# Avogadro Molecule

In 1811 Avogadro put forward a hypothesis that was neglected by his contemporaries for years. Eventually proven correct, this hypothesis became known as Avogadro’s law, a fundamental law of gases.

Molecular Modeling With Avogadro. This is a simple and fun, hands-on activity that demonstrates the basic concepts of computer-based molecular modeling. Using molecular mechanics, small molecules may be modeled by treating the atoms as balls and the bonds connected them as springs. The value of the Avogadro constant was chosen so that the mass of one mole of a chemical compound, in grams, is numerically equal (for all practical purposes) to the average mass of one molecule of the compound, in daltons (universal atomic mass units); one dalton being 1 / 12 of the mass of one carbon-12 atom, which is approximately the mass.

Avogadro is an advanced molecule editor and visualizer designed for cross-platform use in computational chemistry, molecular modeling, bioinformatics, materials science, and related areas. It offers flexible high quality rendering and a powerful plugin architecture. Jul 24, 2018 Avogadro includes over 300 common molecules and molecular fragments to make building larger structures easy. Under the “Build” menu, hold your cursor over “Insert”, and then select “Fragment”. A database of fragments will then pop up (shown below). You can filter the selection if need be. In honor of Avogadro's contributions to molecular theory, the number of molecules per mole of substance is named the ' Avogadro constant ', NA. It is exactly 6.022 140 76 × 1023 mol−1. The Avogadro constant is used to compute the results of chemical reactions.

The contributions of the Italian chemist Amedeo Avogadro (1776–1856) relate to the work of two of his contemporaries, Joseph Louis Gay-Lussac and John Dalton. Gay-Lussac’s law of combining volumes (1808) stated that when two gases react, the volumes of the reactants and products—if gases—are in whole number ratios. This law tended to support Dalton’s atomic theory, but Dalton rejected Gay-Lussac’s work. Avogadro, however, saw it as the key to a better understanding of molecular constituency.

## Avogadro’s Hypothesis

In 1811 Avogadro hypothesized that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. From this hypothesis it followed that relative molecular weights of any two gases are the same as the ratio of the densities of the two gases under the same conditions of temperature and pressure. Avogadro also astutely reasoned that simple gases were not formed of solitary atoms but were instead compound molecules of two or more atoms. (Avogadro did not actually use the word *atom*; at the time the words *atom* and *molecule* were used almost interchangeably. He talked about three kinds of “molecules,” including an “elementary molecule”—what we would call an atom.) Thus Avogadro was able to overcome the difficulty that Dalton and others had encountered when Gay-Lussac reported that above 100°C the volume of water vapor was twice the volume of the oxygen used to form it. According to Avogadro, the molecule of oxygen had split into two atoms in the course of forming water vapor.

## bio-avogadro.jpg

Edgar Fahs Smith Collection, Kislak Center for Special Collections, Rare Books and Manuscripts, University of Pennsylvania

Curiously, Avogadro’s hypothesis was neglected for half a century after it was first published. Many reasons for this neglect have been cited, including some theoretical problems, such as Jöns Jakob Berzelius’s “dualism,” which asserted that compounds are held together by the attraction of positive and negative electrical charges, making it inconceivable that a molecule composed of two electrically similar atoms—as in oxygen—could exist. In addition, Avogadro was not part of an active community of chemists: the Italy of his day was far from the centers of chemistry in France, Germany, England, and Sweden, where Berzelius was based.

## Personal Life

Avogadro was a native of Turin, where his father, Count Filippo Avogadro, was a lawyer and government leader in the Piedmont (Italy was then still divided into independent countries). Avogadro succeeded to his father’s title, earned degrees in law, and began to practice as an ecclesiastical lawyer. After obtaining his formal degrees, he took private lessons in mathematics and sciences, including chemistry. For much of his career as a chemist he held the chair of physical chemistry at the University of Turin.

*The information contained in this biography was last updated on November 30, 2017.*

### Avogadro Copy Molecule

**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[edit]

The law can be written as:

- $V\propto n$

or

- $\frac{V}{n}=k$

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:

- $\frac{{V}_{1}}{{n}_{1}}=\frac{{V}_{2}}{{n}_{2}}$

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.

*k*=

_{B}*R*/

*N*=

_{A}*n R*/

*N*(in each law, properties circled are variable and properties not circled are held constant)

### Derivation from the ideal gas law[edit]

The derivation of Avogadro's law follows directly from the ideal gas law, i.e.

- $PV=nRT$,

### Avogadro Molecules Moles

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

- $\frac{V}{n}=\frac{RT}{P}$.

Compare that to

- $k=\frac{RT}{P}$

which is a constant for a fixed pressure and a fixed temperature. Gitlab readme syntax.

An equivalent formulation of the ideal gas law can be written using Boltzmann constant*k*_{B}, as

- $PV=N{k}_{\mathrm{B}}T$,

where *N* is the number of particles in the gas, and the ratio of *R* over *k*_{B} 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/*n*_{0}, where *n*_{0} is the Loschmidt constant.

### Avogadro's Number Molecules

## Historical account and influence[edit]

**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.

### Ideal gas law[edit]

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 constant[edit]

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'soil 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.

## Molar volume[edit]

Taking STP to be 101.325 kPa and 273.15 K, we can find the volume of one mole of gas:

- $V}_{\mathrm{m}}=\frac{V}{n}=\frac{RT}{P}=\frac{(8.314\text{J}\cdot {\text{mol}}^{-1}{\mathrm{K}}^{-1})(273.15\text{K})}{101.325\text{kPa}}=22.41{\text{dm}}^{3}{\text{mol}}^{-1}=22.41\text{liters}/\text{mol$

For 101.325 kPa and 273.15 K, the molar volume of an ideal gas is 22.4127 dm^{3}⋅mol^{−1}.

## See also[edit]

- 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
- 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

## Notes[edit]

**^**First used by Jean-Baptiste Dumas in 1826.**^**First used by Stanislao Cannizzaro in 1858.

## References[edit]

- ^
^{a}^{b}Editors of the Encyclopædia Britannica. 'Avogadro's law'.*Encyclopædia Britannica*. Retrieved 3 February 2016.CS1 maint: extra text: authors list (link) **^**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.**^**Scheidecker-Chevallier, Myriam (1997). 'L'hypothèse d'Avogadro (1811) et d'Ampère (1814): la distinction atome/molécule et la théorie de la combinaison chimique'.*Revue d'Histoire des Sciences*(in French).**50**(1/2): 159–194. doi:10.3406/rhs.1997.1277. JSTOR23633274.**^**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.