# Dalton's law **Dalton's law**, also called Dalton's law of partial pressures, states that the total [[Pressure|pressure]] of a mixture of non-reacting gases is the sum of the [[Partial_pressure|partial pressures]] of its components, where the partial pressure of each gas is the pressure it would exert if it alone occupied the whole volume at the same [[Temperature|temperature]].[^averill-923] The law follows from the [[Ideal_gas_law|ideal gas law]] applied gas by gas: because ideal-gas molecules do not interact, each component fills the container as though the others were absent, and the pressures add.[^averill-923-924] It is named for the English chemist [[John_Dalton|John Dalton]], who set it out in essays on mixed gases and water vapour read to the Manchester Literary and Philosophical Society in 1801 and printed in 1802.[^dalton1802] On the [[Chemistry]] flagship the law opens Part XI, *Chemical laws*, in the section *Dalton's law of partial pressures*, between the gas laws of Part II and the effusion law treated on [[Graham's_law]]. Its neighbours on the spine are [[Mole_fraction]], [[Heliox]] and [[Henry's_law]], the last of which the microsim carries as a variant. In the microsim below the reader fills a diving cylinder. A fixed charge of 1.60 mol of [[Oxygen|oxygen]] sits in 10.0 L at 293.15 K, and a slider adds [[Helium|helium]] from 0 to 100 mol. Stacked bars answer with `P_i = n_i·R·T/V`, `P_t = Σ P_i` and `X_O2 = n_O2/n_t`: the oxygen segment stays at 3.85 atm however much helium is added, while the helium segment and the total climb past 200 atm and a mole-fraction gauge for oxygen falls toward zero.[^averill-924-925] A second readout applies Henry's law, `c_i = k_H·P_i`, to show how much of each gas would dissolve in water at that partial pressure, which is why the same JSON spec serves the Henry's law page as a variant. ## Formula For a mixture of gases labelled 1, 2, … , *i*, Dalton's law reads `P_t = P_1 + P_2 + … + P_i`.[^averill-923] Each partial pressure obeys its own ideal gas equation, `P_i = n_i·R·T/V`, with *n_i* the amount of that gas in [[Mole_(unit)|moles]], so the total is `P_t = (n_1 + n_2 + … + n_i)·R·T/V`: the mixture behaves as a single ideal gas whose amount is the sum of the amounts.[^averill-923-924] The gas constant is R = 0.082057 L·atm/(K·mol) in the units the worked examples use, or 8.3145 J/(K·mol) in SI.[^averill-904] Dividing the partial-pressure equation by the total gives the second form of the law: the mole fraction of a component, `X_A = n_A/n_t`, equals its pressure fraction, `P_A/P_t = X_A`, so `P_A = X_A·P_t`.[^averill-926] The law is exact for ideal gases and a good approximation for real gases at pressures and temperatures where they are far from condensing; it says nothing about gases that react with one another, whose amounts change on mixing. #### The heliox cylinder The microsim is Example 11 of the Portal Book *General Chemistry*, made adjustable. A deep-diving cylinder of 10.0 L at 293.15 K holds 51.2 g of oxygen, which is 1.60 mol, and 326.4 g of helium, which is 81.55 mol. Each gas fills the cylinder on its own terms: `P_O2 = 1.60 × 0.082057 × 293.15 / 10.0 = 3.85 atm` and `P_He = 81.55 × 0.082057 × 293.15 / 10.0 = 196 atm`, so the gauge reads their sum, 200 atm.[^averill-924-925] The factor R·T/V is the same for both, 2.41 atm per mole (derived), which is why the stacked bars in the microsim grow in proportion to the moles added. With the helium slider at zero the cylinder holds oxygen alone at 3.85 atm and X_O2 = 1; at the book's 81.55 mol the oxygen fraction is 1.60/83.15 = 0.0192 (derived) while its partial pressure has not moved; at the slider's limit of 100 mol the total reaches about 244 atm (derived) and the oxygen fraction falls below 1.6 %. The lesson the bars teach is the one divers live by. The body responds to the partial pressure of oxygen, not to its percentage, and a [[Breathing_gas|breathing gas]] is mixed by partial pressures for the depth at which it will be used; heliox replaces [[Nitrogen|nitrogen]] with helium to avoid the [[Nitrogen_narcosis|narcosis]] that nitrogen produces at high partial pressure, and the same arithmetic governs [[Trimix_(breathing_gas)|trimix]].