in this video we're going to talk about how to calculate the percent composition of an element so let's go over the formula the mass percent is equal to the mass of the element divided by the total mass times 100 now you can calculate the mass percent if you're given the grams or if you're given the molar mass in terms of grams per mole the answer will still be the same in this example we're going to use the atomic weights or the molar mass that can be found in the periodic table so let's begin let's start with c12h22o11 sucrose let's calculate the percent by mass of carbon now the first thing i would recommend doing is finding the molar mass of the entire compound first so let's do that we have 12 carbon atoms 22 hydrogen atoms and 11 oxygen atoms carbon has an atomic mass of 12.01 and hydrogen is 1.008 oxygen 16. so if you type this in exactly the way you see it in your calculator you should get 342.296 grams per mole so that's the molar mass of the entire thing now if you want to find the percent by carbon you need to take the molar mass of all 12 carbon atoms and divide it by the total and then multiply by 100 so each carbon is 12.01 that's the atomic mass the total molar mass is this number that we have 342 0.296 and then we're going to multiply by 100 so 12 times 12.01 that's 144.12 divide that by 342.296 and then take that result multiply it by 100 and you should get 42.1 so that's the percentage by mass of the carbon atoms in sucrose now i'm just going to rewrite the answer on the top so we can reference it later so it's 42.1 percent now let's do the same thing with hydrogen so we need to take the mass of all the hydrogen atoms there's 22 of them each has an atomic mass of 1.008 and divided by the same total mass for the entire compound which is 342.296 and then multiply everything by a hundred percent so 22 times 1.008 that's 22.176 and then divide that by 342.296 and then multiply by 100 this will give you about six point five percent if you round it now let's do the same thing with oxygen so in sucrose there are 11 oxygen atoms each with an atomic mass of 16 then divided by the total molar mass 11 times 16 that's 176 and then divided by the molar mass and multiply by 100 you should get 51.4 so that's the percent by oxygen or the percent by mass of oxygen now if you add up 51.4 42.1 and 6.5 this will give you 100 that's how you can tell if you did everything correctly so now let's move on to that next example let's calculate the percent composition of every element in c5 h9 and o2 so first let's find the mole mass of the entire compound so we have five carbon atoms nine hydrogen atoms one nitrogen atom and two oxygen atoms now let's replace carbon with its atomic mass of 12.01 h is 1.008 nitrogen 14.01 and oxygen it's 16. now 5 times 12.01 is 60.05 9 times 1.008 that's this number and then 2 times 16 is 32 so let's add everything so the total molar mass is 115.132 grams per mole so now that we have that we can calculate the mass percent of every l excuse me every element so let's start with the percent of carbon so it's going to be the five carbon atoms which we could see that it has a mass of 60.05 divided by the total molar mass of 115.132 times 100 percent so it's 52.16 percent by carbon now let's move on to the percent by hydrogen or the percent of hydrogen rather so it's going to be the nine hydrogen atoms which has a mass of 9.072 divided by the same total molar mass of 115.132 times 100 percent and so that's going to be about 7.88 percent now let's do the same for the remaining two elements so let's move on to nitrogen so we have the mass of nitrogen which is uh 14.01 divided by the total times 100 so once you do this a few times it becomes second nature you'll automatically get the hang of it so it's 12.1 percent for nitrogen now let's move on to oxygen the last one there are two oxygen atoms and so the molar mass of those two oxygen atoms is 32 and just as we've been doing before we're going to divide it by the total so nothing has changed except the top number and i got 27 for the value of oxygen so that's the mass percent of oxygen in that compound so now you know how to find the percent composition of every element within a molecular compound and that's it for this problem number two which of the following compounds contain the greatest percentage of carbon by mass is it going to be a b c d or e well the most simplest way to find the answer is to determine the percentage of carbon for each compound let's start with ch4 so the percent of carbon is going to be the mass of carbon there's only one carbon atom and we know the atomic mass is 12.01 divided by the total which is the mass of carbon plus the four hydrogen atoms and then we're going to multiply by 100 percent now let's find the molar mass of ch4 let's start with that first so 12.01 plus 4 times 1.008 that's 16.042 and let's multiply everything by 100 so this is 74.87 percent mass by carbon so let's look at the second example let's see if there's anything that can top that so for b there are two carbon atoms so it's two times 12.01 divided by the total which will be the two carbon atoms and as a total of seven hydrogen atoms five plus two is seven and we have a nitrogen atom as well so let's calculate the molar mass first so for the molal mass i got 45.086 2 times 12 that's going to be 24. so the percentage is 53.3 percent so we could eliminate answer choice b so far a is the highest now let's move on to part c so this time we have five carbon atoms it's gonna be five times twelve point zero one divided by those five carbon atoms and there's a 12 hydrogen atoms 911 and we have an oxygen atom so let's multiply that by 100 percent so five times twelve point zero one that's going to be sixty point zero five and the total molar mass of c5h11oh is 88.146 if i did that correctly so the mass percent of carbon in this sample is 68.1 percent which is still less than 74. so we can get rid of that now let's move on to part d so we have six carbon atoms this time divided by everything else there's 12 hydrogen atoms and six oxygen atoms six times 12.01 that's going to be 72.06 and the molar mass of c6h12o6 that's 180.156 so the percentage is about 40 carbon now the last thing we need to check is carbon dioxide which is probably not going to be more than 50 probably a lot less so we have one carbon which is 12.01 divided by the total the molar mass of co2 is 44.01 so you should get 27.3 percent which is the lowest so therefore the answer is a number three a molecule contains a single atom of nitrogen if the mass percent of nitrogen in this compound is 13.32 percent what is the molar mass of the molecule so how can we figure this out well let's start with the formula the percent of nitrogen is going to equal the mass of nitrogen divided by the total molar mass multiplied by 100 so we have the percentage of nitrogen in this compound it's given to us it's 13.32 now we know that there's a single nitrogen atom and we need to multiply that by the atomic mass of nitrogen which is 14.01 we don't know the molar mass so let's call it some variable x and then we got to multiply everything by 100 so at this point it's basically algebra so what i would prefer doing is dividing both sides by a hundred so this disappears 13.32 divided by 100 is 0.1332 so that's equal to 14.01 divided by x now let's put this over one and let's cross multiply so we have one times 14.01 and that's equal to 0.1332 times x so now to find the value of x let's divide both sides by 0.1332 so the molar mass is 105 point 18 grams per mole so that's the molar mass of the unknown compound so if you have the mass percent of a single element and if you know how many atoms of that element are in the molecule you can calculate the molar mass of the unknown molecule you