Molarity | Intermolecular forces and properties | AP Chemistry | Khan Academy

In this video, we're going to talk about one of the most common ways to measure solute concentration in a solution, and that is molarity. Molarity is defined as the number of moles of solute (the thing that we are dissolving in a solvent) divided by the liters of solution.

Let's just do an example and see if we can calculate the molarity of a solution. So, let's say that I have this container here, and I'm going to dissolve some sodium sulfate in water. Sodium sulfate is the solute, and water is the solvent. Together, they give us the solution. Let's say the total volume of the solution is 250 milliliters.

This solution is made up of, just to give ourselves a bit of a refresher, we have the solvent, which is H2O (it is water in this situation). You might say, "Do we have 250 milliliters of water?" The answer would be not quite, because 250 milliliters is the volume of the water plus the sodium sulfate. So, we're going to have some sodium sulfate in here, and let's say we know that we have 35.5 grams of sodium sulfate. That is the formula for sodium sulfate.

Given this information, how do we figure out molarity? Well, the first thing you might say is, "Okay, I know the number of grams of sodium sulfate. I need to figure out the number of moles." To figure out the number of moles, you'd have to look at the molar mass. You could figure that out from a periodic table of elements, but just to speed us along, I will help you out a little bit here. The molar mass of sodium sulfate is 142 grams per mole.

So, given everything I've now told you, see if you can pause this video and figure out the molarity of this solution. What's the molarity of the sodium sulfate in this solution?

All right, now let's work through this together. First, we want to figure out the number of moles of solute. We can start with the mass of solute that we have right over here. So, we have 35.5 grams of sodium sulfate. Now, if we want to figure out the number of moles, I’m going to multiply this times something that would cancel out the grams. I don’t want grams per mole; I want moles per gram.

I could write this: I could multiply this times, for every one mole of sodium sulfate (Na2SO4), we have 142.04 grams of sodium sulfate. You can see very clearly that that will cancel with that, and we're left with moles of sodium sulfate. So, we'll get a calculator in a second and just take 35.5 and divide that by 142.04.

Then, to figure out molarity, we want to divide by the liters of solution. Up here, we have a calculation for the number of moles, and then the liters of solution: 250 milliliters is the same thing as 0.250 liters of our solution.

Now, we can just use our calculator to figure out what this is: 35.5 divided by 142.04 equals that, and then we divide that by 0.250. I could just throw a 0 in there, and then that gets us that right over there.

Then we can think about how many significant figures we have. We have three over here, we have one, two, three, four, five over here, and we have three over here. So I would say that we have three significant figures. We would round this rightmost 9 over here. If we round that up, we get 1.00. If we were to go to three significant figures, so that gets us 1.00.

Then, you might say, "What are the units here?" What people will normally say is this is 1.00 molar. When you see this capital M right over here, that is the unit for molarity, but they're really talking about the number of moles of solute per liter of solution.

And we are done.