Editing Gas laws

{{short description|List of physical laws relates to gases}}{{More citations needed|date=September 2024}}{{Hatnote|This article outlines the historical development of the laws describing ideal gases. For a detailed description of the ideal gas laws and their further development, see [[ideal gas law]].}}

The laws describing the behaviour of [[Gas|gases]] under fixed [[pressure]], [[volume]], amount of gas, and [[Thermodynamic temperature|absolute]] [[temperature]] conditions are called '''gas laws'''. The basic gas laws were discovered by the end of the 18th century when scientists found out that relationships between pressure, volume and temperature of a sample of gas could be obtained which would hold to approximation for all gases. The combination of several empirical gas laws led to the development of the [[ideal gas law]].

The ideal gas law was later found to be consistent with [[Atomic theory|atomic]] and [[Kinetic theory of gases|kinetic theory]].

== History ==
In 1643, the Italian physicist and mathematician, [[Evangelista Torricelli]], who for a few months had acted as [[Galileo Galilei|Galileo Galilei's]] secretary, conducted a celebrated experiment in Florence.<ref>{{Cite web |last=Lagouge |first=Michel |title=History of Gas Laws |url=https://lagouge.ecole-alsacienne.org/14-15/cahier_texte_1S/Documents/Doc%20C4/History%20of%20Gas%20Laws.pdf}}</ref> He demonstrated that a column of mercury in an inverted tube can be supported by the pressure of air outside of the tube, with the creation of a small section of vacuum above the mercury.<ref>{{Cite web |date=2008-01-23 |title=Torricelli's barometric experiment |url=https://brunelleschi.imss.fi.it/itineraries/multimedia/TorricellisBarometricExperiment.html#:~:text=Torricelli%20filled%20a%20glass%20tube,height%20of%20around%2076%20cm. |access-date=2024-03-21 |website=brunelleschi.imss.fi.it |language=EN}}</ref> This experiment essentially paved the way towards the invention of the barometer, as well as drawing the attention of [[Robert Boyle]], then a "skeptical" scientist working in England. Boyle was inspired by Torricelli's experiment to investigate how the elasticity of air responds to varying pressure, and he did this through a series of experiments with a setup reminiscent of that used by Torricelli.<ref>{{Cite web |last=Purdue University |title=Gas Laws |url=https://chemed.chem.purdue.edu/genchem/topicreview/bp/ch4/gaslaws3.html}}</ref> Boyle published his results in 1662.  

Later on, in 1676, the French physicist [[Edme Mariotte]], independently arrived at the same conclusions of Boyle, while also noting some dependency of air volume on temperature.<ref>{{Cite web |title=Edme Mariotte {{!}} Experimental Physics, Pressure Law & Hydrostatics {{!}} Britannica |url=https://www.britannica.com/biography/Edme-Mariotte |access-date=2024-03-21 |website=www.britannica.com |language=en}}</ref> However it took another century and a half for the development of thermometry and recognition of the absolute zero temperature scale, which eventually allowed the discovery of temperature-dependent gas laws.

==Boyle's law==
{{Main|Boyle's law}}
In 1662, Robert Boyle systematically studied the relationship between the volume and pressure of a fixed amount of gas at a constant temperature. He observed that the volume of a given mass of a gas is inversely proportional to its pressure at a constant temperature.
Boyle's law, published in 1662, states that, at a constant temperature, the product of the pressure and volume of a given mass of an [[ideal gas]] in a [[closed system]] is always constant. It can be verified experimentally using a [[Pressure measurement|pressure gauge]] and a variable volume container. It can also be derived from the [[kinetic theory of gases]]: if a container, with a fixed number of [[Molecule|molecules]] inside, is reduced in volume, more molecules will strike a given area of the sides of the container per unit time, causing a greater pressure.

