 Hi everyone, in this lecture we will be covering two topics one is percentage composition and another one is average atomic mass. So let's start with percentage composition. Suppose we have a compound calcium carbonate. Now calcium carbonate molecular weight is calcium is 40 plus carbon is 12 and oxygen one one atom if we consider it is 16 so 16 into 3. So total will come as 100 grams. One mole of calcium carbonate will have a mass of 100 grams. Now suppose I want to find out the percentage of calcium present in it. Percentage of calcium in CaCO3. This particular thing that I have written here that is known as percentage composition of any element in any compound. So what will be the percentage of calcium in CaCO3? It has a formula. So percentage composition of any element in any compound is given by a formula that is mass of the element in one mole of the compound. Why am I saying one mole? Because I'll take the mass in grams divided by total mass of one mole of the same compound. And as it is a percentage so definitely into 100%. Now we will be calculating for this CaCO3. The percentage composition of each element in calcium carbonate. So percentage of calcium will be what is the mass of calcium that is present in this calcium carbonate we have seen here 40. So 40 upon the total masses 100. So 40 upon 100 into 100. That will give you a percentage of 40. So the amount of percentage of calcium that is present in CaCO3 will be how much? 40%. Similarly we can find for carbon. Carbon how much mass? 12. 12 divided by 100 into 100. That will give you 12%. Next percentage of oxygen. How much of oxygen? What is the mass of the element that is present? 16 into 3. That is 48 in the total mass of the total entire compound is 100 into 100. That will give you 48%. So this is how we calculate the percentage composition of any element in any given compound. Now this was a basic concept. Now based on this particular concept we have to apply it in different questions, numericals. So here we will be practicing a lot of numericals today based on this concept. The first question here is this one. What is the question says insulin contains 3.4 percent of sulphur. Find minimum molecular weight of insulin. Let's try 3.4 percent of sulphur. Find minimum molecular weight of insulin. Now tell me one thing. What do we don't know here? What is the thing that we require? We need, we do not know that how much of sulphur is present in insulin. In order to put the formula that percentage of sulphur in insulin will be equal to mass of sulphur divided by mass of insulin into 100. But we don't know how many sulphur is present basically in insulin. So in these type of questions when they don't mention the number of sulphur of any element that is present in the main compound, then you have to assume that what is the minimum number of sulphur that can be present. Minimum sulphur atoms that can be present is one. Below one it is not possible, right? You break the sulphur into half and then you put half that is not possible. So the minimum atom of sulphur that can be present is one atom. So what is the weight of one atom of sulphur? That is our 32 grams. Now, now we can put this 32 in place of here. So ultimately what we are finding? We are finding the minimum molecular weight only. So let's put percentage of sulphur in insulin is given that is 3.4. That will be equal to 32 upon, let's take the mass of insulin, minimum mass of insulin as x. This we have to calculate. 32 upon x into 100. Now just we have to solve for x. So x will be equal to 32 into 100 divided by 3.4. So when we calculate this, we will get the answer almost equal to 941.17. Grams, if we are talking about one mole of insulin and if we talk about one molecule of insulin, then it will be 941.17 atomic mass unit, unified mass. Okay, we have discussed this before. I hope you have understood this. So this is our answer. Coming on to the next question. Try on its own first. Pause the video. Try on its own. Right. So here the percentage composition of carbon by mole in methane is options are given. Right. So here what can we do? Percentage composition of carbon by mole in methane. So first methane formula is CH4. Now always remember, if I take one mole of methane, it will contain how many moles of carbon and hydrogen. If I take one molecule of CH4, one molecule of CH4 contains one atom of carbon and four atoms of hydrogen. So any molecules, any molecules of CH4 will contain how many atoms of carbon, definitely any atoms of carbon and four into Na atoms of hydrogen. Now why I wrote this? This concept has to be very, very clear. Whenever a compound is given to us, when it is said that one mole of the compound, then you have to see how, what is the atomicity of each one of the element that is given. So if Na molecules of CH4 contains Na