Reducing modal logic to FOL

Question

I was wondering if you could essentially translate modal logic into a logic that doesn't have modal operators, without losing any expressive power, by doing something like saying "Sentence S is necessarily true" means "negating S entails a contradiction" and saying "S is possible" means "S is by itself does not entail a contradiction" and saying "S is necessarily false" means "S by itself implies a contradiction." Is there anything wrong with doing this?