Chemical Equilibrium and Coefficients

[somuchwater]

My question regards chemical equilibrium and reaction quotient.

I have always understood these to measures of the ratios of concentrations, where the equilibrium constant is the ratio at equilibrium and Q is at other points. What I don't understand (and cannot find the solution for this anywhere online) is why we apply the coefficient as an exponent. It makes perfect sense to me that if the equation is say A --> 2B + C, that the equation should be

[2B][C] / [A]. However I don't understand why it is written as [2B]^2 [C] / [A]

For example, if we start with only A, we would get 2Bs and 1 C for every A consumed. This would continue until we hit equilibrium.

So if we start with 10 As and equilibrium is when we have 5 As... wouldn't the final concentrations be

(10 B) (5 C) / ( 5 A)

instead of

(100 B) ( 5 C ) / (5 A)

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[Cawolf]

The "Law of Mass Action" was determined through differential calculus and experimentation.

I personally take van't Hoff's word for it but I found a paper that goes through the math if you really want.

http://www.colorado.edu/engineering/cs/reishus/papers/Adleman08.pdf