using parameters with clear physical meaning: rate constants of the Ps chemical reactions, annihilation rate constants of the different positron states, probability of Ps formation in a quasi-free state, typical formation time of a Ps nanobubble. Such processing of the spectra allowed identification of the dominant interaction of the Ps atom with dissolved oxygen. It turns out to be mainly ortho-para-conversion (Ps → 1/4 p-Ps + 3/4 o-Ps), but not oxidation (Ps + O2 → e+ + O2-). Values of the reaction rate constants are obtained.