in this video we're going to talk about how to find the empirical formula of a compound from percent composition and also how to get the molecular formula if we're given the molar mass so let's start with this problem a compound is composed of 52.14 carbon 13.13 hydrogen and 34.73 percent oxygen by mass what is the empirical formula now let's say that we have a hundred grams of compound 52.14 of 100 grams is basically 52.14 grams so that's how many grams of carbon we have out of a compound that's 100 grams so that means that we have 13.13 grams of hydrogen and 34.73 grams of oxygen so basically when you're given the percent composition simply make it grams base your compound out of 100 grams and you could change the percentage into grams now what you want to do next is you need to convert grams of carbon into moles the atomic mass of carbon is 12.01 grams per mole so you want to set it up this way so that the unit grams will cancel and let me just get my calculator so let's divide 52.14 by 12.01 so you should get 4.34 moles of carbon now let's do the same thing for hydrogen the molar mass of hydrogen is 1.008 grams so that means one mole of hydrogen has a mass of 1.008 grams so let's take 13.13 and divide it by 1.008 so this will give us 13.026 moles of hydrogen lastly we have oxygen the molar mass of which is 16 grams per 1 mole so 34.7 divided by 16 that's 2.171 moles now what you need to do up next is identify which number is the smallest clearly it's the moles of oxygen so what you need to do is divide every quantity that you have by the smallest of the three values in this case the moles of oxygen ideally you want to get a whole number 4.34 divided by 2.171 that is about 2. it's 1.999 but you want to round it to the nearest whole number if possible 13.026 divided by 2.171 is 6. and this is clearly 1. so now we have the subscript for carbon the subscript for hydrogen and the subscript for oxygen so the empirical formula that is the formula with the lowest ratios it's c2 h6 so that's the empirical formula that's how you could find it if you're given the percent composition of an element so that's the answer for part a now let's move on to part b if the molar mass of the compound is 138.204 grams per mole what is the molecular formula so we have the empirical formula now we need to find the molecular formula the first thing we need to do is find the molar mass of the empirical formula so there are two carbons six hydrogens and one oxygen so it's two times twelve point zero one plus six times one point zero zero eight plus 16. so the molar mass of c2h6 is 46.068 so now we need to know what empirical formula or rather what molecular formula corresponds to a molar mass of 138.204 so what you need to do is take the large number and divide it by the small number so if we divide 138.204 by forty six point zero six eight we are going to get three so if you multiply 46 by three you get 132 i mean 138 so therefore to get the molecular formula we need to multiply the subscripts of the empirical formula by three so this is going to give us c6h18o3 and that's how you find the molecular formula from the empirical formula basically you got to divide the molar mass of the molecular formula by the molar mass of the empirical formula whatever number you get multiply the subscripts of the empirical formula by that number and that's going to give you the molecular formula number two a compound consists of 20.32 grams of carbon 5.12 grams of hydrogen and 7.9 grams of nitrogen what is the empirical formula so in the last example we were given a percent composition which we converted to grams anyway here we're given the grams of all the elements in this compound so we're going to follow the same steps of converting each into moles the molar mass of carbon is 12.01 grams for every one mole of carbon so 20.32 divided by 12.01 that's 1.692 moles of carbon so now let's turn our attention to hydrogen the molar mass is 1.008 grams of hydrogen per one mole and so this is going to be 5.079 and finally let's move on to nitrogen we have 7.9 grams of nitrogen and the molar mass is 14.01 so this will give us .5639 moles of nitrogen so now let's divide each number by the smallest of these three values so the smallest is 0.56 so 1.692 divided by 0.5639 that's about 3. 5.079 divided by 0.5629 that's 9 and this is going to be 1. so any empirical formula there should be three carbon atoms nine hydrogen atoms one nitrogen atom so the formula is going to be c3 h9 and one or simply just n so that's the empirical formula now let's find the molecular formula to do that we gotta find the molar mass of the empirical formula first so we have three carbon atoms nine hydrogen atoms one nitrogen atom now let's add up the numbers that we see here so this adds up to 59.112 so that's the molar mass of the empirical formula now we need to find out the molecular formula that corresponds to 236.448 so what you want to do at this point is take the molar mass of the molecular formula and divide it by the molar mass of the empirical formula 236.448 divided by 59.112 that's equal to 4. so therefore we need to multiply the subscripts of the empirical formula by four so three times four is twelve nine times four is thirty six one times four is four so the formula is c12 h36 and 4 so that's the molecular formula that's the answer for part b to this question so now you know how to find the empirical formula and the molecular formula if you're given the percent composition by mass or if you're given the grams of all the elements in the compound thanks for watching you