Law of Partial Pressure - Online Tutor, Practice Problems & Exam Prep

Respiration involves the movement of oxygen and carbon dioxide in the blood, driven by pressure gradients. Dalton's law states that the total pressure equals the sum of individual partial pressures, while Henry's law indicates that gas solubility in a liquid is proportional to its partial pressure. For example, at sea level, the partial pressure of oxygen is approximately 160 mmHg, while it decreases at higher altitudes. Understanding these principles is crucial for grasping how gases diffuse and dissolve in the bloodstream, impacting physiological processes like oxygen delivery and carbon dioxide removal.

Partial Pressure

Alright, folks. We now want to talk about respiration, the movement of oxygen and carbon dioxide in and out of the blood. But before we really get into it, we need to introduce another physics concept, and that is partial pressure. Now again, don't worry. We don't need to get into any advanced calculations here. We just really need to understand how this works conceptually. That's going to be because the movement of gases, and the gases we really care about here are oxygen and carbon dioxide, depends on pressure gradients. Right? That's how gases move in and out of your lungs during ventilation. And for respiration, that's how these gases are going to move in and out of the blood. Now remember that molecules are always going to move down a gradient sort of on their own, and that is a passive process. Now I say that it's a passive process. That's important because we don't need to use cellular energy to get these molecules to cross the membranes in and out of the blood. They do it on their own because of these pressure gradients. They're just going to naturally move down their pressure gradients. So as long as the pressure gradients are all aligned properly, these molecules will move in and out of the blood basically on their own. And when we're talking about this, we want to remember that for diffusion of gas molecules, we are going to care about partial pressure. We are always talking about pressure, not concentration. Now I know for me, that's a little not immediately intuitive because when I think of diffusion, I think of things moving from a high concentration and spreading out on their own until they're in sort of an equally low concentration everywhere. But when we are talking about gas molecules, we don't want to talk about concentration. We want to talk about partial pressure. Alright. So what is partial pressure? Well, Dalton's law of partial pressure, and that Dalton's law, that is a vocab word that you may need to know. Dalton's law of partial pressure says that in a mixture of gases, the total pressure is going to equal the sum of the individual pressures. So if we have a gas that's a mixture like the air around us that's made up of many different types of gas, well, the total pressure in that gas is going to be equal to the sum of gas a plus gas b plus gas c, etcetera. All those pressures added together will equal the total. Alright. Seems pretty straightforward, but let's see what we mean by actually looking at atmospheric pressure. So atmospheric pressure is 760 millimeters of mercury, and we have this table here that we can fill in. And we see on the left, we have the 4 major gases that make up the air around us, nitrogen, oxygen, argon, and carbon dioxide. And it shows here what their concentration is in the air. But, again, for the movement of these molecules, what we really care about is their partial pressure. So to figure this out, well, if 760 millimeters of mercury is the total pressure and about 78% of the gas is nitrogen. Well, to figure out the partial pressure of nitrogen, it's pretty straightforward. We're just going to take 78% of 760. So I'm going to do the math here. We do 0.7808×760 millimeters of mercury, and that gives us 593.4 millimeters of mercury is the partial pressure of atmospheric air due to nitrogen. Alright. Another way to think of that is that if you had a chamber that had atmospheric air in it and it was at 760 millimeters of mercury. If we took away all the other molecules, we just got rid of those molecules, but we kept the same number of molecules of nitrogen, what would the pressure be in that chamber? Well, if it was just the nitrogen in the air and we got rid of everything else, the pressure would be 593.4 millimeters of mercury. Alright. We can keep going down the list here. Next, we have oxygen. That's the next most common gas. You can see here it's about 21% of the air around us. Well, we can do this simple math here. So 21% of 760. So we do 0.2095×760, and that gives me 159.2 millimeters of mercury, is the partial pressure of oxygen in the atmospheric air around us. So again, if you just had the same number of molecules of oxygen in that chamber and got rid of everything else, what would the pressure be? It could be 159.2 millimeters of mercury. Alright. We can keep going. Argon. Argon. We don't really talk about that much. It is about 1% of the air around us, but it doesn't react physiologically. So we generally don't care about it in physiology, but we can do the simple math. So 0.93% of 760 is 0.0093×760, and that gives me 7.1 millimeters of mercury. Carbon dioxide, an incredibly important gas, but you can see it's actually pretty rare in the air around us. It's 0.0004×760 is going to give us this, and that comes out to, with a little rounding here, 0.3 millimeters of mercury is the partial pressure of carbon dioxide. Alright. Now Dalton's law of partial pressure says, now that I figured all those out, if I add them up, what should it equal? Well, I can take the sum, and I'll let you check my math here. It does work. I add all those up. It should equal 760 millimeters of mercury is the total pressure. But again, I can break it into those individual pressures. And why is that important? When we're talking about the diffusion of these molecules, I care about this column. I do not care about this column. I care about the partial pressures. Alright. We're going to see an example where that really makes itself clear why you care about partial pressures coming up. Check it out. I'll see you there.

