Chemistry: Mechanisms

Question

A student proposed the following mechanism for the gas phase reaction of fluorine with chlorine dioxide.

.....step 1.....fast:......2 ClO₂  Cl₂O₄

.....step 2.....slow:....Cl₂O₄ + F₂  2 FClO₂

(1) What is the equation for the overall reaction? Use the smallest integer coefficients possible. If a box is not needed, leave it blank.

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(2) Enter the formula of any species that acts as a reaction intermediate? If none leave box blank:

(3) Complete the rate law for the overall reaction that is consistent with this mechanism.

Use the form k[A]^m[B]ⁿ... , where '1' is understood (so don't write it if it's a '1') for m, n etc.

Rate =

Answer 1

I have a different approach than @Gigi C., and don't agree that you have to have the "data" used to suggest the mechanism. We assume it was generated, and go from there, as follows:

.....step 1.....fast:......2 ClO₂ <==>  Cl₂O₄

.....step 2.....slow:....Cl₂O₄ + F₂ ==>  2 FClO₂

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2ClO₂ + F₂ ==> 2FClO₂ ... equation for overall reaction

(2) Cl₂O₄ is an intermediate

(3) To find the rate law, we look at the slow step and would write the rate law as ...

Rate = k[Cl₂O₄][F₂] HOWEVER, Cl₂O₄ does NOT appear in the overall reaction.

What we can do is to use step 1 which is reversible and at equilibrium to solve for [Cl₂O₄] and then substitute that expression into the rate law for step 2.

From step 1: k1[ClO₂]² = k2[Cl₂O₄]

[Cl2O4] = k1/k2 [ClO₂]² (now substitute this into rate law for step 2)

From step 2: Rate = k3[Cl₂O₄][F₂]

Rate = k3* k1/k2 [ClO₂]²[F₂] and combining rate constants into k' we can write...

Rate = k[ClO₂]²[F₂] and this agrees with the predicted overall reaction

Answer 2

Hi Nicole,

Ahhhh mechanistic organic chemistry. The bane of most students, but my favorite.

1) So the overall reaction equation is just a "summary" equation, if you will. Combine the equations from step 1 and 2, as if it were a math problem. Treat the reaction arrow like an equal sign. See how Cl₂O₄ is present on both sides of the arrow? That means they cancel, leaving you with...

....step 1....fast.... 2 ClO₂ ----> Cl₂O₄

....step 2....slow.... Cl₂O₄ + F₂ ----> 2 FClO₂

2 ClO₂ + F₂ ----> 2 FClO₂

2) A reactionary intermediate is any temporary compound that will eventually be converted into a product. In other words, it is whichever compound that acts is the "middle step." Intermediates are not counted as a reactant or product and are not included in the "summary" or overall reaction equation. So it will be the only compound that was not featured in the overall equation, thus the reactionary intermediate in this problem is the Cl₂O₄

3) So for rate laws, let's first look at the provided equation format: rate = k[A]^m[B]ⁿ , where

k = rate constant

A = concentration of compound A

m = order of reaction for A

B = concentration of compound B

n = order of reaction for B

k, m and n must be determined EXPERIMENTALLY. So if you haven't been given that data, then you would just keep those letters as is. I didn't see that data provided in your question, so double check to see if it's given to you in a data table or maybe you measured it in lab, etc. Considering that the question made a mention about how "1 would be assumed" for m or n, I think you must have been provided with this information somewhere.

A and B come directly from the chemical formulas of the reactants in your reaction equation. So that means A will be [ClO₂] and B will be [F₂].

Plug all of that into the provided form rate = k[A]^m[B]ⁿ

And you'll get rate = k[ClO₂]^m[F₂]ⁿ

Again, this answer (above) is assuming that you were NOT provided with experimental data. You probably were, so go find those numbers and plug them in for your final answer.

If those numbers don't exist anywhere then your teacher might be expecting you to make some logical assumptions about the order of reaction. So let's consider the main "rule" of reaction rate: the slowest step determines the rate of chemical reaction.

....step 1....fast.... 2 ClO₂ ----> Cl₂O₄

....step 2....slow.... Cl₂O₄ + F₂ ----> 2 FClO₂

Logically, we could make the assumption that the fast step (with the ClO₂) would not affect the reaction rate, thus the order for ClO₂ would be 0 (zeroth order). As for the slow step (with the F₂), it would be a reasonable guess to think that the order for F₂ would be 1 (first order), but without experimental data, this is NOT certain.

Assuming that m = 0 (zeroth order) and n = 1 (first order), plug that is and you'll get

rate = k[ClO₂]⁰[F₂]¹ , which simplifies to...

rate = k[F₂]

Again, you MUST check for experimental data to be 100% certain. Take a look around your assignment or notes, or email your teacher directly to ask.

Good luck!

Gigi