The Avogadro's law , even Avogadro's law , Avogadrosches principle or set of Avogadro is a historical from Amedeo Avogadro 1811 -positioned law according to which all gases at the same temperature and pressure in the same volumes of the same number of particles ( atoms with noble gases and metals or Molecules in polyatomic gases). The mean distance between the particles in relation to the range of their interactions must be so great that the interaction is negligible. In this case one speaks of an ideal gas . If the interactions are not negligible, a real gas is obtained .

Avogadro derived this law from the legal relationships found by Gay-Lussac about the compounds of gaseous substances. He differentiated between atoms and molecules and also emphasized that when the elements transition into the gas state, they often only dissolve into molecules, which still consist of several individual atoms, but not into atoms.

## Different formulations

Gases consist of molecules or of atoms. When atoms and molecules are grouped together as "smallest particles", the following applies:

• "The same volumes of all gases contain the same number of tiny particles at the same temperature and pressure ."

From the gas laws of Gay-Lussac and Boyle-Mariotte it follows for a homogeneous gas, i.e. for a type of gas for which temperature and pressure are the same everywhere in the volume:

${\ displaystyle {\ frac {p_ {1} \ cdot V_ {1}} {T_ {1} \ cdot n_ {1}}} = {\ frac {p_ {2} \ cdot V_ {2}} {T_ { 2} \ cdot n_ {2}}} = {\ text {const.}}}$

The set of Avogadro now states that this constant assumes the same value for all gases, it is the universal or universal gas constant R . This cannot be taken for granted because it means:

• "The same number of particles in two different gases always exerts the same pressure at the same temperature and enclosed in the same volume"

Different gases also have different large molar masses , i.e. the particles have different weights. Heavier particles move more slowly at the same temperature, so their speed is lower. Therefore, it is expected that the number of collisions per unit area is smaller to a vessel wall for heavier molecules, but also, it means the transmitted event of an impact pulse is correspondingly larger. The pressure resulting from the impact is the same, that is, the different influences just balance each other out.

It follows that the gas equation

${\ displaystyle p \ cdot V = n \ cdot R \ cdot T}$

applies to all sufficiently diluted gases. It is a general gas equation that applies in particular regardless of the molecular or molar mass and is therefore independent of the substance .

## application

From Avogadro's law it follows indirectly that the density of different gases at the same pressure and temperature is proportional to the molar mass. This also applies to molecules of the same gas, which consist of different isotopes of the elements. This fact applies to uranium enrichment .

Another important application of the law is the determination of molecular or molar masses (often incorrectly referred to as “molecular weights”) by weighing a known volume of gas.

## meaning

### Historical significance and new knowledge

By the end of the 18th century, more precise weighing made it possible to determine the density of gases. With the discovery of electrolysis, water could be converted into two types of gas: oxygen and hydrogen .

According to Lavoisier, all chemical substances are built up from the elementary substances, the elements. The metals known at the time such as silver, copper, lead and tin were classified as elements by Lavoisier. These elements were able to enter into oxygène compounds with the gas in the air , creating compound substances such as lead oxide, tin oxide or copper oxide.

Which substances were elements and which substances were composite substances? Chemists dealt with these questions in the years that followed. The gases were the key to determining the elements.

Since oxygen and hydrogen are different from water vapor, the water that was formed from oxygen and hydrogen in an oxyhydrogen explosion had to be a compound substance.

Avogadro derived this law from the lawful relationships found by Gay-Lussac about the connections between gaseous bodies. Avogadro now established the law that the same number of gas particles are present in the same volume at the same pressure and temperature. He used the terms molécules élémentaires (atoms) and molécules intégrantes (molecules). The law also applied to a composite gas. Avogadro assumed that the elements are also composed. Every molecule of an element in the gas phase should consist of two atoms of the element.

A treatise by André-Marie Ampère appeared three years after Avogadro's publication . At that time, Ampère used the term particle for molecules . Ampère, however, had different views on the particles, assuming that they should consist of at least eight atoms. In 1833, Marc Antoine Gaudin corrected Ampère's atomic theory and, like Avogadro, assumed two atoms for an elementary gas. For other substances like mercury he postulated monatomic particles in the gas phase, for sulfur he assumed six atoms in the gas phase. Since the theories about molecules in the gas phase were quite complex, they were soon forgotten and the majority of chemists around 1845 did not know the ideas of Avogadro.

