[Misha]

Is there a difference in the the electrolysis of molten salts, and aqueous ones?
Such as molten sodium bromide, and aqueous sodium bromide? Are the half-rxns going to be different?

[xiankai]

yes because in aqueous solutions, water is present and hence, involved in electrolysis too. as a result, sodium cannot be obtained as the more reactive hydrogen(or hydronium if u prefer) is displaced instead. however, in concentrated aqueous sodium bromide, u may be able to get sodium displaced instead.

[jdurg]

You will NEVER get sodium to form via aqueous electrolysis.  It will never happen no matter how hard you try and no matter what concentration or salt you use.  The reduction potential for Na+ is about -2.73 volts while that for H+ is about -0.83 volts.  No matter what you do, hydrogen will always be produced.  You can only obtain elemental sodium from electrolysis of the molten salt.  It is thermodynamically and physically impossible to obtain it from anything where water is involved.