Question

For a non-1:1 reaction, such as the one that occurs between sodium and oxygen, how can you determine whether the molar quantity of one of the reactants will act to limit the product yield?

Answer 1

compare the (theoretical) stoichiometric ratio to the actual reactant ratio.

For example 2Mg + O2 --> 2MgO
Now let's say you have 2 moles of Mg and 1 mole of O2. That's the stoichiometric ratio 2:1

If you have 3 moles of Mg and 1 mole of O2, then you can use up 1 mol of O2 and 2 mols of Mg leaving behind 1 mol of Mg excess. Thus the amount of O2 is the limiting factor.
mole ratio is 3:1

If you have 1 mol of Mg and 1 mole of O2, then you will use up 1 mol of Mg and half a mole of O2, leaving 1/2 mole of O2 excess. mole ratio = 1:1

So in summary if actual ratio m:n > stoichiometric ratio a:b, then m is your excess and n is your limiting reagent.
If actual ratio m:n < stoichiometric ratio a:b, then m is your limiting reagent and n your excess.

Best to look at each scenario independently.