=== Statement ===
Boyle's law states that:

{{block indent | text = The volume of a given mass of a gas is inversely related to its pressure when its temperature is kept constant.}}

The concept can be represented with these formulae:
*<math>V \propto \frac{1}{P}</math>, meaning "Volume is inversely proportional to Pressure", or
*<math>P \propto \frac{1}{V}</math>,  meaning "Pressure is inversely proportional to Volume", or
*<math>P V = k_1</math>, or
<math display="block">P_1 V_1 = P_2 V_2</math>
where {{mvar|P}} is the pressure, {{mvar|V}} is the volume of a gas, and {{math|''k''<sub>1</sub>}} is the constant in this equation (and is not the same as the proportionality constants in the other equations).

==Charles' law==
{{Main|Charles's law}}
Charles' law, or the law of volumes, was founded in 1787 by [[Jacques Charles]]. It states that, for a given [[mass]] of an ideal gas at constant pressure, the volume is directly proportional to its [[absolute temperature]], assuming in a closed system.
The statement of Charles' law is as follows:
the volume (V) of a given mass of a gas, at constant pressure (P), is directly proportional to its temperature (T).

=== Statement ===
Charles' law states that:
{{Block indent|quote=The volume of a given fixed mass of a dry gas is directly proportional to its absolute temperature at a constant pressure.}}
Therefore,

* <math>V \propto T\,</math>, or
* <math>{V \over T} = k_2</math>, or
:<math display="block">{V_1 \over T_1} = {V_2 \over T_2}</math>,


where ''"V"'' is the volume of a gas, ''"T"'' is the absolute temperature and ''k''<sub>2</sub> is a proportionality constant (which is not the same as the proportionality constants in the other equations in this article).

==Gay-Lussac's law==
{{Main|Gay-Lussac's law}}
Gay-Lussac's law, Amontons' law or the pressure law was founded by [[Joseph Louis Gay-Lussac]] in 1808.

=== Statement ===
Gay-Lussac's law states that:
{{Block indent|quote=The pressure exerted by a given mass and constant volume of an ideal gas on the sides of its container is directly proportional to its absolute temperature.}}
Therefore,

* <math>P \propto T\,</math>, or
* <math>{P \over T} = k</math>, or

<math display="block">{P_1 \over T_1} = {P_2 \over T_2}</math>,

:where ''P'' is the pressure, ''T'' is the absolute temperature, and ''k'' is another proportionality constant.

==Avogadro's law==
{{Main|Avogadro's law}}

'''Avogadro's law''', '''Avogadro's hypothesis''', '''Avogadro's principle''' or '''Avogadro-Ampère's hypothesis''' is an experimental gas law which was hypothesized by [[Amedeo Avogadro]] in 1811. It related the volume of a gas to the [[amount of substance]] of gas present.<ref name="Britannica">{{cite encyclopedia |entry=Avogadro's law |encyclopedia=[[Encyclopædia Britannica]] |access-date=3 February 2016 |entry-url=http://www.britannica.com/science/Avogadros-law}}</ref>

=== Statement ===
Avogadro's law states that:
{{Block indent|quote=The volume occupied by an ideal gas at a constant temperature is directly proportional to the number of molecules of the gas present in the container.}}
This statement gives rise to the [[molar volume]] of a gas, which at [[Standard temperature and pressure|STP]] (273.15&nbsp;K, 1 atm) is about 22.4&nbsp;L. The relation is given by:

:<math>V \propto n\,</math>, or<math display="block">\frac{V_1}{n_1}=\frac{V_2}{n_2}    \,</math>where ''n'' is equal to the number of molecules of gas (or the number of moles of gas).

==Combined and ideal gas laws==
{{Main articles|Ideal gas law}}
{{ideal_gas_law_relationships.svg}}
The [[combined gas law]] or general gas equation is obtained by combining Boyle's law, Charles's law, and Gay-Lussac's law. It shows the relationship between the pressure, volume, and temperature for a fixed mass of gas:

:<math>PV = k_5 T </math>

This can also be written as:

:<math> \frac {P_1V_1}{T_1}= \frac {P_2V_2}{T_2} </math>

With the addition of [[Avogadro's law]], the [[combined gas law]] develops into the [[ideal gas law]]:

:<math>PV = nRT </math>
:where ''P''  is the pressure, ''V'' is volume, ''n'' is the number of moles, ''R'' is the universal gas constant and ''T'' is the absolute temperature.
:The proportionality constant, now named R, is the [[universal gas constant]] with a value of 8.3144598 (kPa∙L)/(mol∙K).
An equivalent formulation of this law is:
:<math display="block">PV = Nk_\text{B}T </math>
:where ''P'' is the pressure, ''V'' is the volume, ''N'' is the number of gas molecules, ''k''<sub>B</sub> is the [[Boltzmann constant]] (1.381×10<sup>−23</sup>J·K<sup>−1</sup> in SI units) and T is the absolute temperature.

