Okay, what we're going to start looking at now is going more into atomic mass, molar mass, and Avagadro's number. So, some of this was actually in your summer work. One of the things that we defined was the mole um and we are going to be using that in this segment of the material. Okay. So remember we left off with the conversation of isotopes. Um but remember that every element is going to be made up and I shouldn't say every but almost every element has multiple isotopes. There are a few that only have a single isotope. Fos I mean yeah phosphorus is one example that I'm going to just tell you is 100% phosphorus 31. Okay. The other thing that is always key to remember is that the atomic mass of an element listed on the periodic table is the weighted average of all isotopes of that element. So it's really key for you to remember that it's a weighted average. Okay. So these are some common isotope examples just taking from what we did with carbon. You can see carbon is listed on here now and we list the carbon 14% abundance. Um remember that for each of these you could rewrite it as carbon 12 6 carbon 13 6 carbon 14 six and remember that bottom number that six is your atomic number that atomic number I'm going to highlight it here is the same thing as your number of protons and then the difference in the number of neutrons is utilizing the fact that the 12 which is your mass number is the sum of your protons plus your neutrons. Okay, notice the differences in the abundances. Carbon 12 at 98.9, carbon 13 at 1.1, and then carbon 14 at less than 1.1.1%. Okay, some other common isotopes, some names that I would be familiar with if I were you. When we talk about hydrogen, the three common isotopes are H1, H2, and H3. H2 is called dutarium. This is going to come up a lot. I would suggest that you know its name. H3 is tridium. This one also comes up a lot. Okay? And that's throughout many chemistry and biochemistry courses that you're going to see these. Okay? And we'll frequently refer to H1 as just a proton or just hydrogen. Okay. Now, these are just some more examples using uranium. Uranium 238, uranium 235, uranium 234, and just showing you their individual. So, this is the mass of each of those isotopes. And then the percent abundances down here. Okay. So if you look at those percent abundances and you notice that uranium 238 is 99% abundant, you would expect that the the weighted average would be closest to uranium 238 mass. So getting down to the math of this. So the atomic mass of the element that's listed on the periodic table is that weighted average. The way that we're going to find that is that we are going to take the fraction of the isotope for whatever that isotope is. So this fraction, remember this is taking your percent. So let's say it's 40%. Then the fraction is the same as 40 over 100 or 0.4. Okay, so that's what we mean by the fraction of the isotope. And then we're going to multiply it by the mass of that isotope. And then this symbol in the front up here, if you remember, this means the sum. So if there are three isotopes, we do the fraction times the mass for each of the three and then we add them together. Now getting down to the mass itself. One atomic mass unit 1 amu is defined as 112th the mass of a carbon 12 atom at rest. Now remember some things that were in the pre-semester work. A rested carbon 12 atom will have a mass of exactly 12 amu. Okay. And that's because this is our standard. We set this. We chose carbon 12. It used to be oxygen. It used to be hydrogen. But we selected carbon 12 due largely to stability and abundance. Okay. All masses of all isotopes are measured against carbon 12. Okay. Every single isotope has a unique mass and its own natural abundance. that natural abundance is always given to you in the form of a percentage. So you're going to be looking to convert that to the decimal form for all of these problems. So how do we actually measure atomic mass? So we don't continue to do this day by day. Um but one of the ways that we can do this is using a technique called mass spectrometry. So there are different forms of mass spectrometers. Um using ion impact is not as common as it used to be. But one of the easier ways to measure masses for simple compounds is something called ion impact. Okay. The way that it works is that you take a sample and you have to vaporize it. So you have to get it into the gas phase. Okay. Sometimes that's as the form of an aerosol. You put it, you introduce it into a chamber and inside that chamber there is an electron source. And so what will happen is that the atom is going to be ionized by kicking off one or more electrons to give a positive ion. You can also do negative phase as well, but we most frequently measure positive phase. Okay. So now this is true even for things that you would normally expect to form negative ions because we're doing this at high energy. Okay. So we're doing ion impact the mass spectrometer is going to work with the positive ions. Okay. Other forms do not always. So this always is I'm going to use the word relative. Okay. The second thing that happens is that we accelerate those ions. So we speed them up. And the reason why we do that is because we want the ions to have the same kinetic energy. And then what will happen is