I've watched over this Khan video titled "Reactions in Equilibrium" and am still confused on the interpretation of equilibrium. Reactions in Equilirbium
$\ce{N2(g) + 3H2(g) <=>2NH3(g)}$
Whenever I see an equilibrium like the one above, the amounts of each molecule are only what happens at the start of the reaction, correct? In the video, it was made out as if the starting coefficients next to each molecule were what was needed to reach equilibrium. However, each reaction at a different temperature has a different equilibrium constant. With that said, the amount of each molecule will change which also changes the concentration so the amount of $\ce{NH3}$ would not necessarily be 2. He does this in other videos too. He starts off with something such as:
$\ce{aA + bB <=> cC + dD}$
and immediately plugs those into an equilibrium equation. I guess what he is getting at is that we figure out the final concentrations necessary to reach equilibrium but I'm not positive.
Towards the end of the video, arbitrary (I guess) concentration amounts of each molecule were plugged into the formula to output the matching equilibrium constant. He raised each concentration to the power of the starting coefficient for that molecule. If you start out with $\ce{3 H2}$ and you need a wildly different concentration to reach equilibrium, why are we raising the concentration to the power of the starting amount of $\ce{H2}$?
Finally, let's say the concentrations I have for a particular reaction were not the concentrations at equilibrium. If I still plugged them into the equation, that would tell me not only if I were at equilibrium (if I looked up the constant) but also if the forward or backward reactions were favored right?
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