Dalton's Law Calculator – Partial Pressures of Gas Mixtures
Dalton's law of partial pressures says that in a mixture of gases that don't react, each gas pushes on the walls as if the others weren't there, and the total pressure is the sum of those individual pushes: P_total = p₁ + p₂ + … + pₙ. This calculator handles the four jobs the law is used for most often: converting between composition and partial pressures, mixing gases from connected flasks, correcting a gas collected over water, and working out the oxygen pressure a diver or climber actually breathes.
Why each gas acts on its own
John Dalton described partial pressures in the early 1800s while studying moist air and the atmosphere. In an ideal gas the molecules don't attract or repel each other, so each gas obeys the ideal gas law on its own: p_i = n_i R T / V. Add the equations for every gas and you get P_total = n_total R T / V. Divide one by the other and the volume and temperature cancel, which gives the form most people use: p_i = x_i × P_total, where x_i = n_i / n_total is the mole fraction.
The key idea is that pressure counts molecules, not grams. Mix 2 g of hydrogen with 8 g of oxygen and 14 g of nitrogen and the hydrogen is only 8 % of the mass, yet it supplies 57 % of the pressure, because it is 57 % of the molecules.
Mole fraction, volume fraction and pressure fraction
For ideal gases, equal volumes at the same temperature and pressure contain equal numbers of molecules (see the Avogadro's Law Calculator). So volume percent equals mole percent, and both equal the share of the pressure. Dry air is 78.08 % nitrogen and 20.95 % oxygen by volume, so at 1 atm the oxygen partial pressure is 0.2095 atm, or 159.2 mmHg. To convert mass percent or liquid amounts into mole fractions first, use the Mole Fraction Calculator.
Collecting a gas over water
When oxygen or hydrogen is bubbled into an inverted tube over water, it becomes saturated with water vapour. The tube then holds a mixture, so P_inside = P_gas + P_H₂O. At room temperature the vapour is only 2–3 % of the total, but ignoring it overstates the moles of gas by the same 2–3 %. The vapour pressure rises quickly as the water warms: 23.8 mmHg at 25 °C, 55.4 mmHg at 40 °C and 760 mmHg near 100 °C, where the water boils. This tool calculates it with the IAPWS-IF97 equation, the international standard for steam tables. Many lab manuals skip one more correction: if the water inside the tube stands higher than outside, the gas pressure is lower than the barometric pressure by ρ g h.
Connecting flasks
Open a stopcock between two flasks and each gas spreads through the whole volume. Each gas follows Boyle's law on its own, so its pressure falls by the ratio of the volumes. Dalton's law then adds the results. Helium at 2 atm in 1 L joined to neon at 1.2 atm in 3 L gives 0.5 + 0.9 = 1.4 atm.
Diving: oxygen pressure rises with depth
Underwater the gas mix stays the same, but the ambient pressure rises by about 1 bar for every 10 m of seawater, and every partial pressure rises with it. Oxygen becomes toxic at high partial pressure, so divers work to a ppO₂ limit, commonly taught as 1.4 bar for the working part of a dive and 1.6 bar as a maximum. The depth where a mix reaches the limit is its maximum operating depth (MOD). Nitrox has more oxygen than air, so it reaches the limit sooner. Training tables use the round "10 m = 1 bar" rule, which is why their MODs differ from the physics by about half a metre.
Altitude: same 20.95 %, less oxygen
Climb a mountain and the air is still 20.95 % oxygen, but the total pressure falls, so the oxygen pressure falls too. Your airways also saturate the air with water vapour at 37 °C, which takes 6.3 kPa (47 mmHg) off the top before the oxygen gets its share. On the summit of Everest the standard atmosphere gives about 31 kPa, and the inspired oxygen pressure is only about a quarter of its sea-level value.
Where Dalton's law stops working
The law assumes ideal gases. Above about 50 bar real molecules start to interact and the partial pressures become estimates. It also fails for gases that react with each other, such as nitric oxide and oxygen, and for components that condense, like water vapour cooled below its dew point. The next step after partial pressure is Henry's law, which says how much of a gas dissolves in a liquid: the amount is proportional to the gas's partial pressure above it. For the vapour pressure of a solution rather than pure water, use the Raoult's Law Calculator.