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# Gay-Lussac

[gey-luh-sak; Fr. gey-ly-sak]
Gay-Lussac, Joseph Louis, 1778-1850, French chemist and physicist. He was professor in Paris at the Sorbonne, at the Polytechnic School, and at the Jardin des Plantes. Gay-Lussac made two balloon ascensions in 1804, attaining on the second a height of about 7,016 m (23,000 ft), to test the variation of the earth's magnetic field and the composition of the atmosphere at varying altitudes. He made advances in industrial chemistry; in the field of analytical chemistry he improved the methods of analyzing gas mixtures, studied prussic acid and iodine, and isolated cyanogen. With L. J. Thénard he improved Davy's method of isolating alkali metals, showed chlorine to be an element, and isolated boron. In physics he is known especially for his work on gases. In 1802 he discovered independently that a gas at constant pressure expands, for each degree of temperature, by a constant fraction of its volume at 0°C;. This law, first discovered (1787) by J. A. C. Charles, is known as Charles's law or as Gay-Lussac's law (see gas laws). However, Gay-Lussac's name is more commonly associated with another law of gases, the law of combining volumes, which Gay-Lussac was the first to formulate (c.1808). This law states that the volumes of gases that interact to give a gaseous product are in the ratio of small whole numbers to each other and that each bears a similar relation to the volume of the product.
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. One law relates to volumes in chemical reactions while the other concerns the pressures and temperatures of individual gases

## Law of combining volumes

The law of combining volumes states that:

The ratio between the combining volumes of gases and their reaction product, if gaseous, can be expressed in small whole numbers.

Gay discovered this law in 1809. It played a major role in the development of modern gas stoichiometry, and in 1811 Avogadro used Gay-Lussac’s Law to form Avogadro's hypothesis.

## Pressure-temperature law

The other law, discovered in 1802, states that:

The pressure of a fixed mass and fixed volume of a gas is directly proportional to the gas's 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 Kelvin. The law can then be expressed mathematically as:

$\left\{P\right\}propto\left\{T\right\}$
or
$frac\left\{P\right\}\left\{T\right\}=k$

where:

P is the pressure of the gas.
T is the temperature of the gas (measured in kelvins).
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:

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

Charles's Law was also known as the Law of Charles and Gay-Lussac, because Gay-Lussac published it in 1802 using much of Charles' unpublished data from 1787. However, in recent years the term has fallen out of favor since Gay-Lussac has the second but related law presented here and attributed to him. This related form of Gay-Lussac's Law, Charles's Law, and Boyle's law form the combined gas law. The three gas laws in combination with Avogadro's Law can be generalized by the ideal gas law.