 In this video, we'll look at a very simple little calculation in which we express the amount of different elements in a compound as percentage by mass. First, consider a block of pure sodium. The only type of atom in this block is sodium atoms, so we can say that 100% of the atoms are sodium. But because, as human-sized creatures, it's easier for us to measure masses rather than numbers of atoms, it's often more convenient for us to think about the percentage by mass. In this case, it's easy. Because all the atoms are sodium atoms, we can also say that 100% of the mass of this substance is sodium. Okay, now think about table salt, sodium chloride. The formula is NaCl, so that tells you that the ratio of sodium to chloride ions is one to one. That is, in any sample of sodium chloride, half the ions will be sodium and half will be chloride. Okay, so if you have a sample of sodium chloride, what percentage of the mass of that sample will be due to the sodium ions? Is it going to be 50%? Well, we can work it out as a simple percentage using our knowledge of molar masses. To make the calculation easy, let's say we have one mole of sodium chloride. If we work out the molar mass, we'll know the mass of that one mole. So let's first work out the molar mass. The molar mass of sodium is 22.99 grams per mole. The molar mass of chlorine is 35.45 grams per mole and we add them together and we have that the molar mass of sodium chloride is 58.44 grams per mole. So the mass of one mole of sodium chloride is 58.44 grams. Now it's also pretty easy to figure out how much of that is due to sodium and how much to chloride. Now we know that in one mole of sodium chloride, there's one mole of sodium ions and one mole of chloride ions. So of that 58.44 grams, 22.99 grams is sodium from the one mole of sodium ions and 35.45 grams is chloride, one mole of chloride ions. So clearly the mass percent of sodium is not going to be 50% because sodium ions, although there are the same number of them as chloride, sodium ions are lighter. So to work out the percentage by mass of sodium, we simply divide the mass of sodium ions by the total mass of sodium chloride and multiply by 100. So in our mole of sodium chloride, that's 22.99 grams of sodium divided by 58.44 grams of sodium chloride times 100, which gives us 39.34%. Note the four sig figs, which I'm getting from the fact that I've used four sig figs in my molar masses. We can double check where correct by working out the percentage of chloride. If all goes well, those two percentages should add up to 100%. So we say 35.45 divided by 58.44 times 100 and that gives us 60.66%. And yes, those two percentages do add up to 100%. Let's try one more example. We'll determine the percentage by mass of each element in sulfuric acid. So there are a few bits of information we need to collect. We need the formula of sulfuric acid, well that's H2SO4. We need the molar masses of the elements involved, and we need the molar mass of sulfuric acid. Now we can calculate the percentages by mass. So the percentage of hydrogen equals the mass of hydrogen over the total mass of sulfuric acid times 100, and there are two hydrogen atoms in each molecule of sulfuric acid. So that means that if you have one mole of sulfuric acid, there will be two moles of hydrogen atoms contained in it. So the mass of hydrogen in our mole of sulfuric acid equals 2 times 1.008 grams and divided by the molar mass of sulfuric acid 98.072 times 100, and that gives us 2.056%. Note in this calculation that the numbers of moles or atoms are exact numbers. So the fact that there are two hydrogen atoms in each sulfuric acid, that's an exact number of atoms. You can't have part of an atom. So that means they don't affect the significant figures. Okay so let's try oxygen. There are four oxygens in the sulfuric acid molecule, so four moles of oxygen for every one mole of sulfuric acid. So the percentage mass will be 4 times 15.999 divided by 98.072 times 100, which gives us 65.25%. Now we should be able to work out the percentage of sulfur by subtraction. We'll have 100 minus the sum of the other two percentages, and that gives us 32.69%. And if we work out sulfur the full way, we get the same answer, which is great. And our three percentages add up to 100%.