HENRY LAB · C = kH · Pgas · offline · ES5

0 · Hook — one law, three hisses

Pressure writes gas into liquid. Release it wrong and the gas writes back.

One equation predicts a diver's pain, a climber's fog, and a soda's hiss.

By the end you will predict dissolved gas from pressure, then break all three systems on purpose.

Partial pressure means the share of total pressure owned by one gas.

C (mol/L) = kH (mol/L/atm) × Pgas (atm) · at fixed T · Pgas is partial, not total sea-level plasma-like N2 (water estimate) ≈ 0.54 mmol/L · 30 m depth ≈ 2.15 mmol/L · soda at 3 atm ≈ 102 mmol/L CO2

→ Do this: drag the pressure slider in panel 1 first, then come back and read.

Bottom line: dissolved gas follows the partial pressure of that same gas.

1 · Orientation — where Henry sits

Dalton sets the share of each gas. Henry converts that share into dissolved concentration.

Temperature edits the exchange rate kH. Bubbles and blood decide what the number costs.

Some courses call this Henry's theorem; working divers and bottlers say Henry's law.

LawJobInput → output
Daltonsplits total pressuretotal P × fraction → partial P
Henrydissolves each gaspartial P × kH → concentration
Temperature ruleshifts kHwarm liquid → smaller kH → less gas

→ Do this: say aloud “Dalton splits, Henry dissolves” before touching any slider.

Bottom line: Henry never sees total pressure, only each gas and its own kH.

2 · Instruments — eight benches you can break

Every bench runs the same core math. Extremes are safe here and fatal outside.

Teaching model with illustrative tissue and altitude numbers. Not dive, flight, or medical guidance.

Bench 1 · Dissolve any gas

Bench 2 · Diver loader (N2)

Depth pressure uses 10 m per atm (real seawater 10.3).

Bench 3 · Bubble tank — spring the bends

Same 30 m / 20 min dive, two ascents. Fast ascent seeds bubbles; slow ascent lets gas leave quietly.

press a button to run the tank

Bench 4 · Altitude lung

Bench 5 · Soda press

One volume means one litre of CO2 gas (standard conditions) per litre of drink.

sealed

Bench 6 · Warm bath — kH falls

Bench 7 · Trimix — why helium?

Bench 8 · kH direction check

Big kH in C = kH·P means very soluble. Big KH in p = KH·x means barely soluble.

CO2 kH 0.034 (large, soluble) · He kH 0.00038 (small, shy) · N2 KH ~76 kbar (large, shy)

→ Do this: push every slider to both ends and watch which readouts scale in a straight line.

Bottom line: straight-line scaling with partial pressure is the signature you are hunting.

3 · The named trap — the total-pressure slip

Learners multiply kH by total pressure and credit nitrogen with oxygen's pressure.

Henry bills each gas only for its own partial pressure: pN2 = 0.79 × Ptotal in air.

→ Do this: pick “wrong”, note the 27% overcharge, then switch back to “right”.

Bottom line: total pressure is shared; dissolved N2 only answers to the N2 share.

4 · Their codebase — this repo is empty

Checked folder niya: no files, no manifest, no pinned versions to verify against.

So nothing here names your files. The mapping below is where this math would live once you add code.

If you add…Put Henry logic in…Pure function
dive plannerdive/henry.jsdissolved(N2, 0.79 × Pdepth)
altitude aidphysio/oxygen.jsdissolved(O2, frac × Palt)
carbonation toolsoda/carb.jsvolumes(CO2, P, T)

Keep simulation pure and DOM in one boot routine, exactly as this page does.

→ Do this: copy one pure function from this page into your first repo file.

Bottom line: an empty repo means the lesson stays standalone until you pin real code.

5 · Real world — THE WHY (load-bearing)

Three plants run on this law every day. Each has a knob, a cost, and a slider below.

WHY-1 · Diving — nitrogen is a loan shark

At 30 m the pressure is ~4 atm, so blood N2 nears 4× the surface value. A fast ascent leaves no time to repay through the lungs, so N2 becomes bubbles in joints and blood.

The operator moves ascent speed and the safety stop. Dive computers penalise fast ascents with longer stops.

WHY-2 · High altitude — thin air, thin blood

At 5,500 m total pressure halves, so inspired pO2 halves, alveolar follows, and hemoglobin saturation slides down its steep curve. Thinking slows before breathing feels hard.

The operator moves inspired O2: supplemental flow or cabin pressurisation restores pO2 without descending.

Doctors call the shortage hypoxia; many textbooks label this altitude case anoxia.

WHY-3 · Bottling plant — cold and pressure are money

A plant chills syrup to ~4 °C and fills under 3–4 atm CO2, locking in ~3–4 volumes of fizz. A warm fill needs far more pressure for the same fizz and bursts out on opening.

The operator moves fill pressure and chill temperature. Cold saves gas and keeps caps on.

Roll-call — five more rooms with the same knob

Hyperbaric chamber
2–3 atm pure O2 pushes dissolved O2 ~10× to rescue starved tissue.
Spacewalks
Astronauts pre-breathe pure O2 to wash N2 out before low-pressure suits.
Fish farms
Warm noon water holds less O2; aerators restore the partial-pressure drive.
Anaesthesia
Nitrous dose tracks its partial pressure into blood by the same product.
Carbon capture
Pressure-swing absorbers load CO2 at high P and dump it at low P.

Every case is one pattern: pressure sets the dissolved dose, and a careless release turns dose into bubbles or deficit.

→ Do this: set WHY-2 to 5,500 m on air, then raise O2 until the status flips to safe.

Bottom line: control partial pressure and you control what the liquid must carry.

6 · Quiz — can it fail you in every mode?

Eight questions, two per family: law, bends, anoxia, soda. Options shuffle each run.

not attempted

→ Do this: answer all eight, then read the feedback on options you did not pick.

Bottom line: a pass means no family embarrasses you.

7 · Recap + glossary

1 · Formula
C = kH × Pgas at fixed T.
2 · Partial
Use the gas share, never the total.
3 · Bends
Depth loads N2; fast ascent makes bubbles.
4 · Anoxia
Low pO2 starves saturation; add O2 or descend.
5 · Soda
Chill plus pressure stores volumes; opening dumps them.
6 · Heat
Warm liquid holds less gas for every species.
7 · Constants
Large kH loves liquid; large KH hates it.
TermMeaning
Henry's lawdissolved concentration equals kH times that gas partial pressure at fixed temperature
partial pressuretotal pressure times the fractional share of one gas
kHHenry solubility constant in mol per litre per atm for C = kH × P
KHalternate volatility constant in p = KH × x; large means insoluble
solubilityequilibrium dissolved amount at given pressure and temperature
bendsdecompression sickness from N2 bubbles after fast ascent
anoxiatissues starved of O2; here from low inspired pO2 at altitude
nucleationseed site where dissolved gas gathers into a bubble
volumes CO2litres of CO2 gas at standard conditions per litre of drink
saturationfraction of hemoglobin binding sites carrying O2
ascent ratevertical speed upward; fast values raise bubble risk
tissue loadingmodel N2 accumulated in a slow body compartment

→ Do this: cover the table and define each term from the cards alone.

Bottom line: say it with partial pressure or do not say it.