a student did not completely burn all the magnesium and some un-burned magnesium remained. How will this affect the empirical formula found?

Answer:

Mg(s) + N₂(g) + O₂(g) ---> MgO(s) + Mg₃N₂(s)

If you left some Mg₃N₂ in the crucible as product you would calculate a ratio of MgO to contain too little oxygen. When we weigh the final contents we wont know that the contents have more magnesium, we assume it’s pure MgO. Mg₃N₂ does not contain any oxygen, so there would be too little oxygen, but there is magnesium present so there is more magnesium than oxygen. Since we did not completely burn all the magnesium and some un-burned magnesium remained, hence we will find that Mg:O ratio will be too high.