[^averill-924-925] #### Mole fraction and the gauge The second worked number in the microsim's preset list is a [[Natural_gas|natural-gas]] cylinder: 1813 g of methane and 336 g of ethane in 20.0 L at 22 °C give partial pressures of 137 atm and 13.4 atm and a total of 151 atm.[^averill-925] Here the gauge shows only the total, and Dalton's law is what lets a chemist recover the composition from the masses, or the masses from the composition. The mole-fraction form is the one used in the other direction: if the composition is known as fractions, the partial pressure of any component is its fraction times the gauge reading, and no volume or temperature is needed.[^averill-926] The two forms are the same law seen from the two ends of a laboratory problem, and a reader who can move between them can read any gas analysis. In the microsim the gauge for X_O2 is computed as `n_O2/(n_O2 + n_He)`, and its fall while P_O2 stands still is the whole content of the law in one picture; the preset button switches the bars to the methane–ethane case so the reader can check the book's three numbers. #### History Dalton reached the law while studying the [[Atmosphere_of_Earth|atmosphere]] and the behaviour of water vapour in air. In the essays of 1801–1802 he argued that in a mixture each gas behaves as a vacuum toward the others, exerting its own pressure independently, and that the vapour of water in air is simply one more such gas whose partial pressure is set by temperature.[^dalton1802] The same essays contain his measurements of the vapour pressure of water and of the thermal expansion of gases, so the law of partial pressures was born as a piece of meteorology before it became a piece of chemistry. The idea that gases in a mixture act independently was a step toward his atomic theory, and it gave his friend William Henry the framework for the 1803 experiments on the quantity of gas absorbed by water at different pressures, which became Henry's law.[^henry1803] The two laws are usually taught together for that reason, and the microsim carries both. #### Limits and the wet-gas correction The law fails where the ideal gas law fails: at high pressure and low temperature the molecules occupy space and attract one another, and the pressures no longer add exactly.[^averill-904] The 200 atm cylinder of the microsim is treated as ideal for teaching, and the article labels that assumption ILLUSTRATIVE; the [[Van_der_Waals_equation|van der Waals]] correction would move the helium term a few percent, and a filling station uses measured compressibility tables rather than the ideal law. Helium is the closest of the real gases to ideal, its atoms being small and weakly attracting, which is one reason the heliox example holds up as well as it does. The most common laboratory use of the law is the wet-gas correction: a gas collected over [[Water|water]] is mixed with water vapour at the [[Vapor_pressure|vapour pressure]] of water at the bath temperature, so the pressure of the dry gas is `P_gas = P_tot − p_H2O(T)`, read from a table of vapour pressures.[^averill-933-936] Gases that dissolve in or react with water, such as ammonia and hydrogen chloride, cannot be collected this way.[^averill-933-936] ## Volume-based concentration For ideal gases the amount fraction, the pressure fraction and the volume fraction of a component are the same number, because each is proportional to the number of molecules: `n_i/n_t = P_i/P_t = V_i/V_t`, where *V_i* is the volume the component would occupy alone at the total pressure.