Avogadro's law
Avogadro's law (sometimes referred to as Avogadro's hypothesis or Avogadro's principle) or Avogadro-
Ampère's hypothesis is an experimental gas law relating the volume of a gas to the amount of substance of gas
present.[1] The law is a specific case of the ideal gas law. A modern statement is:
Avogadro's law states that "equal volumes of all gases, at the same temperature and pressure, have
the same number of molecules."[1]
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.
The law is named after Amedeo Avogadro who, in 1812,[2][3] 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 gaseous hydrogen and nitrogen contain the same number of atoms 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
Derivation from the ideal gas law
Historical account and influence
Ideal gas law
Avogadro constant
Molar volume
See also
Notes
References
The law can be written as:
or
where
V is the volume of the gas;
n is the amount of substance of the gas (measured in moles);
Contents
Mathematical definition

Relationships between Boyle's,
Charles's, Gay-Lussac's,
Avogadro's, combined and
ideal gas laws, with the
Boltzmann constant
kB =
R
NA
=
nR
N (in each law,
properties circled are variable and
properties not circled are held
constant)
k is a constant for a given temperature and pressure.
This law describes how, under the same condition of temperature and pressure, equal volumes of all gases
contain the same number of molecules. For comparing the same substance under two different sets of conditions,
the law can be usefully expressed as follows:
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 derivation of Avogadro's law follows directly from the ideal gas law,
i.e.
,
where R is the gas constant, T is the Kelvin temperature, and P is the
pressure (in pascals).
Solving for V/n, we thus obtain
.
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 kB, as
,
where N is the number of particles in the gas, and the ratio of R over kB is equal to the Avogadro constant.
In this form, for V/N is a constant, we have
.
If T and P are taken at standard conditions for temperature and pressure (STP), then k′ = 1/n0, where n0 is the
Loschmidt constant.
Derivation from the ideal gas law
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 Amadeo Avogadro in 1811,[4] 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.[5] In 1814, independently from Avogadro, André-Marie Ampère published the same law
with similar conclusions.[6] As Ampère was more well known in France, the hypothesis was usually referred
there as Ampère's hypothesis,[note 1] and later also as Avogadro–Ampère hypothesis[note 2] or even Ampère–
Avogadro hypothesis.[7]
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.
Boyle, Charles and Gay-Lussac laws, together with Avogadro's law, were combined by Émile Clapeyron in
1834,[8] 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 an statistical result from the
movement of atoms/molecules in a gas.
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.[9] His calculation gave
rise to the concept of the Loschmidt constant, a ratio between macroscopic and atomic quantities. In 1910,
Millikan's oil drop experiment determined the 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 of substance. At the
same time, precision experiments by Jean Baptiste Perrin led to the definition of Avogadro's 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.
Taking STP to be 101.325 kPa and 273.15 K, we can find the volume of one mole of gas:
For 101.325 kPa and 273.15 K, the molar volume of an ideal gas is 22.4127 dm3⋅mol−1.
Boyle's law – Relationship between pressure and volume in a gas at constant temperature
Charles's law – Relationship between volume and temperature of a gas at constant pressure
Ideal gas law
Avogadro constant
Molar volume
See also

Gay-Lussac's law – Relationship between pressure and temperature of a gas at constant volume.
Ideal gas – Mathematical model which approximates the behavior of real gases
1. First used by Jean-Baptiste Dumas in 1826.
2. First used by Stanislao Cannizzaro in 1858.
1. Editors of the Encyclopædia Britannica. "Avogadro's law" (http://www.britannica.com/science/Avo
gadros-law). Encyclopædia Britannica. Retrieved 3 February 2016.
2. Avogadro, Amedeo (1810). "Essai d'une manière de déterminer les masses relatives des
molécules élémentaires des corps, et les proportions selon lesquelles elles entrent dans ces
combinaisons" (https://books.google.com/books?id=MxgTAAAAQAAJ&pg=PA58). Journal de
Physique. 73: 58–76. English translation (http://web.lemoyne.edu/~giunta/avogadro.html)
3. "Avogadro's law" (https://www.merriam-webster.com/medical/Avogadro's%20law). Merriam-
Webster Medical Dictionary. Retrieved 3 February 2016.
4. Avogadro, Amadeo (July 1811). "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 de Physique, de Chimie, et d'Histoire Naturelle (in French). 73: 58–76.
5. Rovnyak, David. "Avogadro's Hypothesis" (http://scienceworld.wolfram.com/physics/AvogadrosH
ypothesis.html). Science World Wolfram. Retrieved 3 February 2016.
6. Ampère, André-Marie (1814). "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". Annales de Chimie (in
French). 90 (1): 43–86.
7. Scheidecker-Chevallier, Myriam (1997). "L'hypothèse d'Avogadro (1811) et d'Ampère (1814): la
distinction atome/molécule et la théorie de la combinaison chimique" (http://www.persee.fr/doc/rh
s_0151-4105_1997_num_50_1_1277). Revue d'Histoire des Sciences (in French). 50 (1/2):
159–194. doi:10.3406/rhs.1997.1277 (https://doi.org/10.3406%2Frhs.1997.1277).
JSTOR 23633274 (https://www.jstor.org/stable/23633274).
8. Clapeyron, Émile (1834). "Mémoire sur la puissance motrice de la chaleur" (https://gallica.bnf.fr/ar
k:/12148/bpt6k4336791/f157.table). Journal de l'École Polytechnique (in French). XIV: 153–190.
9. Loschmidt, J. (1865). "Zur Grösse der Luftmoleküle". Sitzungsberichte der Kaiserlichen
Akademie der Wissenschaften Wien. 52 (2): 395–413. English translation (https://web.archive.or
g/web/20060207130125/http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/Loschmidt-1865.ht
ml).
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Notes
References