Avogadro's law is also known as Avogadro's hypothesis or Avogadro's principle. The law dictates the relationship between the volume of a gas to the number of molecules the gas possesses. This law like Boyle's law, Charles's law, and Gay-Lussac's law is a specific case of the ideal gas law. This law is named after Italian scientist Amedeo Avogadro.

Which of the following is a variable in Avogadro's Law, but not in Boyle's, Charles's, and Gay-Lussac's Laws? 2 L sample of gas is determined to contain 0.5 moles of nitrogen. At the same temperature and pressure, how many moles of gas would there be in a 20 L sample? Avogadro’s law, a statement that under the same conditions of temperature and pressure, equal volumes of different gases contain an equal number of molecules. This empirical relation can be derived from the kinetic theory of gases under the assumption of a perfect (ideal) gas. Avogadro’s Law states that: 1 mole of every gas occupies the same volume, at the same temperature and pressure. At STP (standard temperature and pressure), this volume is 22.4 liters At RTP (room temperature and pressure), this volume is 24 dm 3 (liters) We can also say: The molar volume of a gas is 22.4 liters at STP (standard temperature. In 1811, Amedeo Avogadro, who also studied the behaviour of gases when they react, proposed the law which states that: Equal volume of all gases at the same temperature and pressure contain the same number of molecules. The law shows that the volume occupied by a gas depends on the number of molecules it contains at a given temperature.

#### Solution

1. In the year 1811, Avogadro made a distinction between atoms and molecules and thereby proposed Avogadro’s law.
2. Avogadro proposed that, “Equal volumes of all gases at the same temperature and pressure contain an equal number of molecules”.
e.g. Hydrogen gas combines with oxygen gas to produce water vapour as follows:
[ce{underset{text{[2 vol]}}{underset{text{[100 mL]}}{Hydrogen}_{(g)}} + underset{text{[1 vol]}}{underset{text{[50 mL]}}{Oxygen}_{(g)}}->underset{text{[2 vol]}}{underset{text{[100 mL]}}{Water}_{(g)}}}]
cording to Avogadro’s law, if 1 volume contains n molecules, then 2n molecules of hydrogen combine with n molecules of oxygen to give 2n molecules of water, i.e., 2 molecules of hydrogen gas combine with 1 molecule of oxygen to give 2 molecules of water vapour as represented below:
[ce{underset{text{[2 molecules]}}{underset{text{[2n molecules]}}{Hydrogen}_{(g)}} + underset{text{[1 molecule]}}{underset{text{[n molecules]}}{Oxygen}_{(g)}}->underset{text{[2 molecules]}}{underset{text{[2n molecules]}}{Water}_{(g)}}}]
Is there an error in this question or solution?

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

The law can be written as:

${displaystyle Vpropto n,}$

or

${displaystyle {frac {V}{n}}=k}$

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:

${displaystyle {frac {V_{1}}{n_{1}}}={frac {V_{2}}{n_{2}}}}$

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.

Relationships between Boyle's, Charles's, Gay-Lussac's, Avogadro's, combined and ideal gas laws, with the Boltzmann constantkB = R/NA = n R/N (in each law, properties circled are variable and properties not circled are held constant)

### Derivation from the ideal gas law

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

${displaystyle PV=nRT}$,

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

${displaystyle {frac {V}{n}}={frac {RT}{P}}}$.

Compare that to

${displaystyle k={frac {RT}{P}}}$

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 constantkB, as

${displaystyle PV=Nk_{rm {B}}T}$,

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

${displaystyle {frac {V}{N}}=k$.

If T and P are taken at standard conditions for temperature and pressure (STP), then k′ = 1/n0, where n0 is the Loschmidt constant.

## 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.

### Ideal gas law

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'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

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

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

For 101.325 kPa and 273.15 K, the molar volume of an ideal gas is 22.4127 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
• 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

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

## References

1. ^ abEditors of the Encyclopædia Britannica. 'Avogadro's law'. Encyclopædia Britannica. Retrieved 3 February 2016.CS1 maint: extra text: authors list (link)
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'. Journal de Physique. 73: 58–76.English translation
3. ^'Avogadro's law'. 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'. 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'. Revue d'Histoire des Sciences (in French). 50 (1/2): 159–194. doi:10.3406/rhs.1997.1277. JSTOR23633274.
8. ^Clapeyron, Émile (1834). 'Mémoire sur la puissance motrice de la chaleur'. 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.