[^averill-926] This is why gas compositions are quoted "by volume" and why a statement such as "air is 21 % oxygen" can be read directly as a mole fraction of 0.21 and, at sea level, as an oxygen partial pressure of 0.21 atm. Trace components are quoted in parts per million by volume, and the same identity converts them: a concentration of *c* ppmv means a partial pressure of `P_i = c × 10⁻⁶ × P_t`.[^openstax-ch8] The conversion is the practical form in which Dalton's law enters atmospheric chemistry, industrial gas analysis and respiratory physiology, and it is why the microsim's mole-fraction gauge can be read equally as a percentage by volume. #### Exhaled air and Venus Example 12 of *General Chemistry* applies the identity to exhaled breath at a total pressure of 767 mmHg, with mole fractions of 0.740 for nitrogen, 0.151 for oxygen, 0.037 for carbon dioxide and 0.062 for water vapour; the partial pressures are the fractions times 767 mmHg, so nitrogen contributes 568 mmHg, oxygen 116 mmHg and carbon dioxide about 28 mmHg (derived from the book's fractions).[^averill-927-928] One printed line in that example gives 0.031 atm for the carbon dioxide term, but the fraction the book carries forward is 28/760 = 0.037 atm, which is the value the microsim's preset uses.[^averill-927-928] The same example turns to [[Venus]], where the surface pressure is about 90 atm and the mole fractions of carbon dioxide and nitrogen give partial pressures of about 86 atm and 3 atm; the two together account for only about 95 % of the gas, the remainder being minor constituents the example does not list.[^averill-928] #### The Henry's law readout Dissolved gas follows the partial pressure, not the total. Henry's law states that the concentration of a gas dissolved in a liquid at equilibrium is proportional to the partial pressure of that gas above the liquid, `c_i = k_H·P_i`, with a constant *k_H* that depends on the gas, the solvent and the temperature.[^openstax-ch11] The Portal Book *Chemistry: Atoms First* works the case of oxygen in water at 20 °C: exposed to oxygen at 101.3 kPa the water holds 1.38 × 10⁻³ mol/L, so at the partial pressure oxygen has in air, 20.7 kPa, it holds 2.82 × 10⁻⁴ mol/L, a fifth as much.[^openstax-ch11] In the microsim the readout multiplies each partial pressure by a Henry constant and reports the dissolved concentration, so the reader sees that adding helium to the cylinder raises the dissolved helium a diver's tissues would carry without changing the dissolved oxygen at all. That independence is Dalton's law read through Henry's, and it is the physical reason [[Solubility|solubility]] tables list gases one at a time. The variant page treats the dissolved nitrogen at depth in the same way. ## See also - [[Partial_pressure]] - [[Heliox]] - [[Henry's_law]] - [[Mole_fraction]] - [[Breathing_gas]] - [[Ideal_gas_law]] - [[Graham's_law]] - [[Kinetic_theory_of_gases]] ## References [^averill-923]: Averill, B.; Eldredge, P. (2011). *General Chemistry: Principles, Patterns, and Applications*. Chapter 10, "Gases", §10.5, p. 923 (statement of Dalton's law). https://open.umn.edu/opentextbooks/textbooks/general-chemistry-principles-patterns-and-applications [^averill-923-924]: Averill, B.; Eldredge, P. (2011). *General Chemistry: Principles, Patterns, and Applications*. Chapter 10, "Gases", pp. 923–924 (each component obeys P_i = n_i·R·T/V; the total as the sum). https://open.umn.edu/opentextbooks/textbooks/general-chemistry-principles-patterns-and-applications [^averill-904]: Averill, B.; Eldredge, P. (2011). *General Chemistry: Principles, Patterns, and Applications*. Chapter 10, "Gases", pp. 903–904 (the ideal gas law, the values of R, and the conditions under which the