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Gay-Lussac's law (also referred to as Amonton'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: . It is a special case of the ideal gas law. Gay-Lussac is incorrectly 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. 1809). 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.
The law of combining volumes states that, when gases react together they do so in volume which bears simple whole number ratio provided that the temperature and pressure of the reacting gases and their products remain constant
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 two volumes of hydrogen and one volume of oxygen would react to form two 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
could also be expressed as
It can also be expressed in another way of example, 100 mL of hydrogen combine with 50 mL of oxygen to give 100 mL of water vapour. Hydrogen(100 mL) + Oxygen(50 mL) = Water(100 mL)
Thus, the volumes of hydrogen and oxygen which combine (i.e., 100mL and 50mL) bear a simple ratio of 2:1.
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.
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".
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
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:
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 used the formula acquired from ΔV/V = αΔT to define the rate of expansion α for gases. For air he 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.