From what I can ascertain, the formulation of the chemical equilibrium constant is somewhat arbitrary. I don't understand the motivation for putting the stoichiometric coefficients in the exponents. This seems like you are double counting. For instance, if A -> 4B, for every mole of A that decomposes to B produces 4 moles of B. So my reaction would already have a higher amount of B. Then I take those four moles and raise to the 4th power. So if I started with 2 moles of A and 1 decomposed, I would have one mole of A to 4 moles of B. Then I would have a equilibrium constant of 256. How is this superior to not having exponents and just having an equilibrium constant of 4? Or for that matter there are many arbitrary ways I can stick on or not the stoichiometric coefficients. Why not take the 4th root of B over the first root of A?
Edit: Many are saying that this is a duplicate of Law of Mass Action. However, in that question the stoichiometric coefficients just HAPPENED to be the exponents. And as pointed out in the answer the order in the rate law doesn't have to be the same as them. My question is dealing with the Eqilibrium Constant. The Equipibrium Constant is defined such that the stoichiometric coefficients are ALWAYS the exponents. Why?