Attempting to balance a redox reaction using half reactions leaves an unbalanced component

Question

I have this redox reaction that I can't balance using half reaction method.

$$\ce{Mg + HNO3 -> Mg(NO3)2 + N2O + H2O}$$

What I get at the end is

$$\ce{2Mg + 6HNO3 -> 2Mg(NO3)2 + 3N2O +3H2O}$$

I can't get the $\ce{N}$ balanced.

Answer 1

It seems likely that you are starting with the wrong half reactions.

Since this reaction happens in water, separate the ionic species into their ions:

$$\ce{Mg(NO3)2 -> Mg^{2+} + 2NO3-}$$

$$\ce{HNO3 -> H+ + NO3-}$$

Now, one half reaction should involve magnesium (and have no nitrogen anywhere). The other half reaction should involve nitrogen only.

$$\ce{Mg -> Mg^{2+}}$$ $$\ce{NO3- -> N2O}$$