How do you write chemical equation for the neutralization of nitric acid, HNO3, with magnesium hydroxide, Mg(OH)2, first with spectator ions and then without spectator ions?

First you write the "molecular" equation, then the ionic equation, and finally the net ionic equation.

You can read about these equations at

http://socratic.org/questions/what-is-the-net-ionic-equation-of-the-reaction-of-fecl2-with-naoh

Here are the steps for your reaction.

1. Write the molecular equation

We write the equation as if all the reactants were molecules.

2HNO₃(aq) + Mg(OH)₂(s) → 2H₂O(l) + Mg(NO₃)₂(aq

2. Write the ionic equation

We write all the soluble strong electrolytes as ions. H₂O is a weak electrolyte, so we write it as a molecule. Mg(OH)₂ is insoluble, so we write it as a molecule as well.

2H⁺(aq) + 2NO₃⁻(aq) + Mg(OH)₂(s) → 2H₂O(l) + Mg²⁺(aq) + 2NO₃⁻(aq)

3. Write the net ionic equation

Here, we cancel all species that appear on both sides of the equation. We cancel the NO₃⁻ ions.

The net ionic equation is

2H⁺(aq) + Mg(OH)₂(s) → 2H₂O(l) + Mg²⁺(aq)