Rate Law of Multi Step Reaction (Kaplan FL 6)

[Bali]

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So I just took Kaplan FL 6 yesterday, and had a problem with one of the questions.

Consider a reaction that proceeds by four steps:

(fast) A2 + BC --> A2C + B

(slow) B + BC --> B2C

(fast) A2C + B2C --> A2C2 + B2

(fast) A2C2 + B2 --> AB2 + AC2

What is the expression for the rate of the overall reaction?

Now, the correct answer is k[A2][BC]^2.

However, from what I've studied, where you assume the first step goes to equilibrium, set the rates equal solve for , and plug it into the rate for reaction 2, it should be (k[A2][BC]^2)/([A2C]). Why would the [A2C] not be in there? (btw, I'm assuming people know how I got this answer, but if needed I can write out the steps).

After looking at the answer, it seems obvious that A2C wouldn't be in the rate law (because its an intermediate in the overall reaction), but shouldn't this come out in the calculations?

I am aware that you're supposed to rely on critical thinking and not mechanical...math-ing, but I was wondering if I was missing something in how I set my equations up.

Thanks!

ps FL 6 overall sucked. brought me down several points from my last few Kaplan FLs

 

[sangria1986]

.

 

[Bali]

anyone?

 

[quikmaster]

it's just asking for overall reaction not the rate law according to r.d.s

(fast) A2 + BC --> A2C + B

(slow) B + BC --> B2C

(fast) A2C + B2C --> A2C2 + B2

(fast) A2C2 + B2 --> AB2 + AC2

you add all of them up and cancel. corresponding colors cancel.

you're left with A2+ 2BC --> AB2 + AC2 ; k[A2][BC]^2

 

[MT Headed]

Wow, I was going to post a similar question today, but since somebody resurrected this thing, I will join the discussion.

Quik - You are calculating a rate determining step from a balanced chemical equation. This does not work. It is one of the most common mistakes in general chemistry. Look back in your gen chem book, exam krackers, or any other review material. This is one of the most common mistakes and one of the most common traps set up in the MCAT or on any gen chem test. Rate laws can be determined by experimentation or by analyzing the elementary steps ONLY.

bio - So the rate determining step is

B + BC -> B2C

Therefore the rate law is

rate = k[BC].

BC is a legitimate reactant, but B is an intermediate. So go back to the first elementary step. Assuming it is in equilibrium,

k[A2][BC]=k[A2C]

Therefore

= k[A2][BC]/[A2C]

So substituting in the original rate law, we now have

rate = k[A2][BC]^2/[A2C]

Great, we got rid of an intermediate, but now we have another intermediate in our rate law. If you try to get rid of the [A2C] intermediate with the same logic, you can get a few other intermediates or even some products in the rate law, which is equally bad.

I would really like to know, how do you solve something like this?

 

[Preciouzgeek]

it's just asking for overall reaction not the rate law according to r.d.s

(fast) A2 + BC --> A2C + B

(slow) B + BC --> B2C

(fast) A2C + B2C --> A2C2 + B2

(fast) A2C2 + B2 --> AB2 + AC2

you add all of them up and cancel. corresponding colors cancel.

you're left with A2+ 2BC --> AB2 + AC2 ; k[A2][BC]^2

Definitely agree, you have to thoroughly read the question -- it's tricky. If the question stated "What is the rate law for this reaction?" then the overall reaction is given and you would just have to find the rate law by incorporating substitution into the slow step.

BUT, the question given is different because it is asking "What is the rate of the overall reaction?" -- the question hints that the overall reaction is not given, so you have to find the overall reaction (as shown above) and then find the rate law of that.

 

[indianjatt]

Definitely agree, you have to thoroughly read the question -- it's tricky. If the question stated "What is the rate law for this reaction?" then the overall reaction is given and you would just have to find the rate law by incorporating substitution into the slow step.

BUT, the question given is different because it is asking "What is the rate of the overall reaction?" -- the question hints that the overall reaction is not given, so you have to find the overall reaction (as shown above) and then find the rate law of that.

What??? From what I learned in general chemistry, all of these reactions are the mechanisms for the OVERALL reaction so by using the slow step reaction as your rate law and back substituting you are finding the overall reaction, which is what the OP was trying to do. Finding the overall reaction rate isn't different than finding the rate for a simple reaction in a multi-step reaction because it's a process of the overall reaction.

Unless it said what is the reaction rate of the overall reaction assuming it was an elementary reaction, then I could see how they got the answer.

 

[MT Headed]

As a followup, I gave this problem to my gen chem professor, and let him chew on it for a while. He was stumped, and he gave it to the rest of the chemistry faculty, and nobody could figure out WTF was going on. They came back to me and asked where on earth I got this problem.

I do not have access to KaplanFL6. I would be curious what the original question was, including all of the relevant info from the passage. As written in this post, I do not believe the question has a solution.

Does anybody have access to KaplanFL6?
Is the question even posted correctly?
Was there extra information in the passage, like a table of concentrations and reaction times?

MCAT questions just aren't that hard. If this one stumped my entire chemistry department, we are all missing something.

And please, can we agree once and for all that simply adding the elementary equations and deriving a rate law from the net reaction does not work, has never worked, and never will work? It produced wrong answers in gen chem kinetics, it produced wrong answers in ochem kinetics, and there is very little reason to assume that it will suddenly start working on the MCAT.

 

[Preciouzgeek]

What??? From what I learned in general chemistry, all of these reactions are the mechanisms for the OVERALL reaction so by using the slow step reaction as your rate law and back substituting you are finding the overall reaction, which is what the OP was trying to do. Finding the overall reaction rate isn't different than finding the rate for a simple reaction in a multi-step reaction because it's a process of the overall reaction.

Unless it said what is the reaction rate of the overall reaction assuming it was an elementary reaction, then I could see how they got the answer.

Yeah, my fault. Just realized it lol I was praying that's how they derived the solution -- I definitely think we're missing more info from the passage or there's a typo in the post.