TBR GenChem: Kinetics Passage IV #24

[LuminousTruth]

For a catalyst in an industrial system, the number of active sites affects the turnover rate. What can be concluded about the maximum turnover rate of one catalytic site, if the catalyst contains three catalytic sites but the catalyst is NOT saturated with reactant?

A) The maximum turnover rate of one catalytic site is less than one third of the observed turnover rate, assuming the three catalytic sites react equally.
B) The maximum turnover rate of one catalytic site is greater than one third of the observed turnover rate, assuming the catalytic sites react equally.
C) The maximum turnover rate of one catalytic site is exactly one third of the observed turnover rate, assuming the three catalytic sites react equally.
D) The turnover rate of the catalytic site is exactly one third of the observed turnover rate, assuming the three catalytic sites do NOT react equally.

From the passage, "The turnover rate is defined as the rate of the reaction divided by the number of active catalytic sites. The units for turnover rate is reactions per second at the catalytic site."

The answer was "B" (Highlight over)

Can someone explain to me how they got the answer?

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[LoLCareerGoals]

Simple algebra question.
Catalyst could handle more (not saturated with reactant) and has 3 working sites.
Net rate is x. Net max rate Xmax > x.
If all 3 catalytic sites distribute work equally (valid assumption for A through C), then each is currently responsible for x/3, but could in theory do Xmax/3.
A) is Xmax/3 < x/3? No
B) is Xmax/3 > x/3? Yes
C) is Xmax/3 = x/3? No
D) Here our earlier assumptions go out of the window and this question has to be evaluated separately.
If sites are not working equally hard, then we could have x/2, x/4, x/4 type of distribution of load.
The question asks about a turnover rate of the catalytic site...which one? x/2 one? x/4 one? We don't know. Is x/2 = Xmax/3? Maybe. Depends how far from saturation we are. But even if it is, then x/4 def is not equal Xmax/3. So, NO.

Answer B.

 

[Gauss44]

Does "saturated" mean "at a maximum rate"? These 2 ideas seem contradictory, even though context suggests equivalence. Maybe there's a video somewhere.

 

[BerkReviewTeach]

Does "saturated" mean "at a maximum rate"? These 2 ideas seem contradictory, even though context suggests equivalence. Maybe there's a video somewhere.

Yes. Just as when an enzyme is saturated with substrate the reaction reaches Vmax, the same is true for a general catalyst. The turnover rate is the maximum rate at which the catalyst can turn reactant into product, which occurs when the catalyst is saturated with reactant.

 

[allatrope]

Simple algebra question.
Catalyst could handle more (not saturated with reactant) and has 3 working sites.
Net rate is x. Net max rate Xmax > x.
If all 3 catalytic sites distribute work equally (valid assumption for A through C), then each is currently responsible for x/3, but could in theory do Xmax/3.
A) is Xmax/3 < x/3? No
B) is Xmax/3 > x/3? Yes
C) is Xmax/3 = x/3? No
D) Here our earlier assumptions go out of the window and this question has to be evaluated separately.
If sites are not working equally hard, then we could have x/2, x/4, x/4 type of distribution of load.
The question asks about a turnover rate of the catalytic site...which one? x/2 one? x/4 one? We don't know. Is x/2 = Xmax/3? Maybe. Depends how far from saturation we are. But even if it is, then x/4 def is not equal Xmax/3. So, NO.

Answer B.

I still don't understand why Net max rate Xmax > x. I don't understand how a catalyst would work quicker then there is less substrate. My intuition (which is obviously wrong in this case) is that less substrate equates to a lower turnover rate for the enzyme. I would appreciate anyone's help with this!

 

[Lunasly]

Would someone mind expanding on this please. I'm also having a hard time grasping why it is greater than 1/3.

 

[Gauss44]

6/29/2014:

Would someone mind expanding on this please. I'm also having a hard time grasping why it is greater than 1/3.

Me too. I am still stuck on this and don't understand it.

Would someone please explain?

 

[a94wang]

The passage state that turnover rate is defined as the rate of the reaction divided by the number of active catalytic sites.

So what is the difference between maximum turnover rate of one catalytic site and maximum turnover rate of the catalyst. Aren't they the same thing?

If so, why would the maximum turnover rate of one catalytic site be 1/3 maximum turnover rate of the catalyst?

 

[sillyjoe]

You will only see an enzyme or catalyst at it's fastest/maximum rate when it is saturated.

Let's say you are at a toll booth on a busy day and you are waiting in line at the toll because all of the lanes have cars in them. In this scenario we know that the rate of cars going through the tolls would give us the maximum amount of cars passing per unit time through the toll booth since the tolls are all saturated with cars. Lets say for each toll booth the maximum rate it can register payment and allow a car to go through is 25 cars / minute. If there are 3 booths that is a total of 75 cars / minute.

Now lets say we now go to the same toll booth, but at 3:00AM. You will not see as many cars since it's so late and there are hardly cars on the road. Lets say, the rate you would see at this given time is 1 car / minute. If there were three toll booths you would say the total rate at 3:00AM is 3 cars / minute, which is not the MAXIMUM amount of cars that can get through the three the toll booths (75 cars / minute). If someone asked you to calculate the maximum rate of cars passing through the three toll booth's at noon on a busy day you would say it is GREATER than the rate at 3:00AM (75 cars >3 cars).

Similarly, in this example the question specifically states, "What can be concluded about the maximum turnover rate of one catalytic site, if the catalyst contains three catalytic sites but the catalyst is NOT saturated with reactant"

If this were at the maximum rate, one catalytic site would be 1/3rd of the total rate of the catalyst since it makes up only 1 of 3 sites contributing to the rate of the reaction. Think of it as if someone were to ask you the rate of one of the three toll booths above. It would be 1/3rd the rate of all 3 toll booths assuming saturation with cars.

Since it specifies the catalyst is NOT saturated in this reaction we know that the rate of turnover is going to be less than what we would see at saturation (maximum rate). It is like the toll booth at 3:00AM where the rate of cars passing through one toll booth is less than the maximum possible rate at saturation.

 

[bleach121]

Thanks, that makes sense.