Avogadro’s law is a gas law that states that under the same conditions of pressure and temperature, equal volumes of all gases contain the same number of molecules.

Avogadro’s law can be stated as follows:

For a fixed mass of an ideal gas at constant pressure and temperature, the volume and quantity of the gas are directly proportional.

Mathematically it can be expressed as:

V ∝ n

or

V = constant

The law is named after Amedeo Avogadro (1776-1856), who, in 1811, hypothesized that two given samples of an ideal gas with the same volume and at the same temperature and pressure contain the same number of molecules.

Therefore, the number of molecules or atoms in a specific volume of ideal gas is independent of its size or the molar mass of the gas.

Avogadro studied the relationship between the volume and the amount of gas substance present.

The results of certain experiments with gases led him to formulate Avogadro’s law, which states that, under the same conditions of temperature and pressure, equal volumes of different gases contain an equal number of molecules.

Mathematically, this law can be expressed as:

V ∝ n

or

V = constant

where, n·R / V is constant being:

• n is the amount of substance measured in moles
• V is the volume of the gas.

the constant is equal to R·T / p, where p is the absolute pressure of the gas, T is the absolute temperature and R is the ideal or universal gas constant, equal to the product of Boltzmann’s constant and Avogadro’s constant.

In honour to Avogadro, the number of particles (atoms, molecules, ions or other particles) in 1 mole of a substance, 6.02214076·1023, was named after Avogadro as Avogadro’s constant or Avogadro’s number. Avogadro’s constant is one of the IS base units seven and it is represented by NA.

Avogadro’s law  can be used to compare the same substance under two different sets of conditions:

1 / n 1 = V 2 / n 2

## Solved exercises on Avogadro’s law

1) A helium balloon is inflated to a volume of 1.5 liters. Helium is a very light gas so it gradually escapes through the walls of the balloon. A few days later the volume of the balloon is 0.75 liters and it is determined that at the end there are 0.03 moles of helium,

How many moles of helium were in the newly inflated balloon?

(consider that the pressure and temperature at the time of the measurements were the same as at the beginning).

Solution:

Since the pressure and temperature are constants in this exercise, the volume is related to the number of moles. Therefore, Avogadro’s law can be used:

V1/n1 = V2/n2

n1/V1 = n2/V2

n1 = (n2 · V1)/V2

n1 = (0.03 moles · 1.5 L) / 0.75 L = 0.5 moles

When the helium balloon was inflated there were 0.5 moles.

2) What volume do 2 million (2 x 106) molecules of Oxygen gas, O2, occupy under normal conditions of pressure and temperature?

Solution:

Under normal conditions: 22.4 L of O2 contains Avogadro’s number of molecules = 6.022·1023 molecules.

The O2 molecules are transformed to moles of O2 molecules and then through Avogadro’s law the moles of molecules are transformed to liters of the gas.

(2 x 106 O2 molecules) · (1 mol O2)/(6.022·1023 molecules) · 22.4 L / 1 mol O2 = 7.439·10-17 L