Partial pressure and mole fraction explained
How partial pressures add to a total, how mole fractions split it back, and worked examples for air, scuba gas, and lab mixtures.
The idea behind Dalton's Law
In a mixture of gases that do not react, each gas behaves as if the others were not there. It spreads through the whole container and exerts its own pressure, called its partial pressure. Dalton's Law says the pressure you actually measure is just the sum of those partial pressures. This holds well for the ideal-gas conditions found in most everyday and classroom settings, where molecules are far apart and interact weakly.
From partial pressures to a total
If you know each gas's partial pressure, adding them gives the total. Suppose a tank holds gases at 2, 3, and 5 in the same unit; the total pressure is 10. To find each gas's mole fraction, divide its partial pressure by that total, which gives 0.2, 0.3, and 0.5. Those fractions describe how the moles of gas are shared out, and they always sum to 1 because every gas is counted once.
From a total back to partial pressures
The relationship also runs the other way. Given a total pressure and the mole fraction of each gas, multiply the total by each fraction to recover its partial pressure. A mixture at a total of 10 with mole fractions 0.2 and 0.8 has partial pressures of 2 and 8. This is the mode to use when a datasheet lists composition as percentages, since a percentage is simply a mole fraction times one hundred.
Where this shows up in practice
Dry air is roughly 78 percent nitrogen, 21 percent oxygen, and 1 percent argon by moles, so at one atmosphere the partial pressures are close to 0.78, 0.21, and 0.01 atm. Divers use the same idea to track the partial pressure of oxygen in a breathing mix, and chemists use it when a gas is collected over water and the water vapor adds its own partial pressure. In each case the total is only meaningful once you know how the components share it.