Rate determining step Help!

Link to Q:

https://imgur.com/t7vDi8C
https://imgur.com/Gk7G3ID

I'm stuck on part b) of this question which is shown on the 2nd link.

How do I find what the rate determining step is? I've tried doing this and I thought the answer would be step 1.

This is because the first step would be a slow reaction where you form the reactive intermediate X. This step is important because this reactive intermediate is carried over to next step, step 2.

If the first step doesn't happen then we know that step 2 and step 3 can't proceed then.

However this is wrong and the rate determining step is actually step 2. I don't really understand why that is. Could someone please help tell me why it is step 2?

This is what the MS is saying as well: https://imgur.com/NpvhCG9

Any help would be really appreciated! Thanks!

Reply 1

Yatayyat

I tried finding the overall reaction that takes place by adding up all the intermediate steps that are involved, so this gave me:

2NO + 2H2 ---> N2 + 2H2O (intermediate species X and Y cancel out)

And also noting that the rate equation is rate = k [NO2]^2

, which was given at the start of the Q.

I read up on my textbook that there is a rule where in the slowest step, the molecularity (i.e. number of moles of a particular molecule) will equal to the order of reaction with respect to that reactant. So maybe I see why step 2 is the answer because it has H2 involved which is part of the rate equation as well as being 1st order as shown in step 2.

And if I summed up steps 1 and 2 alone together then I get: 2NO2 + H2 ---> Y, this also does look in proportion to the rate equation as again I see there is 2 moles of NO2 which indicates that it should be 2nd order in the rate equation which it is.

So is this similar to how they come with the answer in the MS?

Reply 2

Kian Stevens

Some extra background information:

•

The rate-determining step is made up of only the terms in the rate equation.
This may seem a bit startling at first, as in these questions you most likely won't have one step which consists of each of those terms.
However, the good thing is that we can combine multiple steps and cancel intermediates out to make one big slow step, which consists of everything in the rate equation... This is the rate-determining step.

•

The rate equation only describes elementary reactions.
An 'elementary reaction' is one where reactants go straight to products, with no intermediates being formed in the process. However, the steps in mechanisms have intermediates. So, building on above, this means that steps must be combined together to remove intermediates; this results in an elementary reaction, as well as the rate-determining step, which will therefore fully satisfy the rate equation.

•

Multiple steps can and will occur simultaneously.
As much as one step may produce an intermediate and another one consume it, the intermediates are produced and consumed at the same time; this means that Step 2 doesn't have to wait for Step 1 to complete or anything. The elementary reaction resulting from combining the two steps will show this to be the case too. Hence, your logic about steps needing to wait so that intermediates can be 'carried over' isn't quite right.

(You don't need to learn about elementary reactions, I only described them to help with above explanations)

So, let's get started!
The rate equation consists of [NO]² and [H₂]. This means that the rate-determining step consists of two molecules of NO and one molecule of H₂, i.e. 2NO + H₂

\rightarrow

...
This is problematic of course, as you don't have a step consisting of each term in the rate equation. Let's look at the steps closely and see how we can tackle the problem:
Step 1: NO + NO

\rightarrow

X
Step 2: X + H₂

\rightarrow

Y (THIS IS SLOW)

Why is Step 2 slow? Well, as we know from Step 1, X is produced. Due to X being an intermediate, it is subsequently used up in Step 2, meaning that Steps 1 and 2 are simultaneous. Since Steps 1 and 2 are simultaneous, we can deduce an elementary reaction by combining them both together:

•

Step 1 + Step 2 = (NO + NO $\rightarrow$ X) + (X + H₂ $\rightarrow$ Y) = NO + NO + H₂ + X $\rightarrow$ X + Y

•

X cancels out on both sides, leaving: NO + NO + H₂ $\rightarrow$ Y = 2NO + H₂ $\rightarrow$ Y

Alternatively, if it's easier for you to think of it this way, you can substitute Step 1 into Step 2 like so:

•

Step 1: NO + NO $\rightarrow$ X

•

Step 2: X + H₂ $\rightarrow$ Y

•

$\therefore$ NO + NO + H₂ $\rightarrow$ Y = 2NO + H₂ $\rightarrow$ Y

Hence, even though Step 2 in the exam paper is X + H₂

\rightarrow

Y, it is equivalent to 2NO + H₂

\rightarrow

Y, simply due to Steps 1 and 2 being simultaneous.
Your explanation would therefore be that Step 2 satisfies the rate equation, as its stoichiometry is in proportion to the rate equation, so Step 2 is the rate-determining step.

It simply takes a bit of logic and reasoning to realise that multiple steps are simultaneous, and so can be combined to produce the rate-determining step.

(edited 5 years ago)

Reply 3

Yatayyat

Original post by Kian Stevens

Some extra background information:

•

\rightarrow

...
This is problematic of course, as you don't have a step consisting of each term in the rate equation. Let's look at the steps closely and see how we can tackle the problem:
Step 1: NO + NO