# Gay-Lussac's law

The expression Gay-Lussac's law is used for each of the two relationships named after the French chemist Joseph Louis Gay-Lussac and which concern the properties of gases, though it is more usually applied to his law of combining volumes, the first listed here. The first law relates to volumes before and after a chemical reaction while the second concerns the pressure and temperature relationship for a sample of gas often known as Amontons' Law.

## Law of combining volumes

Under STP, a reaction between three cubic meters of hydrogen gas and one cubic meter of nitrogen gas will produce circa two cubic meters of ammonia

The law of combining volumes states that, when gases react together to form other gases, and all volumes are measured at the same temperature and pressure:

The ratio between the volumes of the reactant gases and the products can be expressed in simple whole numbers.

For example, Gay-Lussac found that 2 volumes of Hydrogen and 1 volume of Oxygen would react to form 2 volume of gaseous water. In addition to Gay-Lussac's results, Amedeo Avogadro theorized that, at the same temperature and pressure, equal volumes of gas contain equal numbers of molecules (Avogadro's law). This hypothesis meant that the previously stated result

2 volumes of Hydrogen + 1 volume of Oxygen = 2 volumes of gaseous water

could also be expressed as

2 molecules of Hydrogen + 1 molecule of Oxygen = 2 molecules of water.

The law of combining gases was made public by Joseph Louis Gay-Lussac in 1808.[1][2] Avogadro's hypothesis, however, was not initially accepted by chemists until the Italian chemist Stanislao Cannizzaro was able to convince the First International Chemical Congress in 1860.[3]

## Pressure-temperature law

This law is often referred to as Amontons' Law of Pressure-Temperature after Guillaume Amontons, who, between 1700 and 1702, discovered the relationship between the pressure and temperature of a fixed mass of gas kept at a constant volume[4][5][6] Amontons discovered this while building an "air thermometer".

The pressure of a gas of fixed mass and fixed volume is directly proportional to the gas's absolute temperature.

Illustration of pressure varying with temperature.

Simply put, if a gas's temperature increases, then so does its pressure if the mass and volume of the gas are held constant. The law has a particularly simple mathematical form if the temperature is measured on an absolute scale, such as in kelvins. The law can then be expressed mathematically as:

${P}\propto{T}$

or

$\frac{P}{T}=k$

where:

P is the pressure of the gas
T is the temperature of the gas (measured in Kelvin).
k is a constant.

This law holds true because temperature is a measure of the average kinetic energy of a substance; as the kinetic energy of a gas increases, its particles collide with the container walls more rapidly, thereby exerting increased pressure.

For comparing the same substance under two different sets of conditions, the law can be written as:

$\frac{P_1}{T_1}=\frac{P_2}{T_2} \qquad \mathrm{or} \qquad {P_1}{T_2}={P_2}{T_1}.$

Because Amontons discovered the law beforehand, Gay-Lussac's name is now generally associated within chemistry with the law of combining volumes discussed in the section above. Some introductory physics textbooks still define the pressure-temperature relationship as Gay-Lussac's law.[7][8] Gay-Lussac primarily investigated the relationship between volume and temperature and published it in 1802, but his work did cover some comparison between pressure and temperature.[9] Given the relative technology to both men, Amonton was only able to work with air as a gas, where Gay-Lussac was able to experiment with multiple types of common gases, such as oxygen, nitrogen, and hydrogen.[10] Gay-Lussac did attribute his findings to Jacques Charles because he used much of Charles's unpublished data from 1787 - hence, the law became known as Charles's law or the Law of Charles and Gay-Lussac[11] However, in recent years the term has fallen out of favor.

Gay-Lussac's (Amontons') Law, Charles' Law, and Boyle's law form the combined gas law. These three gas laws in combination with Avogadro's Law can be generalized by the ideal gas law.

## References

1. ^ Gay-Lussac (1809) "Mémoire sur la combinaison des substances gazeuses, les unes avec les autres" (Memoir on the combination of gaseous substances with each other), Mémoires de la Société d'Arcueil 2: 207-234. Available in English at: Le Moyne College.
2. ^ http://www.chemistryexplained.com/Fe-Ge/Guy-Lussac-Joseph-Louis.html
3. ^ Hartley, Harold (1966). "Stanislao Cannizzaro, F.R.S. (1826 – 1910) and the First International Chemical Conference at Karlsruhe". Notes and Records of the Royal Society of London 21: 56–63. doi:10.1098/rsnr.1966.0006.
4. ^ Barnett, Martin K. (Aug 1941), "A brief history of thermometry", Journal of Chemical Education 18 (8): 358, Bibcode:1941JChEd..18..358B, doi:10.1021/ed018p358. Extract.
5. ^ http://web.fccj.org/~ethall/gaslaw/gaslaw.htm
6. ^ See:
7. ^ Tippens, Paul E. (2007). Physics, 7th ed. McGraw-Hill. 386-387.
8. ^ Cooper, Crystal (Feb. 11, 2010). "Gay-Lussac's Law". Bright Hub Engineering. Retrieved from http://www.brighthubengineering.com/hvac/26213-gay-lussacs-law/ on July 8, 2013.
9. ^ Crosland, Maurice P. (2004). Gay-Lussac: Scientist and Bourgeois. Cambridge University Press. 119-120.
10. ^ Astimov, Issac (1966). Understanding Physics - Motion, Sound, and Heat. Walker and Co. 191-192.
11. ^ Gay-Lussac (1802) "Recherches sur la dilatation des gaz et des vapeurs" (Researches on the expansion of gases and vapors) Annales de Chimie 43: 137-175. On page 157, Gay-Lussac mentions the unpublished findings of Charles: "Avant d'aller plus loin, je dois prévenir que quoique j'eusse reconnu un grand nombre de fois que les gaz oxigène, azote, hydrogène et acide carbonique, et l'air atmosphérique se dilatent également depuis 0° jusqu'a 80°, le cit. Charles avait remarqué depuis 15 ans la même propriété dans ces gaz ; mais n'avant jamais publié ses résultats, c'est par le plus grand hasard que je les ai connus." (Before going further, I should inform [you] that although I had recognized many times that the gases oxygen, nitrogen, hydrogen, and carbonic acid [i.e., carbon dioxide], and atmospheric air also expand from 0° to 80°, citizen Charles had noticed 15 years ago the same property in these gases; but having never published his results, it is by the merest chance that I knew of them.) Available in English at: Le Moyne College.
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