 Chemical reactions happen at many different speeds, they can be fast like when you turn on your gas burner and ignite it, it immediately catches fire or it can be slow like the slow rusting of an old abandoned car. But how exactly do we measure the speed or the rate of a chemical reaction? How do I put a value to how fast this reaction is happening or how slow this one is happening? So in this video we are going to see how we record and measure the rate or the speed of a chemical reaction. So how do we measure the speed or the rate of a chemical reaction? Well, in any chemical reaction there are these reactants that are converted into the products. So out here we have some reactants and during the course of the reaction it gets converted into the products. Now this conversion can be fast or it can be slow. So the speed or the rate of a chemical reaction should be thought of as how fast the reactants get converted into the products in the course of a chemical reaction. So how do we measure how fast the reactants convert into the products? Well, we can do that by checking for the change in the amount of reactants that is happening per unit time in the course of this reaction. A greater change in the amount of reactants means that the conversion is happening faster and so greater will be the speed of the reaction. Now instead of checking for the change in the amount of reactants, we could have instead checked for the change in the amount of products per unit time. And similarly we could have said that a greater change in the amount of products per unit time means a faster conversion of the reactants into the products and so a greater speed of the reaction. So the speed of a chemical reaction can be thought of in terms of the change of the reactants per unit time and this is commonly referred to as the rate of disappearance of the reactants or in terms of the change in the amount of products per unit time which is referred to as the rate of appearance of the products. Let us now take a few examples to help us understand better. Let us say we have a hypothetical reaction in which some gas A converts into the gas B. Now let's assume that initially at time t equal to 0, I had 10 moles of air. So there are 10 moles of air out here initially and let's assume that after 10 minutes all of this air gets converted into B. So in this reaction 1 mole of air gives 1 mole of B. So 10 moles of air on complete reaction in 10 minutes gives me 10 moles of B. So how do we calculate the rate of this reaction? The rate of this reaction. So the rate of a reaction can be thought of in terms of the rate of disappearance of the reactants or in terms of the rate of appearance of the products. So let us try and calculate the rate of disappearance of air out here. Now the rate in disappearance of air is the change in the amount of air per unit time. And change in the amount of air out here can be measured in terms of the change in moles. So the rate of disappearance of air can be thought of as the change in the moles of air by change in time. Right. So now if I ask you what the rate of disappearance is, you can say that 10 moles of air disappears in 10 minutes. So the rate of disappearance of air is 10 moles in 10 minutes. So it's going to be 1 mole per minute. Let me bring this out here. So the rate of disappearance of air you would say is 1 mole per minute. However, if we use this formula then change always represents final minus of initial. So change in moles will be n final minus of n initial while change in time will be t final minus of t initial. So if I now plug in the values the final moles of air is 0 while initially I had 10 moles of air. The final time is 10 minutes and the initial time is assumed to be 0. So the rate of disappearance of air will come out to be minus of 10 by 10. So it will come out to be minus of 1 mole per minute. Right. So should we call the rate of disappearance of air as 1 mole per minute or should we call it as minus of 1 mole per minute? What do you think it should be? Well, the rate of disappearance of air will be 1 mole per minute and not minus of 1 mole per minute because 1 mole is disappearing per minute not minus of 1 mole. So to correct this what we are going to do is we are going to introduce a negative sign in front of this formula. So it's going to be minus of this which will be minus of this which will ultimately come out to be 1 mole per minute. So the rate of disappearance of air should be written as minus of change in moles by the change in time. Similarly, the rate of appearance of B can also be thought of as change in moles of B by the change in time. So should we put a minus sign out here? Before we think about that just by looking at this data let us try and think about the rate of appearance of B. Well, 10 moles of B appears in 10 minutes. So the rate of appearance of B is again 10 mole in 10 minutes. So it's 1 mole per minute, right? Now if we use this formula change is final minus of initial. So it's n final by minus of n initial by t final minus of t initial. So finally I have 10 moles of air and initially I had 0 divided by 10 minus of 0. So this will come out to be plus of 1 mole per minute, right? So the rate of appearance of B using this formula comes out to be plus of 1 mole per minute as expected. So we don't need to put a minus sign out here and just to drive home my point, let me write it as plus of change in moles by change in time. Now instead of calculating the change of A and B in terms of moles, we could have done it say in terms of concentration or in terms of pressure. For example, out here we had 10 moles of air in a 2 liter container. So instead of saying that we have 10 moles, we could have said that we have 10 moles in 2 liters that is 5 molar of air. Molarity is number of moles per unit volume. So we had 10 moles in 2 liter. So in 1 liter we had 5 moles. So it's 5 molar of air. Now after 10 minutes, we again had 10 moles of B. So instead of saying 10 moles, we could have said 10 moles in 2 liters. So we could have said that we had 5 molar of B. So now instead of calculating the rate of disappearance in terms of moles per unit time, we could have also calculated it in terms of the change in concentration of air per unit time, right? So out here 5 molar of air disappears in 10 minutes. So by unit time, the rate of disappearance will be 0.5 molar per minute. Similarly the rate of appearance of B can also be measured in terms of the change in concentration of B per unit time, which will also come out to be 0.5 molar per minute out here. Similarly we can also calculate the rate in terms of the change in pressures, especially if the reactants are gases. So out here initially we had 10 moles of air. So we had 10 moles in a 2 liter container at a temperature of 100 Kelvin. So using the ideal gas equation, we can calculate the pressure which will come out to be 41 atm. So initially I had 41 atm of air. Now after 10 minutes all of the air converted into B and we had 10 moles of B. So again if we use the ideal gas equation, we will find that the pressure of B comes out to be equal to 41 atm. So the rate of disappearance of air and the rate of appearance of B in terms of pressure will be 41 atm by 10 minutes, so it will be 4.1 atm per minute. So even this will come out to be 4.1 atm per minute. Now we generally express rates in terms of concentration or pressure and not in terms of moles because it turns out as we will see in a later video that rates of reactions depends upon the molecular density that is the number of molecules per unit volume rather than on the absolute number of moles. Both concentration as well as pressure gives us an idea about the molecular density. So rates is generally expressed in terms of concentration or in terms of pressure. So out here the rate of the reaction can be thought of to be equal to the rate of the disappearance of air which will also be equal to the rate of appearance of B which will be equal to 0.5 molar per minute or 4.1 atm per minute or 1 mole per minute. Let us take one more example. Let us say that out here initially I had 10 molar of air and let's assume that after 5 minutes the concentration of air becomes 0 while that of B and C increases to 20 molar and 10 molar respectively. So what will be the rate of disappearance of air, the rate of appearance of B and the rate of appearance of C in this case? You can pause the video and think about the answer. So 10 molar of air disappears in 5 minutes so the rate of disappearance of air will be 10 by 5 which will be 2 molar per minute, right? Similarly 20 molar of B appears in 5 minutes so the rate of appearance of B will be 20 divided by 5 which will be 4 molar per minute. Also 10 molar of C appears in 5 minutes so the rate of appearance of C will be 10 by 5 which will be equal to 2 molar per minute. Now what will be the rate of reaction in this scenario? Do we say that it's 2 molar per minute or is it 4 molar per minute or is it something else? So how do we report the rate of reaction in such a scenario when the rate of reactants and the rate of the products are not equal? We will explore this question in detail in the next video.