Dalton's Law

When two or more gases that do not react chemically are mixed together in a container, each gas behaves as though it alone occupies the entire volume. This fundamental observation, formalized by the English chemist John Dalton in 1801, is known as Dalton's Law of Partial Pressures. It states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of each individual gas in the mixture. A partial pressure is simply the pressure that a particular gas would exert if it were the only gas present in the same volume at the same temperature. The concept of partial pressure arises directly from the kinetic molecular theory of gases. Because ideal gas molecules are assumed to have negligible volume and to exert no attractive or repulsive forces on one another, the collisions of one type of molecule with the container walls are completely independent of the collisions made by any other type of molecule. Each gas therefore contributes to the total pressure in proportion to the number of its molecules present — that is, in proportion to its mole fraction in the mixture. This makes Dalton's Law a powerful quantitative tool for analyzing gas mixtures in chemistry, meteorology, medicine, and industrial processes. One of the most important practical applications of Dalton's Law in the chemistry laboratory is the collection of gases over water. When a gas is bubbled through water and collected by water displacement, the gas becomes saturated with water vapor. The total pressure measured inside the collection vessel is the sum of the pressure of the desired gas and the vapor pressure of water at that temperature. To find the true pressure of the collected gas, the vapor pressure of water (a well-tabulated quantity) must be subtracted from the total pressure. This correction is essential for accurate quantitative work, including molar mass determinations and stoichiometric calculations.

Key takeaways
  • Defining Partial Pressure
  • Stating Dalton's Law Mathematically
  • Mole Fraction Relationship
  • Collecting Gas Over Water
  • Real-World Relevance

Defining Partial Pressure

The partial pressure of gas A in a mixture (P_A) is the pressure gas A would exert if it alone occupied the entire volume V at the same temperature T. Using the ideal gas law: P_A = n_A RT / V, where n_A is the number of moles of gas A. Each component gas has its own partial pressure calculated the same way.

Stating Dalton's Law Mathematically

For a mixture of gases A, B, C, …, the total pressure P_total = P_A + P_B + P_C + … This is exact for ideal gases and an excellent approximation for real gases at moderate pressures. Adding partial pressures is equivalent to adding all n_i terms: P_total = (n_A + n_B + n_C + …) RT / V = n_total RT / V.

Mole Fraction Relationship

The mole fraction of component A is defined as χ_A = n_A / n_total, where n_total = n_A + n_B + n_C + … The mole fraction is dimensionless and always lies between 0 and 1; the sum of all mole fractions in a mixture equals 1. The partial pressure of any component equals its mole fraction multiplied by the total pressure: P_A = χ_A × P_total. This relationship lets chemists quickly calculate partial pressures from composition data without knowing the volume or temperature separately.

Collecting Gas Over Water

In a typical pneumatic trough experiment, a gas such as hydrogen (\ce{H2}) generated by a chemical reaction displaces water in an inverted graduated cylinder. The gas collected is actually a mixture: the desired gas plus water vapor at equilibrium with liquid water. The vapor pressure of water, P_H2O, depends only on temperature and is found in standard tables (e.g., at 25 °C, P_H2O = 23.8 mmHg; at 20 °C, P_H2O = 17.5 mmHg). Applying Dalton's Law: P_gas = P_total − P_H2O. The corrected P_gas is then used in ideal gas law calculations to find moles or molar mass of the collected gas.

Real-World Relevance

Dalton's Law applies across many fields. In scuba diving, the partial pressures of \ce{O2} and \ce{N2} in compressed air increase with depth, explaining nitrogen narcosis and oxygen toxicity. In medicine, blood oxygen levels are reported as the partial pressure of oxygen (P_O2). Meteorologists use the concept of partial pressure of water vapor to define relative humidity. Industrial gas mixtures — such as syngas (\ce{H2} + \ce{CO}) and air separation products — are routinely characterized using partial pressures.

