Relationship between k and k'

[Jessie Hsu 1C]

I remember writing this down for the reaction A + B + C --> P when B and C are in large excess.
"since rate = k[A]ⁿ[B]_o^m[C]_o^l = k'[A]ⁿ, then k = k'/([B]_o^m[C]_o^l)"
Is there a reason why we don't use the initial concentration for [A] ?

[Steph Du 1H]

I think it is because since our pseudo rate law = k'[A]^n, [A] is actually changing. So we aren't looking at the initial concentration of [A]. [B] and [C], on the other hand, we consider to be constant since they are in large excess.

[Lea Chamoun 2J]

I think that it is because when finding the rate law for a reaction with multiple reactants, an experiment needs to be set up to determine the rate of the reaction in respect to each reactant individually. When finding the rate law in respect to A, the amount of reactant A is small compared to B and C. You assume that the concentrations of B and C do not change by a measurable amount over the course of the reaction. So the initial concentrations of B and C will not be much different than the final because there is so much more of B and C than there is A. the rate of the reaction depends on the concentration of A when it is small, so it's concentration is going to change as the reaction proceeds.

[EmilyGillen_1A]

I am not sure if this is right, but when the instructions say B and C are in excess it implies that A is not (meaning all of A gets used up in the reaction). There is so much concentration of B and C you use the initial concentration because their overall concentration does not change enough. For A, though, there is a small amount present so you want to measure the change of overall concentration (which will be more noticeable than the changes for B and C) instead of the initial concentration.

[allyssa bradley 1H]

I really like Lea's explanation! When we have problems with rate law and multiple reactants, we need to derive different k's to get our final k. If we weren't able to use a different reactant concentration for one and constant for the others, we would have way too many moving variables to come up with a system of equations that was actually useful to us! So, like Lea said, our other reactants are added in huge excess so that we can just get change in one reactant, and that reactant changes in each trial (so in your example, [A] is different from [A] knot, but we would do 2 more trials with B and C changing).