Law of Partial Pressure Example 1

For this example, it says the following gas mixtures are contained in 2 chambers separated by a permeable membrane. For each gas listed, draw an arrow in the direction you would expect the molecules to move by diffusion. Alright. So for each gas, we have a mixture of nitrogen, hydrogen, helium, and oxygen in different concentrations. And for gas a and gas b, it tells us the concentration of each gas, and it tells us the partial pressure of each gas. Alright. So to figure this out, what are we gonna use? Well, I'm going to go right ahead right away and I'm going to sort of put red through this concentration because when we're talking about the diffusion of gases, we said we do not care about concentration. We care about partial pressure. Right? So these numbers here are all we care about. So let's just go down the line.

Nitrogen here, partial pressure of 300 millimeters of mercury in gas a, partial pressure of 400 millimeters in gas b. In which way is nitrogen going to move? Well, it's going to move down its pressure gradient. So that means it's going to move from the right to the left. Alright. Now quick look, let's just check out these concentrations. The concentration is actually greater in gas a than in gas b. So it's actually moving against its concentration gradient, but we don't care about that. We care about the partial pressures, so we know it's moving from the right to the left. Alright.

Hydrogen, well, we have a 100 millimeters of mercury, partial pressure in gas a, and 100 millimeters of mercury is the partial pressure in gas b. So which way is it going to move? Well, the partial pressure is going to be equal. So there is no net movement of hydrogen in this case, so I'm not going to draw an arrow. We can check these concentration gradients again though. Well, we can see if we went by concentration gradient, you might think that it's going to move to the right down its concentration gradient, but we don't care about concentration. We care about partial pressure.

Next up, helium. Alright. Helium in gas a has a partial pressure of 75 millimeters of mercury. In gas b, it has a partial pressure of 50 millimeters mercury. Which way is it going to go? It's going to move down its partial pressure gradient. So it's going to move to the right. Alright. In this case, that's the way that you might think that it would go by the concentration gradient, but again we don't care about the concentration gradient, so who cares. Alright.

Finally, we have oxygen. Oxygen partial pressure in gas a is 25 millimeters of mercury. In gas b, it's 450 millimeters of mercury. So which way is oxygen going to move? It's going to move down its pressure gradient. It's going to move towards the left. And again, I don't care about the concentration gradient. I'm not even going to look at it.

Finally, let's just look at the total here. So total movement, net movement of molecules across this membrane, well, all we care about is the pressure. So the total pressure here in gas a is 500 millimeters of mercury. Total pressure in gas b, way bigger, 1000 millimeters of mercury. So the net movement of molecules is going to be from the right towards the left in that direction. Alright. The big takeaway here though, right, do not worry about the concentrations when you're talking about the movement of gases. You worry about the partial pressures.

Gas A and Gas B are both mixtures separated by a permeable membrane. Gas A contains 40% nitrogen at a partial pressure of 300 mm Hg. Gas B contains 80% nitrogen at partial pressure of 200 mm Hg. Given this information, in which direction do you expect to see a net movement of nitrogen and why?

• A. From Gas A to Gas B because the total pressure of Gas A is greater than Gas B.
• B. From Gas B to Gas A because Gas B has a higher concentration of nitrogen than Gas A.
• C. From Gas B to Gas A because 80% of 200 mm Hg > 40% of 300 mm Hg.
• D. From Gas A to Gas B because the partial pressure of nitrogen in Gas A is greater than in Gas B.

