Avogadro's Law: Formula and Derivation Explained with Solved Examples

Have you ever noticed that a balloon expands when more air is blown into it? This simple observation is explained by Avogadro's Law, one of the fundamental gas laws in chemistry proposed by the Italian scientist Amedeo Avogadro, this law explains the relationship between the volume of a gas and the number of molecules present in it. It forms an important part of the ideal gas equation and helps students understand the behaviour of gases under constant temperature and pressure. 

This article Avogadro's formula, derivation, graphical representation, molar volume, real-life examples, applications and limitations of Avogadro's Law.

Table of Contents 

• What is Avogadro’s Law
• Examples of Avogadro's Law
• Formula and Graphical Representation of Avogadro's Law
• What is the Molar Volume of a Gas
• Applications of Avogadro's Law
• Limitations of Avogadro's Law
• Solved Examples on Avogadro's Law

What is Avogadro’s Law 

Avogadro's Law, also called Avogadro's hypothesis or Avogadro's principle, states that:

"Equal volumes of all gases, at the same temperature and pressure, contain an equal number of molecules."

In other words, the volume occupied by a gas is directly proportional to the number of moles of the gas, provided the temperature and pressure remain constant.

Mathematical Statement

[V∝n]

where:

• (V) = Volume of gas
• (n) = Number of moles
• Temperature and pressure remain constant

Key Points

• Volume increases when the number of moles increases.
• Volume decreases when the number of moles decreases.
• Temperature and pressure must remain constant.
• Applicable mainly to ideal gases.

Examples of Avogadro's Law

1. Inflation of a Balloon:As more air is blown into a balloon, the number of gas molecules increases.As a result, the volume of the balloon also increases.

2. Human Respiration:During inhalation, more air enters the lungs.The increase in the number of gas molecules causes the lungs to expand.

3. Deflation of Vehicle Tyres:When air escapes from a punctured tyre, the number of gas molecules decreases.Consequently, the volume decreases and the tyre collapses.

4. Inflating Air Mattresses and Sports Balls; Adding air increases the number of moles of gas, causing an increase in volume.

Suggested Read: Helium and Hydrogen Gas 

Formula and Graphical Representation of Avogadro's Law

The mathematical expression of Avogadro's Law is: V∝n
or Vn=k

where (k) is a constant.

For two different conditions:

 V1n1=V2n2
where:

• ( V1) = Initial volume
• ( n1) = Initial number of moles
• ( V2) = Final volume
• ( n2) = Final number of moles

Graphical Representation

When the number of moles is plotted on the x-axis and volume on the y-axis, a straight line passing through the origin is obtained.

This graph shows that volume and number of moles are directly proportional.

Derivation of Avogadro's Law

Avogadro's Law can be derived from the ideal gas equation:

PV=nRT

where:

• (P) = Pressure
• (V) = Volume
• (n) = Number of moles
• (R) = Universal gas constant
• (T) = Absolute temperature

Rearranging the equation:

 V=nRTP
Since pressure and temperature are constant,

RTP=k

Therefore,V=kn
or Vn=k
Hence, volume is directly proportional to the number of moles, which verifies Avogadro's Law.

Also Read: Boyle’s Law

What is the Molar Volume of a Gas?

According to Avogadro's Law, one mole of any gas occupies the same volume under identical conditions of temperature and pressure.

At STP (Standard Temperature and Pressure)

• Temperature = 273.15 K
• Pressure = 1 atm

One mole of any ideal gas occupies: 22.4 L

Therefore,

1 mole of any gas occupies 22.4 litres at STP.

This volume is called the molar volume of a gas.

Applications of Avogadro's Law

Avogadro's Law has several practical applications:

• In chemistry, Avogadro's Law helps scientists determine molecular masses and calculate the volumes of gases.
• In industries, it plays an important role in the storage, transportation, and manufacturing of compressed gases.
• Did you know that oxygen cylinders used in hospitals are also based on the principles of Avogadro's Law? It helps in understanding respiratory systems and medical gas supply.
• Meteorologists use this law to study the behaviour of gases present in the atmosphere.

Even in our daily lives, Avogadro's Law can be observed when balloons expand, tires are inflated and other inflatable objects change their volume with the amount of air inside them.

Limitations of Avogadro's Law

Although Avogadro's Law works well for ideal gases, it has certain limitations.

• Real Gases Deviate from Ideal Behaviour;At very high pressures and low temperatures, intermolecular forces become significant and gases do not obey Avogadro's Law exactly.
• Heavy Gases Show Greater Deviations;Lighter gases such as hydrogen and helium follow the law more closely than heavier gases.
• Constant Temperature and Pressure are Required;The law is valid only when temperature and pressure remain unchanged.

Solved Examples on Avogadro's Law

Example 1

One mole of helium occupies 1.5 L. What volume will be occupied by 3.5 moles of helium at constant temperature and pressure?

Given:

• ( V1=1.5 L)
• ( n1=1 mol)
• ( n2=3.5 mol)

Using Avogadro's Law:

 V1n1=V2n2

 V2=V1n2n1
V2=1.5×3.51
 V2=5.25 L

Answer: The final volume is 5.25 L.

Example 2

A tyre contains 10 moles of air occupying 40 L. Due to puncture, the volume decreases to 20 L. Find the number of moles remaining.

Given:

• ( n1=10 mol)
• ( V1=40 L)
• ( V2=20 L)

Using:

 V1n1=V2n2

 n2=V2n1V1

 n2=20×1040

 n2=5 mol

Answer: The tyre contains 5 moles of air.

Read More: Molarity and Molality 

We have learned that Avogadro's Law is one of the fundamental gas laws  in chemistry that establishes a direct relationship between the volume of a gas and the number of moles present at constant temperature and pressure. Proposed by Amedeo Avogadro,this law forms the basis for understanding molar volume and the behaviour of ideal gases.