 In the last video, we saw that we could describe a chemical reaction in terms of the rate of disappearance of the reactants or in terms of the rate of appearance of the products. But what exactly is the overall rate of this reaction? In fact, is there even a way to describe the rate of this reaction as a whole? So in this video, we are going to see how we define the rate of a reaction and we will realize that because of our definition, the rate of a reaction ultimately depends upon the stoichiometric coefficients that we use to balance our reaction. To understand, let us take a hypothetical reaction A giving me B. Now let's assume that initially, at time t equal to 0, the concentration of A was say 10 molar. Let's assume that no B was formed as of yet, so the concentration of B is 0 molar. Now let us say that after 1 minute, some of this A converted into B and the concentration of A dropped down from 10 molar to say 8 molar. So in 1 minute, 2 molar of A got reacted. And if you look at this reaction, 1 molar of A will give me 1 molar of B, so 2 molar of A on complete reaction will lead to the formation of 2 molar of B. Right. Now looking at this data, if I ask you to calculate the rate of disappearance of A, what would your answer be? Well, you can be like, hey, 2 molar of A disappears in 1 minute, so the average rate of disappearance of A is going to be 2 molar per minute. Right. Similarly, if I ask you to calculate the rate of appearance of B, you can say that since 2 molar of B is formed in 1 minute, so the rate of appearance of B is going to be 2 molar per minute. Right. Now if I ask you to tell me what the overall rate of this reaction is, rate of the reaction, then what would your answer be? Well, out here the rate of disappearance of A is 2 molar per minute, the rate of appearance of B is also 2 molar per minute, so 2 molar of the reactants get converted into 2 molar products in 1 minute. So maybe we can put down the overall rate of the reaction as also 2 molar per minute. Seems reasonable. Right. Let us now take a totally different reaction, say P giving me twice Q. Now even in this reaction, let us assume that initially the concentration of P was 10 molar and the concentration of Q was 0 molar. Now to keep things simple, let us say that after 1 minute, the concentration of P also drops down from 10 molar to 8 molar. So what will be the concentration of Q after 1 minute? Well, out here in this reaction, 1 molar of P gives 2 molar of Q, so 2 molar of P on complete reaction will give me 4 molar of Q. Right. So out here if we try to calculate the rate of disappearance of P, 2 molar of P disappears in 1 minute. So the rate of disappearance of P is going to be 2 molar per minute, right. Now what would be the rate of appearance of Q in this case? Now out here 4 molar of Q is produced in 1 minute, so the rate of appearance of Q is going to be 4 molar per minute, right. Now again if I ask you what the overall rate of the reaction is in this scenario, what would your answer be? Well out here the rate of disappearance of P and the rate of appearance of Q is clearly not equal. This time 2 molar of the reactants give rise to 4 molar of the products in 1 minute. So what would you say that the overall rate of the reaction is? Do you say that it's 2 molar per minute or is it 4 molar per minute or is it something else? In fact, what does the overall rate of a reaction even mean? To highlight this confusion let me take one more reaction. Let us say we have a reaction 2e giving me thricef plus g and just to keep things simple let us assume that initially we had 10 molar of e and 0 molar each of f and g. Now after 1 minute let us again assume that the concentration of e drops from 10 molar to 8 molar. So 2 molar of e gets reacted in 1 minute. And looking in this reaction we can say that 2 molar of e gives me 3 molar of f and 1 molar of g. So 2 molar of e on complete reaction is going to give me 3 molar of f and 1 molar of g. Right. So out here the rate of disappearance of e is going to be equal to 2 molar per minute. The rate of appearance of f is going to be 3 molar per minute while the rate of appearance of g is going to be 1 molar per minute. So we can very clearly have very different rates of reactants and rates of products. But what's not very apparent is how we can calculate the overall rate of a reaction. Let us now for a moment step back and analyze these 3 reactions. Let us start by analyzing the rate of the reactants and the rate of the products for this reaction. Now out here if we divide each of these rates with their respective stoichiometric coefficients. So if we divide rate of e by 2, rate of f by 3 and rate of g by 1, g has a