These equations are exact only for an [[ideal gas]], which neglects various intermolecular effects (see [[real gas]]). However, the ideal gas law is a good approximation for most gases under moderate pressure and temperature.

This law has the following important consequences:
# If temperature and pressure are kept constant, then the volume of the gas is directly proportional to the number of molecules of gas.
# If the temperature and volume remain constant, then the pressure of the gas changes is directly proportional to the number of molecules of gas present.
# If the number of gas molecules and the temperature remain constant, then the pressure is inversely proportional to the volume.
# If the temperature changes and the number of gas molecules are kept constant, then either pressure or volume (or both) will change in direct proportion to the temperature.

==Other gas laws==
;[[Graham's law]]: This law states that the rate at which gas molecules [[diffusion|diffuse]] is inversely proportional to the square root of the gas density at a constant temperature. Combined with Avogadro's law (i.e. since equal volumes have an equal number of molecules) this is the same as being inversely proportional to the root of the molecular weight.
;[[Dalton's law]] of [[partial pressure]]s: This law states that the pressure of a mixture of gases simply is the sum of the [[partial pressures]] of the individual components. Dalton's law is as follows:
:
:<math> P_\textrm{total} = P_1 + P_2 + P_3 + \cdots + P_n \equiv \sum_{i=1}^n P_i ,</math>
:
:and all component gases and the mixture are at the same temperature and volume
:where ''P''<sub>total</sub> is the total pressure of the gas mixture
:''P''<sub>i</sub> is the partial pressure or pressure of the component gas at the given volume and temperature.
:
;[[Amagat's law]] of [[Partial gas volume|partial volumes]]: This law states that the volume of a mixture of gases (or the volume of the container) simply is the sum of the partial volumes of the individual components. Amagat's law is as follows:
:
:<math> V_\textrm{total} = V_1 + V_2 + V_3 + \cdots + V_n \equiv \sum_{i=1}^n V_i ,</math>
:
:and all component gases and the mixture are at the same temperature and pressure
:where ''V''<sub>total</sub> is the total volume of the gas mixture or the volume of the container,
:''V''<sub>i</sub> is the partial volume, or volume of the component gas at the given pressure and temperature.
:
;[[Henry's law]]: This states that at constant temperature, the amount of a given gas dissolved in a given type and volume of liquid is directly proportional to the [[partial pressure]] of that gas in equilibrium with that liquid. The equation is as follows:
:
:<math> p = k_{\rm H}\, c</math>
:
;[[Real gas law]]: This was formulated by [[Johannes Diderik van der Waals]] in 1873.

== References ==
{{Reflist}}

*{{Cite book |author1=Castka, Joseph F. |author2=Metcalfe, H. Clark |author3=Davis, Raymond E. |author4=Williams, John E. | title=Modern Chemistry | publisher=Holt, Rinehart and Winston | year=2002 | isbn=0-03-056537-5}}
*{{Cite book | author=Guch, Ian | title=The Complete Idiot's Guide to Chemistry | publisher=Alpha, Penguin Group Inc. | year=2003 | isbn=1-59257-101-8 | url=https://archive.org/details/completeidiotsgu00guch }}
*{{Cite book | author=Zumdahl, Steven S | title=Chemical Principles | publisher=Houghton Mifflin Company | year=1998 | isbn=0-395-83995-5 | url=https://archive.org/details/chemicalprincipl00zumd_1 }}
*[https://www.chem.fsu.edu/chemlab/chm1045/gas_laws.html FSU(Florida State University)]
==External links==
*{{Commonscat-inline}}

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[[Category:Gas laws| ]]
[[Category:History of thermodynamics]]