Texas Tech University
The Rate Law - Example 1


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Solis Elam or complicated question where we have three reactors this time and they're asking us what is the order off reaction with respect to ch four. What is the overall order off the reaction and what this decay constant? So let's what we're What we need to do is now. We're given four different experiments and we have different values for the concentrations and the initial rates, and you find number them. There's going to be experiment number one experiment number to experiment number three and experiment number four. Now I can I just need to pick to experiment and compare their rates, which to Should I choose, I would go with one and two at first because what we have over here the concentration of CH four is not changing concentration off. All too, is not changing. The only thing that changed is the concentration off NH tree so we can solve for an H trees power. Say this is M. This is N and this is X. So what I mean is, we can solve for n. So let's write this rates to do I buy rates. One equals to what we have 0.12 the white by 0.30 and is going to be equal to four. And this will be equal to que de ch four concentration for the second one the N H four concentration for the second one and the 02 concentration for the second one. Do I buy ch four concentration for the first one NH four concentration for the first one and all to concentration for the first one. And now, if you rights um case cancel thes air the exact same because these sports are 0.10 point 01 So what we're going to have is 0.2 to the poor off end. Do I buy 0.1 to the poor off? And if you write them in the same power 0.2 0.1 the poor off and And this is going to be to to the poor off ends again to support and equals to four so and equals Tutut. So is everything all right here? Can you see that what we did was basically to use the experiment one and two and compare them to each other look at the ratios and then sold for end. The reason why we did this is ch four. Concentration and all to concentrations are not changing. So it will be easier for us to pick one and two. Now, this is a little bit the hardest way to do, uh, such questions. But in the same time, these air the safest fate, you cannot just fail using this comparison method. But I'm also going to show you a shorter method than this. If you are, you don't even need to be good at mental math that much. What you're supposed to do is just look at this. What happens between these two this is multiply by four from 1 to 2, right? And what happens here not changing, not changing, multiplied by two. But there's a power off end. So to to the poor, off n equals 24 c. This is very faster and easier. But then again, you cannot fail using this, uh, first method that we used. So let's full soul for the other ones. Let's say let's soul for em. So which was am I going to pick? I would pick one and four. The reason for that is, if you look at one and four or two is the same and on a stree is going to be doubled. But we already know that the end equals to two. So we need to solve for this last one on Lee. So basically, what happens in this bigger one is what is the multiplier? This is multiplied, um, from 0.0 32 0.0 120 times four and firms your points, your 1. 22 0.4 80 times in the before. So there is a time 16 over here. Basically, what we did was 0.480 divided by 0.0 30. I picked these two numbers. This is 16 times. So now what I'm going to do is the 16 equals two. This guy is doubled to the poor off N N N s to times. This guy is cause report four to the poor off em. So, to the power of to is going to be 4 16 equals to four times four to the power of em. Four equals two four to the poor of em. Hence m it close to one. So just by dividing this last value by the first value, I get 16 and then I just simply no, that end is going to be too so to the blood off, too, because this is doubled. But overall, the greatest Collier pulled and ch four is quadrupled. What is m just solving for em? And this also gives us the answer. The order off reaction With respect to ch four, this is going to be one. So what is X? We need to find X to find the overall order. So let's look at um, let's look at the experiment. Very only it the so two changes so normally it's 0.1 But at the Experiment three, it's 0.4 So let's pick experiments to. And three. This is not changing. This is getting doubled. So there is to the poor of one, and this is getting doubled to the poor off one. So what we right over here, if you will. Solving for X, we have 0.24 do I? By 0.12 equals to two and two equals two thes two ratios just going to write to to the part off one because our M s one multiplied by eggs. This is cause report for the power of X. So what is exe? Basically two divided by 21 equals 24 to the power off X. Therefore, eggs equals to zero. Can you see that this X zero hence, it means the concentration off oxygen is just not affecting to the overall reaction. Even if you increase it, the reaction is just not going to change. It's just going to change with the, uh, concentration off ch four over here in X between experiment and tree and lastly list soul for okay. And how are we? How you're going to do that is actually pretty simple. Let's write our red law. First rates equals two que ch four to the poor off once NH tree to the power of to or two to the port of Sierra. So if you're going to just put the numbers for Experiment one, the rate is going to be 0.0 trees. Here. This equals two R K that we weren't sold for and our ch four 0.1 and our NH tree is your 0.1 to the power of to this time and 0.1 to the part of Sierra. So there's going to be just one. So solving four k equals two 0.0 tree zero Do I buy 0.1 times 0.1 to the power of to. And if we solve for K, what we're going to get is three times 10 to the power of three.

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