Graphing
Texas Tech University
Chance of rate with time - Overview


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So let's talk about reaction rates normally, what its speed, How we define speed. If you can remember, speed is, let's say through this road. This guy is walking and he's walking with the Speed V and this entire road is X. So the speed is going to be the road he needs to take over the time how fast this guy is taking this entire way. But in reactions we're not talking about like a speed. A guy is running rather, we're talking about the reaction consumption. So let's say we have this beaker that was a horrible beaker. Let's say we have this speaker, and again we have inside some blues and some reds. So what may happen in this B girl Flowers is after some time, they they're going to be Les Bleus because they got consumed and they're going to be less reds because they reacted with the blues. But instead they gave us yellows. So how we can write this, for example, react, react in a plus, reacting be would give us two products, see? So how fast the sea we get into this speaker or how fast we lose this? A. And B are actually showing us the speed off the reaction. So what? I mean by the speed off the reaction in mathematical way. So it's basically think off. We have a and we have B and we have see and these air going to change over time. Let's say this is our time in terrible at zero. At the very first, let's say we have Vermijl off a bumble off B and zero C because we don't have any. And when I say more, think about this is in one liter so we can change it into the concentration Modularity the say in 10 seconds you're going tohave 0.8 a zero point eight b illness, say 0.4, See at 20 seconds. Let's say we have 0.6 a 0.6 B and zero point eight c this time. So if you look at this trend, what happens is for every Von mall off A we get one, matloff, because what is the change? Here it is 0.8 minus one. So for looking at the changes, what you need to do is you need to look at the final minus initial. So this is the changing the concentration for the very first time in terrible. And this is going to be point to and for B, this is also point to but foresee, it is going to be 0.4. No, of course. This is 0.8 minus one. This is going to be a negative number. So this is going to be negative 2.2 and this is going to be a positive 0.4 and the change in time is over here. 10 seconds and over here also 10 seconds. So for A and B are getting consumed the same rate, which means they're basically going with one toe one ratio, whereas we get to off see, because for every 10.2 we get 0.4. So let me modify this a question by saying we get to see now writing this mathematically, what we have is the concentration off a. The change in the concentration which we show with the Greek letter Delta and this is the brackets is our concentration over some period of time. So what is this? This is the average rates. Now, what is the average rate off? The change of, um, A is basically over here. If you look at is going to be, the change is going to be minus 0.2 over the time period. 10. What we're going to get is negative 0.2 Now, this is the every trade, but this is not the average straight off disappearance. So the average rate off disappearance is going to be equal to a negative sign at the first Delta A over tea, which is going to be a negative sign again. 0.2 or 10 native Point to. So this is going to give us a plus sign this time 0.0 team. So there's every great off disappearance off A is going to give us. Basically, the average rate off the reaction when we're talking about this every great off disappearance or the average rate off disappearance be, which is going to be the same. The concentration change over the time period and this is going to be negative 0.2 over the time period. So let's talk about the speed in a mathematical term in this right, our equation a plus be use us see, and that's right a table. So the concentration off a remember we show it with brackets and the units for this is going to be polarity. And what Miller to US. Number of moles over some volume. And we have concentration of B in polarity and we have concentration off, see similarity and in our table. He also are going to have a time interval. Let's say this guy is in seconds. So what we're going to do at the time? Zero initially in the beaker. What we have is just a and B. You don't have seat. I'm just going to give an arbitrator number like one. Morrissey. Let's say this is also on instance, you don't have any. See, this is your so in 10 seconds, let's say this guy drops to 0.8. This guy dropped 0.8. This guy is increasing to 0.2 another 10 seconds. This guy goes to 0.6 0.6 and 0.4. Let's go all more. 0.40 point four and zero point six. Now let's look at the average rate off appearance off. See? So rates off. Appearance off. See, is going to be the change in concentration off. See how we show the change this Greek letter Delta in the concentration off scene over the change in time. So I'm just going to put Delta t. So let's located. Let's look at four. The first in Terrible. And let's say this every trade off appearance in the first 10 seconds period. So let's show it as what is the Delta Psi? You first look at the final and then look at the initial so in our first case is going to be 0.2 minus zero final mine. Essential over was our delta t thin minus. See you and this is going to give us 0.2 over 10, and this is going to give us zero point 02 So this gives us the rate off opinions of sin and this rate off appearance off C has to be the same with the rate off disappearance off a. So let's solve it for a this time rates off appearance. Excuse me in this case is going to be disappearance off a and this is going to be Delta concentration off A or Delta T. And what's our concentration off A. In the first 12th interwar final minus insure 0.8 minus one. And what is the seconds? 