 Let us now try and solve a numerical. The decomposition of ammonia on a metal surface is a zero-order reaction, okay. If for the reaction 2 times of ammonia giving me N2 plus 3 times of H2, so this is the decomposition reaction we are talking about. So if for this reaction the rate constant K is 2.5 into 10 to the power minus of 4 moles per liter per second. So the rate constant for this reaction is also given. And if the initial concentration of ammonia was 4 molar, so initially if we had 4 molar of ammonia then find question number A, the concentration of ammonia after 1 hour and question number B, the half life of ammonia that is the time required for ammonia to drop by 50% of its initial value, okay. So in part A we need to find out the concentration of ammonia after 1 hour while in part B we need to find out the time that is required for the concentration of ammonia to drop by 50% of its initial value, okay. So let's try and solve this. Let me first write this equation out here. So we have 2 times of ammonia that decomposes to give me N2 plus 3 times of H2. Now this is a zero-order reaction according to the question and the rate constant for this reaction, the rate constant K is given as 2.5 into 10 to the power minus of 4 mole per liter per second, 2.5 into 10 to the power minus of 4 mole per liter is smaller. So it's 2.5 into 10 to the power minus of 4 molar per second. Now it's given to us that initially at time t equal to zero the concentration of ammonia was 4 molar and we need to find out the concentration of ammonia after 1 hour. We need to find out what the concentration of ammonia will be after 1 hour. So how do we solve this? Well to figure out how much ammonia will be left after 1 hour we need to find out the rate at which this ammonia is getting decomposed into the products, right. So if we can figure out the rate at which ammonia gets converted into the products then maybe we can find out the amount of ammonia that is going to be left after 1 hour. So how do we figure this out? Well we know that because this is a zero order reaction, so the rate of this reaction can be written as the rate constant K multiplied by the concentration of the reactant which is ammonia out here raised to the power zero, right because this is a zero order reaction. Now anything to the power zero is going to be equal to 1. So this basically means that the rate of this reaction is independent of the concentration of ammonia and it is simply going to be equal to the rate constant K. So whatever be the concentration of ammonia in this reaction the rate of the reaction is always going to be equal to a constant and this is going to be equal to this particular value which is 2.5 into 10 to the power minus of 4 molar per second. So this is going to be equal to 0.00025 molar per second. So whatever be the concentration of ammonia out here the rate of reaction is going to be equal to 0.0025 molar per second. Now that we know the rate of the reaction can you figure out the concentration of ammonia that will be left after 1 hour. You can pause the video and see if you can come up with the answer. Now because the rate of reaction is 0.00025 molar per second. So one might say that in 1 second the amount of ammonia that is getting converted into the products is 0.00025 molar, right. Now because this is a zero order reaction this rate will always be constant. So if in 1 second 0.00025 molar of ammonia gets converted into the products then in 1 hour which is 60 minutes and which is nothing but equal to 60 into 60 seconds. So in 1 hour which is 3600 seconds the amount of ammonia that is going to get converted into the products the amount of ammonia that is going to be that is going to react is going to be 0.00025 multiplied by 3600 molar, right. So this much of ammonia is going to get converted in 1 hour. So if you do the math this will come out to be equal to 0.9 molar. So one might say that in once again 0.0025 molar of ammonia gets converted into the products. So in 1 hour 0.9 molar of ammonia will get converted. So the amount of ammonia that is going to be left the concentration of ammonia that is going to be left after 1 hour it's clearly not going to be equal to 4 molar it's going to be less than that. So it's going to be 4 molar minus of 0.9 molar that has reacted. So the amount of ammonia that is going to be left will be equal to 3.1 molar, right. So the amount of ammonia that is going to be left after 1 hour one might say that this is going to be equal to 3.1 molar. Well if you too came up with this particular answer then this is actually not the right answer. There is something wrong that we are doing out here. Can you spot where we are going wrong? Well we are saying that because the rate of this reaction is 0.0025 molar per second so we are saying that in once again 0.0025 molar of ammonia is getting converted into the products. So we are saying that the rate at which ammonia is getting converted into the products which is the rate of disappearance of ammonia. We are saying that the rate of disappearance of ammonia is equal to the rate of the reaction, right. However this statement is not true. The rate of the reaction and the rate of disappearances of the reactants and the products are two separate things and in fact the rate of the reaction is actually defined as the rate of disappearances of the reactants or the products divided by their respective tesometric coefficients which in this case is 2. The coefficient of ammonia is 2. Now we have talked a lot about the rate of a reaction in our videos so feel free to check them out if you want a quick refresher. So now for this particular reaction the rate of disappearance of ammonia, the rate of disappearance of ammonia is actually going to be equal to 2 times the rate of reaction So it's going to be 2 times the rate of reaction and the rate of reaction is 0.0025 molar per second. So this will actually come out to be equal to 0.005 molar per second, right. So the rate of disappearance of ammonia is not 0.0025 molar per second but it's 0.005 molar per second. So in once again actually 0.005 molar of ammonia is getting converted into the products and so in one hour the amount of ammonia that is going to react that is going to get converted is going to be 0.005 into 3600. So this will actually come out to be equal to 1.8 molar. So the concentration of ammonia that is left after one hour is going to be 4 molar minus of 1.8 molar that has reacted so minus of 1.8 molar so the answer will actually be equal to 2.2 molar, right. So the correct answer for this question is 2.2 molar. Let us now come to the second part of the question. We are asked to calculate the half-life of ammonia. And what is half-life? Half-life is defined as the time required for concentration of ammonia to drop by 50% of its initial value. So half-life is actually the time that is required for the concentration to drop by 50% of its initial value. So out here the initial concentration was 4 molar. So the half-life is the time required. So we now need to find out the time for this concentration to drop by 50%. Now 50% of 4 is 2 molar. So I need to find out the time that is required for 2 molar of ammonia to react, right. Or in other words we can say that we need to find out the time after which the concentration of ammonia that is going to be left is going to be equal to 2 molar. So can you figure this out? I am sure that you can. You can pause the video and see if you can come up with the correct answer. Well out here we have seen that the rate of disappearance of ammonia is 0.005 molar per second, right. So we know that for 0.005 molar of ammonia to react it takes 1 second. So now we need to find out the time that is required for 2 molar of ammonia to react, right. So for 2 molar of ammonia to react we can use our unitary method. And the time that is going to be required is going to be 1 divided by 0.005 multiplied by 2. So this is going to be this many seconds. So if you do the math this will come out to be 4000 seconds. So the half life we generally call it t half or t 50%. So the t half out here is going to be 4000 seconds and if you want to do it in minutes it's going to be 4000 divided by 60 which is going to be equal to 66.66 minutes. And if you want to do it in hours you can again divide this by 60. So this is going to be 66.66 by 60 hours. So this is going to come out to be equal to 1.11 hours. So the time required for concentration of ammonia to drop down by 50% from 4 molar to 2 molar is 1.11 hours.