Thursday, January 25, 2007
AP: the catalyst and the rate constant
Occasionally, some interesting conundrums are posed in class; such an enigma was expressed today. I decided to "read the book" in order to clarify my answer and, though I found no explicit answers in any of the lofty tomes of chemistry, I can finally infer the correct answer to the problem presented today.
The question was: since catalysts LOWER the activation energy required for an effective collision, and the Arrhenius equation RELATES activation energy to the rate constant as follows: ln k = -Ea/RT + lnA, doesn't a catalyst increase the value of the rate constant?
I had to reply, "No", because of the unexplained DOGMA that ONLY TEMPERATURE can ever, ever, ever affect the rate constant for a reaction. That is, was, and always will be true, Now, however, I can clarify why a catalyst doesn't affect the rate constant (and here is the source of the conundrum) of the GIVEN reaction (the one WITHOUT the catalyst)!
Since a catalyst provides (say it together) "an alternative chemical pathway" for the same net reaction, the catalyst is IN THE RATE LAW of the ALTERNATE (catalyzed) reaction which has its own GREATER rate constant (compared to the SEPARATE and DISTINCT rate constant of the uncatalyzed reaction).
For example,
uncatalyzed reaction rate law: rate = k [A]
catalyzed reaction rate law: rate = k'[Q]{A] , where "Q" is the catalyst in the rate-determining step.
and k' is a greater number than k. So the catalyst DID NOT affect the ORIGINAL rate constant; the catalyzed reaction has its own different (and greater) rate constant.
In contrast, TEMPERATURE increases do NOT change the mechanism of a given reaction, so they do increase the SAME reaction's rate constant by increasing the number of effective collisions per second occurring in the reaction.
The end.
Now, I can sleep better.
The question was: since catalysts LOWER the activation energy required for an effective collision, and the Arrhenius equation RELATES activation energy to the rate constant as follows: ln k = -Ea/RT + lnA, doesn't a catalyst increase the value of the rate constant?
I had to reply, "No", because of the unexplained DOGMA that ONLY TEMPERATURE can ever, ever, ever affect the rate constant for a reaction. That is, was, and always will be true, Now, however, I can clarify why a catalyst doesn't affect the rate constant (and here is the source of the conundrum) of the GIVEN reaction (the one WITHOUT the catalyst)!
Since a catalyst provides (say it together) "an alternative chemical pathway" for the same net reaction, the catalyst is IN THE RATE LAW of the ALTERNATE (catalyzed) reaction which has its own GREATER rate constant (compared to the SEPARATE and DISTINCT rate constant of the uncatalyzed reaction).
For example,
uncatalyzed reaction rate law: rate = k [A]
catalyzed reaction rate law: rate = k'[Q]{A] , where "Q" is the catalyst in the rate-determining step.
and k' is a greater number than k. So the catalyst DID NOT affect the ORIGINAL rate constant; the catalyzed reaction has its own different (and greater) rate constant.
In contrast, TEMPERATURE increases do NOT change the mechanism of a given reaction, so they do increase the SAME reaction's rate constant by increasing the number of effective collisions per second occurring in the reaction.
The end.
Now, I can sleep better.