Balancing a reaction with unknown products I'm given this equation in word form:

$$\ce{sodium (s) + water (aq) -&gt; unknown~products (s/g/aq)}$$

and I have to convert this to a chemical equation. I understand how to covert this normally, that equation can hence be represented by:

$$\ce{Na + H2O -&gt; unknown~products\:(s/g/aq)}$$

This is indeed a single displacement reaction so it should become (according to what I know so far) $\ce{Na2O + H2}$ but after doing some research, I got that it should be:

$$\ce{Na + H2O -&gt; NaOH + \frac{1}{2}H2}$$ or $$\ce{2Na + 2H2O -&gt; 2NaOH + H2}$$

I'm lost now, where did $\ce{NaOH}$ come from? Especially the H since there is no reason for hydrogen to be present.

Please explain why and how to balance this reaction or convert this and what factors to look at when dealing with these types of equations.
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.