stoichiometric coefficient of 1 then we will see that all these values turn out to be equal. Rate of e by 2 will be 1 molar per minute, rate of f by 3 will also be 1 molar per minute, rate of g by 1 will also be equal to 1 molar per minute. So all these rates come out to be equal. Now this relationship exists because if we look into this reaction we will realize that by the time 2 molar of e completely reacts, 3 molar of f would have formed in the same time. Right. So by the time, let me get some space out here. So by the time 2 molar of e completely reacts, 3 molar of f gets formed. So by the time 1 molar of e gets completely reacted, 3 by 2 molar of f would have formed. Right. So the rate of formation of f will always be equal to 3 by 2 times the rate of disappearance of e. So from here we can write that r of f by 3 will be equal to r of e by 2, r of f by 3 will be equal to r of by 2. Similarly if we look at e and g, by the time 1 molar of g would have formed, 2 moles of e would have reacted in the same time. So the rate of disappearance of e will always be 2 times the rate of formation of g. Right. So the rate of e by 2 will always be equal to rate of g by 1. So rate of e by 2 will be equal to rate of g by 1. So we can conclude by saying that by the time 2 molar of e completely reacts, 3 molar of f and 1 molar of g would have formed. So the rate of disappearance of e by 2 will be equal to the rate of formation of f by 3 which will be equal to the rate of formation of g by 1. Similarly even in this reaction if I divide these rates with the stoichiometric coefficient, these values will come out to be the same. So rate of p by 1 is 2 molar per minute, rate of q by 2 is also 2 molar per minute. So this will be 2 molar per minute. Now even out here we can see that this relation will always be true because by the time 1 molar of p completely reacts, 2 molar of q would have formed. So the rate of formation of q is 2 times the rate of disappearance of p. So if we divide the rate of formation of q by 2, we will get the rate of disappearance of p. Similarly, in this reaction, rA by 1 will be equal to rB by 1 which out here will be 2 molar per minute. Now chemists all over the world have agreed to call these values that we get by dividing the rate of the reactant or the product by its respective stoichiometric coefficient. Chemists all over the world have agreed to call this value the rate of the reaction. So for this reaction, the rate of the reaction by definition is 1 molar per minute. For this, the rate of the reaction by definition is 2 molar per minute. And the rate of the reaction out here is 2 molar per minute. So to summarize for any chemical reaction, the rate of disappearances of the reactants and the rate of appearance of the products can have very different values. So if we had to put a value to the overall rate of the reaction, how do we do that? Well, for any chemical reaction, the rate of the reactants and the rate of the products divided by their respective stoichiometric coefficients will always be equal and this value is assumed to be the overall rate of the reaction. So whenever we say that a reaction, say this one under certain conditions, has a rate of reaction say 0.3 molar per minute, then what we really mean is that under these conditions, the rate of disappearance of nitrogen is 1 times the rate of reaction. So it will be 0.3 molar per minute. The rate of disappearance of hydrogen will be 3 times the rate of reaction, so it's going to be 0.9 molar per minute, while the rate of appearance of ammonia will be 2 times the rate of reaction, which will be 0.6 molar per minute. So the rate of the reaction is simply a neat way of representing the rate of disappearances of the reactants and the rate of appearances of the products for the given reaction. Now because the rate of reaction will always be directly proportional to the rate of the reactants or the rate of appearances of the products, so any change in these values will always be reflected in the rate of the reaction. So say we carried this reaction at some other conditions and under these conditions if we assume that everything was happening here twice as fast, the rates of disappearances of the reactants or the rate of appearances of the products were 2 times these values. So this reaction is happening twice as fast and if we calculate the overall rate of reaction out here, this will be equal to 0.6 by 1 or 1.8 by 3 or 1.2 by 2, which will be equal to 0.6 molar per minute. So under these conditions this reaction is happening twice as fast, which will be reflected in the overall rate of reaction, which will now be 0.6 molar per minute instead of 0.3 molar per minute.