Dalton’s law in diving: partial pressures of oxygen and nitrogen

Before a nitrox dive, you analyze your cylinder and work out a depth you must not pass: 33 m (111 ft) for EAN32. The mix in the tank stays the same throughout the dive, but the pressure of each gas in it rises with depth, and your body reacts to that pressure.

What is Dalton’s law?

Dalton’s law states that the total pressure of a gas mixture equals the sum of the partial pressures of the gases in it. Each gas behaves as if it were alone, and its partial pressure is its fraction of the mix times the absolute pressure.

Air is about 21% oxygen and 78% nitrogen, plus about 1% other gases, which dive calculations count with nitrogen: 21% and 79%. At the surface, 1 bar (1 ata), the ppO2 of air is 0.21 and its ppN2 0.79, which add up to 1.

Why does partial pressure matter to divers?

Partial pressure matters because your body responds to the partial pressure of a gas, not to its percentage. The percentage in your tank never changes during the dive; the partial pressure rises with every meter.

• Oxygen: at high partial pressures, oxygen can cause a convulsion, sometimes without warning. Underwater, that can mean losing the regulator and drowning. DAN calls a ppO2 of 1.4 or less the “green light” region for open-circuit scuba and says recreational divers should not exceed 1.6.
• Nitrogen: more of it dissolves in your tissues (Henry’s law), and narcosis deepens. DAN ties nitrogen narcosis to a raised partial pressure of nitrogen; on air, most divers notice it around 30 m (100 ft).
• Contaminants: a trace of carbon monoxide that’s harmless at the surface acts more strongly with depth.
• Breath-hold diving: on the way up, the ppO2 in your lungs falls with the pressure, which is why a blackout, especially after hyperventilating, often strikes during the ascent.

Try a question from the app

nitrox and narcosis

A guest says: “On EAN32 I’ll have less nitrogen, so less narcosis, and I can go deeper than on air.” How do you answer?

1. AHe’s right: his equivalent air depth is shallower, so narcosis is too
2. BNitrox cuts nitrogen loading, not narcosis, and its MOD is shallower
3. CHe’s right, provided he stays under a ppO2 of 1.6 at depth
4. DHe’s wrong: nitrox actually increases nitrogen loading

Show the answer

Answer B. Equivalent air depth applies to nitrogen loading. Oxygen is probably narcotic too, so narcosis is planned as for air. And at 1.4, EAN32’s MOD is 33 m (111 ft), shallower than the 40 m (130 ft) recreational limit on air.

What is the partial pressure formula?

The partial pressure formula is partial pressure = fraction × absolute pressure. Rearranged, it answers three questions:

1. Partial pressure = fraction × absolute pressure: what am I breathing here?
2. Fraction = partial pressure ÷ absolute pressure: what’s the richest mix for this depth?
3. Absolute pressure = partial pressure ÷ fraction: what’s the deepest depth for this mix?

Then depth = (absolute pressure − 1) × 10 m, or × 33 ft, in seawater. Use fractions (0.32), not percentages (32). Every gas formula sits on one page in the dive theory formulas cheat sheet.

How do you calculate a nitrox maximum operating depth?

You calculate a nitrox maximum operating depth (MOD) by dividing the ppO2 limit by the oxygen fraction, subtracting 1 and multiplying by 10 m or 33 ft, then rounding down. The usual limits are 1.4 for the dive and 1.6 as a contingency, never a target. Some agencies and operators set lower limits: use the one you trained with.

Try a question from the app

MOD of EAN32

What is the maximum operating depth of EAN32 for a ppO2 of 1.4?

1. A43 m
2. B40 m
3. C34 m
4. D33 m

Show the answer

Answer D. 1.4 ÷ 0.32 = 4.375 bar; (4.375 − 1) × 10 = 33.75 m, rounded down to 33 m. 43 m forgets to subtract the atmosphere; 40 m is the limit at 1.6; 34 m rounds up and crosses 1.4.

Each diver analyzes their own cylinder and marks the mix and MOD on it. The full picture is on oxygen toxicity and nitrox.

What are the common Dalton’s law mistakes?

• Using gauge pressure. At 20 m (66 ft), 0.21 × 2 = 0.42 is wrong; the ppO2 is 0.63.
• Using percentages. 1.4 ÷ 32 = 0.044 means nothing. Use 0.32.
• Forgetting the atmosphere. 4.375 × 10 = 43.75 m (144 ft) is about 10 m (33 ft) too deep. Subtract 1 first.
• Rounding a MOD up. For EAN32, 34 m (112 ft) already crosses 1.4.
• Treating 1.6 as a plan. It’s a contingency limit.

Which dive course covers Dalton’s law?

In Octo, partial pressures first appear in the Advanced Open Water nitrox lesson: ppO2 limits and MOD. The Divemaster level covers Dalton’s law in full: best mix, contaminants and equivalent air depth. Agencies split this material differently, so check your own course. To test yourself, try the Advanced Open Water practice questions, then the Divemaster ones.

Frequently asked questions

Does the percentage of oxygen in my tank change with depth?

No. Air stays about 21% oxygen at every depth, and EAN32 stays 32%. Only the partial pressure rises: the same fraction times a higher absolute pressure. At 30 m (99 ft), the ppO2 of air is 0.21 × 4 = 0.84, four times its surface value.

What ppO2 limit do recreational divers use?

Recreational divers usually keep the ppO2 at or below 1.4 during the dive and treat 1.6 as an absolute maximum, for contingencies only. DAN describes 1.4 or less as the “green light” region for open-circuit scuba and says recreational divers should not go above 1.6. Some agencies and operators set lower limits.

What is the difference between Dalton’s law and Henry’s law?

Dalton’s law tells you how much pressure each gas in your breath exerts. Henry’s law tells you how much of that gas dissolves in your body, in proportion to that partial pressure. You need Dalton first to get the ppN2, then Henry to see what your tissues do with it.

Does nitrox reduce nitrogen narcosis?

Don’t count on it. Nitrox has less nitrogen, so it loads your tissues less, but oxygen is probably narcotic too, and how much is still debated. The prudent approach is to plan narcosis as if you were breathing air, and to respect the MOD of your mix.

Sources

1. LibreTexts Chemistry (UC Davis), Dalton’s Law (Law of Partial Pressures)
2. Nicholas Bird, Back to Basics, DAN Alert Diver (2014)
3. DAN, Oxygen Toxicity
4. NOAA National Ocean Service, How does pressure change with ocean depth?