Short Answer

Avogadro’s law states that equal volumes of all gases, at the same temperature and pressure, contain an equal number of molecules. This means the volume of a gas is directly proportional to the number of moles present when temperature and pressure remain constant.

According to Avogadro’s law, if you double the number of moles of a gas, its volume will also double under the same conditions. This law helps in understanding gas behaviour, calculating gas volumes, and performing gas-related stoichiometric calculations.

Detailed Explanation

Avogadro’s Law

Avogadro’s law is a fundamental principle in gas chemistry that explains the relationship between the volume of a gas and the number of moles of gas present. Formulated by Amedeo Avogadro in 1811, the law states:

“Equal volumes of all gases, under the same temperature and pressure, contain equal numbers of molecules.”

This statement highlights the idea that gas volume depends only on the number of particles (moles) and not on the type of gas. It provides a simple way to understand how gases behave and how their volumes change when the amount of gas changes.

Key idea of Avogadro’s law

The main concept is a direct proportionality between gas volume (V) and number of moles (n):

V ∝ n
or
V = kn

where k is a constant when temperature and pressure are fixed.

This means:

• More moles of gas → greater volume
• Fewer moles of gas → smaller volume
• Doubling moles → doubles volume
• Halving moles → halves volume

The type of gas does not matter. A litre of hydrogen contains the same number of molecules as a litre of oxygen under the same conditions.

Why gases follow Avogadro’s law

Gas molecules are spread far apart with large gaps between them. Because of this:

• The actual size of gas molecules is very small compared to the space they occupy.
• The identity (type) of the gas does not affect volume under equal conditions.
• Adding more gas molecules increases the number of collisions and requires more space, causing the gas to expand.

These properties explain why all gases behave similarly and follow Avogadro’s law.

Mathematical form of Avogadro’s law

The mathematical expression of the law is:

V₁ / n₁ = V₂ / n₂

This equation helps compare two different states of gas when the number of moles changes.

Example:
If 1 mole of a gas occupies 22.4 L at STP, then 2 moles will occupy:

V₂ = (2 moles × 22.4 L) / 1 mole = 44.8 L

Avogadro’s law and molar volume

Avogadro’s law helps define molar volume—the volume occupied by one mole of gas.
At STP (0°C and 1 atm):

• 1 mole of any gas occupies 22.4 litres

This value comes directly from Avogadro’s idea that equal volumes of gases contain equal numbers of molecules.

Avogadro’s law in the ideal gas equation

The ideal gas equation PV = nRT includes Avogadro’s law within it.
When pressure (P) and temperature (T) are constant:

V = (nRT) / P

Since R, T, and P stay constant:

V ∝ n

This matches Avogadro’s law perfectly, showing how deeply the law is connected to gas behaviour.

Importance of Avogadro’s law

Avogadro’s law is widely used because it:

1. Helps calculate gas volumes

Knowing moles makes it easy to find volume, and vice versa.

2. Supports atomic theory

It gave strong proof that gases are made of tiny particles (molecules).

3. Helps determine molar mass

Chemists analyse gases to find the molar mass of unknown substances.

4. Is essential in gas stoichiometry

It simplifies calculations for reactions involving gases.

5. Assists in chemical formula determination

Avogadro’s ideas helped understand how atoms combine in molecules.

Examples showing Avogadro’s law

Example 1: Doubling moles

1 mole of gas → 22.4 L
2 moles of same gas → 44.8 L
Volume doubles because moles doubled.

Example 2: Half the moles

0.5 moles of gas → 11.2 L
Volume halves with moles.

Example 3: Comparing different gases

1 L of helium and 1 L of nitrogen at same T and P contain the same number of molecules, even though the gases are different.

Limitations of Avogadro’s law

Although very useful, Avogadro’s law works best at:

• Low pressures
• Moderate temperatures

At high pressure or very low temperature, gases deviate from ideal behaviour due to intermolecular forces and volume of gas particles.

Conclusion

Avogadro’s law states that at the same temperature and pressure, equal volumes of gases contain equal numbers of molecules. It shows a direct relationship between gas volume and moles and is essential for gas stoichiometry, molar volume calculations, and understanding gas behaviour. The law is a cornerstone of modern chemistry and has many practical applications in laboratories, industry, and scientific research.