In this video, we'll look at mole fraction. We'll learn what it is and how to calculate it, and then in the next video, we'll do some practice problems. So, mole fraction. Mole fraction is a way to describe the concentration of different parts, also known as components, of a solution.
Let's take a look at an example solution. Most solutions have two parts or components. They have a solute that dissolves in a solvent. Now, the solute and solvent are different chemicals. In this example, we'll say that the solute is chemical A and the solvent is chemical B.
In a solution, we usually know how much of each of these chemicals is solute. chemical we have or we can figure it out in this example we have 2.0 moles of the solute chemical a and we have 6.0 moles of the solvent chemical B now we can calculate mole fraction for either a or for B let's start out by calculating the mole fraction for the solute for chemical a and here is the equation for the mole fraction of chemical A. This symbol here, the x with the A down here is a symbol for mole fraction of A.
You can pronounce this as x sub A. Now, let's take a look at the numbers here. On the top of the fraction we have the number of moles of A, 2.0 moles.
And on the bottom of the fraction we have the total moles in the solution. So we have the moles of A plus the moles of B. This equation makes sense if you think about fractions because when we're talking about fractions we're talking about a part compared to a whole and in this fraction up here we have the part of the solution that comes from A and then down here we have the whole solution.
We have A and B together the total, the whole thing. Now, when we do this math, we end up with 0.25. Pay attention to units here.
Oh, wait. There are no units. Is that correct? Yeah, it is. Let's look at how this happens.
Now, technically before we divide we add these two values together and here's what we get in this in between step. We get 2.0 moles on top and then we get this. plus this which gives us 8.0 moles so this is the in between or the intermediate step and it gives us moles over moles so the moles cancel out there are no units on the final answer we get what we call a dimensionless quantity so mole fraction has no units okay so this is how we calculate mole fraction of a We can do the same thing and calculate the mole fraction of b. And here is what that equation looks like.
We have on top of the fraction, we have the moles of b, 6.0 moles. And then on the bottom, we have the total number of moles in the solution, 2.0 plus 6.0. And when we do this math, we get...
0.75. You can probably see what's going on here. When we calculate the mole fraction of B, we put the number of moles of B on top, and then on the bottom, the total number of moles, number of moles of A, plus the number of moles of B.
When we calculate the mole fraction of A, we put the number of moles of A on top, and then the total number of moles on the bottom. Here's something else to keep in mind about mole fraction. Since these two mole fractions represent the two parts of the solution, when we add them together we get one or the whole. So, these are two examples of how we can calculate mole fraction for different components of a solution. But how can we write a general equation that we can refer to whenever we need to calculate mole fraction?
Here is an equation that you'll often see in textbooks or in lectures. We have mole fraction x sub a and here a is any chemical that we're calculating mole fraction for. So A might be water, it might be sodium chloride, or it might be some kind of sugar. So we have the mole fraction of A equals the number of moles of A, and that's little n sub a divided by the total moles the total number of moles in the solution and this is the abbreviation for that so you can always plug values into this equation to figure out the mole fraction there's some other versions of this equation that you might run into as well. Here is kind of an abbreviated version of this equation that just has the symbols instead of the words.
And there's another version of the mole fraction equation that you might run into. I don't like this one as much. All right, this has mole fraction of a equals moles of a divided by moles of a plus moles of b.
Now, this is exactly what we did here. So why don't I like it? Well, here's why.
This equation only works when you have a solution that has two parts or components. We had two parts. In this example, we had a and b.
But that's not always the case. There are solutions out there that have three or four or even five different parts. And in that case, this isn't a good equation because it only works if you have two components. So that's why I don't like it so much.
Because we often, or at least sometimes, run into solutions that have more than two components, I like these equations instead that just have the total number of moles on the bottom. These equations work no matter... how many different parts or components you have in your solution. So, this is how we calculate mole fraction.
These are some equations. Now, let's apply these equations and do some practice problems.