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# Molecular mass percentage

## Video transcript

- So let's say that we have some glucose, the sugar in your blood that allows you to think, and do things, and watch this video, and allows me to make this video. And so, one molecule of glucose has six carbons in it, it has 12 hydrogens in it, and it has six oxygens in it. Now what I'm curious about is by mass, what percentage of a glucose molecule is carbon, what percentage is hydrogen, and what percentage is oxygen? And to do that, I'm gonna first take a stab at it where I'm just gonna use kind of the round numbers, the approximations. Now we've already talked about atomic weight, and atomic mass, and how we define it by the carbon 12 isotope, and how a neutron isn't exactly one atomic mass unit, or a proton isn't exactly one atomic mass unit, but for a lot of purposes, that's a very close approximation. So, let me write this down. So for the sake of this one, this is going to be kind of an overview, kind of get the idea, and then we'll do other examples where we get more precise, where we use the actual atomic weights, which is going to be more indicative of the elements as you will find them in earth, or the molecules, even, as you would find them on earth. So we're just going to assume, which isn't a bad assumption, that one proton, or one neutron, is approximately equal to one atomic mass unit, and I've sometimes used the notation amu, that's what I remember using, but it's actually the more modern notation for the unit is just the u. Sometimes an atomic mass unit is referred to as a Dalton, so you'll see that. That's still referring to atomic mass unit, or you could use kind of the older prefix, I guess you could say, or units amu, but this is the modern atomic mass unit that I'm talking about, not like one of the older ones, that are defined based on oxygen or hydrogen. This is the atomic mass unit where carbon 12, the carbon 12 isotope is exactly 12 atomic mass units, but I'll use the more modern notation. So if we assume that, let's just think about what the mass is of each of the constituents, so how much of the mass is made up by carbons, how much of the mass is made up by hydrogens, and how much is made up by oxygens? Well, carbon, let's do carbon first. So carbon has, by definition, it has six protons, that's what makes it carbon, six protons and the most typical isotope is six neutrons, and even if you were going to a periodic table, and you were to look up the atomic weight, you would find that it's very close to six plus six, which is 12. If you look up on a periodic table, you'd get 12.011, because that is weighting the various isotopes, and so, carbon, each of them has an atomic, we can assume carbon has an atomic mass, for the sake of this video, as 12, so six carbons are going to have an atomic mass collectively, be six together, six times 12 is, six times 12 is 72 atomic mass units. Now let's do the same thing for the hydrogens and the oxygens. So, hydrogen is, actually the typical isotope of hydrogen we find on earth is one proton, and zero neutrons. That's kind of what's neat about hydrogen, it's kind of a proton with an electron buzzing around, and the bulk of the mass is made up by the proton. The electron has almost a negligible mass if you're considering protons and neutrons. And so for the sake of our assumptions here, and this isn't exact, a hydrogen's atomic mass, we could say, is one atomic mass unit. Now if you're going on the periodic table, you'd see that's pretty close, 1.0079 is the atomic weight of hydrogen. Once again, this is based on the various isotopes of hydrogen as found on earth, and it is based on the idea that the electron does contribute a little bit, and a proton by itself is not exactly one atomic mass unit. The atomic mass unit is now defined that carbon 12 isotope is exactly 12 atomic mass units, but this is not the definition, but this is a useful way to think about it. So if each of the hydrogens is roughly one atomic mass unit, that means that 12 of the hydrogens are going to be 12 atomic mass units. And now let's do the same thing with the oxygen. Oxygen has... Actually, let me write it over. So oxygen has, by definition, eight protons, and the most typical, most of the oxygen on earth, also has eight neutrons, although there are other isotopes. There are eight neutrons, and so oxygen has an atomic weight, if we assume this way, of 16 atomic mass units. We'll see that's not exactly right. If you look at a periodic table, the atomic weight is 15.999, and we could be more precise and do that, but this is at least a rough way of getting it quickly, or of kind of getting a rough estimate, and it's really not that rough. Oxygen's atomic mass, we could say is 16, and so six oxygens are going to be 16 times six, which is 96 atomic mass units. And so, what's the mass of a molecule of glucose? Well, if we assume these numbers right over here, it's gonna be 72 plus 12 plus 96. I'm just adding the mass of the constituents, and that's going to be, what is that, 84 plus 96, which is 180, so this right over here is 180 atomic mass units, or 180 Daltons. Now let's try to answer our question. What percentage of this 180 is carbon? Well, 72 out of the 180 is carbon. So let's write that down. So, 72 of the 180 is carbon, 72 of the 180, which is equal to what? I have my calculator here. Let's see, 72 divided by 180 gets us 0.4, which is 40 percent, so this is 40 percent. 40 percent of a glucose molecule's mass is made up by carbon, based on the assumptions that we've done so far. Now what about hydrogen? Well, we could do the exact same idea. 12 180ths, which is equal to, get my calculator out, so 12 divided by 180 gets us 0.066, and it just keeps repeating on and on forever, so it's roughly, this is equivalent to 6.7 percent. So this right over here, I'll just say it's approximately 6.7 percent, and then the remainder, as a percentage, should be oxygen, but let's just verify that. So the oxygen is going to be 96, the same color, the oxygen is going to be 96 of the 180 atomic mass units, and so, that is going to be 96 divided by 180 gets us 0.533333, which is roughly 53.3 percent, so, approximately 53.3 percent. And so, once again, I did not use the precise atomic weights in the periodic table below, where this over here would have been 12.011, this over here would have been 1.0079, this over here would have been 15.999, but these numbers are awfully close, and it's much easier to do the math with it, and if we use these numbers instead, we get a pretty good estimate of what percentage, and it's a very good estimate, of what percentage of this molecule by mass is carbon, hydrogen, or oxygen. And you see, even though there are the same number of oxygens and carbons, there's a larger percentage by mass, because each oxygen has a larger mass. More than half of the mass of a glucose molecule is oxygen. And then in second place comes the carbon, and then hydrogen, there's a ton, well not a ton, there's 12 hydrogen, there's twice as many as there are carbons or oxygens, but because hydrogen has so much smaller of a mass, that it represents a much smaller percentage of the total mass of the molecule.