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{{Short description|Relationship between volume and amount of a gas at constant temperature and pressure}}
'''Avogadro's law''' (sometimes referred to as '''Avogadro's hypothesis''' or '''Avogadro's principle''') or '''Avogadro-Ampère's hypothesis''' is an experimental [[gas laws|gas law]] relating the [[volume]] of a gas to the [[amount of substance]] of gas present.<ref name="Britannica">{{cite encyclopedia |entry-url=http://www.britannica.com/science/Avogadros-law |entry=Avogadro's law |encyclopedia=[[Encyclopædia Britannica]]| access-date=3 February 2016}}</ref> The law is a specific case of the [[ideal gas law]]. A modern statement is:
<blockquote>
Avogadro's law states that "equal volumes of all gases, at the same [[temperature]] and [[pressure]], have the same number of [[molecule]]s."<ref name="Britannica"/>
For a given mass of an [[ideal gas]], the volume and amount (moles) of the gas are [[directly proportional]] if the temperature and pressure are constant.
</blockquote>
The law is named after [[Amedeo Avogadro]] who, in 1812,<ref>{{cite journal | first = Amedeo | last = Avogadro | author-link = Amedeo Avogadro | title = Essai d'une manière de déterminer les masses relatives des molécules élémentaires des corps, et les proportions selon lesquelles elles entrent dans ces combinaisons | journal = Journal de Physique | year = 1810 | volume = 73 | pages = 58–76 |url = https://books.google.com/books?id=MxgTAAAAQAAJ&pg=PA58 }} [http://web.lemoyne.edu/~giunta/avogadro.html English translation]</ref><ref name="US Definition">{{cite web|url=https://www.merriam-webster.com/medical/Avogadro's%20law | title=Avogadro's law | website=[[Merriam-Webster]] Medical Dictionary | access-date=3 February 2016}}</ref> [[Hypothesis|hypothesized]] that two given samples of an ideal gas, of the same volume and at the same temperature and pressure, contain the same number of [[Molecule|molecules]]. As an example, equal volumes of gaseous [[hydrogen]] and [[nitrogen]] contain the same number of molecules when they are at the same temperature and pressure, and display [[ideal gas]] behavior. In practice, [[real gas]]es show small deviations from the ideal behavior and the law holds only approximately, but is still a useful approximation for scientists.
==Mathematical definition==
:<math>n = \frac{PV}{RT}</math>▼
The law can be written as:
:<math>V \propto n</math>
or
:<math>\frac{V}{n} = k</math>
where
*''V'' is the [[volume]] of the gas;
*''n'' is the [[amount of substance]] of the gas (measured in [[mole (unit)|moles]]);
*''k'' is a [[Constant (mathematics)|constant]] for a given temperature and pressure.
This law describes how, under the same condition of [[temperature]] and [[pressure]], equal [[volume]]s of all [[gas]]es contain the same number of [[molecule]]s. For comparing the same substance under two different sets of conditions, the law can be usefully expressed as follows:
:<math>\frac{V_1}{n_1} = \frac{V_2}{n_2}</math>
[[Category:Chemistry]]▼
[[Category:Thermodynamics]]▼
The equation shows that, as the number of moles of gas increases, the volume of the gas also increases in proportion. Similarly, if the number of moles of gas is decreased, then the volume also decreases. Thus, the number of molecules or atoms in a [[specific volume]] of ideal gas is independent of their size or the [[molar mass]] of the gas.
{{Ideal gas law relationships.svg}}
=== Derivation from the ideal gas law ===
The derivation of Avogadro's law follows directly from the [[ideal gas law]], i.e.
:<math>PV = nRT ,</math>
where ''R'' is the [[gas constant]], ''T'' is the [[Thermodynamic temperature|Kelvin temperature]], and ''P'' is the pressure (in [[Pascal (unit)|pascals]]).
Solving for ''V/n'', we thus obtain
:<math>\frac{V}{n} = \frac{RT}{P}.</math>
Compare that to
which is a constant for a fixed pressure and a fixed temperature.
An equivalent formulation of the ideal gas law can be written using [[Boltzmann constant]] ''k''<sub>B</sub>, as
:<math>PV = N k_\text{B} T,</math>
where ''N'' is the number of particles in the gas, and the ratio of ''R'' over ''k''<sub>B</sub> is equal to the [[Avogadro constant]].
In this form, for ''V/N'' is a constant, we have
:<math>\frac{V}{N} = k' = \frac{k_{\text{B}}T}{P}.</math>
If ''T'' and ''P'' are taken at [[standard conditions for temperature and pressure]] (STP), then ''k''′ = 1/''n''<sub>0</sub>, where ''n''<sub>0</sub> is the [[Loschmidt constant]].
