Mechanism and Rate Law of Cl2 Reaction: Find the Answer

[dolpho]

Homework Statement

The proposed mechanism for a reaction is

Cl2 => 2 Cl (Fast)

Cl + H2S => HCl + HS (Slow)

Cl + HS => HCl + S (Fast)

Which of the following would be a rate law for the reaction?

The Attempt at a Solution

From other questions I've done the rate law for the reaction is always the slow step or rate-determining step. My answer was;

k[Cl-][H₂S]

But the answer is k[Cl2]1/2[H2S]

I don't really understand how they got that answer. Any help would be appreciated!

 

[epenguin]

Homework Statement

The proposed mechanism for a reaction is

Cl2 => 2 Cl (Fast)

Cl + H2S => HCl + HS (Slow)

Cl + HS => HCl + S (Fast)

Which of the following would be a rate law for the reaction?

The Attempt at a Solution

From other questions I've done the rate law for the reaction is always the slow step or rate-determining step. My answer was;

k[Cl-][H₂S]

But the answer is k[Cl2]1/2[H2S]

I don't really understand how they got that answer. Any help would be appreciated!

And we don't understand how you got yours!

As you haven't given any reasoning.

However it may help to ask if there is one slow step what can you say in general about the species undergoing fast reactions that precede the first step?

 

[dolpho]

And we don't understand how you got yours!

As you haven't given any reasoning.

However it may help to ask if there is one slow step what can you say in general about the species undergoing fast reactions that precede the first step?

Well I've been reading a bunch of stuff that just says that the rate determining step is the only thing that matters when it comes to the rate law. However I might be missing a piece since I can't really understand why I got the last question wrong. The k[Cl2]1/2[H2S] is really confusing me.

For my answer I just put the atoms present in the slow step. I don't really know if I have to do anything with those atoms like relate them to the fast steps or overall reactions...

 

[epenguin]

For my answer I just put the atoms present in the slow step. I don't really know if I have to do anything with those atoms like relate them to the fast steps or overall reactions...

I didn't see you had done that, because for not having written any reasoning or derivation I took the [Cl-] to be a mistyping for [Cl₂]. There is no Cl- or Cl^- appearing anywhere in this mechanism, only Cl, chlorine atoms.

So I will take it you meant to write k[Cl][H₂S] .

That is OK. But actually chlorine atoms will normally be very few and practically unmeasurable. Practically all the chlorine will be Cl₂ although the very small amount of Cl atoms are what drive the reaction. So you have to work out what is the [Cl] to put into the above expression, in terms of the measurable [Cl₂]

Try and work that out and if you can't I'm sure there are examples of something similar in the stuff you've read.

 

[JohnRC]

For all mechanisms like this, just considering the slow step is not enough.

What you have to do is to think about reactive intermediates -- that is species that are both created and destroyed in the reaction mechanism, and that never build up to particularly high concentrations.

When you manage to find a reactive intermediate, you then apply a steady state approximation to its concentration, and work through some algebra.

(2) The rate equation that you eventually require will be an expression that only involves the reactants.

(3) Cl^– is not involved in this reaction; it involves chlorine atoms, which are quite different to chloride ions (one electron fewer, and much more reactive)

(4) The reaction scheme that you have written does not give the rate law embodied in the answer. Are you sure that the first step was not Cl₂ <==> 2 Cl ? a very important difference!
(In a realistic mechanism for this reaction HS + Cl₂ ==> S + HCl + Cl would also figure, but that is not relevant when facing a test question.)