### Avogadro’S Law States That At A Given Temperature And Pressure, What Quantity Is Constant?

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• 19 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. 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,” 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, 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.

Ideal gas law – Boyle, Charles and Gay-Lussac laws, together with Avogadro’s law, were combined by Émile Clapeyron in 1834, 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.

### How is Avogadro’s law related to the ideal gas equation?

Derivation –

1. Avogadro’s law can be derived from the ideal gas equation, which can be expressed as follows:
2. PV = nRT
3. Where,
• ‘P’ is the pressure exerted by the gas on the walls of its container
• ‘V’ is the volume occupied by the gas
• ‘n’ is the amount of gaseous substance (number of moles of gas)
• ‘R’ is the
• ‘T’ is the absolute temperature of the gas
• Rearranging the ideal gas equation, the following equation can be obtained.
• V/n = (RT)/P
• Here, the value of (RT)/P is a constant (since the temperature and pressure kept constant and the product/quotient of two or more constants is always a constant). Therefore:
• V/n = k
• Thus, the proportionality between the volume occupied by a gas and the number of gaseous molecules is verified.

Avogadro constant – 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. 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 the Avogadro 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,