Pressures: Dalton’s and Henry’s Laws

We previously looked at Dalton's law of partial pressure. Well, now we need to add another law to the mix here. We're going to be looking at Dalton's law and Henry's law, and that's because these two laws together explain the movement of molecules by respiration, and that's what we really care about. We're really interested in how these oxygen molecules and carbon dioxide molecules move in and out of the blood. Alright. So let's look at these 2, Dalton's law. We're actually going to restate it here just slightly to be a little closer to how we've been using it. So we're going to say that Dalton's law says that the partial pressure of a gas is equal to its percent composition multiplied by the total pressure. Remember, that's how we calculated those partial pressures of the gases that make up atmospheric air. We looked at their percent composition, we multiplied it by total atmospheric pressure, and that gave us the individual partial pressures. Alright. Well, now to this, we're going to add Henry's law. And Henry's law says that the amount of a gas that dissolves in a liquid is proportional to the partial pressure. Alright. Well, hopefully for respiration, you see why that's important. We're interested in getting these gas molecules, oxygen and carbon dioxide, in and out of the blood. We're worried about how do they dissolve into the blood. Henry's law tells us that to know how that works, we have to understand the partial pressure. Now, two quick notes about Henry's law here: two other things play a factor in how easily things go into a liquid. First off is just, well, let's say here the specific values depend on the solubility. Some gas molecules are just more soluble than others are, and also temperature. Now while temperature is important for Henry's law, it's actually not important physiologically, because we have homeostasis and our body's temperatures are constant. So at a constant temperature, we don't need to worry about that variable for figuring out how all this works. Okay. So let's look at these two laws and see how they work together. So first off, Dalton's law. Well, if we're at sea level, the total pressure is going to be 760 millimeters of mercury. Now to represent that, we have a chamber here, and we have gas molecules represented by sort of balls in that chamber, and we have oxygen molecules represented by those red balls in the chamber there. And oxygen is about 21% of the atmospheric air. So to figure out the partial pressure of oxygen, we take that 21% and multiply it by 760 millimeters mercury, that atmospheric air. So it comes out to 160 millimeters of mercury. Now previously when we looked at that, we had a number that was a little bit more specific. For our purposes here, that's that's close enough. Alright. So 160 millimeters of mercury is the partial pressure of oxygen at sea level, but what if you're not at sea level? What if you're on a mountain in Colorado, for example? Alright. Well, on a mountain in Colorado, the atmospheric pressure is closer to 500 millimeters of mercury. So here to represent that, we have this same chamber, but we have proportionally fewer molecules in that chamber because the pressure is less. Now, importantly, though, we have the same percentage of those molecules are oxygen. The percent composition on that mountain is still, I'm sorry, is still 21% oxygen. So to figure out the partial pressure of oxygen, we take that 21%. We multiply it now by 500 millimeters of mercury. So it gives us, in this case, a 105 millimeters of mercury. Right? So the percent composition in both cases is the same, but the partial pressures are very different. Right. Well, let's see how this works with Henry's law. So we're going to take the same chamber, but now we're going to add some water on the bottom of it. So we have the same number of molecules in there. It's still at 760 millimeters of mercury. It's still 21% oxygen, and that partial pressure of oxygen is still 160 millimeters of mercury. Alright. We have one more line there on the bottom. We're going to come back to that in just a second. But we do the same thing for that mountain in Colorado. Well, now we have fewer total molecules up in that chamber, but it's still over this water. Well, the part the I'm sorry. The percent composition of oxygen, that's still 21%. The, partial pressure of oxygen is still 105 millimeters of mercury. But if you look at these, what does Henry's law say about which one of these chambers is going to have more oxygen dissolved in the water? Well, Henry's law says that how much of that oxygen actually dissolves in the water is proportional to that partial pressure. So at sea level, more oxygen dissolves. Up on that mountain in Colorado, well, the partial pressure is less, less dissolves. Again, even though the percent composition is the same, we care about the partial pressures. And maybe now that makes sense, even though it's still 21% of the air is oxygen on that mountain in Colorado. Well, now you know why you might feel a little lightheaded when you're at that altitude. Alright. Dalton's law and Henry's law. I understand remembering the names of laws can be a little confusing sometimes. We have a quick memory tool here for you. Though the way I say it, I say Dalton divides the pressure, Henry hydrates it. Remember, Dalton's law says that we can take that total pressure and divide it up into those individual partial pressures. Henry hydrates it. Henry's law tells us that knowing those partial pressures tells us how much of those gases go into solution. Alright. We'll practice this more like always. I'll see you there.

