The Sum of the Parts
Formulated by John Dalton in 1801, Dalton's Law of Partial Pressures states that in a mixture of non-reacting gases, the total pressure exerted is equal to the simple sum of the partial pressures of all the individual gases in the mixture.
Imagine a container filled with nitrogen and oxygen. The nitrogen atoms are bouncing around exerting a certain pressure on the walls, completely ignoring the oxygen atoms. The oxygen atoms are doing the same, ignoring the nitrogen. The total pressure you measure on a gauge is simply the combined force of both gases hitting the walls.
Breathable Atmospheres
- SCUBA Diving: This is a matter of life and death for deep-sea divers. Air is roughly 78% nitrogen and 21% oxygen. At sea level ($1 , \text{atm}$), the partial pressure of oxygen ($P_{O2}$) is $0.21 , \text{atm}$. However, at $40 , \text{meters}$ underwater ($5 , \text{atm}$ of total pressure), Dalton's law dictates that the $P_{O2}$ spikes to $1.05 , \text{atm}$. If a diver goes too deep on standard air, the partial pressure of oxygen becomes so high that it becomes acutely toxic and causes lethal seizures. Divers must mix special gases with less oxygen to survive.
- Mount Everest: At the summit of Everest, the air is still exactly 21% oxygen. However, the total atmospheric pressure is only about $0.33 , \text{atm}$. Therefore, the partial pressure of oxygen drops to a suffocating $0.07 , \text{atm}$, which is why almost all climbers require supplemental oxygen tanks to force the partial pressure back up to survivable levels.
- Anesthesia: Anesthesiologists use Dalton's law constantly to precisely balance the partial pressures of oxygen, nitrous oxide, and vaporized anesthetic drugs being delivered to a patient during surgery.
The Formula
Example Calculation
A sealed tank contains a mixture of Helium, Neon, and Argon. A pressure gauge on the helium line reads $20,000 , \text{Pa}$. The neon line reads $50,000 , \text{Pa}$. The argon line reads $30,000 , \text{Pa}$.
- Simply sum the partial pressures: $20,000 + 50,000 + 30,000 = 100,000 , \text{Pa}$.
The total pressure inside the master tank is exactly $100,000 , \text{Pa}$ (roughly $1 , \text{atm}$).