I'm learning about rate law and equilibrium, and the textbook really hammers in that the exponents for the rate law must be determined experimentally - you can't just use the coefficients from the balanced equation. In a generic reaction aA + bB -> cC + dD:
rf = kf[A]w[B]x
rr = kr[C]y[D]z
It is not always the case that w = a, x = b etc.
Equilibrium is then described as the point that the forward reaction is occurring at the same rate as the reverse reaction. For the same reaction as above, we set the two rates to equal each other.
rf = rr
kf[A]w[B]x = kr[C]y[D]z
Kc = kf / kr = [C]y[D]z / [A]w[B]x
I'm told that the exponents here are based on the coefficients of the balanced equation, such that w = a, x = b, y = c, and z = d. This seems to be in direct opposition to what I read earlier about the rate law, as equilibrium is just built from two rates.
Why is this?