Polyelectrolyte solutions of Na-doped single-wall carbon nanotube (SWNT) salts are studied by Raman spectroscopy. Their Raman signature is first compared to undoped SWNT suspensions and dry alkali-doped SWNT powders, and the results indicate that the nanotube solutions consist of heavily doped (charged) SWNT. Raman signature of doping is then used to monitor in situ the oxidation reaction of the nanotube salt solutions upon exposure to air and to an acceptor molecule (benzoquinone). The results indicate a direct charge-transfer reaction from the acceptor molecule to the SWNT, leading to their gradual charge neutralization and eventual precipitation in solution. The results are consistent with a simple redox titration process occurring at the thermodynamical equilibrium.