10 minus year. Now, there's one more trick to this one. Since this is the rate off disappearance, we put a negative sign to the behind. So what we're going to get is a negative ***. There's 0.2 over 10, and this is going to be 0.2 exact same number for these two. Now, if you will, I'm going Thio, erase this part and so a little bit of a different example in the same table just to make it a little bit more clear. Let's look at the rate of disappearance off B in the entire time in. Terrible. So what is our entire time Interval. 10 seconds. 20 seconds. Church of seconds. Right. So this number is actually going to be Turkey 2010 0. So since this is the rate off disappearance off, be what you're going to use again. A negative sign and let's look at B. Final is over here this time 0.4 minus initial is over here. One divided by final 30 seconds. Initial zero. So this is going to give us negative negative 0.6. Divide, apply 30 and again it's going to give us zero point 02 Now these numbers are the same, but please don't be puzzled. This is Onley for this very specific example where one more moles off a is getting reacted with one moles off B gives us warm ALS of C. Now let's just generalize what we have done here so far. Let's see a plus to be ghost to, let's say one over four. See, now you're going to understand why I gave those numbers. What we want to write is a generalized term for rate, which in units off polarity over seconds, the change off the concentration in time is going to be. Since this is the disappearance, you want to put a negative concentration change in a over just the time this is going to be equal to negative. But since we have to, what we're going to right over here is a 1/2 concentration difference. Change and be Let's put our brackets over the change in time. So why did I put this one or two? If you think about it for everyone? A to B is getting reacted for as a guest disappeared twice as much B is getting disappeared. That's why we put this one or two over here and in the same logic. Now I want to flip this 1/4. This is going to be four. The change in concentration c over the change in time notice. There's no negative term over here because this is the appearance. So again, let's think about this, as does disappears. Let's say this guy was one more Mueller at first and then this is 0.8 final minus initial is going to give us a negative value. And with this negative report, this overall is going to be a positive term over here. Let's say this zero at first and then becomes one inthe e other time in terrible. So final minus initial is going to be a positive number. So here again, we have a positive number. This is going to be a postive overall, so all these are going to be equal to each other. Now, if you want to think off why they have this one or two or four, these numbers flipped. You can just memorize it as it is if you like Thio, But I don't like memorization that much. So I would just go with an example in my mind, like real quick. Let's say what we had is a from one to get 0.8 and we have B from one to get 0.6. Now, this difference is 0.2, and this difference is 0.4. And this say this all happens in 10 seconds again. So let's write what we have so far. What is the rate gonna be for for a This is going to be the Delta concentration off A. So this is going to be 0.8 minus one divided by time 10 and there's a negative over here. And let's check if this is equal to negative 1/2 and then the concentration change off be in this, uh, in this case is going to be negative 0.4 and over 10 seconds in trouble. So what we have over here is negative. Negative 0.2 over 10. Is it equal to negative 1/2, 0.4 over 10th. So these negatives make a positive. This canceled this guy, and this is going to be 0.2 so 0.2 equals to 0.2 if you get confused. If you should put one or two or two here, just do it like me. Give a very simple example and tested. So in this case, this is going to be flipped and our general role this rights a A plus be gives us C C plus. The the So is a general old rates. If it is on the left hand side, there's a negative one over a Delta A over Delta T equals to native will Never be Delta be over Delta T equals Now on the right hand side, we have one over. See Delta See over Delta T equals two one over the Delta. Concentration off the with the change in time.

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