# Ideal Gas Equation

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Physik
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JoVE Core Physik
Ideal Gas Equation

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The state variables for gas under study are pressure, volume, temperature, and the number of moles.

Avogadro's law states that the gas volume is proportional to its number of moles at constant temperature and pressure.

Similarly, Boyle's law expresses that the pressure is inversely proportional to the volume of the gas for a given number of moles and at constant temperature.

Furthermore, Charles's law gives the relationship between the volume and temperature of the gas at constant pressure and a given number of moles.

Similarly, Gay-Lussac's Law states that the pressure of a gas is proportional to its temperature for a given number of moles and at constant volume.

These four laws combined give the ideal gas equation. The proportionality constant is the universal gas constant, with a value of 8.314 joules per mole kelvin in the SI units. It is independent of the type of gas under the study.

The ideal gas equation describes any gas at higher temperatures and low pressures.

## Ideal Gas Equation

The ideal gas equation is an equation of state that relates the state variables pressure, volume, temperature, and the number of moles of a hypothetical gas. This equation is a combination of four empirical laws, namely Boyle’s Law, Charles’s Law, Avogadro’s Law, and Gay-Lussac’s Law. When the proportionalities of the above four empirical laws are combined, it results in a single proportionality constant known as the universal gas constant.

This gas constant is the same for all real gases under certain conditions. The value of the universal gas constant is

but, when the ideal gas equation is used in chemical calculations, the value of the universal gas constant is

The ideal gas equation describes the nature of any real gas when its density is low enough or its temperature is high enough that it is far from liquefaction.

In real-world situations, the ideal gas law is applied to a sample of gas with a constant number of molecules; for instance, the gas may be in a sealed container. If the number of moles are constant, then the ratio of pressure multiplied by volume to the temperature of a gas is constant. In such cases, the ratio of pressure multiplied by volume to the temperatures in two different states of the gas can be equated. Here, the temperature must be expressed in kelvin, and the pressure must be absolute pressure, which is the sum of gauge pressure and the atmospheric pressure.

The ideal gas equations can also be expressed in terms of Boltzmann's constant as

Here, kB is Boltzmann’s constant, and NA is Avogadro's number. The ideal gas equation can be derived using the kinetic theory of gases. The ideal gas equation is closely related to energy. The units on both sides of the equation are joules.