==Historical account and influence==
'''Avogadro's hypothesis''' (as it was known originally) was formulated in the same spirit of earlier empirical gas laws like [[Boyle's law]] (1662), [[Charles's law]] (1787) and [[Gay-Lussac's law]] (1808). The hypothesis was first published by Amedeo Avogadro in 1811,<ref>{{Cite journal |last=Avogadro |first=Amedeo |date=July 1811 |title=Essai d'une maniere de determiner les masses relatives des molecules elementaires des corps, et les proportions selon lesquelles elles entrent dans ces combinaisons | journal=Journal de Physique, de Chimie, et d'Histoire Naturelle |language=fr |volume=73 |pages=58–76}}</ref> and it reconciled [[Dalton atomic theory]] with the "incompatible" idea of [[Joseph Louis Gay-Lussac]] that some gases were composite of different fundamental substances (molecules) in integer proportions.<ref name="Hypothesis">{{cite web|url=http://scienceworld.wolfram.com/physics/AvogadrosHypothesis.html|title=Avogadro's Hypothesis|last=Rovnyak|first=David|website=Science World Wolfram|access-date=3 February 2016}}</ref> In 1814, independently from Avogadro, [[André-Marie Ampère]] published the same law with similar conclusions.<ref>{{Cite journal|last=Ampère|first=André-Marie|author-link=André-Marie Ampère|date=1814|title=Lettre de M. Ampère à M. le comte Berthollet sur la détermination des proportions dans lesquelles les corps se combinent d'après le nombre et la disposition respective des molécules dont les parties intégrantes sont composées|journal=Annales de Chimie| language=fr| volume=90| issue=1|pages=43–86}}</ref> As Ampère was more well known in France, the hypothesis was usually referred there as '''Ampère's hypothesis''',<ref group="note">First used by [[Jean-Baptiste Dumas]] in 1826.</ref> and later also as '''Avogadro–Ampère hypothesis'''<ref group="note">First used by [[Stanislao Cannizzaro]] in 1858.</ref> or even '''Ampère–Avogadro hypothesis'''.<ref>{{Cite journal| last=Scheidecker-Chevallier |first=Myriam |date=1997 |title=L'hypothèse d'Avogadro (1811) et d'Ampère (1814): la distinction atome/molécule et la théorie de la combinaison chimique|journal=Revue d'Histoire des Sciences| language=fr |volume=50 |issue=1/2 |pages=159–194 |jstor=23633274 |doi=10.3406/rhs.1997.1277 |url=http://www.persee.fr/doc/rhs_0151-4105_1997_num_50_1_1277}}</ref>
Experimental studies carried out by [[Charles Frédéric Gerhardt]] and [[Auguste Laurent]] on [[organic chemistry]] demonstrated that Avogadro's law explained why the same quantities of molecules in a gas have the same volume. Nevertheless, related experiments with some inorganic substances showed seeming exceptions to the law. This apparent contradiction was finally resolved by [[Stanislao Cannizzaro]], as announced at [[Karlsruhe Congress]] in 1860, four years after Avogadro's death. He explained that these exceptions were due to molecular dissociations at certain temperatures, and that Avogadro's law determined not only molecular masses, but atomic masses as well.
=== Ideal gas law ===
Boyle, Charles and Gay-Lussac laws, together with Avogadro's law, were combined by [[Benoît Paul Émile Clapeyron|Émile Clapeyron]] in 1834,<ref>{{Cite journal|last=Clapeyron|first=Émile|author-link=Émile Claperyon|date=1834|title=Mémoire sur la puissance motrice de la chaleur|url=https://gallica.bnf.fr/ark:/12148/bpt6k4336791/f157.table|journal=Journal de l'École Polytechnique|language=fr|volume=XIV|pages=153–190}}</ref> giving rise to the ideal gas law. At the end of the 19th century, later developments from scientists like [[August Krönig]], [[Rudolf Clausius]], [[James Clerk Maxwell]] and [[Ludwig Boltzmann]], gave rise to the [[kinetic theory of gases]], a microscopic theory from which the ideal gas law can be derived as a statistical result from the movement of atoms/molecules in a gas.
=== Avogadro constant ===
Avogadro's law provides a way to calculate the quantity of gas in a receptacle. Thanks to this discovery, [[Johann Josef Loschmidt]], in 1865, was able for the first time to estimate the size of a molecule.<ref>{{cite journal |last=Loschmidt |first=J. |author-link=Johann Josef Loschmidt|year=1865|title=Zur Grösse der Luftmoleküle|journal=Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften Wien|volume=52|issue=2|pages=395–413}} [https://web.archive.org/web/20060207130125/http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Loschmidt-1865.html English translation].</ref> His calculation gave rise to the concept of the [[Loschmidt constant]], a ratio between macroscopic and atomic quantities. In 1910, [[Robert Andrews Millikan|Millikan's]] [[oil drop experiment]] determined the [[Elementary charge|charge]] of the [[electron]]; using it with the [[Faraday constant]] (derived by [[Michael Faraday]] in 1834), one is able to determine the number of particles in a [[Mole (unit)|mole]] of substance. At the same time, precision experiments by [[Jean Baptiste Perrin]] led to the definition of the Avogadro number as the number of molecules in one [[gram-molecule]] of [[oxygen]]. Perrin named the number to honor Avogadro for his discovery of the namesake law. Later standardization of the [[International System of Units]] led to the modern definition of the [[Avogadro constant]].
==Molar volume==
{{main|Molar volume}}
At [[standard temperature and pressure]] (100 [[kPa]] and 273.15 [[kelvin|K]]), we can use Avogadro's law to find the molar volume of an ideal gas:
:<math>V_\text{m} = \frac{V}{n} = \frac{RT}{P} \approx
\frac{\mathrm{8.3145\ \frac{J}{mol\cdot K} \times 273.15\ K}}{\mathrm{100\ kPa}} \approx
\mathrm{22.711\ L/mol}</math>
Similarly, at [[Standard atmosphere (unit)|standard atmospheric pressure]] (101.325 kPa) and 0 [[Celsius|°C]] (273.15 K):
:<math>V_\text{m} = \frac{V}{n} = \frac{RT}{P} \approx
\frac{\mathrm{8.3145\ \frac{J}{mol\cdot K} \times 273.15\ K}}{\mathrm{101.325\ kPa}} \approx
\mathrm{22.414\ L/mol}</math>
==See also==
* [[List of eponymous laws]]
== Notes ==
<references group="note" />
==References==
{{Reflist}}
{{Mole concepts}}
{{Authority control}}
[[it:Volume molare#Legge di Avogadro]]
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