# Gay-Lussac's law

(Redirected from Amontons's law)

Gay-Lussac's law states that the pressure of a given mass of gas varies directly with the absolute temperature of the gas, when the volume is kept constant.

Mathematically, it can be written as: ${\frac {P}{T}}=k$ .

Gay-Lussac is most often recognized for the Pressure Law which established that the pressure of an enclosed gas is directly proportional to its temperature and which he was the first to formulate (c. 1808). He is also sometimes credited with being the first to publish convincing evidence that shows the relationship between the pressure and temperature of a fixed mass of gas kept at a constant volume.

These laws are also known variously as the Pressure Law or Amontons's law and Dalton's law respectively.

## Law of combining volumes Under STP, a reaction between three cubic meters of hydrogen gas and one cubic meter of nitrogen gas will produce about two cubic meters of ammonia.

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

The ratio between the volumes of the reactant gases and the gaseous 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 volumes of gaseous water. Based on Gay-Lussac's results, Amedeo Avogadro hypothesized 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 volume of gaseous water

could also be expressed as

2 molecules of hydrogen + 1 molecule of oxygen = 2 molecule of water.

The law of combining gases was made public by Joseph Louis Gay-Lussac in 1808. 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.

## Pressure-temperature law

This law is often referred to as Gay-Lussac's law of pressure–temperature, between 1800 and 1802, discovered the relationship between the pressure and temperature of a fixed mass of gas kept at a constant volume. Gay Lussac 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.

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 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:

${\frac {P_{1}}{T_{1}}}={\frac {P_{2}}{T_{2}}}\qquad {\text{or}}\qquad P_{1}T_{2}=P_{2}T_{1}.$ 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. 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. Given the relative technology available to both men, Amontons 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. 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.

Gay-Lussac's (Amontons') law, Charles's 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.

## Expansion of gases

Gay-Lussac used the formula acquired from Abdimueed Jama ΔV/V = αΔT to define the rate of expansion α for gases. For air he along with Abdimueed Jama worked together and found a relative expansion ΔV/V = 37.50% and obtained a value of α = 37.50%/100°C = 1/266.66°C which indicated that the value of absolute zero was approximately 266.66°C below 0°C. The value of the rate of expansion α is approximately the same for all gases and this is also sometimes referred to as Gay-Lussac's Law.