atoms of carbon and four Na atoms of hydrogen, this Na molecules means what? One mole of CH4. So I can say one mole of CH4 contains one mole of carbon atom. This is one mole of CH4, that is molecules. But here when I say one mole of carbon, I am talking about carbon atoms and four moles of hydrogen atoms. So now it is clear. See, so total moles, so whenever percentage by moles they are asking, so it will be percentage of carbon by moles will be equal to moles of carbon upon total moles present into hundred of course percentage it is. Moles of carbon is how many? One. And what is the total moles present in this, total moles of atoms present in this CH4? One plus four, that is five. So one upon five into hundred. So the percentage of carbon by moles is equal to 20%. This is our final answer. Coming on to the next question, read the question. An unknown chlorohydrocarbon, an unknown chlorohydrocarbon has 3.55% of chlorine in each molecule of hydrocarbon has one chlorine atom only. So they have specified here clearly that one molecule contains one chlorine only. So one chlorine mass is 35.5. So 35.5, so percentage of chlorine will be equal to mass of chlorine that is present in one molecule that is 35.5 upon the total mass of the molecule that we can take as X into 100. So this percentage of chlorine is given to us 3.55. So we can say 3.55 is equal to 35.5 divided by X into 100. Now solve for X. This X is our what? X is our mass of the unknown hydrocarbon. So when we solve for X, 3.45.5 into 100 divided by 3.55. So what it will give? It will be cancelled with 10 and then 10 to the power 3. 10 to the power 3 is the mass of the unknown hydrocarbon that we have got. Now try to analyse this. That 10 to the power 3 grams of the hydrocarbon contains, contains 35.5 grams of chlorine. Correct? Just now we have found out right? We have put 35.5 here and that's how we have found out X that is the mass of one molecule of the hydrocarbon. So we can say 10 to the power 3 grams of hydrocarbon contains 35.5 grams of chlorine. So 1 gram, the question is chlorine atoms present in 1 gram of chlorohydrocarbon. So 1 gram of hydrocarbon contains how much grams of chlorine? 35.5 upon 10 to the power 3 grams of chlorine. So this much amount will be of chlorine will be present in 1 gram of hydrocarbon. But that is not the question. In question what they are asking? Chlorine atoms present in 1 gram. So we just need to convert this weight of chlorine into chlorine atoms. Now go back to mole concept. One formula I have given N is equal to W by MW that is equal to N upon NA that is equal to volume in litres at STP upon 22.7. So here we have weight and I need to find out N. So if we equate these two formulas we will get our answer. Let's see weight is given as 35.5 into 10 to the power minus 3 I can write divided by molecular weight of chlorine that is 35.5 again that will be equal to our N. This N signifies the number of chlorine atoms divided by avogadro's number that is 6.023 into 10 to the power 23. So just we have to solve for N now. So N will be equal to here this one will get cancelled 6.023 into 10 to the power 23 into 10 to the power minus 3. So our answer will be 6.023 into 10 to the power 20 atoms of chlorine in how much gram of hydrocarbon in 1 gram of the unknown hydrocarbon. I hope you have understood. So according to this what should be the answer? Which one should be the answer? Option D should be the our answer. Next question. Okay this you can try on your own first because it is similar to that of what we have done just now. Caffeine contains 28.9 by mass of nitrogen. This is nitrogen. Find the number of atoms of nitrogen in one molecule of caffeine. Now one information I forgot to write here that is molecular weight of caffeine is given that is 194. It is given in the question. Now what should we do? We have to find out the now here we will not consider that the minimum amount of nitrogen that can be present is 14 because minimum atom of nitrogen that can be present is 1. We cannot say here because they have already given the molecular weight of caffeine. So we don't need to assume over here. They have already given it. Okay. So we will take the amount of nitrogen present in this caffeine as X. So X upon 194 into 100 will be our percentage of nitrogen that is nothing but 28.9. Now we will calculate what is X. So X will be equal to 28.9 into 194 divided by 100. So you calculate this what will be the upon calculation we will get as 56 grams. 56 grams. Now what are they asking? Find the number of atoms of nitrogen in one molecule of caffeine. Now this 194 grams means this is the molecular weight. So this means one mole. Correct. So we can say one mole of caffeine contains 56 grams of nitrogen and 56 grams of nitrogen means how many moles. Calculate again n is equal to W upon Mw. W is this 56. 