Avogadro's Law

Avogadro's law Avogadro's hypothesis or Avogadro's principle is a basic postulate in chemistry which relates the volume of the gas to the number of molecules or atoms within a sample. It was stated by Italian physicist Amedeo Avogadro in 1811, and it is highly significant in knowing the behaviour of gases. From the gas law to the interactions of molecules, Avogadro's Law is a fundamental principle that tells us about the behaviour of gases and how they will interact under different conditions.

1.0Avogadro's Law: Statement and Meaning

Avogadro's Law Statement: "Equal volumes of all gases, at the same temperature and pressure, contain an equal number of molecules."

In simple words, Avogadro's Law of Gases means that the volume of gas(V) is directly proportional to the no. of gas molecules(n) when the temperature and pressure are constant for an ideal gas. Mathematically, The law can be expressed as: 

$V_1\propto n$

If dealing with two gases, say, for example, Gas 1 and Gas 2, The equation for both gases can be rewritten to form Avogadro’s law formula:

$V_1\propto n_1$

$V_1\propto n_2$

Here, 

• V₁ and V₂ represent the volumes of two different gases, and 
• n₁ and n₂ represent their respective number of moles of the gases. 

Since, under the same temperature and pressure, both the equations are proportional. Hence, both equations can be equated as: 

$\frac{V_1}{n_1}=\frac{V_2}{n_2}$

Avogardro’s Constant

Avogadro's constant (N_A) is the number of particles (like atoms or molecules) in one mole of a substance. It is a fundamental constant in chemistry that connects the macroscopic (The Volume of the Gases) and microscopic (number of moles) concepts. The value of Avogadro's constant is approximately N_A = 6.022 × 10²³.

This constant allows chemists to relate the number of molecules in a sample to the amount of substance (moles) and its mass.

2.0Avogadro's Law Derivation

Avogadro’s Law derivation includes the use of the equation of ideal gas, a fundamental equation of science which describes the behaviour of ideal gases. The equation of ideal gas can be written as: 

PV=nRT

Here:

• P is the pressure of the gas,
• V is represented as the volume of the gas,
• n is represented as the number of moles of gas,
• R is the ideal gas constant,
• T is the temperature in Kelvin.

The ideal gas equation can be rewritten as: 

$\frac{V}{n}=\frac{RT}{P}$

Now, According to the statement of Avogadro’s law, the temperature and pressure are constant and, therefore, RTP  (\frac{RT}{P}) can be written as “k”, which is a constant. 

$\frac{V}{n}=k$

$V\propto n$

3.0Graphical Representation of Avogadro’s Law

In the Graphical Representation of Avogadro’s Law, there would be a straight-line graph with the number of moles (n) on the x-axis and the volume (V) of the gas on the y-axis. The line is straight, and as the number of moles increases, so does the volume proportionally, showing the directly proportional relation between both the components of the law if the temperature and pressure remain constant.

4.0Applications of Avogadro's Law

• Molar Volume: At Standard Temperature & Pressure (STP), one mole of an ideal gas has a specific volume of 22.4 litres. This relationship is a result of Avogadro's law. It helps in determining the volume of gas produced or consumed in a chemical reaction.
• Atomic Theory: Avogadro's law was a significant contribution to the development of atomic theory. It supported the idea that gases are made up of discrete molecules and not continuous substances. This laid the foundation for the later development of the atomic model by John Dalton and others.
• Stoichiometry in Chemistry: Avogadro's law is essential in stoichiometric calculations, where it helps chemists determine the amounts of reactants & products in chemical reactions, especially involving gases.
• Linking the Macroscopic and Microscopic Worlds: The law bridges the gap between the macroscopic quantities that we can measure (like volume and pressure) and the microscopic world of molecules. It allows us to understand how many molecules are present in a sample of gas from its volume.
• Avogadro's Constant in Other Fields: Avogadro's constant plays a crucial role in various scientific fields, such as material science, nanotechnology, molecular biology, and even in calculating the number of atoms in a given mass of material.

5.0Avogadro's Law Example: Numerical

Problem 1: A sample of helium gas at a temperature of 300 K occupies a volume of 10.0 litres. If the amount of gas is increased to 2 moles, what will the new volume of the gas be, assuming temperature and pressure remain constant?

Solution: Given that: 

Initial Volume (V₁) = 10L 

Initial Moles of gas (n₁) = 1 mole 

Final moles of gas (n₂) = 2 moles 

Using the Avogadro’s law: 

$\frac{V_1}{n_1}=\frac{V_2}{n_2}$

$\frac{10}{1}=\frac{V_2}{2}$

$V_2=10\times 2=20L$

Problem 2: A balloon filled with carbon dioxide gas occupies a volume of 12 litres at a pressure of 1 atmosphere and a temperature of 298 K. If the amount of gas is increased from 2 moles to 4 moles, what will the new volume be, assuming temperature and pressure remain constant?

Solution: Given that, 

Initial volume (V₁​) = 12 L

Initial moles (n₁) = 2 moles

Final moles (n₂) = 4 moles

Using the law, 

$\frac{V_1}{n_1}=\frac{V_2}{n_2}$

$\frac{12}{2}=\frac{V_2}{4}$

$V_2=6\times 4=24L$