that they are then passed through a tube, a curved tube that's in the presence of an electromagnet. Now remember these ions have charge. So charge is going to be attracted to or deflected by this electromagnet. And it's actually going to be done so based on the overall charge because it's possible to get + 1 + 2 + 3 um but also the mass. Okay, the lighter they are, the more they are deflected. Um and then we do time of flight. So we measure how fast those individual ions at masses reach what we call the detector. Okay. So once it reaches the detector we actually use um a mathematical transformation to give us the information and what we would see is an output that looks like this. Now notice over here on this side it says relative abundance. So the tallest peak is our base peak. It just has the highest abundance. So sometimes this will say 100% abundance but it doesn't really mean 100. It's 100 because it's the highest and the others are measured rel like in height relativity to that. So it's like a height differential. Along the bottom you see mass to charge. So this is mass divided by + one. So we're not having to adjust the masses. We're saying that at that base peak, the mass is 98. Okay? And so each one of these would be an individual isotope. So we would have isotopes ranging from 92 to 100. Okay? So if we go to one that's actually for a given element with that information, we can see that this massspec output. So we would call it a mass spectrum and this is specifically for zirconium. It has one, two, three, four, five lines. So it has five isotopes. The tallest one where our base peak is, that's the one with the greatest abundance. and then we measure the other abundances of those against it to figure out what the percentages are. Okay, but that's the information that you're given. You're given all of these. So, zirconium 90 is this peak here. All right, zirconium 91 is this peak here. Zirconium 92, zirconium 94 and zirconium 96. Okay, so those are your individual peaks and what you see is their identity, their percent abundance and then their actual mass. Okay. So, what we're going to do now is we're going to actually calculate the atomic mass of zirconium using those numbers so that you can see how to plug it in. Okay. So, I'm going to do that on the next slide just so that we have space. So, remember what we're going to do to get the atomic mass going. I could keep it's going to be equal to the sum over n values the fraction the fractional abundance times the mass of the isotope. and then we're going to add them up. So for zuconium, so I'm just going to write it out as atomic mass of zirconium and I'm going to take each of those numbers. So for zirconium 90, we had 51.5%. So 0.515 that's my percent abundance times the atomic mass 89.9047 amu keeping our units plus the atomic mass of zirconium 91 which is 0.112 because it's 11.2% 2% abundant time 90.9056 amu plus zirconium 92 the percent abundance is 17.1 so.171* 9.9050 amu plus zirconium 94 4 0.174 because it's 17.4% abundant time 93.9064 amu and then zirconium 96 0.028 because it's 2.8% abundant times 95.9083 amu. Okay, so if you notice each of those atomic masses are not exactly 90, not exactly 91, not exactly 92, and so forth, but they're very, very close. Okay, so when I add all of these together and I put them in to my calculator, I get 91.22 amu. And then if I look at the periodic table, that value is 91.22 amu. And so therefore, we can see that it matches. Okay. Now I only rounded to two digits or two decimal places I should say. Um the limitation is not in the percentages for these. Um usually the limitation is in the instrument. So we could have reported it to four because each one of these values has four um decimal places. And those percent abundances, they're usually just rounded for you um in these problems. So it's not overly important that we get that sigfig completely correct on these. Okay. So this example is something that I'm going to encourage you to try for yourself and then we can rework it in class and I'll have the solution on another slide. But it says chromium which has an atomic mass of 51.9961 amu. So, this is its actual atomic mass. Actually, we're not I'm going to just do this one for you. Okay, this is its actual atomic mass. This comes from the periodic table. I'm going to put PT over it for periodic table. It consists of four isotopes with the following given masses. And then it says the first two have abundances of 4.41% and 83.46% respectively. Estimate the other two abundances. Okay. So, what I'm going to do is I'm going to stop this and I'm going to start a video to show you how to work this problem. Okay. But realize first and foremost when we have those abundances, like if you want to start out with your isotopes and then you want to put their masses and then their percent abundances where it says here that, you know, we have the first two have the abundances of those respectively. That means that they're in the same order. So my first two masses were 49.941 amu. That means that one is the 4.41%. And then the second one which was 51.9405 amu that one is 83.46% abundant. And what we're doing is we're following the order of listing because it matches our order of our percent abundances because we've used the word respectively.