Atomic Mass: Introduction

In this video, we are going to talk about

atomic

mass

. Now, sometimes people call

atomic

mass

by other names; your teacher might call it one of these things. Atomic mass is a really important characteristic of elements. Each element, such as copper, oxygen, sulfur, etc., has its own atomic mass and the atomic mass is the number written below the sign of the element in the periodic table. Now, atomic mass is an average, it is an average of the masses of several different atoms, but it is a special type of average called a weighted average and this is different from the type of average that you probably already learned about in mathematics.

So to really talk about and understand atomic mass, we first need to understand weighted averages, what they are, and how to calculate them. So let's start by talking about the weighted average using a car analogy. So let's imagine that there is a type of car called Lemona and the Lemona is called Lemona because it looks like a lemon and has a very distinctive shape. For the purposes of this video, we will imagine that Lemona comes in two models, Lemona GX and Lemona GXL and these two models have different features that are unique to each of them.

The GX is blue, the GXL is red and this is a luxury model. It has massaging seats and platinum swivel wheels, while this one only has cloth seats and cheap aluminum wheels. Either way, although these are different models that have different features, they are both Lemonas because they have this distinctive lemon shape. In this sense, Lemonas' models are very similar to the isotopes of an element. Copper, for example, comes in two models, Copper 63 and Copper 65. Both isotopes of Copper have the same number of protons, twenty-nine, because the atomic number of Copper is 29. But they have different numbers of neutrons.

So as long as we have 29 protons, we will get copper. It doesn't matter how many neutrons you have, just like if you are shaped like a lemon, the car is a Lemona and it doesn't matter what other characteristics that car has. That's all we're going to talk about with isotopes right now, but keep in mind that the models of a car are very similar to the isotopes of an element. Anyway, we said that atomic mass is going to have a lot to do with the idea of ​​averages. So let's think about the averages of these two cars.

The Lemona GX weighs 4,000 pounds while the Lemona GXL weighs 5,000 pounds. It's probably the platinum spinning wheels that really add to that weight. So let's say you have this question. What is the average weight of the two cars? Knowing what you probably already know about averages, you could do these calculations. You could take 4,000 pounds for the GX, add it to the 5,000 pounds for the GXL, and then divide it by two because we have two things here. That would give it an average of 4,500 pounds, giving us a fair number between the weights of the two models. So I'll refer to this as a regular average, it's a type of average that you probably already learned to do.

Now, what if I complicated this problem a little more by giving you additional information? Let's say there is not the same amount of GX and GXL. Perhaps because the GXL is a little more expensive, there are many fewer of them. If we look at all the Lemonas that have been sold everywhere, only five percent of them are GXL, while the vast majority, ninety-five percent, are GX. We could show them graphically. If we were to pull 100 Lemonas at random from the street, all the blue ones would be GX, while the red ones would show GXL. Obviously there are many more but these are a hundred taken at random and we can see the same thing in a pie chart with only five percent GXL and the vast majority ninety-five percent are GX.

So there's that. Now let's take this information into account when we are asked this question. What is the average weight of Lemonas taking into account the quantity of each model? Now we have to calculate an average that is different from the regular average that we did here because in this case we found a number that was right between 4000 and 5000, but if we take into account the amount of each of these, is it really fair to say that the average weight is 4500, right in the middle of these two weights? Because there are many more Lemona GX and they weigh less, we need to come up with an average that takes this into account and gives us a number that is not right in the middle but closer to this because there are many more of them.

This is how we do it. This is where we get to the idea of ​​weighted average. So to calculate the weighted average, I'll take the amount Lemona G weighs, which is 4,000 pounds, and then multiply it by the abundance percentage. Abundance is just a fancy word that means how much of something you have. So here we have ninety-five percent of the total Lemonas are GX, so I'm going to multiply that by the abundance of GX. I have to convert this percentage to decimal. So the decimal point would be here, I move it two spaces to the left to get 0.95.

This expression is the GX contribution of which I own 95 percent. Now I'm going to take that and add it to the amount I have of the GXL. So I'm going to take his weight, which is 5,000 pounds, and multiply it by his abundance, also expressed as a decimal. Again the decimals are here, I'm going to move them two spaces to the left so I have 0.05 and this right here is the GXL which represents 5 percent of my total. I multiply these two things and then do the sum and I'll end up with a weighted average of 4,050 pounds. Now, as you can see, here is an average that takes into account the weights of both models, but it also takes into account how much we have of each and, because there are many more GXs, the average is not right. the medium, that average is much closer to the weight of the GX.

And since there are few GXLs, their weight doesn't have much of an impact on this final average. I want to say it's higher than 4000, but it's not right in the middle, so this calculation is what we call a weighted average where we take into account the amount or abundance of what we have of each thing. Now that we learned how to do weighted averages with different types of cars, let's talk about how to do weighted averages with different isotopes of an element. So, the atomic mass is a weighted average of the masses of all the isotopes of a given element.

Copper, as we said previously, has two versions or models, Copper 63 and Copper 65. Like Lemona, these two versions of Copper or these two isotopes of Copper have different masses. So the mass of Copper 63 is about 63 amu and the mass of Copper 65 is about 65 amu, but like Lemona, we do not have the same number of atoms of Copper 63 and Copper 65. If we randomly drew 100 atoms of copper in the world, we find that 69 percent of them are Copper 63. Here my 100 copper atoms and the 63 are represented by blue dots. And we would find that 31 percent of them are 65 copper atoms.

So the point is that you pull a random copper atom from somewhere in the world and it can be 63 or 65. You have a 69 percent chance of getting Copper 63 and a 31 percent chance of getting Copper 65. So to find the atomic mass, we need to do a weighted average calculation that takes into account the mass of each of these isotopes but also their percentage abundance and this is how we do it. will. Do you remember how we did it with Lemona? What we do is start with the dough. So Copper 63, I'll make 63 uma. Now I multiply it by its abundance expressed as a decimal.

Sixty-nine percent moves the decimal two points to the left and I have 0.69 and this expression here is for Copper 63. Now I'm going to add that to Copper 65. I'm going to make 65 amu multiplied by its abundance. 0.31 expressed as a decimal and just to keep track of this I will put Copper 65 (Cu-65) here. Now the math really isn't that difficult, the complicated part is just setting it up. Multiply this, multiply this and add them together, I will get 63.62 amu. Now look at this, 63 and 65, if we did a regular average we would get a number right in the middle, 64, okay?

But there are many more 63s, so that will mean that the weighted average won't be right in the middle, it will be closer to 63 and that's exactly what we see. We see a weighted average that is not 64 but is closer to 63 because we have more of these and the heavier Copper 65s do not contribute as much to this weighted average. Now I told you that this number here on the periodic table represents the atomic mass. You may be wondering why the atomic mass I calculated here was 63.62 and not the 0.55 I see here. Well, the reason is that I took some shortcuts here.

I used cleaner numbers so they wouldn't confuse you as much when we first did the math. It turns out that copper 63 doesn't actually weigh exactly 63 amu, but actually weighs 62.93. It is also not abundant at 69 percent, but it is at 69.17. So it's just a few extra decimals at the end that I chose to omit for these calculations because they're a bit annoying. The same goes for 65, where the numbers are not the perfectly nice pairs I used for this problem, but the point is that when you take these numbers into account and do the weighted average calculation, you end up with an atomic mass. in amu that is exactly the same as what is found in the periodic table.

So now that you understand what a weighted average is, how to calculate it, and how to calculate atomic mass, you're ready to watch practice problems on this topic in other videos.