Avogadro’s Law: Definition, Formula, Graphical Representation, Derivation, Limitations and Examples

When you inflate a balloon, the gas molecules are added to it. The result is that the volume of the balloon increases and the number of molecules in your lungs decreases accordingly. This gas phenomenon is based on Avogadro's law.

What is Avogadro’s Law?

Avogadro’s law is a gas law. It states that the total number of molecules/atoms of a gas is directly proportional to the volume occupied by the gas at constant temperature and pressure. 

Avogadro’s Law is also known as Avogadro’s Hypothesis or as Avogadro’s Principle. This law is also associated with the ideal equation of the gas due to the reason that it links pressure, volume, temperature along with the amount of the substance of a gas.

The Avogadro’s law is named after an Italian Scientist; Amedeo Carlo Avogadro who discovered the fact that the two different types of gases occupy the same quantity of volume at a constant temperature, as well as pressure, must contain an equal number of molecules or atoms.

Formula and Graphical Representation of Avogadro’s Law

At any constant pressure and temperature, Avogadro’s Law can be expressed as:

V ∝ n

So, the formula of Avagadro’s Law can be given as-

V/n = k

Here,

V denotes the volume of gas,

n indicates the amount of gas (in moles) and 

k is the constant. 

Accordingly, if there is an increase in the amount of gaseous substance, there will be an increase in volume which is occupied by the gas and it can be calculated with the formula given below:

V₁ /n₁ = V₂/n₂ (=K, according to Avogadro’s Law)

The following graphical representation can be used to understand Avogadro’s Law Formula:

The straight line in the graph indicates that zero moles of gas will occupy zero volume. Hence, both volume and amount of substance are directly proportional

Derivation of Avogadro’s Law

Avogadro’s Law can be expressed can be derived from the ideal gas equation. The Ideal gas equation can be expressed as:

PV = nRT

Here, 

P indicates the pressure exerted on the wall of the container by the gas.

V indicates the volume that has been occupied by gas.

n indicates the total amount or total number of moles of the gaseous substance

R indicates to the Universal gas constant

T indicates the absolute temperature of the gas

The equation of ideal gas can be rearranged and the following equation can be stated:

V/n = (RT)/P

Here, (RT)/P is a constant as no change of temperature and pressure takes place & the product of two or more constants always remains a constant.

Hence, 

  V/n = K

So it can be stated that the definition of Avogadro’s Law and proportionality of the amount of gaseous substance and the Volume occupied is verified.

Avogadro’s Law: Molar Volume of a Gas

According to Avogadro’s Law, the ratio of the amount of gaseous substance and volume of gas at constant temperature and pressure is denoted by K. So,

K = (RT)/P

Under standard conditions, T= 273.15K and P=101.325 kilopascals

Therefore, the volume of one mole of gas at STP= 8.314 J.mol -1.K-1273.15 K(101.325 k Pa)= 22.4 Litres 

So, the volume occupied by one mole of a gas at STP is 22.4 liters

Read Also: Charles Law Important Notes

Example of Avogadro’s Law

The respiration process is one of the great examples of Avogadro’s law. When we inhale, there is an increase in the molar quantity of the air in our lungs. This leads to an increase in lungs volume and our lungs expand.

A balloon filled with helium weighs much less than an identical balloon filled with air. Both balloons contain the same number of molecules. Helium atoms have a lower mass than either oxygen molecules or nitrogen molecules in the air, so the helium balloon is lighter.

Limitations of Avogadro’s Law?

• The Avogadro’s Law is perfectly applicable only on the ideal gases
• In case of the real gases, at very low pressure or at very high volume, the law provides an approximate relationship between the total number of molecules/atoms of the gas and the volume of gas.
• The ratio of volume to mole is a little bit more for real gases in comparison to ideal gases at High Pressure and Low temperature.
• Gases such as Hydrogen & Helium have relatively low molecular masses to follow Avogadro’s law in comparison to the other gases.

Check Important Notes for Avogadro’s Law (Volume-Amount Relationship)