Very Common Mole Questions

In this video I want to talk about two types of

very

common

questions

about

mole

s. These two types of

questions

don't really fit into the other categories we've talked about, but they appear all the time on assignments, in textbooks, on quizzes, and especially on tests and exams. Well, here's the first one. What is the mass in grams of a single oxygen atom? Well, this is the type of question that asks us to calculate the mass of a single atom of some element. Here, we will use Oxygen as an example. Now, to solve problems like this, you have to get different information about

mole

s, okay?

The first one will be about dough, right? We are talking about the mass of a single oxygen atom. What do we know about the mass of oxygen? Well, we can look up Oxygen on the periodic table and we can zoom in on this number, 16.00, which tells us the molar mass of Oxygen. It tells us how much a mole of oxygen weighs in grams. So we can say that from this periodic table information, 1 mole of oxygen atoms weighs 16.00 grams. But we are not talking about a mole of Oxygen atoms, we are talking about a single Oxygen atom, one Oxygen atom.

So what do we know about the number of oxygen atoms in a mole? Well, you may know that 1 mole of oxygen atoms contains 602 hexillions of oxygen atoms which we often abbreviate as (6.02 x 10^23). Now we want to combine these two data to create a third data, okay? Look at this. We know two things here. On the one hand, we know that one mole of oxygen atoms weighs 16.00 grams and we also know that one mole of oxygen atoms contains 602 hexillion oxygen atoms, so we can combine these two data to say that 602 hexillion atoms of oxygen weigh 16.00 grams. grams, okay?

We can even take this and express it as an equation, as a relationship here. We can say that 6.02 times 10 to the power of 23 oxygen atoms is equivalent or its equivalent to 16 grams (6.02 x 10 ^ 23 oxygen atoms = 16.00 grams). Now look at this last thing I drew. This right here is an equation or a relationship that we can convert into a conversion factor that will allow us to go from the number of oxygen atoms that we have to grams, okay? So I'm going to use this equation as a conversion factor to go from one oxygen atom to a certain number of grams.

This is how I'm going to do it. Let's start here, I'm going to make 1 oxygen atom and now I'm going to multiply it by a conversion factor made from this relationship. I want to get rid of the oxygen atoms at the top here, so I'll write this relationship as a conversion factor with the oxygen atoms at the bottom. So I'm going to take this part here, 6.02 x 10^23 oxygen atoms, put it at the bottom and make my fraction here a little bit longer. Then I'm going to put the other side of the ratio on top, 16.00 grams. And now when I work through the calculations here, the oxygen atoms at the top, the oxygen atoms at the bottom, they're going to cancel out and that's going to leave me with grants, which is exactly what I want.

I'm just going to rearrange this so we can go over the calculations. So you write this down and you probably want to solve it by putting it on the calculator. You can write it like this, although you don't actually have to multiply it by 1 because multiplying something by 1 doesn't actually change its value, but it's totally up to you. You put this in, you'll get this as an answer, this E-23 in calculator language just means this multiplied by 10 to the power of negative 23 and then we're going to take this number and round it to three. important characters.

Here we don't worry about significant figures in 1 because this is a counting number. We are saying 1 oxygen atom, it is not a measurement, so it has an infinite number of significant figures. Let's round this to three significant figures because there are three in 6.02, which has the fewest significant figures. So we round this up to 2.6, we have the 5 here, so we round up because of the 7, 2.66 times 10 at least 23 (2.66 X 10^-23). And what are our units? They are grams. That's what we're left with after the conversion factors. Here is our final answer in scientific notation and if we write it in normal decimal notation, we can see that it is a

very

, very, very, very small number. 2.66 X 10^-23 grams, the mass of a single oxygen atom.

So the key to solving that problem was being able to take this information and write conversion factors with it, okay? We knew that 1 mole of oxygen weighed this amount and we know how many oxygen atoms there are in 1 mole. So we can take this information and write these two conversion factors. It could allow us to go from the number of oxygen atoms to grams and back and forth. What mass of Mercury has the same number of atoms as 64.2 grams of Calcium? I don't know about you, but I find the wording of this question very confusing, so I want to try to explain what you are really trying to ask here so you can understand how to solve it.

So we have Mercury and we have Calcium. We can look them up on the periodic table and this number here, the molar mass, tells us how much one mole of each of these types of atoms would weigh. So here, Mercury, we know that one mole of Mercury (602 hexillion Mercury atoms) would weigh 200.6 grams and for Calcium here, one mole of Calcium atoms (602 hexillion Calcium atoms) weighs 40.08 grams . So here's the main point, the main point is that 200.6 grams of Mercury and 40.08 grams of Calcium have the same number of atoms, okay? The masses are different. This weighs a lot more, it's a lot lighter, but the point is that even though the masses are different, the number of atoms is the same because 602 hexillion mercury atoms weigh that much and 602 hexillion calcium atoms weigh that much, okay? ?

So we can say that this amount of Mercury and this amount of Calcium have the same number of atoms. What really begs the question is that X grams of Mercury and 64.2 grams of Calcium have the same number of atoms, right? That's not really a question but it's a statement, okay? It's like how much Mercury has the same number of atoms as 64.2 grams of Calcium. This amount of Mercury and this amount of Calcium have the same number of atoms. Does this amount of Calcium and how much Mercury have the same number of atoms? So this is how we are going to solve it.

We are going to do two steps. Step 1: Let's ask, how many atoms are there in 64.2 grams of calcium? And then we are going to take that number of atoms that are in this amount of calcium and we are going to ask, if we had that number of Mercury atoms, how much would it weigh? So let's start here with the first part. Well, I'll start here with 64.2 grams of calcium. And now I want to know how many atoms are in them. So I'm going to multiply it by a conversion factor that I can get from this information here.

I want to get rid of the grams, so I'm going to put grams in the background. I'm going to make 42.08 grams of calcium and then on top of that I'm going to put 6.02 x 10^23 atoms. So now we have grams of calcium here, grams of calcium here, they will cancel out and I will be left with calcium atoms. I can put this into the calculator, I get this as my answer, and I'll round it to three significant figures to get 9.64 x 10^23, okay? 9.64 x 10^23 calcium atoms. This is the number of calcium atoms in this amount of calcium. Now the next thing I want to do here is ask, if we had this many Mercury atoms, how much would they weigh?

So we have so many calcium atoms. If we had that amount of Mercury, how much would it weigh? So this is how we will do it. Take this and we'll multiply it by a conversion factor that we can write from this information. It tells us how much a certain number of Mercury atoms weigh. So we'll multiply that by 6.02 x 10^23 Hg atoms at the bottom and then multiply it by 200.6 grams of mercury at the top. And now the Mercury atoms at the top, the Mercury atoms at the bottom, cancel, I'm left with grams of Mercury. The calculations I am going to do are these.

I pull this out of the calculator and my final answer rounded to three significant figures is 321 grams of Mercury and that tells us how much Mercury, what mass of Mercury would have the same number of atoms as 64.2 grams of Calcium.