 In this video, we are now going to look at how the concentration of the reactant changes with time for a zero order reaction. So if I have a zero order reaction say A giving me products and let's say that initially at time t equal to zero, I started this reaction with say, let's say I started this with 200 molar of air. So in this video, we'll try and figure out the concentration of air that is going to be left after a certain time t. So I want to know what will be the concentration of A after a certain time, let's say 10 minutes. So how can we figure that out? Let's see. Let's start by asking ourselves what exactly is a zero order reaction. So if this reaction is a zero order reaction, then this means that the rate of the reaction is going to be equal to the rate constant K multiplied by the concentration of the reactant raised to the power zero, right? So this basically means that the rate of the reaction is simply going to be equal to the rate constant K because anything to the power zero is going to be equal to one. So for a zero order reaction, the rate of the reaction is a constant. It's equal to the rate constant K, right? So what does this mean? So let's say that for this particular zero order reaction, let's say that the rate of the reaction was found out to be equal to 2 molar per minute. So this means that when I started this reaction, when I had 200 molar of air, then this reactant air was getting converted into the product at a rate of 2 molar per minute. So per minute, 2 molar of air was getting converted into the products. Now if I leave this reaction and if I come back say after one hour, and if I again check the rate of reaction, I'll find out that even now, this air is getting converted into the products at 2 molar per minute. So even after one hour per minute, I'll still see that 2 molar of air is getting converted into the products. So the rate of reaction for a zero order reaction doesn't change and is constant throughout the course of the reaction. Now this is actually kind of special because generally in a chemical reaction, this rate of reaction does change with time and generally as the reaction keeps progressing, the rate of the reaction slowly keeps decreasing. However, this is not the case for a zero order reaction. Their rates are constant throughout the course of the reaction and we have talked a lot about this in a previous video. So feel free to check it out if you want a quick refresher. So now that we have established what constant rate means, let us try and figure out the concentration of air out here. After a certain time, let's say after 10 minutes. So after 10 minutes, what do you think will be the concentration of air? You can pause the video and see if you can come up with the answer. So in this particular reaction, we know that per minute, 2 molar of air is getting converted into the products, right? And whatever happens, this rate always remains constant. So in 10 minutes, we can say that the amount of air that has converted is going to be 10 times of 2 molar. So this is going to be equal to 20 molar, right? So in one minute, 2 molar of air gets converted into the products and because the rate is constant, so in 10 minutes, 20 molar of air would have gotten converted into the product, right? So the amount of air that is left after 10 minutes, it's not going to be equal to 200 molar clearly. So it's going to be equal to 200 minus of this value. So it's 200 minus of 10 times of 2. So this is going to be equal to 200 minus of 20. So it's going to be equal to 180 molar, right? So the amount of air that is going to be left after 10 minutes, it's going to be equal to 180 molar, pretty straightforward, right? So now let's try and see if we can make up a general formula for this. So now instead of saying that initially I had 200 molar of air, let's say that the initial concentration of air, let's say that this was a naught. And let's say that after some time t, so after some time t, let us say that the concentration of air dropped down to say 80. So 80 is the concentration of air after some time t, while a naught is the concentration of air that I had initially. Now if the rate of the reaction is equal to the rate constant, so let's keep the rate constant as k. So what will be the concentration of 80 after some time t? What is this formula going to look like? Well clearly it's not going to be equal to a naught, right? It's going to be lower than a naught. And if a rate of the reaction is k, so it means k molar of air is getting reacted per unit time. So in one minute if k molar of air is getting reacted, then in t minutes, the amount of air that is going to be reacted is going to be equal to k times of t, right? So the concentration of air that is going to be left after some time t is going to be equal to a naught minus of kt. So this is how the concentration of the reactant changes with time for a zero order reaction. Let us now take a look at this particular zero order reaction. Even out here the rate of the reaction is equal to the rate constant k, which is given to be 2 molar per minute. Let us now try and figure out the concentration of air that will be left after 5 minutes. You can also pause the video to come up with your answer. Well out here the rate of reaction is 2 molar per minute. So we might be tempted to say that in one minute the concentration of air that gets reacted is 2 molar. So in one minute we might be tempted to say that 2 molar of air gets reacted. And so in 5 minutes the amount of air that is going to get converted into the products is going to be 2 times of 5. So this is going to be equal to 10 molar and therefore after 5 minutes the concentration of air that is going to be left will be equal to 100 minus of 10 which is going to be equal to 90 molar. Now this is actually not the correct answer. In fact we are making an error out here. Can you spot what we are doing wrong? So when I say that in one minute 2 molar of air gets converted into the products. So what we have out here is the rate of disappearance of air. So this is actually talking about, it is actually telling us about the rate of disappearance of air. It is telling about the rate at which air is getting converted into the products. Now the rate of disappearance of air need not always be equal to the rate of the reaction. We know from our previous videos that the way the rate of reaction is defined, it is actually a hypothetical quantity which is defined as the rate of disappearance of the reactants or the products divided by the respective stoichiometric coefficients. So out here the stoichiometric coefficient is 2. So the rate of reaction will be the rate of disappearance of air divided by 2. This is how it is defined. If you want to know more about what rate of reaction is and how it is defined, you can check out the video we did earlier for a quick refresher. So from here we can say that for this particular reaction, the rate of disappearance of air is actually 2 times the rate of reaction. So it is going to be equal to 2 times the rate constant k. So this is actually going to be equal to 2 times of this value. So this will be 4 molar per minute. So the rate of disappearance of air is not 2 molar per minute, but it is instead 4 molar per minute. So per minute 4 molar of air is getting converted into the products and not 2 molar. So in one minute 2 molar of air does not get converted into the products. In fact 4 molar of air gets converted. So 4 molar of air gets converted into the products. So in 5 minutes, the amount of air that would have reacted would be 4 times of 5. So this is going to be equal to 20 molar. So 20 molar of air reacts in 5 minutes. So the concentration of air that is left after 5 minutes is going to be 100 minus of 20. So this is going to be equal to 80 molar. So for this particular reaction, we cannot write the general formula simply as 80 is equal to N0 minus of kT where k is the rate constant of the reaction. We cannot simply write it like this because the rate of disappearance of air out here is not equal to the rate constant k, but it is in fact equal to 2 times of k, right? So the correct equation for this particular reaction would be N0 minus of 2 times of kT. In fact let me use yellow so it is 2 times of kT where 2 is the stoichiometric coefficient of air. So to summarize if you have a zero order reaction, AA giving me products, then in this scenario the rate of reaction will not be equal to the rate of disappearance of air. In fact the rate of reaction will be equal to the rate of disappearance of air divided by air. So this implies the rate of disappearance of air will be equal to A times the rate of reaction. So this will be equal to A times the rate constant k. So therefore the concentration of air at any time T will be equal to the concentration of air that we took initially A0 minus the rate of disappearance of air which is A times of k multiplied by the time T.