Hey people,
This topic is a bit difficult for me. Could someone explain it using this problem? I just know that we're looking at the slowest reaction, I think, and setting up a few equations for it, but unfortunately I don't understand exactly how that works.
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Hello, can someone please explain to me how to solve this problem?
So our reaction consists of two steps
A3 = 3 A
2 A + B ⟶ Something
wherein the first step proceeds rapidly and the second slowly.
With this indication I get abdominal pain right away. If the object is to be completely detachable, then the steps specified must be elementary steps, i.e. they must proceed in a molecular manner just as without an intermediate step. The second step would then require three molecules to collide in exactly the right way, which is extremely unlikely — two-strokes are common, but three-strokes are so rare under civilized conditions that the reaction rate is ≅0. This is all the more true when presumably A3 is only partially disintegrated, that is to say c(A) is small and two A atoms have no realistic chance of reacting with one another.
Let us assume that the example is meant as I understand, even if it is very practical (or an absurdly rare exception from the rule of thumb)
In this case, the speed law is something like v=k⋅c2(A)⋅c(B), because it depends only on the speed-determining step (the slowest). However, we need to express c(A) by c(A3) because this is the starting material.
The first reaction is an equilibrium reaction, so I assume that it is in the same weight. It then has an equilibrium constant K, and K=c3(A)/c(A3) applies, and from this it follows that c(A)=3√(K⋅c(A3)), i.e. the concentration of A is proportional to the third root of c(A3). There is also an approximation in it, namely that the DIssociation of A3 takes place only to a small extent; Otherwise, c(A3) would have to be reduced by the decayed part, i.e. K=c3(A)/(c(A3)-1⁄3c(A)) and I do not think that the purpose of the task is. In the extreme case that the decay is almost complete, c(A)≅3c0(A3) would apply, and there is no third root.
If we take small decay, then we continue to count on the third root. We already know that the reaction rate will be proportional to c2(A), so we get an exponent 2⁄3 for c(A3). The entire constants do not play a major role here because all of them are absorbed by the speed constant k.
we therefore get out of an innumerable reaction order 12⁄3; that is typical of all reactions in which a molecule in not-speed-determining step disintegrates into several identical fragments, for example radical chain reactions.
Disclaimer:
I don’t understand much about kinetics, so a mistake of thinking is not excluded.