Molarity vs. molality

Let's talk about the difference between two words molarity and molality. So the first one has obviously, a little r in it, and the other has an l in it. And in fact, sometimes when people say it quickly, it's hard to even hear which one they just said, so just make sure you listen carefully because there is a slight difference, actually, two little differences that we'll talk about. So molarity, let's start there, is really talking about moles of something, some particle, over 1 liter of solution. And I haven't been writing out liter of solution, but that is what is meant, so one liter of solution, that is molarity. Now, molality is slightly different, so let me do it in a different color. Molality is actually the moles, again-- so that part is the same-- over 1 kilogram-- so this is now actually looking at mass-- 1 kilogram of solvent, so not solution, but solvent. And so let me make that very clear. So this is 1 liter of solution. This is 1 kilogram of solvent. So both are looking at the same numerator, but the denominator is different. So let me actually draw out an example of what this might look like. Let's say we have our solution down here, and let's say it's mostly water, so I'm going to fill this in with water, and let's fill it in more quickly using a little air brush. So let's say this is our solution of water. I'm going to make it nice and even. You can see the line that it goes up to. So this is carefully measured out, and I'm going to put 1 mole of something, and we can decide whatever that something is going to be. And in this case, I don't know, let's say we decide to put some urea in there, little molecules of urea. And we know the urea is something our body uses to get rid of nitrogen, so something that we throw into urine and actually even sounds like urine. So I'm going to put some molecules of urea in here, and we're going to make our urea, I don't know, let's say kind of a pink color. This is our urea, and this is 1 mole of it. So I'm only going to draw a few of the little molecules, but you know that whenever I say there's a mole that must mean that there's 6.02 times 10 to the 23rd of these molecules in here, so lots and lots of molecules. So 1 mole, this refers to 6.02 times 10 to the 23rd, so lots of molecules hanging out in our solution now. And so let me actually then now cut and paste this. We're going to cut and paste this over to the other side, so that's over here, and we'll move this underneath here. So you know this is exactly the same, right? So this is just the exact same solution, and I still have my little pink urea. And now on this side, let's say I measure this out and check the level here. Let's say this level right here is exactly 1 liter. Well then, I would say this solution has 1 mole of urea in 1 liter of solution, so we have 1 molar solution of urea. So that's our molarity. Right? So so far so good. And these are little ureas just to make sure that we're clear about that. So this is our molarity, but what about the other side, our molality? So for that, I actually need to use a little eraser. So imagine now that I actually removed all the urea because I don't want the solution, I just want the solvent. I just want the part that is water. I don't care about the molecules. I just want to first get 1 kilogram of the solvent. So to do that, I've got to get rid of all my urea. So I take out all the little molecules of urea, and immediately you can't imagine that the water is actually going to allow those little holes to be like that. They're going to fill in those holes immediately. So right away, those holes are going to get filled in, right? So let's fill them in with water, so the water rushes into those holes and fills them in. But in doing so, in filling in these little holes, of course, the level falls. Right? You actually have a little bit less water. So you actually drop the level of water a little bit, so let me erase some water up here because the water level falls just a little bit to fill in all those holes of solvent that I took away or all the holes of urea that I pulled out. So now my level is fallen, and so if I was to measure this, let's say this is less than 1 liter. Let's say it's 0.99 liters. It's going to be very close, but it's going be slightly less, right? so let's say about 0.99 liters. So it's a little bit less than a liter. And remember, 1 liter equals 1 kilogram. So for water and most temperatures, 1 liter for a water, 1 liter equals 1 kilogram. So I guess I have to ask the question, does this equal 1 kilogram? Well, the answer is no, right? It actually equals about 0.99 kilograms. It's actually slightly less than a liter. So that's going to weigh less than 1 kilogram, just 0.99 kilograms. So now I have really 1 mole of urea. Thinking back to how much I dumped in, I had put in 1 mole of urea. I'm just going to let it hover here because this is where it was right before it fell into my water. 1 mole of urea was going in to only 0.99 kilograms of water. And so if that's the case, then my molality is actually going to be slightly different. It's going to be 1 mole of urea over 0.99 kilograms of solvent, of water. And so 1 divided by a number slightly less than 1 will be a little bit more than 1, so my molality will actually be maybe let's say 1.01 or thereabout. It will be just slightly upwards of 1, and that will be the molality. So they're very similar, right? Like 1 molarity, in this case was, was going to equal just a little bit higher molality and that's because we know that the molecules of urea take up a little bit of volume and that makes the overall volume of the solvent a little bit less. So that's the key difference, and if you think about this really when you're talking about blood and things that are dissolved into blood, most clinicians will jump back to molarity because it's just easier to work with and you don't actually have to figure out the exact amount of solvent. You can just think about the solution. So most of the clinicians or doctors and nurses will think in terms of molarity, but most of the time when you're working in a lab setting and you can be more precise, people think about molality.