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K is the normal rate constant for a reaction, let's say for rate = k[A]N[B]M[C]L. However, if [B]0 and [C]0 >> [A]0, we can say that rate = k'[A]N, and that the reaction is a pseudo-first order reaction. Comparing the two, we can see differences in the units of k, with k' having units of L2*mol-2*s-1 and k having units of s-1.
Yes so because k is the reaction constant for the forward reaction k' is the reaction constant for the reverse reaction. Thus the equilibrium constant K for the forward direction is equivalent to k/k'. This can be determined because at equilibrium of a+b --> c + d, the rate of the forward reaction (k[a][b]) = the rate of the reverse reaction, k'[c][d] and when these are set equal to one another [c][d]/[a][b] = k/k'= K
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