Calculate your own osmolarity

Now let's say that you have a vial of plasma. And I'm actually going to label it as we go. We've got some sodium floating in here and you've got some anion in purple over here. And this could be anything that really binds to sodium. So if this is some negatively charged ion, maybe chloride, or bicarb, those are the two most common. And you've also got, let's say, some glucose in here. And maybe some urea, or we call it urea nitrogen as well. So you've got a few things floating around the plasma and someone asks you, well, what is the total osmolarity of the plasma? And you know that this is in units of osmoles per liter blood, Actually, I should write liter plasma to be more accurate. Since that's what we're talking about here. So per one liter of plasma. And these are the units that we have to think about to answer this question, is, what are the osmoles per liter of plasma? So let's go through this. And I'm going to give you some lab values and we'll see how based on just a few lab values and really just four of the most representative solutes, or most important solutes, we can get a pretty close guesstimate of the osmolarity. So you don't actually need to know every single osmole that's in your plasma. You can figure it out based on four of the most important ones. So let's go with the first one, sodium. And let's say the lab tells you, well, your sodium value-- and I'm going to write the labs in kind of this grey color, somehow that reminds me of the lab-- let's say they say the sodium value is 140 milliequivalents per liter. So how do you take that and make it into osmoles per liter? Well, our denominator is already OK. But immediately, you can say, OK, well 140 millimoles per liter is what that equals. And you know that because sodium is a monovalent. It's only got one charge. If it's monovalent, then that means that the equivalents equal the moles. And now that you're in moles, you can actually go across to osmoles. You could say 140 osmoles or milliosmoles per liter. And you know that because once sodium is in water, it acts the same way that you would expect it to act. It doesn't split up or anything like that because it's one particle. So it acts as a single particle. One particle. So if it's one particle, it's going to have 140 milliosmoles per liter. And we've effectively gotten one quarter of this problem done. Because all we need to do is take the four different solutes that we've identified and add them up together. So we've figured out sodium. And now let's move on to the anion. And the trick to the anion is just thinking of it as sodium. It's almost the same as sodium, but just the reverse. So we know that it's going to be 140. We're going to use 140 as the number here. Because our assumption is that sodium is a positive charge and for every one positive charge, you need one negative charge. So we're going to assume that all the negative charges are coming from these anions. And these would be things like we said, things like chloride or bicarb, something like that. So again, we don't actually get these numbers or even need these numbers, we simply take that 140 and we multiply by 2 and assume that the other half is going to be some anion. Now we actually have to convert units still. We have to get over to milliosmoles per liter. And so we know that the anion is going to be monovalent and that gets us to millimoles. And we use the same logic as above. We just say, OK, well if that was millimoles and it's still one particle, meaning it's not splitting up when it hits water and going in two different directions, in a sense, having twice the effect, we're going to end up with 140 milliosmoles per liter, just as before. So this is our second part done, right? So two parts are done. We figured out the sodium and we figured out the anion. Now let's go over to glucose. So let's figure out how to get glucose as units from what the lab gives us, which I'll tell you in just a second, into something more usable. So how do we actually get over to something usable? Let me actually, switch over. There we go. Make some space on our canvas. So let's say we have our glucose here. And the lab calls us and says, hey, we just got your lab result, it was 90 milligrams per deciliter. It's actually a very, very common lab value or common range for a glucose lab value. One thing we have to do right away is figure out how to get from milligrams to moles. And you know that this is what glucose looks like. This is the formula for it. So to get the overall weight, the atomic weight, you could say, well, let's take 6, because that's how many carbons we have, times the weight of carbon, which is 12, plus 12, because that's what we have here, times the weight of hydrogen, which is 1, plus 6, times the weight of oxygen. And