According to Avogadro’s Law, all gases have an identical number of molecules in an equal volume at a given temperature and pressure. Amedeo Avogadro, an Italian chemist, and physicist, first described the law in 1811. Amadeo Avogadro was a scientist from Italy in the 1800s. When chemistry was just starting to become its science field, he made important contributions to it. His work was done around the same time as that of Jacques Charles, Robert Boyle, and others. The Ideal Gas Law is based in part on Avogadro’s Law, which is a hypothesis he came up with.

**What is Avogadro’s Law?**

The quantity (number of moles) and volume of an ideal gas are directly proportional to each other for a given mass of the gas at constant temperature and pressure, according to the modern definition of Avogadro’s law. Avogadro’s law connects temperature, pressure, volume, and substance amount for a certain gas, which makes it closely related to the ideal gas equation. The behaviour of particles in an ideal gas, which lacks mass and is not attracted to one another, can be explained by the collisions between gas molecules and the container’s walls.

Real gases do not, of course, exist in an ideal state, but since they are so little and are surrounded by so much space, it is difficult to estimate their size and mass, which is why it is not important. As a result, under most circumstances, most gases behave quite “ideally.”

**Avogadro’s Law Formula**

According to Avogadro’s rule, a gas’s volume, V, is inversely related to its particle count, n. This link can be described mathematically as follows:

**V ∝ n**

Mole counts are used by chemists to determine the number of atoms and molecules. The quantity of particles that make up a mole of a substance is known as Avogadro’s number or NA. It has been established through numerous investigations that NA has a particle density per mole of 6.02 × 1023.

In other words, the volume V to the number of gas particles n ratio equals a proportionality constant k.

\(\frac{V}{n}\) = k

Thus,

**\(\frac{V1} {n1}\) =\(\frac{V2} {n2}\)**

This equation says that when the number of particles in a gas changes from n1 to n2, the volume also changes from V1 to V2.

**Derivation of Avogadro’s Law**

The ideal gas equation, which can be written as follows, can be used to figure out Avogadro’s law:

**PV=nRT**

Where,

P= the pressure that the gas puts on the walls of its container

V= volume that the gas did take up

n=number of moles of gas

R= gas constant

T= absolute temperature

If you rearrange the equation for an ideal gas, you will get the following equation:

\(\frac{V}{n}\) = \(\frac{RT}{P}\)

The value of RHS (Right Hand Side) is constant. Then,

**\(\frac{v}{n}\) = k**

So, the relationship between the amount of space a gas takes up and the number of molecules in the gas is proven.

**Graphical Representation**

There is a straight-line relationship between the volume of a gas and the number of moles of gas particles. At the same temperature and pressure, as the volume of gas goes up, so does the number of moles of gas.

**Moles to Grams**

The following formula shows how to change from moles to g, which is another common unit of measure:

Moles = \(\frac{grams}{molar mass}\)

To figure out what a substance’s molar mass is, you have to use the useful periodic table. It can be worked out by adding up the masses of all the atoms in the substance. For example, if you need to figure out the molar mass of NaCl, you would:

Na has a mass number of 22.99 g/mol.

Cl’s mass number is 35.45 g/mol.

So, the molar mass of NaCl is 22.99 plus 35.45, which equals 58.44 g/mol.

**Molar Volume of a Gas**

The formula for the ideal gas law, PV = nRT, can be used to find the molar volume, or V, of a gas. In this equation, P is the pressure, n is 1 mol, R is the universal gas constant, and T is the temperature in Kelvin. The value of R will change depending on the pressure and volume units that are used.

**Examples of Avogadros Law**

A great example of Avogadro’s law is the way that we breathe. When a person breathes in, the molar amount of air in their lungs goes up, and so does the volume of their lungs (expansion of the lungs). The way car tires lose air is another common example of Avogadro’s law. When the air that was trapped in the tire gets out, the amount of air in the tire goes down. This causes the gas to take up less space, which causes the tire to lose its shape and deflate.

**What are the Limitations of Avogadro’s Law?**

Even though it works perfectly for all ideal gases, Avogadro’s law only tells us how the real gases relate to each other. The difference between how real gases behave and how they should behave tends to get bigger as pressure and temperature go up. Hydrogen and helium, which are gases with low molecular masses, follow Avogadro’s law better than molecules with higher molecular masses.

**Solved Exercises on Avogadro’s Law**

Question 1. At 25°C and 2.00 atm, a sample of 6.0 L holds 0.5 moles of a gas. What is the final volume of the gas if 0.25 moles more are added at the same pressure and temperature?

Solution. Avogadro’s law:

\(\frac{V1}{n1}\) = \(\frac{V2}{n2}\)

V1= initial volume = 6.0 L

n1= initial number of moles = 0.5 mole

V2= final volume = x L

n2= final number of moles= 0.5 + 0.25 = 0.75 mole

\(\frac{6.0}{0.5}\) = \(\frac{x}{0.75}\)

x = \(\frac{6.0 × 0.75}{0.5}\)

x= 9 L

Question 2. A puncture takes away half of the volume of a tire with 10 moles of air and a 40-litre volume. How much air is left in a tire that has been deflated?

Solution. Avogadro’s law:

\(\frac{V1}{n1}\)= \(\frac{V2}{n2}\)

V1= initial volume = 40 L

n1= initial number of moles = 10 mole

V2= final volume = 20 L

n2= final number of moles= x mole

\(\frac{40}{10}\) = \(\frac{20}{x}\)

x= \(\frac{20 × 10}{40}\)

x= 5 moles

**FAQs on Avogadro’s Law**

Question 1. What does the law of Charles law say?

Answer. Avogadro’s law looks at the relationship between the amount of gas (n) and the amount of space it takes up (V). It’s a direct relationship, which means that the amount of moles in a gas is proportional to how much space it takes up.

Question 2. Explain Avogadro’s idea?

Answer. Avogadro’s law says that when the temperature and pressure are the same, the same number of molecules are found in equal volumes of different gases. Under the assumption of an ideal gas, the kinetic theory of gases can be used to figure out this empirical relationship.

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