Jean Baptiste Dumas used vapor density to determine the atomic mass of a large number of substances. Charles Frédéric Gerhardt formulated formulas for hydrogen chloride , water, ammonia and carbon dioxide from vapor density . He compared the determined atomic masses with the atomic masses of Berzelius and then found differences. Gerhardt related the atomic mass to hydrogen . Berzelius used oxygen as a reference point . To explain the deviations in the atomic masses, Gerhardt assumed that an organic molecule needs two parts by volume in the gas phase. ${\ displaystyle H = 1}$${\ displaystyle O = 100}$

Only Stanislao Cannizzaro rediscovered the work of Avogadro. It was important to realize that certain gas molecules can transform into the elements at higher temperatures and thus falsify measurements. By determining the vapor density of diethyl zinc , which was first presented by Edward Frankland , the correct interpretation of the molecules in the gas phase succeeded. He concluded that hydrogen in the gaseous state must not be present as an atomic gas, but as an H 2 molecule. Other gases such as oxygen and nitrogen also had to be in molecular and not in atomic form. He also concluded that the atomic mass of metals had to be twice as high as previously stated.

Thanks to the findings of Cannizzaro, the molecular masses of many volatile organic substances could be determined in the subsequent period, so that the structure clarification of substances was significantly improved.

Avogadro's views did not come into their own until nearly half a century after they were first formulated. Since the molar masses are of fundamental importance, this law provided a secure foundation for the further expansion of chemistry. Avogadro's law was therefore of great importance, especially for chemistry in general. But it is also important for physics, especially for the kinetic gas theory , which was further developed by James Clerk Maxwell .

### Today's meaning

Nowadays molar masses are determined almost exclusively with the help of the mass spectrometer , so that the law is no longer used for this purpose today. But it has a didactic value and is in the thermal equation of state of ideal gases

${\ displaystyle p \ cdot V = n \ cdot R_ {m} \ cdot T}$

- albeit hidden - included (here in the form of the general gas equation).

## Literature sources

1. Lorenzo Romano Amadeo Carlo Avogadro: Essai d'une manière de déterminer les masses relatives des molécules élémentaires des corps, et les proportions selon lesquelles elles entrent dans les combinaisons . In: Journal de physique, de chimie, d'histoire naturelle et des arts . tape 73 , 1811, pp. 58–76 ( digitized in the Google book search).
2. ^ André-Marie Ampère: Lettre de M. Ampère à M. le comte Berthollet sur la détermination des proportions dans lesquelles les corps se combined d'après le nombre et la disposition, respectively des molécules dont les parties intégrantes sont composées . In: Annales de chimie . tape 90 , 1814, ISSN  0365-1444 , p. 43–86 ( digitized as PDF ).
3. AM Gaudin: Recherches sur la Structure intime des Corps inorganiques définis, et Considérations générales sur le rôle que jouent leurs dernières particules dans les principaux phénomenès de la nature, tels que la conductibilité de l'élctricite et de la chaleur, le magnétisme, la refraction (simple or double) et la polansation de la lumière . In: Annales de chimie et de physique . tape 52 , 1833, ISSN  0365-1444 , p. 113–133 ( digitized in the Google book search).
4. ^ J. Dumas: Mémoire sur quelques points de la théorie atomistique . In: Annales de chimie et de physique . tape 33 , 1826, ISSN  0365-1444 , p. 337–391 ( digitized in the Google book search).
5. ^ Charles Gerhardt: Considerations sur les equivalents de quelques corps simples et composés . In: Annales de chimie et de physique, 2nd ser. tape 7 , 1843, ISSN  0365-1444 , p. 129-143 ( digitized on Gallica ). Charles Gerhardt: Considerations sur les equivalents de quelques corps simples et composés (I) . In: Annales de chimie et de physique, 2nd ser. tape 7 , 1843, ISSN  0365-1444 , p. 238–245 ( digitized on Gallica ).