Here it says consider the following elementary steps. What is the rate law of the reaction mechanism? So when this reaction mechanism we have three elementary steps, the first one is a fast step, the second one is a slow step and the last one, the third step is also a fast step.

Now if we take a look, it says step one, we need to locate the slow step of the reaction mechanism. So the slow step is this. Right here we're going to say as long as the reactants are not intermediate, their coefficients equal the reaction orders of the rate law. So looking at the reactants here, we'd say K rate equals K NO2. The coefficient here is a 1 to the one and then N2O5 to the one. But we have an issue. One of our reactants is an intermediate. This intermediate, this intermediate. Remember, intermediates cancel out, so we could have stopped at step one if the reactants were not intermediates. But because they are, we have to continue to Step 2.

Now if a reactant is an intermediate, which we saw, you're going to cancel out with the product intermediate and we did that with the Fasttab before, now we're going to say step three. If Step 2 happens, use the elementary step possessing the product intermediate. Here we're going to say for that elementary step, the coefficients of the reactants still equal the reaction orders, and for that elementary step, the coefficients of the products equal the inverse, the inverse of the reaction orders. So let's see what that means.

Alright, so if we come back up here, my NO2 reactant got cancelled out by this NO2 product and we kind of have to make up for what we just lost. So this here took away the reactant that I needed. So I'm going to take both of its reactant and its product to make up for that loss. So if we if we if we look at everything, what do I have now? Well here I have an N2O5 that I originally had as a reactant and now I have a newly gained N2O5 also as a reactor. So how many total moles of N2O5 do I have? 21 from here that I just gained and one here that I originally had. So in essence their coefficient is 2 because I have two moles of it.

Coming down here we say that our new rate law is equal to KN2O5 to the two because again, I have two moles of it, one that I originally had plus one that I gained later on. And then let's look at what else we took. We also took this one mole of NO3, but here it is not a reactant, it is a product. We're going to say here bringing it down to our rate law. If it were reacting, it'd be NO3 to the one. But because it is a product, we said that it equals the inverse. So instead of being one, it's to the -1.

This can be a bit tricky. This happens anytime one of our reactants is an intermediate have to do this making up process what we just lost. So here the rate law would be rate equals KN2O5 to the two and NO3 to -1 right? So this would be our new and official rate law.