law fails). https://open.umn.edu/opentextbooks/textbooks/general-chemistry-principles-patterns-and-applications [^averill-926]: Averill, B.; Eldredge, P. (2011). *General Chemistry: Principles, Patterns, and Applications*. Chapter 10, "Gases", p. 926 (mole fraction; P_A = X_A·P_t). https://open.umn.edu/opentextbooks/textbooks/general-chemistry-principles-patterns-and-applications [^averill-924-925]: Averill, B.; Eldredge, P. (2011). *General Chemistry: Principles, Patterns, and Applications*. Chapter 10, "Gases", Example 11, pp. 924–925 (the heliox cylinder: 3.85 atm, 196 atm, 200 atm). https://open.umn.edu/opentextbooks/textbooks/general-chemistry-principles-patterns-and-applications [^averill-925]: Averill, B.; Eldredge, P. (2011). *General Chemistry: Principles, Patterns, and Applications*. Chapter 10, "Gases", p. 925 (the methane–ethane cylinder: 137 atm, 13.4 atm, 151 atm). https://open.umn.edu/opentextbooks/textbooks/general-chemistry-principles-patterns-and-applications [^averill-927-928]: Averill, B.; Eldredge, P. (2011). *General Chemistry: Principles, Patterns, and Applications*. Chapter 10, "Gases", Example 12, pp. 927–928 (exhaled air at 767 mmHg; the 0.031/0.037 atm discrepancy). https://open.umn.edu/opentextbooks/textbooks/general-chemistry-principles-patterns-and-applications [^averill-928]: Averill, B.; Eldredge, P. (2011). *General Chemistry: Principles, Patterns, and Applications*. Chapter 10, "Gases", p. 928 (the atmosphere of Venus at 90 atm: 86 atm CO₂, 3 atm N₂). https://open.umn.edu/opentextbooks/textbooks/general-chemistry-principles-patterns-and-applications [^averill-933-936]: Averill, B.; Eldredge, P. (2011). *General Chemistry: Principles, Patterns, and Applications*. Chapter 10, "Gases", pp. 933–936 (gases collected over water; Table 10.4 vapour pressure of water). https://open.umn.edu/opentextbooks/textbooks/general-chemistry-principles-patterns-and-applications [^openstax-ch8]: Flowers, P.; Neth, E.; Robinson, W.; et al. (2019). *Chemistry: Atoms First*, 2nd ed. OpenStax. Chapter 8, "Gases", pp. 363–420 (Dalton's law of partial pressures; page to pin). https://open.umn.edu/opentextbooks/textbooks/chemistry-atoms-first [^openstax-ch11]: Flowers, P.; Neth, E.; Robinson, W.; et al. (2019). *Chemistry: Atoms First*, 2nd ed. OpenStax. Chapter 11, "Solutions and Colloids", pp. 545–596 (Henry's law and the dissolved-oxygen example; page to pin). https://open.umn.edu/opentextbooks/textbooks/chemistry-atoms-first [^dalton1802]: Dalton, J. (1802). "Experimental essays on the constitution of mixed gases; on the force of steam or vapour from water and other liquids in different temperatures, both in a Torricellian vacuum and in air; on evaporation; and on the expansion of gases by heat." *Memoirs of the Literary and Philosophical Society of Manchester*, vol. 5 (read October 1801). [^henry1803]: Henry, W. (1803). "Experiments on the quantity of gases absorbed by water, at different temperatures, and under different pressures." *Philosophical Transactions of the Royal Society of London*, vol. 93. <!-- MATTERSIM:BEGIN g33 — Matter & Energy Cluster microsim (framework build, specs/sims/Dalton's_law.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework):** *Dalton's law* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/matter/Dalton's_law.html" data-title="Dalton's law"></div> *Built from `MICROSIM_GUIDE/specs/sims/Dalton's_law.json`; part of the [[PORTAL_Matter|Matter portal]] spine (section sims and See-also variants).* <!-- MATTERSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Dalton's_law) : [Wikitube](https://en.wikitube.io/wiki/Dalton's_law) · pinned revision [1357855600](https://en.wikipedia.org/w/index.php?oldid=1357855600) · 2026-09-11 ## Previous hub tags Hubs: `Life_Physics`. 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