 In this video, let us solve these problems to better understand the concept of moles. So the first problem we have on our hands is finding the number of atoms in four moles of carbon. Now, a mole of anything is like a dozen of anything. If I ask you how many bananas in a dozen bananas, you will say 12. How many apples in two dozen apples? You will say two times 12, that is 24 apples. Similarly, number of anything in one mole of that thing, so one mole of carbon will have 6.022 into 10 to the power 23 carbon atoms. That's the only difference. In a dozen, we have 12 and in a mole, we have 6.022 into 10 to the power 23. A huge number of atoms, but still the concept is still the same. So to find the number of atoms in four moles of carbon, all we need to do is multiply this with four. So in four moles of carbon, we will have four times 6.022 into 10 to the power 23 carbon atoms. That is it. All we needed to do was multiply this number which we call the Avogadro's number with the number of moles four to find the number of atoms. Alright, let's move on to the next question. The next question is to find the mass of four moles of helium. So in this one, we're relating mass with moles and this is a very important concept. This will help us understand why did we define mole to be this weird number, 6.022 into 10 to the power 23. Why this? Why not anything else? Okay, the advantage of defining one mole as this number is that when we take these many atoms of hydrogen, that is when we take one mole of hydrogen, do you know what is its weight? Its weight is one gram. When we take one mole of helium, do you know what its weight is? Its weight is four grams. Similarly, one mole of lithium is seven grams and you don't have to take my word for these numbers. You can take one mole of hydrogen that is you can take Avogadro's number and multiply it with the mass of one atom of hydrogen. Just find it online and if you multiply these two numbers, you will get one gram similarly for helium and similarly for lithium. If you have studied your periodic table, you might recognize these numbers one four seven. These are the atomic masses of hydrogen, helium and lithium. So what this definition of mole allows us to do is it allows us to simply write the mass of one mole of anything as the atomic mass unit of that thing. Let us see. So here we have helium. Helium has an average atomic mass of four atomic mass units. This means there are four grams in one mole of helium and this is also what we call the molar mass. The molar mass of helium is four grams. But anyways, we have four grams in one mole of helium. So what will be the mass of four moles of helium? One mole has a mass of four grams. So four moles, simple unitary method, will have a mass of 16 grams and we are done. The mass of four moles of helium is 16 grams. This is the power of the definition of mole. You will get used to it as you do more and more problems. For now, let us move to the third problem. Here we are asked the number of atoms in 28 grams of N2. So this is the first time we are dealing with a molecule here N2. And we are given the mass of that molecule. Okay, first let's see what is the mass of one mole of this molecule. If I look at the periodic table, I can see that the mass of one atom of nitrogen is 14u. This means that there are 14 grams in one mole of nitrogen, 14 grams per mole. U is the same as grams per mole. 14 grams of nitrogen in one mole of nitrogen. Here we have N2. N2 has two atoms of nitrogen, NN, right? So one mole of the nitrogen molecule will have double the mass of one mole of nitrogen atoms. So one mole of nitrogen molecule will have a mass of 28 grams, double of this. So if one mole of nitrogen molecules has 28 grams and we are asked what is the number of atoms in 28 grams of nitrogen, the first thing we have seen is this is one mole of nitrogen molecule. That is 6.022 into 10 to the power 23 nitrogen molecules. But because we are asked atoms, and we have to be careful in these type of questions about noticing these words of atoms or molecules, because we are asked atoms, we will multiply this number by 2. So 2 into 6.022 into 10 to the power 23 nitrogen atoms. Each molecule has two atoms. So we simply multiply this by 2. So these many nitrogen atoms in 28 grams of nitrogen gas or N2 molecules. Finally let us look at this last problem. Here we have the number of moles of H atoms in 32 grams of methane. Again we have a molecule. This is CH4. So first let us find the molar mass of this molecule because we are dealing with masses. So first let's find the molar mass that is mass of one mole of CH4. So CH4 is made of one carbon and four hydrogens. So the molar mass of CH4 will be the molar mass of one carbon plus four times the molar mass of hydrogen. Again from the periodic table one atom of carbon is 12 U. This means that one mole of carbon will be 12 grams. This is the molar mass. So 12 grams plus four times one atom of hydrogen is one atomic mass unit. So one mole of hydrogen will be one gram. So four times one gram. This is equal to 16 grams. So this is one mole of CH4. This is the mass of one mole of CH4. All right. We are given here 32 grams of CH4. This means this is double of this. So we have two moles of methane here. This is the same as saying we have two moles of methane here. So we have two moles of CH4 and each atom of the CH4 will have four hydrogens attached to it. So if we have one mole of the CH4 we have four moles of hydrogen atoms. And in two moles of CH4 we will have eight moles of hydrogen atoms because for each methane molecule we have four hydrogen atoms. So for two moles of CH4 we will have eight moles of hydrogen atoms. So the answer here for this fourth part is eight moles of hydrogen atoms. So I hope this is clear and this shows you the power of the concept of moles.