Law of Partial Pressure Example 2

In this example, it tells us that when climbers summit Mount Everest, they often use an oxygen mask to increase the amount of O₂ they inhale with each breath. Then it says the table below gives the concentration of oxygen and atmospheric pressure under three conditions. Use the table to calculate the partial pressure of oxygen under each condition, then answer the questions below. Alright. So we have this table here, and our columns are for sea level, Everest with supplemental oxygen, and Everest without supplemental oxygen.

And then our rows here are the concentration of oxygen, the total atmospheric pressure, and then what we need to calculate, the partial pressure of oxygen. Alright. So let's just do these one by one. We're going to go through first here for sea level. So at sea level, the concentration of oxygen is 20.9%, and the total atmospheric pressure is that familiar 760 millimeters of mercury.

Alright. So how do we figure out the partial pressure from those two numbers? Well, we multiply them. Alright. So I'm going to take 0.209 and multiply that by 760 millimeters of mercury. I don't have room in this box for my units, but we should write them in if we can. And that is going to give me right about 159 millimeters of mercury. That is my partial pressure of oxygen at sea level. Alright. Let's do the same thing for Everest with supplemental oxygen.

So it says here the concentration of oxygen that someone's breathing into that mask is going to be as high as 50%. I'll just note that's kind of an unrealistically high percentage at the top of Mount Everest even with an oxygen mask, but for this problem, we're going to go with it. So, you know, they're breathing in 50% oxygen, but the total atmospheric pressure is only 235 millimeters of mercury. Alright? A lot less.

So what's our partial pressure of oxygen in that scenario? Well, what we're going to do is we're going to take 50%, so 0.5, and multiply that by that 235, and that gives us 117.5 millimeters of mercury of oxygen that those people would be breathing in with that supplemental oxygen. Alright. Next, Everest without supplemental oxygen. Alright.

So just up there on Everest with no oxygen with you. Well, the concentration of oxygen, it's the same at sea level, the same percentage, 20.9% oxygen up there on top of Everest. But here the total atmospheric pressure is again way lower. We're there at that 235 millimeters of mercury. So how do we figure it out?

Well we multiply them together. 0.209 times 235. That's going to give me right about 49 millimeters of mercury. Alright. So those are my partial pressures. I have 159, 117.5, and 49 there. So moving on. Next question we have here, it says, using the information from the table, under which two scenarios would you expect the amount of oxygen dissolved in the blood to be most similar? Alright. Well, look at those numbers.

Which one do you think the amount of oxygen dissolved in the blood would be most similar? Well, I can sort of tell just by looking at it, but I'm actually going to do the math out here. So I'm just going to write it down, 159. We have 117.5, and we have 49. And so the difference between these is what I can do.

The difference between these two is 41.5, and the difference between these two is 68.5. Remember, we learned that what dissolves into the blood is dependent on the partial pressure. So we're just looking at here which two partial pressures are the closest. So that means that sea level and Everest with O₂, that's what I would expect the concentration of oxygen dissolved in the blood to be most similar because those partial pressures are closest to each other. Alright.

Final questions here. It says, what law allowed you to calculate the partial pressures? Okay. So in that first part when we're calculating partial pressures, what law was that? Well, that was Dalton's Law of Partial Pressures. Dalton's Law of Partial Pressures, that's what tells us that we can take the concentration of a gas, multiply it by the total pressure, and that will give us the partial pressure for that gas. Alright. Then we have what law allows you to predict how much oxygen would be dissolved in the blood. Well, what's the name of that law? That is Henry's Law.

