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The law of Avogadro , also called Avogadro principle, is a law that applies to ideal gases and that was enunciated by a scientist of the nineteenth century called Amedeo Avogadro. This law establishes that two equal volumes of different gases that are in the same conditions of temperature and pressure, will contain the same number of gaseous particles.

This means that if we have two balloons, one filled with helium and the other with oxygen, and both balloons have the same volume , the same pressure and the same temperature, then there will be the same number of gaseous helium atoms in the first balloon. than oxygen molecules in the second.

Another way to state Avogadro’s law is to say that, if the pressure and temperature are kept constant, the volume of a gas will be proportional to the number of moles. This is represented in mathematical form as:

This formula can be rearranged to V / n = k, that is, the relationship between volume and number of moles remains constant as long as P and T are constant.

## Conditions under which Avogadro’s law is fulfilled

This law applies exactly to ideal gases. These are gases formed by point particles (that do not occupy a volume in space) that do not interact with each other in any way.

As its name indicates, this type of gas does not exist in reality but in our imagination. They are a simplified “idea” of what we think of as a gas. However, there are some conditions under which a real gas, such as air, behaves ideally: at very low pressures and at very high temperatures.

Low pressures make the volume occupied by the particles of a gas negligible compared to the size of the container, while high temperatures make the particles move so fast that they do not have time to interact when they cross each other.

Under these conditions, most gases comply with Avogadro’s law with good accuracy.

One of the most important contributions of Avogadro’s law was that it allowed to demonstrate the existence of elemental gases formed by more than one atom such as O 2 or H 2 . This contributed to the advancement of atomic theory.

On the other hand, Avogadro’s law also allows establishing relationships between the molecular weights of different gases, since it implies that the mass of equal volumes of different gases measured at the same temperature and pressure is proportional to the mass of each particle of each gas.

So just by weighing samples of two gases that occupy equal volumes at the same temperature and pressure, the relationship between their molar masses can be obtained.

## Examples of Avogadro’s law in everyday life

### Party balloons

We have all seen a clown at a children’s party inflating helium balloons to distribute among the children. These balloons are at approximately the same temperature. If two party balloons are filled to the same pressure and both are the same size, Avogadro’s law ensures that both balloons will have the same number of moles of helium.

On the other hand, if one of the balloons is larger than the other, it will have a greater volume and, according to Avogadro’s law, it will have a greater amount of helium particles inside.

### The tires of a car

No matter what gas they are filled with, the tires on opposite sides of a car are always filled to the same final pressure of around 32 psi.

In addition, it is always ensured that both rubbers are the same, so they will have the same volume. Thus, according to Avogadro’s principle, we can say that both tires will contain the same number of gaseous particles.

### An air-filled syringe

Suppose we have an open syringe filled with 50 cm 3 of air. Because it is open, the inside of the syringe and the outside (the surroundings) are at the same temperature and pressure.

Now suppose we press the plunger of the syringe and move it until 10 cm 3 is read . Because the syringe is uncapped, air escapes from the tip as the plunger moves, so the number of air particles within the syringe decreases along with the volume.

Since neither the pressure nor the temperature are changing, Avogadro’s law can be applied to relate the final volume to the amount of air particles that remain inside the syringe. This relation is:

Rearranging this equation, we obtain that:

This result means that, if we reduce the volume inside the syringe to one fifth while keeping P and T constant, then the number of moles or particles present inside at the end of the process will also be one fifth of what was originally.