that's going to equal-- this is 72, this is 12, and this is 96, and add them all up together, and we get-- 180. So we have 180 atomic mass units per glucose molecule. Which means, if you think back, which means that one mole of glucose equals 180 grams. And since these are way, way bigger than, I mean this is grams, and we're talking about milligrams over here, so I'm going to just switch it down by 1,000. So one millimole of glucose equals 180 milligrams. All I did was divide by 1,000. So now I can take this unit and actually use our conversions. I could say, well, let's multiply that by 100 and-- let's say, one millimole rather, one millimole per 180 milligrams, that'll cancel the milligrams out. And I also have to get from deciliters to liters, right? So I've got to go 10 deciliters equals 1 liter. And that'll cancel my deciliters out. So I'm left with-- and this 10 will get rid of that 0-- so I'm left with 90 divided by 18, which is 5 millimoles per liter. And, just as above, I know that the glucose will behave as one particle in water, in solution. So it's going to be 5 osmoles, or milliosmoles, actually. 5 milliosmoles per liter. And that's the right units, right? So I figured out another part of my formula. And I'll show you the actual formula at the end of this, but I wanted to work through it piece by piece. So we've done glucose now and we're ready for our last bit, so let's do our last one, which is going to be urea. Specifically, the lab is not going to call us about urea, it's going to call us about blood urea nitrogen. And actually, it matters what this means. So what that exactly means is that they're measuring the nitrogen component of urea. And so they'll call you and say, well, we measured it and the value came to 14 milligrams per deciliter. Something like that, so let's say that's the amount of urea we find in our little tube of plasma. How do we convert that to moles per liter like we did before? Well, again, it'll be helpful if I draw out a molecule of urea. So we have something like this. A couple nitrogens. And this is what urea looks like. It's a pretty small molecule. A couple nitrogens, carbon, and oxygen. And these nitrogens have an atomic mass unit of 14 apiece. So that's 14. And this is 14 over here, as well. So what the lab actually measures is just this part. It's just measuring the two nitrogens. It's not measuring the weight of the entire molecule. So all it's going to give you is the weight of the nitrogens that are in the molecule. So what that means is that we say, OK, well, that tells us that one molecule of urea is going to be 28 atomic mass units of-- I'm going to put it in quotes-- urea nitrogen. Because that's the part of urea that we're measuring and that means that one mole of urea is going to be 28 grams of urea nitrogen. And because, again, this is much, much more than what we actually have, let me divide by 1,000. So one millimole equals 28 milligrams of urea nitrogen. So that's how we figure out the conversion. And I do the exact same thing as above. I say, OK, well, let's times-- let's say, I want to get rid of the milligrams, right? So 1 millimole divided by 28 milligrams, and that'll get rid of my milligrams. And I'll take, let's say, 10 deciliters over 1 liter and that'll help me get rid of my deciliters. And so then I'm left with 14 over 28, which is 0.5. And then times 10, so that's 5. 5 millimoles per liter. And as I've done a couple times now and we know that it's the urea nitrogen or the urea is going to act and behave like one molecule or one particle when it's in water, it's not going to split up or anything like that, so that means that it's going to basically be 5 milliosmoles per liter. And so I figured out the last part of my equation. So going back to the top, we have sodium. And this turned out to be a total of 140 milliosmoles per liter. And then for our anion, we had 140 milliosmoles per liter. And then for our glucose, we had 5 milliosmoles per liter. And for our urea, we had 5 milliosmoles per liter. So adding it all up, our total comes to 140 times 2 plus 10. So we get, if I do my math correctly, I think that's 290 milliosmoles per liter. That's the answer to our osmolarity. Our total osmolarity in the plasma is 290 milliosmoles per liter. Now that was kind of the long way of doing it. Let me give you a very, very quick and dirty way of doing it. Let me actually make some space up here. You could do the exact same problem, you could say, well, this osmolarity equals, you could say, sodium times 2, plus glucose, divided by 18, plus BUN divided by 2.8. And that takes all of those conversions and simplifies it down. So if you ever get your sodium value, your glucose value, and your BUN, and you want to quickly calculate your osmolarity, now you know the fast way to do it.