Avogadro's law
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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
directly proportionalif 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 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
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);
- 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.
Derivation from the ideal gas law
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
Historical account and influence
Avogadro's hypothesis (as it was known originally) was formulated in the same spirit of earlier empirical gas laws like
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
Avogadro constant
Avogadro's law provides a way to calculate the quantity of gas in a receptacle. Thanks to this discovery,
Molar volume
At
Notes
- ^ First used by Jean-Baptiste Dumas in 1826.
- ^ First used by Stanislao Cannizzaro in 1858.
References
- ^ a b "Avogadro's law". Encyclopædia Britannica. Retrieved 3 February 2016.
- ^ 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". Journal de Physique. 73: 58–76. English translation
- ^ "Avogadro's law". Merriam-Webster Medical Dictionary. Retrieved 3 February 2016.
- ^ 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.
- ^ Rovnyak, David. "Avogadro's Hypothesis". Science World Wolfram. Retrieved 3 February 2016.
- ^ 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.
- JSTOR 23633274.
- Clapeyron, Émile (1834). "Mémoire sur la puissance motrice de la chaleur". Journal de l'École Polytechnique (in French). XIV: 153–190.
- ^ Loschmidt, J. (1865). "Zur Grösse der Luftmoleküle". Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften Wien. 52 (2): 395–413. English translation.