56 divided by molecular weight of nitrogen that is 14. So it will come around 4. So one mole of caffeine contains 4 moles of nitrogen and 4 moles of nitrogen. So one mole contains 4 moles of nitrogen. So we can say that one molecule. So this one mole is Na molecules. So Na molecules contain 4 Na atoms of nitrogen. So one molecule will contain how many? One molecule will contain 4 Na divided by Na. That will be our 4 atoms. 4 atoms of nitrogen. Again I am repeating this once more. One mole of caffeine contains 56 grams of nitrogen. So if we convert this 56 into moles it will be 4 moles of nitrogen. So we can say Na molecules of caffeine contains 4 Na atoms of nitrogen. So one molecule will contain how many? One molecule will contain 4 Na upon Na that is 4 atoms of nitrogen. So this is our final answer. Moving on. Now this question I would like you to try on your own and tell me the answer. Okay. I will not solve this. This will be your homework. This will be your assignment. Okay. This is very similar. Very similar to that of the one we have done before. Okay. I hope you have noted down this question. You can take a screenshot if you want to write. Next question. Next question is an organic compound gives 0.220 grams of carbon dioxide and 0.126 grams of H2O on complete combustion. Okay. So here any organic compound X upon this is our organic compound. So upon combustion it has given CO2 plus H2O and definitely we don't know whether it is a hydrocarbon or whether it is any organic compound containing oxygen nitrogen as well. We don't know if there is any other products also. So we are considering this is definitely containing carbon and hydrogen and whatever carbon is present here that carbon is going to this CO2 and whatever hydrogen is present here that hydrogen is going to contribute in this H2O and according to law of conservation of mass how much ever quantity of carbon is present here that same if all of the carbon is going in CO2 only then these two should be same and same goes for hydrogen as well. Understanding this part is very very important. Now 0.220 grams of CO2 it is given. So this amount of CO2 now we know that 44 grams of CO2 contains how much carbon? 12 grams of carbon. So 1 gram of CO2 will contain 12 upon 44 grams of C carbon. So this is we are doing unit factor method. So here 0.220 grams of CO2 will contain how many? How much how much grams of carbon? 12 upon 44 into 0.220 grams of carbon. So that will give you around 0.06 grams 0.06 grams. Now this 0.0 using this 0.06 grams in in the question you can see if the percentage of carbon is 24 percent. So percentage of carbon in the organic compound they have given I have the amount of like weight of carbon that is present actually. So I can easily find out the mass of organic compound. So 0.06 upon x into 100 is equal to percentage of carbon that is our 24. So from here if we calculate x, x will be 6 upon 24 that is nothing but 0.25 grams. So this is the weight of our organic compound that is present. Now next this carbon part we have solved now come to H2O. H2O 18 grams of H2O contains how much hydrogen? 2 grams of hydrogen. Now 1 gram of H2O will contain how much hydrogen? 2 upon 18 grams of hydrogen. Now how much is given in the question? 0.126. So 0.126 grams of H2O will contain how much hydrogen? 2 upon 18 into 0.126 grams. When we calculate this entire thing we will get the value as 0.014 grams. So this much amount of hydrogen is present in the organic compound. Now it is very easy to find the percentage of hydrogen that will be equal to mass of hydrogen that is 0.014 upon the mass of the organic compound which we just now found out that is 0.25 into 100. So when we calculate this entire thing we will get 5.6 percent. Let us see the question what they have told. Okay now see here this is an integer type question. It's an integer type question where they are they have said percentage hydrogen is dash into 10 to the power minus 1. So you have to change this answer accordingly. So if you put here 56 then only this entire thing will give you back 5.6. So here the answer will be 56. Okay the answer will be 56. Right. Right. Now so this was all about our percentage composition. Next coming on to our second topic of our video today that is our average atomic mass. Average atomic mass. Now like we are saying that the mass of oxygen is 16 grams or mass of carbon is 12 grams or mass of chlorine is 35.5 grams. So when we closely look at periodic table there the mass generally suppose we are talking about let's say potassium. For potassium the mass they will write as this 39.098 and the atomic number will be 19. Okay for chlorine it is 35.45. For carbon it is around 12.02. So what is this decimal point? How is this coming in a fraction? So for this we need to understand a