ShmoopTube

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And here’s your Shmoop du jour, brought to you by limits, know ‘em, love ‘em, [Students listening in class]

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and maybe test ‘em every once in a while… But you didn’t hear that from us.

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Assume that a reaction occurs by the mechanism given below. What is the rate law for the

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reaction?

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And here are your potential answers: To figure out the rate law, we need to consider [Spoiler alert sign and Pause button sign post]

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which step in the mechanism limits the rate of the overall reaction, which is called the

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“rate limiting step.” …Creativity isn’t exactly a chemist's [A girl awarded a least creative trophy]

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strong suit… Anyway, the rate limiting step is kind of

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like your grandpa at the grocery store. You can’t walk down the aisle any faster than [Grandpa walks slowly down an aisle and blocks people]

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grandpa… And neither can anyone else. Good thing grocery carts don’t have horns.

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Just like your grandpa limits your rate of walking, the slowest step in a chemical reaction

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mechanism limits the rate of the overall reaction. In this case, we know that the second step,

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C reacts to form D, is the slow step. The rate of the overall reaction will be equal

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to the rate of this second step. So the second step is a first order reaction [Chemist pouring a substance into an erlenmeyer flask]

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with only one reactant, C. That means the rate law for this step is

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The rate equals the rate constant times the concentration of C

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And that’s the rate of our overall reaction! Ta-da!

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But wait, that isn’t one of the final answer choices! What kind of a cheap trick is this? [magician reaches into tophat and hand is bitten by a rabbit]

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Well… Remember that C is an intermediate species in this reaction. Our overall rate

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law can’t include any intermediate species, so we need to rewrite this equation in terms

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of the reactants, species A and B.

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The first step in the reaction mechanism, an equilibrium between A and B

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and C, is fast. We can assume this step is at equilibrium, so the rate at which A and [A+B on one side of see-saw and C on the opposite]

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B are consumed is equal to the rate at which C is formed: In equation form, that means:

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the rate constant times concentration of a times concentration of b equals the rate

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constant times the concentration of c. Equality for all As, Bs, and Cs! [A, B, C and D letters in the street and D runs away]

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Ds can get lost. Anyway, we already figured out that the overall

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reaction rate = the rate constant times the concentration of C.

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Now we know that the rate constant times the concentration of C equals

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the rate constant times the concentration of a times the concentration of b. That means

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our overall reaction rate is the rate constant times concentration of a times

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concentration of b! Long, concentration-filled story short, that

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means C is the correct answer. So next time you’re eating some delicious [Kid jumps up on a kitchen counter for cookies]

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fresh-baked cookies, maybe you should make sure the rate limiting step is your dignity

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and not how quickly your mom can work that frosting knife.

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