Dalton’s Law

Dalton’s Law of Partial Pressures describes the behaviour of gases within a mixture when no chemical reactions occur between the constituent components. 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. First formulated by John Dalton and published in 1802, the law established a foundational principle in physical chemistry and contributed significantly to the development of the ideal gas model and later kinetic molecular theory.
Dalton’s observations were based on experimental investigations into gas behaviour and vapour pressures. His empirical findings formed a major part of the early nineteenth-century efforts to quantify gaseous properties using measurable physical parameters. The principle remains fundamental to modern chemistry, physics, meteorology, and engineering, especially in systems involving gas mixtures such as the atmosphere, industrial gas processing, and respiratory physiology.

Fundamental Principle

Dalton’s Law asserts that each gas in a mixture behaves independently and exerts a pressure as though it alone occupied the entire volume. This pressure is known as the partial pressure. The total pressure exerted by the mixture is therefore the arithmetic sum of all partial pressures.
Mathematically, the relationship is expressed as:p_total = p₁ + p₂ + p₃ + … + pₙ,where each pᵢ denotes the partial pressure of an individual component in a mixture containing n gases.
A related expression links partial pressure to the mole fraction of the component:pᵢ = xᵢ × p_total,where xᵢ is the mole fraction of gas i in the mixture. This formulation shows that the proportion of each gas directly determines its contribution to the overall pressure.

Concentration and Volume Relationships

Dalton’s Law also allows concentrations of gases in a mixture to be related to the total pressure. If cᵢ represents the volumetric concentration of component i, then:
pᵢ = p_total × cᵢ.
This expression is useful for determining the amount of an individual gas when the total pressure and composition are known. Such calculations underpin many analytical techniques, including the measurement of atmospheric pollutants, the calibration of gas mixtures, and quantitative assessments in chemical engineering.

Behaviour of Real Gases and Limitations

While Dalton’s Law accurately models ideal gases under standard conditions, real gases deviate from ideal behaviour, particularly at high pressures. Under such conditions, intermolecular forces and the finite size of molecules become significant enough to influence the pressure exerted. Molecules are forced closer together, reducing free volume and increasing attractions or repulsions between particles. These effects cause measured pressures to depart from the predictions of Dalton’s Law.
The greatest deviations arise when:

• pressures are high,
• temperatures are low,
• intermolecular forces (e.g., van der Waals forces) are strong, or
• gas molecules occupy a non-negligible proportion of the total volume.

Corrections for such deviations are incorporated into alternative models such as the van der Waals equation and other real-gas equations of state.

Applications and Scientific Importance

Dalton’s Law is central to various scientific and practical fields. Its principles are used in:

• Atmospheric science, for calculating the partial pressures of atmospheric gases and understanding humidity, vapour pressure, and weather processes.
• Respiratory physiology, where oxygen and carbon dioxide partial pressures govern gas exchange in the lungs and tissues.
• Chemical engineering, in the design of gas separation units, combustion systems, and industrial gas mixtures.
• Diving physiology, including decompression modelling and assessments of inert gas narcosis.
• Environmental monitoring, where pollutant concentrations rely on partial pressure calculations.