Chapter 1 showed that the pressure on you rises by about 1 bar for every 10 m you go down. But the gas you breathe is not one gas. Air is mostly nitrogen and oxygen, and deeper dives add helium. Dalton’s law says how the pressure is shared between the gases in a mix. That share is what your body responds to.
Dalton’s law in one sentence
In a mix of gases, each gas pushes as if it were there on its own, and those pushes add up to the total pressure.
The push of one gas is called its partial pressure. A mountain climber shows why it matters. At about 5500 m the air is still 21% oxygen, but the air pressure is only about 0.5 bar. So each breath holds about half as much oxygen as at sea level, and the climber gets out of breath. The percentage stayed the same. The partial pressure of oxygen fell.
Working out a partial pressure
A partial pressure is the gas’s share of the mix multiplied by the total pressure. Your body responds to partial pressure, so this is the sum behind every gas limit in diving.
The fraction belongs to the mix and does not change with depth. The absolute pressure does. So every partial pressure rises as you go down.
Think of it like splitting a restaurant bill: each person pays their share, and the shares add up to the total.
- Oxygen
- Nitrogen
- Helium
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Air at the surface
Air is about 21% oxygen and 79% nitrogen. At the surface the total pressure is 1 bar. So the PO2 is 0.21 × 1 = 0.21 bar and the PN2 is 0.79 × 1 = 0.79 bar.
The 2 partial pressures add up to the total of 1 bar. That is Dalton’s law.
Air at 30 m
At 30 m the absolute pressure is 4 bar. The mix has not changed, so the PO2 is 0.21 × 4 = 0.84 bar and the PN2 is 0.79 × 4 = 3.16 bar.
It is the same air as at the surface. But each gas in it now acts on your body 4 times as strongly.
Limits are partial pressures
What a gas does to your body depends on its partial pressure, not its percentage. So the oxygen limits in diving are all partial pressures:
- below 0.16 bar there is too little oxygen. This is hypoxia, and you can pass out. 0.16 is the minimum PO2;
- 1.4 bar is the working PO2, the usual maximum while you swim at the bottom of a dive;
- 1.6 bar is the contingency or deco PO2, the usual maximum at rest during decompression stops: planned pauses on the way up that give your body time to release gas.
Air at 30 m, at 0.84 bar, is well inside these limits.
Trimix at 60 m
At 60 m the absolute pressure is 7 bar. Air there would give a PO2 of 0.21 × 7 = 1.47 bar, over the working PO2.
Trimix is a mix of oxygen, helium and nitrogen. Trimix 18/45 is 18% oxygen and 45% helium. Its PO2 at 60 m is 0.18 × 7 = 1.26 bar, inside the limit. Helium takes the place of most of the nitrogen, so the PN2 falls to 0.37 × 7 = 2.59 bar.
Equivalent narcotic depth
At depth, nitrogen and oxygen make you feel drunk and think less clearly. This is inert gas narcosis. Helium does not cause it. In trimix 18/45 at 60 m, the oxygen and nitrogen add up to 0.55 × 7 = 3.85 bar. Air gives that same total at 28.5 m.
That depth is the mix’s equivalent narcotic depth (END): the depth where air would feel as narcotic as the mix. Divers set a maximum END, so this is a partial pressure limit too.
Every gas limit is a partial pressure
Each limit a diver plans to is a partial pressure. Each has its own chapter later in the book.
- Too much oxygen. A high oxygen partial pressure can cause a seizure without warning. A long exposure can also harm the lungs. Chapter 6 and chapter 7 cover these. The deepest you can take a mix before it reaches its oxygen limit is its maximum operating depth (MOD). For air at a PO2 of 1.4 it is about 56.7 m. For nitrox 32, a mix with 32% oxygen, it is 33.75 m. DiveLogic rounds a MOD down to the whole metre, so 56 m and 33 m. Chapter 4 shows how to work it out.
- Too little oxygen. A mix with little oxygen, such as trimix 10/70, has a PO2 of only 0.10 × 1 = 0.10 bar at the surface. You cannot breathe it there. It is used only below the depth where its PO2 reaches 0.16 bar.
- Narcosis. Narcosis gets stronger as the PN2 rises, and many divers count oxygen too. Divers limit it with a maximum END. Chapter 8 covers it.
Choosing a mix means choosing percentages that keep every one of these partial pressures inside its limit at the depths you plan. Chapter 4 describes the mixes divers use.
Try it
Choose a depth and a mix. The bar shows the absolute pressure split by gas. The gauges show the PO2 against the 0.16 bar floor and the 1.4 and 1.6 bar limits, and the equivalent narcotic depth. Try air at 60 m. Then find a trimix that brings both gauges back inside their limits.
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Where the law comes from
John Dalton (1766-1844) taught mathematics in Manchester and kept a daily weather record for over 50 years. He wanted to know why the gases in the air stay mixed instead of settling into layers by weight. In 1801 he told the Manchester Literary and Philosophical Society his answer: each gas in a mix behaves as if the others were not there. The paper was printed in 1802.
What to remember
- Dalton’s law: each gas in a mix has its own partial pressure, and the partial pressures add up to the total pressure.
- Partial pressure is the gas’s fraction multiplied by the absolute pressure. The fraction (FO2, FN2, FHe) stays fixed; the partial pressure (PO2, PN2, PHe) rises with depth.
- Your body responds to partial pressure. Air at 30 m has 4 times the oxygen and nitrogen partial pressures of air at the surface.
- Every gas limit is a partial pressure: a PO2 of at least 0.16, at most 1.4 working and 1.6 at rest, and a maximum END for narcosis.
Checking a mix at depth
DiveLogic’s mix at depth tool uses Dalton’s law on any mix. Enter the oxygen and helium percentages and a depth. It gives the oxygen partial pressure, the equivalent narcotic depth and the gas density (how hard the gas is to breathe), each against its limit.
Sources
- Dalton J. (1793). Meteorological Observations and Essays. London.
- Dalton J. (1802). Experimental essays on the constitution of mixed gases; on the force of steam or vapour from water and other liquids in different temperatures, both in a Torricellian vacuum and in air; on evaporation; and on the expansion of gases by heat. Memoirs of the Literary and Philosophical Society of Manchester 5(2): 535-602.