# Avogadro's law Formula

Definition: The Italian chemist Amedeo Avogadro created law in the 19^{th} century for describing the relation between the volume of gases and the amount of substance. Thus, the Avogadro's law says that "Equal volumes of all gases, at the same temperature and pressure, have the same number of molecules."

The above statement means that the volume of a gas is directly proportional to the number of moles of gas when the temperature and pressure are held constant.

Formula: The Avogadro's law can be expressed through the next mathematical equation:

V = k . n

Where V is the gas volume, n is the number of gas' moles and k is a constant, which is defined as RT/P, where R is a constant called the constant of the gases (8.314 kg m2 s^{-2} K^{-1} mol^{-1}), T is the temperature in Kelvin and P is the pressure. Thus, the Avogadro's expression can be rewritten as the most famous expression for the ideal gas law:

P V = n RT

Uses: The ideal gas law is extensively use in chemistry for doing basic calculation of the pressure or the quantity of gas present in any vessel or recipient. More importantly, this law has suffered some fits or optimization for correcting the ideal behavior (which is almost impossible to have in real systems) for a more real behavior. The basic equation remains, but some corrections factors are added and the resulting expression is using for chemical and process engineers for doing industrial calculations.

Example: 10 L of Helium gas is in X recipient and we know the Helium number of atoms is 0.965 mol. If the amount of gas is increased to 0.9 mol, what new volume will result at the same temperature and pressure?

P and T are constants, so P_{1} T_{1} = P_{2} T_{2} and PT = n R / V

n_{1} R / V_{1} = n_{2} R / V_{2} → V_{2} = n_{2} V_{1} / n_{1} = 10 L x 0.9 mol / 0.965 mol = 9.33 L

Considerations: The Avogadro's law allow to observe many changes at any gas system because it has many parameters that can be altered. Temperature, pressure, amount of mass and volume are 4 important parameters for studying gases. In general, P and V are inversely proportional, so if P increases, it can be due a decrease of the volume which comprised the gas. Also, temperature and P and V are inversely proportional.

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