In this tutorial, i want to talk about two very common types of questions about moles. these two types of questions don’t really fit into the other categories we’ve talked about but they show up all the time on homework, in textbooks, on quizzes and particularly on tests and exams. Okay, here’s the first one. What is the mass in grams of a single atom of oxygen? Okay, this is the type of question that asks us to calculate the mass of a single atom of some element. Here, we’re going to use Oxygen as the example.
Now in order to solve problems like this, you have to pull in a few different pieces of information about moles, okay? The first one is going to be about mass, right? We’re talking about the mass of a single atom of Oxygen. What do we know about the mass of Oxygen? Well we can look up Oxygen on the periodic table and we can zoom in to 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 information on the periodic table,.
1 mole of oxygen atoms weighs 16.00 grams. but we’re not talking about a mole of oxygen atoms, we’re talking about a single atom of Oxygen, 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 hexillion Oxygen atoms which we often abbreviate as (6.02 x 10^23). Now we want to combine these two pieces of information to make a third piece of information, okay? Check this out. 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 pieces of information to say that 602 hexillion Oxygen atoms weigh 16.00 grams, okay? We can even take this and express it kind of like an equation, kind of like a relationship here. We can say 6.02 times 10 to the 23rd Oxygen atoms equals or its equivalent to 16 grams (6.02 x 10^23 Oxygen atoms = 16.00 grams). Now check out this last thing that I drew. This thing here is an equation or a relationship.
That we can turn into a conversion factor that will let us go from the number of oxygen atoms 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. Here’s how I’m going to do it. Let’s start here, I’m going to do 1 oxygen atom and now I’m going to multiply that by a conversion factor made from this relationship. I want to get rid of Oxygen atoms which is on top here so I’m going to write this relationship as a conversion factor with Oxygen atoms.
On the bottom. so i’m going to take this part here, 6.02 x 10^23 oxygen atoms, put that on the bottom, and make my fraction here a little bit longer. Then I’m going to put the other side of the relationship, 16.00 grams, on top. And now when I work through the math here, Oxygen atoms on the top, Oxygen atoms on 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 through the math. So you write this.
Out and you probably want to solve it by putting it into the calculator. you can type it in like this although you don’t really have to multiply it by 1 here because multiplying something by 1 doesn’t really change its value but it’s totally up to you. You put this in, you’re going to get this out as an answer, this E23 in calculator language just means this times 10 to the negative 23rd and then we’re going to want to take this number and round it to three significant figures. We don’t worry about significant figures in 1.
Here because this is a counting number. we’re saying 1 oxygen atom, it’s not a measurement, so this has an infinite number of significant figures. We’re going to round this to three significant figures because there are three in 6.02 which has the fewer numbers of significant figures. So we round this to 2.6, we have the 5 here so we round up because of the 7, 2.66 times 10 to the negative 23rd (2.66 X 10^23). And what are our units? They are grams. That’s what we’re left over with after the conversion factors. Here’s our final answer.