Dalton's law

Dalton's law (also called Dalton's law of partial pressures) states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of the individual gases.^[1] This empirical law was observed by John Dalton in 1801 and published in 1802.^[2] Dalton's law is related to the ideal gas laws.

Formula

Mathematically, the pressure of a mixture of non-reactive gases can be defined as the summation: $p_{\text{total}}=\sum _{i=1}^{n}p_{i}=p_{1}+p_{2}+p_{3}+\cdots +p_{n}$ where $p 1$ , $p 2$ , ..., $p n$ represent the partial pressures of each component.^[1]

$p_{i}=p_{\text{total}}x_{i}$ where $x i$ is the mole fraction of the ith component in the total mixture of n components.

Volume-based concentration

The relationship below provides a way to determine the volume-based concentration of any individual gaseous component $p_{i}=p_{\text{total}}c_{i}$ where c_i is the concentration of component i.

Dalton's law is not strictly followed by real gases, with the deviation increasing with pressure. Under such conditions the volume occupied by the molecules becomes significant compared to the free space between them. In particular, the short average distances between molecules increases intermolecular forces between gas molecules enough to substantially change the pressure exerted by them, an effect not included in the ideal gas model.

Dalton's Law vs. Real Case

Feature	Dalton’s Law (Ideal Case)	Real Case (Non-Ideal)
Molecular Volume	Assumes gas particles have zero volume; they are treated as point masses.	Particles have finite volume, which becomes significant at high pressures.
Intermolecular Forces	Assumes no attraction or repulsionbetween molecules.	Van der Waals forces (attraction) exist, which can reduce the impact force against container walls.
Pressure Summation	Ptotal is exactly the sum of P1+P2+...	Ptotal is usually lower than predicted due to attractive forces "pulling" molecules back.
Collision Type	Perfectly elastic; no kinetic energy is lost.	Collisions are nearly elastic, but intermolecular "stickiness" affects momentum transfer.
Best Conditions	High temperature and low pressure.	Low temperature and high pressure (where deviations are maximized).
Mathematical Model	Ideal Gas Law: PV=nRT	Van der Waals Equation: (P+an²/V²)(V−nb)=nRT

The most significant breakdown of Dalton's Law in these scenarios:

When a gas is close to its boiling point, intermolecular forces are at their strongest.
At extreme depths, the partial pressures of nitrogen and oxygen don't perfectly follow linear math, which is critical for calculating decompression sickness risks.
Dalton’s law strictly applies to non-reacting gases. If you mix NH3 and HCl, they react to form solid NH4Cl, and the pressure drops drastically, violating the additive principle entirely.

References

^ ^a ^b Silberberg, Martin S. (2009). Chemistry: the molecular nature of matter and change (5th ed.). Boston: McGraw-Hill. p. 206. ISBN 9780073048598.
^ J. Dalton (1802), "Essay IV. On the expansion of elastic fluids by heat," Memoirs of the Literary and Philosophical Society of Manchester, vol. 5, pt. 2, pages 595–602; see page 600.

[Silberberg-1] Silberberg, Martin S. (2009). Chemistry: the molecular nature of matter and change (5th ed.). Boston: McGraw-Hill. p. 206. ISBN 9780073048598.

[2] J. Dalton (1802), "Essay IV. On the expansion of elastic fluids by heat," Memoirs of the Literary and Philosophical Society of Manchester, vol. 5, pt. 2, pages 595–602; see page 600.

[1]

[2]

v t e Distillation
Principles	Raoult's law Dalton's law Reflux Fenske equation McCabe–Thiele method Theoretical plate Partial pressure Vapor–liquid equilibrium
Industrial processes	Batch distillation Continuous distillation Fractionating column Spinning cone
Laboratory methods	Alembic Kugelrohr Rotary evaporator Spinning band distillation Still
Techniques	Azeotropic Catalytic Destructive Dry Extractive Fractional Reactive Salt-effect Steam-based Vacuum-based

Formula

Volume-based concentration

Dalton's Law vs. Real Case

See also

References