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Rate Law for Reversible Reaction Without Reaction Mechanism

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RH111:
Hi all,

I have been stuck on a chemical kinetics question for quite some time (the question is #26 from the 2021 USNCO local exam).

We are given a reversible reaction A + B  ::equil:: C and are told the forward reaction is kf[A]. We are asked to find the rate law for the reverse reaction.

I think there is not information to identify the reverse rate law because (from what I understand) we know nothing about the reaction mechanism, which is necessary for us to use the steady-state approximation.

My questions are on the following right now:
1. Is the provided information enough for us to identify the reaction mechanism ourselves?
2. Do we even need to know the reaction mechanism to identify the reverse rate? If not, how do I approach this? Is there some theory involved?

Any help is appreciated, thanks!
~RH111

Orcio_87:
In thermodynamical equilibrium rate of forward reaction is equal to rate of the reverse reaction.

Since forward reaction is dependent on concentration of A, this excludes zero-order reaction for degradation of C.

In theory it is possible that reverse reaction is second-order reaction (v ~ [C]2), but there are no points directing that.

In my opinion A is the most accurate answer.

RH111:
Thank you for your response! If it helps to work backward, the correct answer according to USNCO is B: Rate = kr*[C]/[.B].

After some more research, I came across an equation (in Raymond Chang's AP Chemistry) that says the kf/kr = KC. Using this yields the correct answer. Is this equation applicable to any reversible equation, and does anyone know why it holds true? Also, how can we determine this without knowing the reaction mechanism?

Thanks!
RH111

Orcio_87:
Sorry for misdirection. I just assumed earlier that since forward reaction doesn't depend on B, B must be constant. I think that answers A and B is just a different way how the rate constant is written, but of course maybe B is more accurate.


--- Quote ---Is this equation applicable to any reversible equation, and does anyone know why it holds true? Also, how can we determine this without knowing the reaction mechanism?
--- End quote ---

It is applicable, but only for one intermediate stage.

For overall reaction it is K = (kf1 x kf2 x kf3 x ...) / (kr1 x kr2 x kr3 x ...), where kf1 is 1st step forward reaction constant, kr1 is 1st reverse reaction consant and K - equilibrium (thermodynamical) constant for reaction as overall.

Orcio_87:
Sorry for misdirection. Reverse reaction is dependent on B, since B doesn't occur in forward reaction rate (this would give different rate constants and Kc = kf / kr won't be true).

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