Avogadro's Law is the relation which states that at the same temperature and pressure, equal volumes of all gases contain the same number of molecules. The law was described by Italian chemist and physicist Amedeo Avogadro in 1811.

## Avogadro's Law Equation

There are a few ways to write this gas law, which is a mathematical relation. It may be stated:

k = V/n

where k is a proportionality constant V is the volume of a gas, and n is the number of moles of a gas

Avogadro's law also means the ideal gas constant is the same value for all gases, so:

constant = p_{1}V_{1}/T_{1}n_{1} = P_{2}V_{2}/T_{2}n_{2}

V_{1}/n_{1} = V_{2}/n_{2}

V_{1}n_{2} = V_{2}n_{1}

where p is pressure of a gas, V is volume, T is temperature, and n is number of moles

## Implications of Avogadro's Law

There are a few important consequences of the law being true.

- The molar volume of all ideal gases at 0°C and 1 atm pressure is 22.4 liters.
- If pressure and temperature of a gas are constant, when the amount of gas increases, the volume increases.
- If pressure and temperature of a gas are constant, when the amount of gas decreases, the volume decreases.
- You prove Avogadro's Law every time you blow up a balloon.

## Avogadro's Law Example

Say you have 5.00 L of a gas which contains 0.965 mol of molecules. What will be the new volume of the gas if the quantity is increased to 1.80 mol, assuming pressure and temperature are held constant?

Select the appropriate form of the law for the calculation. In this case, a good choice is:

V_{1}n_{2} = V_{2}n_{1}

(5.00 L)(1.80 mol) = (x)(0.965 mol)

Rewriting to solve for x give you:

x = (5.00 L)(1.80 mol) / (0.965 mol)

x = 9.33 L

## Sources

- Avogadro, Amedeo (1810). "Essai d'une manière de déterminer les masses relatives des molécules élémentaires des corps, et les proportions selon lesquelles elles entrent dans ces combinaisons."
*Journal de Physique*. 73: 58–76. - Clapeyron, Émile (1834). "Mémoire sur la puissance motrice de la chaleur."
*Journal de l'École Polytechnique*. XIV: 153–190.