Texas Tech University
The Rate Law - Example 2


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So let's make a very simple example. Let's say we have the concentration of chlorine in polarity and let's say we have the initial rates and Mueller t over seconds. So let's say once this is zero this initial rate in zero, if this is 0.1, we have zero point zero 10 zero points to zero point Sierra too. And zero points four zero point 04 Now what we want to do is to draw a graph and the graph actually very similar to the graph that we had in the previous video. This is going to be and rates versus concentration off chlorine graph. So if you look at what's happening here, you will see at zero we have zero at 0.1, we have 0 10 doubled. His amount rate is doubled, double this amount. Creators doubled. So this is off first order reaction. So that's right. Thes 0.1 is going to correspond to 0.1 0.2 is going to correspond to 0.2 and lastly, 0.4 is going to correspond to 0.4 Now, if you want to find the rate constant K. Are we going to do that now? Let's look at thes. What What are these? This is experiment number one. This is a different experiment. Number two. This is a different experiment. Number three and it's a different experiment. Number four. Why, I'm stressing this different experiment is because this is concentration versus initial rate. So the issue of race are different in different concentrations. So what was all right? Law rates for the first order equals two. Okay, A to the part of one. So r k if you sold four K, what we have is rates. Do I buy the concentration off are chlorine So this a is actually going to be chlorine? And over here, the rate what? We have eyes. Let's pick experiment number two. Let's say this is going to be zero point 0 10. Do I buy 0.1 and there's going to be 0.1 now. What if I accidentally picked a different one? Well or purposefully, it does not matter. Even though the initial race change the rate constant K does not change. Let's look for experiment for what we will have over here. 0.4 do I? By 0.4 this is again 0.1, so they just do not change it all. So let's make another example that is concentration off. Let's say this time, bro Mean and initial rates. And let's say this is 0.10 point two and 0.4. Again. Where is the initial rate? Is 0.10 point 10.1? Do you remember what that was? Changing With the concentration, the interest rate doesn't change. Does basically k borough mean to the power zero this time? Because the amount of bro mean in different experiments just does not change insured rate. So we can just conclude this as a zero or the reaction. And let's make one more example there. Let's say this time, I'll Dean, let's go with seven. A group concentration off paradigm versus and this is immoral, etc. Versus initial rates. And let's go with this. So what we're going to have let's say over here is your appoint one 0.2 and 0.4 and what we would have 0.1 0.4 zero points. 16 now what's happening once I double this number. This is getting, um, multiple. Bye bye. Four over here. Once I doubled this number two, this is getting multiply by four to So this is getting multiplied by to to the poor of two. As I multiply this by two. So this is going to be our rates equals two K Hello, Dean, to the power of to now, How did I How did I come off with this part of two in a better mathematical senseless ST So let's number these again. Let's say this is one to and three. Let's see rates off three divided by rates off to and these are going to be equal to okay, I to the poor off end Now we don't know it. Let's let's assume the ver Just not way. Didn't guess good enough and we still don't know what this is. So I'm just going to write to the poor off end and is going to be for the rate three and is going to be k I to the poor roof and and is going to be 482 now what is great? Three is going to be 0.16 And what this rate to There's going to be 0.4 and there's going to be equal to Kay's are the same. So I cancel them. And what I'm going to just right over here is going to be a The I three is 0.4 to the power off end. Divided by two is going to be 0.2 to the poor off end. So what we will have over here is this guy, Do I buy This guy is four. Now, this is going to be equal to to to the power off. And if you can remember how we can write, this is 0.4 divided by 0.2 to the common pour off n and 0.4 divide by 0.2 is two. Now we want to solve for n If you guys remember, we can take the logarithm and how that happens is we take the longer term off both sides. But if I want to find the end, I will take a look at him base to so longer it's him two based four is going to be equal to in. And if you guys also can remember how I can. You can just always user calculator if that's going to be easier for you. But how you can write this look to to to based to to the power of to a lot of twos Here, this equals two log to base to and bays and the same number is just going to give us one. So this is going to be too, so our N is going to be equal to two.

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