 In this video, we'll look at how to work out the molecular formula of a compound if you know the empirical formula and the molar mass of the compound. Let me explain the key to the problem. To turn a molecular formula into an empirical one, you simplify the ratio of elements by dividing through by a common factor. For instance, to work out the empirical formula of hydrogen peroxide, we divided H2O2 through by 2 to give HO. This means that the molar mass of the empirical formula is half that of the true molar mass. Hence, if you divide the true molar mass, the molar mass of the molecular formula, by the molar mass of the empirical formula, you'll rediscover the factor that was used to simplify the molecular formula. So if you can find out the molar mass of the molecular formula and the molar mass of the empirical formula, then you can find out the simplifying factor. And that would then allow you to turn the empirical formula back into the molecular formula and discover what the compound was. Let's try an example. A compound is known to have the empirical formula CH2O. This is not helpful since there are many compounds with this empirical formula. Acetic acid, lactic acid and glucose are among them. However, its molar mass is determined to be 180.2 grams per mole. And it's molecular formula and hence its identity. Okay, so first write down what you know. We know that the empirical formula is CH2O, and we know that the molar mass of the molecular formula, the true formula, is 180.2 grams per mole. What we need to discover is what factor should we multiply the empirical formula by to get the molecular formula? Well, let's work out the molar mass of the empirical formula to start off with. It's 12.01 carbon plus 2 times 1.008, that's two hydrogens, plus 15.999 for the oxygen, which gives us 30.025 grams per mole. Now we'll take the true molar mass, 180.2, and divide it by the molar mass of the empirical formula, and this equals 6. That means that the molecular or true formula was divided through by 6 to give the empirical formula. So we reverse that process and we get that the true formula is C6H12O6, which is the formula for glucose. Now let's try a problem where we go all the way from percentage composition through to the molecular formula. A smelly compound with a molar mass of 88.11 grams per mole is purified. On elemental analysis it's found to contain 54.53 percent carbon, 9.15 percent hydrogen, and the balance oxygen. Determine its molecular formula and find out its name. So the way we're going to tackle this problem is first to determine the empirical formula from the mass percentage information, and then to use the true molar mass to determine the molecular formula. So we'll go back to our little rhyme. First we'll write out the percentages, calculating that oxygen must be 36.32 percent as we go. Next we convert those to masses and then to moles, which gives me a mole ratio of 4.54 moles of carbon to 9.08 moles of hydrogen to 2.27 moles of oxygen. Now we divide through by 2.27, which is the smallest of the three numbers, to simplify the ratio, and that gives us 2 to 4 to 1, which is a whole number ratio so it doesn't need any further work. So our empirical formula is C2H4O. Next we need the molar mass of that empirical formula. And that gives us 44.052 grams per mole. And now I divide the true molar mass by the empirical molar mass, 88.11 over 44.052, and that equals 2. So that means I need to multiply the empirical formula by 2. And that gives me a molecular formula of C4H8O2, which you'll find, if you hunt around, is the formula for butyric acid, which is found in rancid butter and parmesan cheese and charmingly vomit. Incidentally, as a metabolic product in the human gut, it's also been found to suppress colorectal cancer, so perhaps you should eat more parmesan cheese.