The Key Equation

Ptotal=P1+P2+P3+⋯=∑iPi=∑iχiPtotalP_{\text{total}} = P_1 + P_2 + P_3 + \cdots = \sum_i P_i = \sum_i \chi_i P_{\text{total}}
  • P_{\text{total}} — Total pressure (Pa, atm, mmHg, or kPa): The measured pressure of the entire gas mixture acting on the container walls.
  • P_i — Partial pressure of component i (Pa, atm, mmHg, or kPa): The pressure component i would exert if it alone occupied the same volume at the same temperature.
  • \chi_i — Mole fraction of component i (dimensionless): Ratio of moles of component i to total moles in the mixture; χ_i = n_i / n_total. All mole fractions sum to 1.
  • n_i — Moles of component i (mol): Amount in moles of the individual gas species i present in the mixture.

Worked Example

Problem. A student collects 245 mL of gas over water at 22 °C. The atmospheric pressure is 754 mmHg. The vapor pressure of water at 22 °C is 19.8 mmHg. The gas is produced by the reaction: \ce{Zn(s) + H2SO4(aq) -> ZnSO4(aq) + H2(g)}. (a) Calculate the partial pressure of the dry hydrogen gas. (b) Calculate the number of moles of \ce{H2} collected.

P\ceH2=734.2 mmHg;n\ceH2=9.77×10−3 molP_{\ce{H2}} = 734.2\ \text{mmHg};\quad n_{\ce{H2}} = 9.77 \times 10^{-3}\ \text{mol}

Answer. The partial pressure of dry hydrogen is 734.2 mmHg (0.966 atm), and approximately 9.77 × 10⁻³ mol of H₂ was collected.

Figure
Diagram
Dalton's Law: Gas Mixture Pressure and Mole FractionsContainer APure N₂n = 2 molP(N₂) = 0.60 atmContainer BPure O₂n = 1 molP(O₂) = 0.30 atmMixtureN₂ + O₂n = 3 mol totalP_total = 0.90 atm+=Mole Fraction Calculationχ(N₂) = 2/3 = 0.667P(N₂) = 0.667 × 0.90= 0.60 atm ✓χ(O₂) = 1/3 = 0.333P(O₂) = 0.333 × 0.90= 0.30 atm ✓P_total = P(N₂) + P(O₂) = 0.60 + 0.30 = 0.90 atm
Origins · 1 minJohn Dalton and how this was discovered
JD
John Dalton
1766–1844 · British (English)

John Dalton published his law of partial pressures in 1801, demonstrating that each gas in a mixture exerts pressure independently of the others. This work grew from his meticulous meteorological observations and his broader atomic theory (1803), in which he proposed that all matter is composed of indivisible atoms with characteristic masses — the first modern quantitative atomic theory in chemistry. Dalton was one of the first scientists to study color blindness systematically — a condition he himself had. For many years, color blindness was colloquially called 'Daltonism' in his honor. After his death, his eyes were preserved and, in 1995, DNA analysis confirmed he lacked the pigment gene for medium-wavelength (green) sensitive cones.

  • The Ideal Gas Law (PV = nRT) — Dalton's Law is derived directly from the ideal gas law: each component gas obeys PV = nRT independently, so partial pressures simply add to give the total pressure.
  • Kinetic Molecular Theory of Gases — The kinetic molecular theory provides the microscopic justification for Dalton's Law: ideal gas molecules do not interact, so each species contributes independently to the pressure through its own molecular collisions with the container walls.
  • Vapor Pressure and Evaporation — When collecting gas over water, the vapor pressure of water must be subtracted from the total pressure using Dalton's Law. Understanding what vapor pressure is and why it depends on temperature is essential for this correction.
  • The Mole Concept and Avogadro's Law — Mole fractions, which link composition to partial pressure, are built on the mole concept. Avogadro's Law (equal volumes of gases at the same T and P contain equal numbers of molecules) is a related principle that also supports the additive nature of partial pressures.