# 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. 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 amount of gas at a fixed volume is directly proportional to its temperature in kelvins.

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 is 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 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:

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

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Law was also known as the Law of Charles and Gay-Lussac, because Gay-Lussac published it in 1802 using much of Charles' unpublished data from 1787.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.