Dalton's Law of Partial Pressures

Core Idea

In a gas mixture, each gas exerts its own partial pressure as if it occupied the container alone; total pressure is the sum of all partial pressures. Partial pressure of a gas equals its mole fraction times the total pressure. This principle explains vapor pressure above solutions and gas collection over water.

Explainer

From kinetic molecular theory, you know that gas pressure results from molecules colliding with container walls. In a mixture of gases — say, nitrogen and oxygen in a flask — each type of molecule bounces off the walls independently of the others. Nitrogen molecules do not "know" oxygen is present, and vice versa. Dalton's law of partial pressures formalizes this insight: the total pressure of a gas mixture equals the sum of the individual partial pressures, where each gas's partial pressure is the pressure it would exert if it alone occupied the entire container. Mathematically: P_total = P₁ + P₂ + P₃ + ...

The bridge between partial pressure and composition is the mole fraction (χ). The mole fraction of gas A in a mixture is simply the moles of A divided by the total moles of all gases: χ_A = n_A / n_total. Because pressure is proportional to the number of moles (from the ideal gas law, PV = nRT), the partial pressure of gas A is its mole fraction times the total pressure: P_A = χ_A × P_total. If air is 78% nitrogen by moles and atmospheric pressure is 1.00 atm, then the partial pressure of nitrogen is 0.78 × 1.00 = 0.78 atm. Note that all mole fractions in a mixture must sum to 1, and all partial pressures must sum to the total pressure — these are useful checks on your arithmetic.

A classic application is collecting a gas over water. When you produce hydrogen gas in a reaction and collect it by displacing water in an inverted bottle, the gas in the bottle is not pure hydrogen — it is a mixture of hydrogen and water vapor. The total pressure inside the bottle (equal to atmospheric pressure) is the sum of the partial pressure of hydrogen and the vapor pressure of water at the experimental temperature. To find the partial pressure of the dry hydrogen, you subtract the water's vapor pressure (looked up in a table) from the total: P_H₂ = P_total − P_H₂O. From there, you can use the ideal gas law with the partial pressure of hydrogen alone to calculate the moles of H₂ collected.

Dalton's law appears throughout chemistry and beyond. In respiratory physiology, the partial pressure of oxygen decreases at high altitude because total atmospheric pressure drops — even though the mole fraction of O₂ remains 21%. This is why climbers need supplemental oxygen. In scuba diving, increased total pressure at depth raises the partial pressure of nitrogen, increasing the amount that dissolves in blood — a direct setup for Henry's law, which you will study next. Mastering the relationship between mole fraction, partial pressure, and total pressure gives you a versatile tool for any situation involving gas mixtures.