Dalton’s law states that the total pressure of a gas mixture equals the sum of the pressures each gas would exert on its own. If you have a container with three different gases, each one pushes on the walls independently, and the total pressure is simply all those individual pushes added together. The formula is straightforward: P(total) = P₁ + P₂ + P₃ + … for however many gases are in the mix. Each of those individual values is called a partial pressure, meaning the pressure that gas would exert if it occupied the same volume at the same temperature all by itself.
How Partial Pressure Works
A gas exerts pressure because its molecules are constantly bouncing off surfaces. In a mixture, each type of molecule bounces around independently of the others. Nitrogen molecules don’t “know” oxygen molecules are there. They collide with the container walls at the same rate regardless. This independence is the key insight behind Dalton’s law: each gas contributes to the total pressure in proportion to how much of it is present, and you can calculate each contribution separately.
To find a gas’s partial pressure, you multiply the total pressure by that gas’s fraction of the mixture. Earth’s atmosphere at sea level has a total pressure of about 760 mmHg. Dry air is roughly 78% nitrogen, 21% oxygen, 0.93% argon, and 0.03% carbon dioxide. So nitrogen’s partial pressure is about 593 mmHg (760 × 0.78), and oxygen’s is about 160 mmHg (760 × 0.21). Those partial pressures, along with the small contributions from argon, carbon dioxide, and trace gases, add up to the full 760 mmHg you’d read on a barometer.
Why It Matters for Breathing
Dalton’s law is the reason altitude makes you breathless. The percentage of oxygen in the air stays at 21% whether you’re at the beach or on a mountaintop. What changes is the total atmospheric pressure, and that drags down oxygen’s partial pressure with it. At sea level, inspired oxygen has a partial pressure of about 160 mmHg. On the summit of Mount Everest, where atmospheric pressure drops to roughly 250 mmHg, the partial pressure of inspired oxygen falls to around 43 mmHg. That’s barely a quarter of what your lungs are used to, which is why climbers at extreme altitude experience blood oxygen saturations as low as 55%, compared to the normal 95% or above.
Inside your lungs, the math gets one more adjustment. The air you breathe in picks up water vapor as it travels through your airways. At body temperature, water vapor exerts a pressure of 47 mmHg. Your body subtracts that from the available atmospheric pressure before oxygen gets its share. So the partial pressure of oxygen in the tiny air sacs of your lungs (the alveoli) works out to about 100 mmHg at sea level, not 160. Carbon dioxide, meanwhile, has an alveolar partial pressure of roughly 40 mmHg, generated almost entirely by your own metabolism rather than from inhaled air.
These partial pressure differences are what drive gas exchange. Oxygen moves from the alveoli (100 mmHg) into the blood, where its partial pressure is lower. Carbon dioxide moves the other direction, from the blood (where it’s around 45 mmHg) into the alveoli (40 mmHg) and then out with each exhale. Without the pressure gradients Dalton’s law describes, gases would have no reason to cross from air into blood or back again.
Applications in Scuba Diving
Divers experience Dalton’s law in a potentially dangerous way. As you descend underwater, the total pressure increases by about one atmosphere for every 10 meters of depth. The percentages of gases in your tank stay the same, but the partial pressure of each gas climbs. Breathing regular air at 30 meters means nitrogen’s partial pressure roughly quadruples compared to the surface, which is why nitrogen narcosis (a drunk, disoriented feeling) becomes a risk at depth.
Oxygen toxicity follows the same principle. At the surface, oxygen’s partial pressure of about 0.21 atmospheres is perfectly safe. But at depth, or when breathing oxygen-enriched mixtures, the partial pressure can climb past 1.4 atmospheres. Above that threshold, the central nervous system can react with symptoms ranging from nausea and tunnel vision to seizures and loss of consciousness. Underwater, a seizure is life-threatening. Dive planning relies heavily on Dalton’s law to calculate exactly how deep a diver can go on a given gas mixture before oxygen’s partial pressure crosses into the danger zone.
A Simple Calculation Example
Suppose you have a rigid container holding three gases at a total pressure of 2.0 atmospheres. The mixture is 60% gas A, 30% gas B, and 10% gas C. Dalton’s law tells you the partial pressures are:
- Gas A: 2.0 × 0.60 = 1.2 atm
- Gas B: 2.0 × 0.30 = 0.6 atm
- Gas C: 2.0 × 0.10 = 0.2 atm
Add them up: 1.2 + 0.6 + 0.2 = 2.0 atm. The partial pressures always sum to the total. This works whether you’re solving a chemistry problem, calibrating an anesthesia machine, or planning a technical dive.
When the Law Breaks Down
Dalton’s law assumes gases behave “ideally,” meaning the molecules don’t attract or repel each other and don’t take up meaningful space in the container. For most everyday conditions, this assumption holds well. Air at room temperature and normal pressure follows Dalton’s law almost perfectly.
The law becomes less accurate at very high pressures and very low temperatures. Under those conditions, gas molecules are squeezed close enough together that attractive forces between them start to matter. These forces slightly reduce the pressure a gas exerts compared to what the ideal calculation predicts. Push the conditions far enough, and the gas will condense into a liquid, at which point it’s no longer a gas at all and the law no longer applies. For practical purposes in chemistry, biology, and diving, Dalton’s law is reliable across the range of pressures and temperatures you’re likely to encounter.