Counting Atoms: Intro to Moles Part 2

In this video, we are going to see how we can use

moles

to count the number of

atoms

we have in something. For example, here I have a container with a bunch of carbon chunks. I want to know how. How many carbon

atoms

do I have here? You will learn how to solve it here. So just a quick review of

moles

. A mole is kind of like a dozen except there are 12 things in a dozen and there are 602 hexillion things in a mole and we often abbreviate this number in scientific notation as 6.02 times 10 to the 23rd power (6.02 x 10^23 ).

Now let's look at a mole. Right here I have one mole of sulfur atoms, which is roughly equivalent to 602 hexillions of sulfur atoms. Now this is pretty crazy because this is a huge amount of sulfur atoms. Here's my question, how do I know there are 602 hexillion sulfur atoms here, right? I couldn't rule them out for two reasons. First, the atoms are too small, we can't even see them with a very powerful microscope, so there is no way I could have seen the atoms and counted them. Second, even if you could count sulfur atoms, there are so many things in a mole that it would take 20 quadrillion years to count from 0 to one mole.

So even if you could see these atoms, there would be no way you could count them. However, I'm pretty sure there are about 602 hexillion sulfur atoms here. How do I know that? Well, we're going to learn more about this, but it turns out that I can calculate how much one mole weighs, 602 hexillions of sulfur atoms, and then I can put this on a scale and weigh the number of sulfur atoms. Let's talk a little more about this so it makes a little more sense. Well, here's an analogy. Let's say I work in a candy factory and when someone places an order, my job is to count all the candy he ordered.

One day, a rush job comes in for 10,000 jelly beans and the person who placed this order wants exactly 10,000 jelly beans. What a pain this is going to be, right? I have to count 10,000 jelly beans! This is going to take all day! What could make my life so much easier? One thing that would be really amazing is if you knew how much 10,000 jelly beans weighed. And what would happen if you discovered that 10,000 jelly beans weigh 27,130 grams? That would be really amazing because all you would have to do is put a large bag on a scale and put the jelly beans in until you get 27.130 grams.

In other words, instead of having to count, if I know how much 10,000 jelly beans weigh, all I have to do is weigh that amount. We can do exactly the same thing here with the moles. I told you that there are about 602 hexillion sulfur atoms here, of course I didn't count them, that's because I know that 602 hexillion sulfur atoms weigh about 32.07 grams, so all I have to do is put this container on a scale, weigh it. I take out 32.07 grams and I will know that I have approximately 602 hexillion of them. So how did I know that one mole of sulfur atoms weighed 32.07 grams?

Well, all you have to do is look at the periodic table. If I look up sulfur on the periodic table, I have the name of the element and the abbreviation and stuff and then I have this number down here. This is what we call molar mass and this number down here tells us how much one mole of this element weighs in grams. So 32.07 is what one mole weighs or 602 hexillions of sulfur atoms. Now let's go back to the candy factory. Imagine I get all kinds of orders for all kinds of different sweets. I can calculate how much 10,000 of many different types of candy weigh.

So, for example, you may have to make M&M's one day and you may discover that 10,000 M&M's weigh 8,770 grams. They weigh less because an M&M is much lighter than a jelly bean, so 10,000 of them will weigh less. On the other hand, a candy like one of these malted chocolate balls weighs much more than jelly beans, so 10,000 malted balls will weigh much more, 154,600 grams. The same thing happens with atoms, some are lighter and some are heavier. So carbon, for example, is a little lighter than sulfur and 602 hexillions of carbon atoms only weigh about 12.01 grams because carbon atoms are lighter than sulfur atoms.

On the other hand, something like zinc atoms are heavier than sulfur atoms, so 602 hexillions of zinc atoms or one mole of zinc atoms weigh 65.38 grams and, just as I did with sulfur , I know how much moles of carbon and zinc weigh because I can look. atoms in the periodic table. So here we have Carbon, 12.01 is its molar mass, that's how much a mole weighs, and Zinc, 65.38 and that tells me how much a mole of Zinc weighs, 602 hexillions of atoms. So if I want 602 hexillion, one mole, of any type of atom, all I have to do is look at the periodic table and find out how much one mole of that atom weighs and I don't have to count any atoms, all we have What to do is weigh this amount on a scale.

This is like me being a slacker in the candy factory. I don't want to have to count these jelly beans or M&Ms, so I can just weigh them. I can count everything by weighing it and that's what I do with these atoms: I count by weighing their molar masses. Now that we know how to calculate how much a mole of atoms weighs, let's go back to the original question I asked at the beginning of the video. I have a lot of Carbon here in this container. I want to know how many carbon atoms are here.

Let's see how we respond to this. Okay, how many carbon atoms do I have in this container? Well, let's think about moles of carbon. I look up Carbon in the periodic table and discover that one mole weighs 12.01 grams and I also know that in that mole there are 602 hexillions of atoms. The first thing I want to know is how many moles of Carbon do I have here? To find out, we can weigh a little, okay? I know that one mole weighs 12.01 grams, so let's weigh this and calculate how many moles we have in total. I put this on a scale and find that there are 31.87 grams of carbon atoms here.

That's more than a mole. If we had 12.01 grams of carbon, we would have one mole, but we have more than that, so let's figure out how many moles we have in total. We'll do this by taking 31.87 grams, the total mass of carbon atoms here, and dividing it by 12.01 grams, which is what one mole weighs. When we do that, we get 2.654 moles, so that's how many moles of carbon I have here. Well, we'll take this number and keep it because it's going to be important for what we do next. So how many carbon atoms do we have here?

Well, we know that in each mole there are 602 hexillions of atoms but here I have 2,654 moles. However, this is not too difficult because all I have to do is multiply 2.654 by the number of atoms in a mole. So I can make 2.654 moles times 602 hexillions of atoms. So this is a little annoying because I have all these zeroes, so I'm going to rewrite this using a shortened version in scientific notation. I'm going to multiply this by 6.02 times 10 to the power of 23, which is typically the version of 602 hexillion that we want to use when doing math. When I do this, I can just plug it into a calculator and I'll get 1.60x10^24 carbon atoms.

Sometimes when you see things in scientific notation, it can be a little scary, so let's take this out of scientific notation and this is the number of carbon atoms we have when we put all those zeros in. One hep-billion six hundred hexillion carbon atoms. This is how we can use moles to calculate the number of atoms we have in something. We can calculate how many moles we have by weighing it and then once we know how many moles we have, all we have to do is multiply it by the number of things in a mole and we get our final answer.