Oxidation Reduction (redox) Balancing

[krackers]

When balancing oxidation reduction reactions involving acids or bases, what (in the case of acids) allows you to add H+ ions to one side of the reaction and H2O to the other, or in the case of bases, OH- and H2O to balance out hydrogen/oxgen? Normally you are not allowed to just add random compounds to either side of the equation.

I suspect this has something to do with the ability of H+ to grab oxygen atoms to form H2O, as similarly with 2OH- to supply Oxygen atoms and give H2O, as demonstrated by these two reactions:
2H^{+}\; +\; O^{2-}\; -->\; H_{2}O

2OH^{-}\; -->\; H_{2}O\; +\; O^{2-}

However, is this the real reason? And instead of using H+ ions for the acids, wouldn't it be more appropriate to use the hydronium ion, H3O+?In case the question is not clear, here is an example reaction.

MnO_{4}^{-}\; +\; I^{-}\; -->\; I_{2}\; +\; Mn^{2+}

One of the half reactions would be:

5e^{-}\; +\; MnO_{4}^{-}\; +\; 8H^{+}\; ->\; Mn^{2+}\; +\; 4H_{2}O

However, in this half reaction what allows you to add H+ to one side and H2O to the other?

 

[Borek]

These reactions usually take place in water, and typically in either low or high pH - so you can safely assume there is plenty of H₂O and H⁺/OH^- around. As there is plenty of them, they can be between reactants and products and you won't even notice changes in their concentrations.