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# Molecular weight percentages

## Video transcript

- Let's figure out what percentage of a benzene molecule by mass is made up of the carbons, and what percentage is made up by the hydrogens. And as we see, each molecule of benzene has six carbons and six hydrogens in it. And I encourage you to pause the video now, and use a periodic table, we'll be a little bit more precise in this video, we'll use the actual atomic weight to calculate the molecular mass, or you should say the molecular weight of a benzene molecule, and then figure out what percentage of that is from carbons, and what percentage of that is from hydrogens. So I'm assuming you have had your go at it, so let's first think about what percentage is from the carbons, or let's see what the carbon contributes to the mass. So you have six carbons, so the C six is going to be six times, and if we get our periodic table out, we see that the atomic weight of carbon, is 12.011, so the weighted average of all the isotopes as found on Earth, and we've talked a lot about that, 12.011 atomic mass units, this is going to be 12.011 atomic mass units, and the contribution from hydrogen, the contribution from hydrogen, let me do that in yellow... The contribution from hydrogen, from the six hydrogens, is going to be six times the atomic weight of hydrogen, which is 1.0079, by this periodic table that I have right here, once again, the weighted average of all the isotopes, et cetera, et cetera, 1.0079. 1.0079, and so, the molecular weight of this whole thing, a typical benzene molecule, if you were to take the weighted average of all of its molecular masses, based on the prevalence of the different isotopes on Earth, well, you would just say it's just going to be the sum of these two things. It is going to be six times 12.011 plus, six times 1.0079, and then what is that going to give us? Well, let's see, let's get a calculator out, so let me clear that, so 12.011 times six gives us 72.066, so this right over here. is 72.066, and actually, I probably could have done that in my head, well anyway, let's look at what we have from the hydrogen, so the hydrogen are going to be six times 1.0079 gets us to 6.0474, plus 6.0474, now we're going to add them together, but since I only go to the thousandth place in terms of precision here, if I care about significant figures, significant digits, then I'm only going to go three spaces to the right of the decimal, but let's add these two together, so I'm going to get 6.0474, plus 72.066 equals, and I'm just going to go three to the right, so 78.113, so this is equal to, 78.113 atomic mass units, that's the molecular mass of a molecule of benzene, now what percentage is from the carbon? Well, it's going to be equal to the 72.066 over the 78.113 which is equal to, all right, so let me just clear this. So 72.066 divided by 78.113 is equal to 0.9225, it keeps going on and on and on, but in terms of percentages, this is going to be, and let's say I want to keep my precision, so I have five significant digits in both the numerator and the denominator, so I can have five significant digits in the answer, so it's not .92259, .92259 if I were to round this eight up, because I have this six here. So this is 0.92259 which is, let me see, this is approximately equal to since I'm now rounding, and this is equal to 92.259 percent carbon. Now, the remainder is going to be hydrogen, of course we can figure that out, that's going to be 6.0474 divided by the 78.113, which is going to get us, so let me clear it out. So 6.0474 divided by 78.113, is equal to 0.07741, and let's see I have five significant digits in either case, so this is going to be, 0.07742. 0.07742, did I do that right? I have trouble remembering these numbers. Let's see, 0.0774, and then I round that one up because I have an eight in the next place over, so four, two, which if I were to express as a percentage, and this is five significant digits right here, one, two, three, four, five, as a percentage is equal to, and this is roughly, since I'm rounding, this is going to be 7.742 percent, and these roughly do add up to 100 percent. So most of the mass here, even though you have an equal number of carbons and hydrogens, most of the mass here is from the carbons, and a little over 92 percent of the mass is from the carbons.