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The Ideal Gas Law describes the state of gases under ideal circumstances when gas molecules are visualized in a certain way. Because conditions in the real world do not match the hypothetical state of the molecules in the Ideal Gas Law, it is only an approximation.

The law describes the state of a gas in terms of temperature, pressure and volume, which are related according to a law formulated by Emile Clapeyron in 1834. It is most accurate for monatomic gases at high temperatures and low pressures. Other equations more precisely describe the actual state of specific volumes of gas.

**The Equation**

According to the equation, the pressure of a gas times the volume of a gas is equal to the number of moles of a gas times the temperature of the gas, times a constant, R. It is written:

PV = nRT.

**Definitions**

- A mole is the mass in grams of a pure substance that is equal to its atomic mass. For example, Carbon-12 has an atomic mass of 12, so therefore a mole of carbon atoms is 12 grams. The letter n symbolizes moles in the Ideal Gas Law equation.
- Avogadro's constant is 6.0221 x 10^23 per mole. It expresses the number of elementary entities, usually atoms or molecules, per mole of a substance. In other words, it is the number of atoms in twelve grams of Carbon-12.
- Boltzmann's constant is 1.38066 x 10^ -23 joules per Kelvin. It defines the relationship between temperature and kinetic energy in an ideal gas.
- The constant R is equal to Avogadro's constant times Boltzmann's constant.

**Hypothetical conditions**

For the purposes of the Ideal Gas Law, there are no collisions between molecules or atoms and no intermolecular attractive forces. The gas molecules are visualized as hard impenetrable spheres that may collide but do not otherwise interact.

**Emile Clapeyron**

Emile Clapeyron was born in 1799 in Paris. He trained as an engineer at the Ecole des Mines. He then worked in Russia, improving the road system, and also taught advanced mathematics in St. Petersburg schools. Back in France ten years later, he taught as a professor and designed locomotives and steel bridges.

Professor Clapeyron derived the Ideal Gas Law as a synthesis of earlier laws. Robert Boyle described the relationship of pressure and volume. Jacques Charles and Joseph Louis Gay-Lussac described the relationship between temperature and pressure. Clapeyron described the relationship of all three.

**The concept of the Ideal Gas Law**

As a gas is heated, the heating adds energy to its molecules. Therefore, the energized molecules begin to move faster. Their increased motion pushes outward, and produces more pressure in a gas that is confined so that its volume must stay the same. If the gas is allowed to expand, on the other hand, more energy will equal more volume. Volume changes are inverse to pressure changes, but are directly proportionate to the number of atoms or molecules in a given volume of the gas, and directly proportionate to the constant R.

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