term which is called isotopes. Isotopes are substances having we have studied in the lower classes same atomic number but different mass number. Different mass number. Right. So now in case of suppose we will take the example of chlorine here first. Chlorine exist in form of two isotopes one is Cl35 another one is Cl37. Cl37. Cl37. But the question is why is the mass of this chlorine is taken as 35.45. How is it coming? So to understand this we need to understand one concept that is these two isotopes are present in nature in a certain abundance certain quantity which we call as percentage abundance. Generally Cl35 is present in a percentage abundance of 75 percent and Cl37 is present in a percentage abundance of 25 percent. So now if I let's analyze this a little bit. Suppose this particular thing is our 35 this is 36 and this is 37. Now consider this as what can I say percentage abundance we consider this as a influence like who has more influence. You can see here this 35 has more influence or more weightage. So that's why if we take just the average of this these two. Okay it will come exactly in the between that is 36 but it is not 36. So we are not definitely not taking the average of these two. If you take the average 35 plus 37 by 2 it will come 36. But the mass of chlorine is not 36. It is more towards this 35. It is around somewhere here or more precisely here 35.45. So it is 35.45. Why it is more towards this 35? Because this person has more influence this is present in more quantity the percentage is 75 percent. So the mass is little bit towards this 35 and not 37. Now how do we calculate this average atomic mass? What is the formula for this? So average atomic mass is equal to the sum of the sum of percentage abundance into mass number divided by 100. So if I calculate that for chlorine we have seen that the two two possibilities are there one is chlorine 35 one is chlorine 37. So 35 into the mass number of one into its abundance that is 75 plus mass number of another that is 37 into its abundance that is 25 divided by 100. So when you calculate this when you solve this you will get a value of exactly 35.45. So this is the main significance of whatever this is in our periodic table. So whenever you get confused looking at how is this point and all fractional all is coming. So you remember that it is coming from all the isotopes they have taken the average atomic mass but not simple average. Okay it is not a simple average it depends on the percentage abundance of each isotope as well. Right coming on to a question based on this this is the simplest form of question that can come. They will give you the mass number they will give you the percentage abundance and you have just have to calculate the average atomic mass this is the simplest form of question that can come. Now look at this question average atomic mass of magnesium is 24.3 fine very good average atomic mass they have given to us that is 24.3 grams. Magnesium has three isotopes MG 24, MG 25 and MG 26. Okay percentage abundance of MG 24 is 70 79% okay find the percentage abundance of M26 sorry this will be MG okay this will be MG and this will be percentage abundance. Okay so we need to find out the percentage abundance of MG 26. So let's take the percentage abundance of MG 26 as X okay X. Now in the formula we will put all this so 24 into 79 plus 25 into what can we do we can take this as X percentage abundance we have taken as X fine. Okay one thing we can do here see when we add all these values it should come 100% okay if it has only three isotopes then upon adding this it should come 100%. So first we will find out 79 plus percentage of MG 25 plus X. X is what the percentage abundance of MG 26 is equal to 100. So from this find out percentage of MG 25 percentage of MG 25 in terms of X. So it will come around 100 minus 79 minus X 100 minus 79 is 21 minus X. So now you have got everything in terms of X. So now just we have to solve it solve for X putting in the formula. So mass number of MG 24 into abundance of MG 24 that is 79 plus mass number of MG 25 that is 25 into abundance that is 21 minus X plus mass number of MG 26 26 into its abundance that is our X divided by 100 should be equal to it is already given the average atomic mass is given it will be 24.3 that's all now it is all done. So just now we have to solve for X. So when you solve for X you can do it on your own the X will come around 9%. So ultimately we have got our answer but suppose they have told you to calculate percentage MG 25 as well then you know that percentage MG 25 will be equal to 21 minus X and X just now you have found out 9%. So 21 minus 9 will be how much? 12% okay. So this is how we approach the questions of percentage composition and average atomic mass. Thank you everyone see you in the next lecture.