Positrons and electrons sometimes exist as the unstable species positronium (Ps) in living organisms. The time it takes for Ps to annihilate represents the Ps lifetime and it varies depending on the surrounding electron density. The Ps lifetime may add new biological information to PET scan information. To discuss the feasibility of quantifying (free) radicals in vivo by the Ps lifetime, we used a clinical PET system to make Ps lifetime measurements in aqueous solutions containing radicals. The results suggested that differences in radical concentrations in aqueous solutions of the order of a few mM could be quantified by the Ps lifetime if the counting statistic of the time difference spectra was more than 108 events. This concentration was much higher than the radical concentration generated in the physiological functions of living organisms. We concluded that quantification of radicals generated in vivo by using the Ps lifetime is practically hopeless.