Dalton's Law Partial Pressure Calculator

This wonderful law was given by John Dalton in 1801. It states that in a mixture of non-reacting gases, the total pressure exerted by the mixture is equal to the sum of the partial pressures of the individual component gases. The partial pressure of a gas is the pressure it would exert if it alone occupied the entire volume of the container at the same temperature. The law works because gas molecules are far apart and behave independently of each other, ignoring intermolecular attractions. PTotal = P1 + P2 + P3 + … + Pn

There are two simple methods. Method 1 (direct): if you know each partial pressure, just add them up. Method 2 (using mole fraction): Pi = xi × PTotal, where xi = ni / nTotal is the mole fraction. Example: a 5 L vessel contains 2 mol N2 and 3 mol O2 at 300 K. PTotal = (nTotalRT)/V = (5×0.0821×300)/5 = 24.6 atm. Then PN2 = (2/5)×24.6 = 9.84 atm and PO2 = (3/5)×24.6 = 14.76 atm. Pi = xi · PTotal where xi = ni/nTotal

Respiration is essentially gas exchange driven by partial-pressure differences. Air at sea level (760 mm Hg) contains roughly 21% oxygen, so PO2 in inhaled air is about 159 mm Hg. In the alveoli, PO2 drops to ~104 mm Hg while PO2 in the venous blood is only ~40 mm Hg — oxygen therefore diffuses from alveoli into blood. Conversely, CO2 at higher partial pressure in blood (46 mm Hg) diffuses into the alveoli (40 mm Hg) and is exhaled. Without Dalton's law, we cannot explain breathing in physiology.

In distillation we separate liquids based on differences in vapour pressure. When a mixture of two volatile liquids boils, the vapour above is itself a mixture of gases. The total vapour pressure equals the sum of the partial vapour pressures of each component (Raoult's law combined with Dalton's law): PTotal = xAP°A + xBP°B. The component with higher vapour pressure (more volatile) has a larger partial pressure in the vapour and therefore distils over first. This is the key principle used to separate alcohol from water or different fractions of crude oil.

Dalton's law assumes that the gases in a mixture do not chemically interact — only physical mixing occurs. If the gases react, the number of moles of each component changes continuously: some are consumed, others are produced, and the total moles of the mixture itself may change. In such a situation, the partial pressures keep changing with time, so we cannot simply add fixed values. For example, in 2 NO + O2 → 2 NO2, the total pressure decreases as the reaction proceeds because 3 mol of gas become 2 mol.

They blend together very neatly. For each component gas in the mixture, the ideal-gas equation gives PiV = niRT, so Pi = niRT/V. Adding these for all components: PTotal = (n1 + n2 + … + nn)RT/V = nTotalRT/V. So Dalton's law is essentially the ideal-gas law applied separately to each gas and then added. This also leads to the concept of mole fraction: Pi/PTotal = ni/nTotal. Pi · V = ni · R · T

Two situations arise. (a) If the partial pressures are given, simply add: PTotal = P1 + P2 + … + Pn. (b) If the moles, volume and temperature are given, use the ideal-gas law on the total: PTotal = (nTotalRT)/V. Always make sure all gases are at the same temperature and volume before applying the law. If a gas is collected over water, remember to subtract the vapour pressure of water (saturated water vapour) to get the dry-gas pressure.

At high altitude (say, on Mount Everest at 8848 m), the total atmospheric pressure falls to about 250 mm Hg compared with 760 mm Hg at sea level. The mole fraction of oxygen is still ~21%, but its partial pressure drops to only about 53 mm Hg. This is too low for efficient diffusion of O2 into the blood, causing breathlessness and altitude sickness. Climbers therefore carry oxygen cylinders, which raise the PO2 in the inhaled air. Dalton's law is indispensable in pulmonary medicine and aviation.