Henry's Law lets us take those partial pressures, and it tells us that how much will dissolve is going to be dependent on those partial pressures. And we had a little memory tool to remember these to remember. We said that Dalton divided the pressure and Henry hydrated it. Dalton, you can break up that total pressure into partial pressures. Henry, it tells you how much is going to go into a liquid.

Alright. So that hopefully helps you better understand a little bit how to use these partial pressures. And you also know if you climb Mount Everest, bring that oxygen with you.

Air in the alveoli is approximately 5.2% CO₂. Given that information along with the total air pressure in the alveoli, which law would allow you to calculate the partial pressure of CO₂?

• A. Henry’s Law.   
• B. Dalton’s Law.
• C. Purkinje’s Law.
• D. Boyle’s Law.

How is Henry’s law related to the amount of gas that can be exchanged in the alveoli?

• A. Henry’s law states that the small volume of the alveoli will cause an increase the total pressure, allowing gases to be more easily dissolved by the blood.
• B. Henry’s law allows us to predict the relative amount of a gas that will dissolve in the blood when given its partial pressure.
• C. Henry’s law states that molecules will always move towards an area of lower pressure.
• D. Henry’s law states that, in a mixture, the total pressure can be divided into the partial pressures of each gas; this determines how much of each gas will be absorbed by the blood.

Gas A is 40% oxygen and 10% CO₂. It has a total pressure of 500 mm Hg. Gas A is in contact with a with a liquid containing oxygen at a partial pressure of 100 mmHg and CO₂ at a partial pressure of 25 mm Hg. In which direction will O₂ and CO₂ diffuse in this situation?

• A. Oxygen will dissolve into the liquid, while CO₂ will move from the liquid into the gas.
• B. CO₂ will dissolve into the liquid, while O₂ will move from the liquid into the gas.
• C. Both O₂ and CO₂ will move from the gas into the liquid.
• D. Both O₂ and CO₂ will move from the liquid into the gas.

Here’s what students ask on this topic:

What is Dalton's Law of Partial Pressure and how is it applied in respiration?

Dalton's Law of Partial Pressure states that in a mixture of gases, the total pressure is equal to the sum of the partial pressures of each individual gas. In respiration, this law helps us understand how gases like oxygen (O₂) and carbon dioxide (CO₂) move in and out of the blood. For example, atmospheric pressure at sea level is 760 mmHg, and the partial pressure of oxygen (21% of air) is calculated as 0.21 × 760 mmHg = 160 mmHg. This partial pressure drives the diffusion of oxygen into the blood.

How does Henry's Law relate to the solubility of gases in the blood?

Henry's Law states that the amount of a gas that dissolves in a liquid is proportional to its partial pressure. In the context of respiration, this means that the higher the partial pressure of oxygen (O₂) in the alveoli, the more oxygen will dissolve into the blood. For example, at sea level, the partial pressure of oxygen is about 160 mmHg, leading to more oxygen dissolving in the blood compared to higher altitudes where the partial pressure is lower.

Why is partial pressure more important than concentration in gas diffusion?

In gas diffusion, partial pressure is more important than concentration because gases move according to pressure gradients, not concentration gradients. Partial pressure represents the force exerted by a specific gas in a mixture, driving its diffusion across membranes. For instance, oxygen diffuses from the alveoli (high partial pressure) into the blood (lower partial pressure) due to the pressure gradient, facilitating efficient gas exchange during respiration.

How do Dalton's and Henry's laws explain the effects of high altitude on respiration?

At high altitudes, atmospheric pressure is lower, reducing the partial pressure of oxygen. According to Dalton's Law, if the total pressure drops, the partial pressure of oxygen also drops. Henry's Law then indicates that less oxygen will dissolve in the blood at these lower partial pressures. This explains why people may experience hypoxia or light-headedness at high altitudes, as less oxygen is available for bodily functions.

What is the partial pressure of oxygen at sea level and how is it calculated?

At sea level, the atmospheric pressure is 760 mmHg, and oxygen makes up about 21% of the air. The partial pressure of oxygen (P_O2) is calculated using Dalton's Law: P_O2 = 0.21 × 760 mmHg = 160 mmHg. This partial pressure is crucial for driving the diffusion of oxygen from the alveoli into the blood during respiration.