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'''[[Amedeo Avogadro|Avogadro]]'s law''' (sometimes referred to as '''Avogadro's hypothesis''' or '''Avogadro's principle''') is an experimental [[gas laws|gas law]] relating [[volume]] of a gas to the [[amount of substance]] of gas present. A modern statement of Avogadro's law is:
<blockquote>


Avogadro's law states that, "equal volumes of all gases, at the same temperature and pressure, have the same number of molecules".
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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>
which 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]] equal to RT/P, where R is the universal gas constant, T is the Kelvin temperature, and P is the pressure.  As temperature and pressure are constant, RT/P is also constant and represented as ''k.'' This is derived from the [[ideal gas law]].
 
This law explains 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>
 
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.
 
The law is named after [[Amedeo Avogadro]] who, in 1811,<ref>{{cite journal | first = Amedeo | last = Avogadro | authorlink = Amedeo Avogadro | 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 | year = 1810 | volume = 73 | pages = 58–76 |url = http://books.google.com/books?id=MxgTAAAAQAAJ&pg=PA58#v=onepage&q&f=false }} [http://web.lemoyne.edu/~giunta/avogadro.html English translation]</ref> 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 molecules. As an example, equal volumes of molecular [[hydrogen]] and [[nitrogen]] contain the same number of molecules when they are at the same temperature and pressure, and observe [[ideal gas]] behavior. In practice, real gases show small deviations from the ideal behavior and the law holds only approximately, but is still a useful approximation for scientists.
 
==Mathematical definition==
Avogadro's law is stated mathematically as:
 
:<math>\frac{V}{n} = k</math>
Where:
:''V'' is the volume of the gas(es).
:''n'' is the [[amount of substance]] of the gas.
:''k'' is a proportionality [[Physical constant|constant]].
 
The most significant consequence of Avogadro's law is that the [[Gas constant|ideal gas constant]] has the same value for all gases. This means that:
:<math>\frac{p_1\cdot V_1}{T_1\cdot n_1}=\frac{p_2\cdot V_2}{T_2 \cdot n_2} = constant</math>
Where:
:''p'' is the [[pressure]] of the gas in the cell
:''T'' is the [[temperature]] in [[kelvin]] of the gas
 
==Ideal gas law==
A common rearrangement of this equation is by letting ''[[Gas constant|R]]'' be the proportionality constant, and rearranging as follows:
:<math>pV = nRT</math>
 
This equation is known as the [[ideal gas law]].
 
==Molar volume==
Taking [[Standard Temperature and Pressure|STP]] to be 101.325 [[kPa]] and 273.15 K, we can find the volume of one [[Mole (unit)|mole]] of a gas:
 
:<math>V_{\rm m} = \frac{V}{n} = \frac{RT}{p} = \frac{(8.314 \mathrm{ J} \mathrm{ mol}^{-1} \mathrm{ K}^{-1})(273.15 \mathrm{ K})}{101 325 \mathrm{ Pa}} = 22.41 \mathrm{ dm}^3 \mathrm{ mol}^{-1}</math>
 
For 100.000 [[kPa]] and 273.15 K, the molar volume of an ideal gas is 22.712 dm<sup>3</sup>mol<sup>−1</sup>.
 
==See also==
* [[Boyle's law]]
* [[Charles's law]]
* [[Combined gas law]]
* [[Gay-Lussac's law]]
* [[Ideal gas]]
 
==References==
{{reflist}}
 
==External links==
*[http://chimge.unil.ch/En/mat/1mat12.htm Avogadro's law] at the University of Fribourg
*[http://www.rsc.org/chemsoc/timeline//pages/1811.html Avogadro's law] at the Royal Society of Chemistry
 
[[Category:Gas laws]]
[[Category:Amount of substance]]
 
[[it:Volume molare#Legge di Avogadro]]

Latest revision as of 09:10, 25 December 2014


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