Balancing a reaction with unknown products
Water is normally a mix of hydroxide and hydrogen, at very dilute levels.  For example, neutral water (pH of 7) is 10-7 of OH- and H3O+ ions.  Add sodium and it combines with the OH-.  The loss of electrons by sodium are available to the hydrogen ions, which combine to make hydrogen gas.  Sodium in metal form is so reactive, it will sustain this reaction even at the low hydroxide levels in pure water, and even in slightly acidic seawater.