Dalton's law
Summary
Dalton's law says the total pressure of a mixture of ideal gases equals the sum of the partial pressures of its components, each acting as if it alone filled the container. Most testable: partial pressure = mole fraction × total pressure.
Detail
Meaning: In an ideal gas mixture the particles do not interact, so each gas exerts the pressure it would exert if it alone filled the container at the same temperature. Total pressure is the sum of these partial pressures. At fixed T and V, a gas's pressure is proportional to its moles, so its share of the total pressure equals its share of the moles. Real gases follow the law closely at low pressure and high temperature.
Equation: Ptotal = P₁ + P₂ + P₃ + …, and Pᵢ = XᵢPtotal, where Pᵢ is the partial pressure of gas i (Pa; atm and mmHg are also used), Xᵢ = nᵢ/ntotal is its mole fraction (unitless), and n is moles (mol).
On the MCAT: Air is about 21% O₂, so PO₂ ≈ 0.21 × Ptotal, and it falls at altitude as Ptotal falls. For a gas collected over water, Pdry gas = Patm − PH₂O, using the water vapor pressure at that temperature. Partial pressures also drive gas exchange in respiration and set how much gas dissolves in a liquid (Henry's law).
Common confusion: Partial pressure depends on moles, not on a gas's molar mass or identity, so equal moles of H₂ and CO₂ contribute equal partial pressures. Adding an inert gas at constant volume and temperature raises Ptotal but leaves the other gases' partial pressures unchanged.
Sources
- Chemistry: The Central Science
- Chemistry (Zumdahl)
- General Chemistry (Ebbing and Gammon)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.