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The number of units in one mole of any substance is called Avogadro’s number or Avogadro’s constant. It is equal to 6.022140857×1023. The units may be electrons, ions, atoms, or molecules, depending on the character of the reaction and the nature of the substance.

So, if you wanted to know the number of particles in 3 moles of a substance, the value would be:

= 3 x 6.023 x 1023

= 1.81 x 1024 particles

Simply put, it creates a bridge between the macroscopic world and the microscopic world by relating the amount of substance to the number of particles. It also provides the relationship between other physical constants and properties. Some of them are:

• The relationship between the gas constant R and the Boltzmann constant kB: R=kBNA
• The relationship between the Faraday constant F and the elementary charge e: F=NAe
• The relationship between atomic mass unit u and molar mass constant Mu: 1u=Mu/NA

In chemistry, we always take a macroscopic approach to measuring stuff. We measure the total volume of a substance, or the temperature, or the mass of a substance and general things along those lines. But if we look at this from the atomic level, knowledge of velocity and momentum of particles are important. The atomic mass is important. Avogadro’s number connects both of these.

## How was Avagadro’s Number Determined?

Avagadro grew up during the important period of development of chemistry. Chemists such as John Dalton and Joseph Louis Gay-Lussac began to understand the basic properties of atoms and molecules, and they debated how these infinitesimally small particles behaved. Gay-Lussac’s law of combining volumes particularly interested Avagadro.

Tinkering around with the ramifications of this law, Avogadro expected that with the goal for this to be valid, equivalent volumes of any two gases at a similar temperature and weight must hold an equivalent number of particles. And the only way to confirm that this law could be true was if there was a difference between atoms and molecules and that some elements, such as Nitrogen, actually exist as molecules ( N2 rather than simply N). Given, Avogadro didn’t have words such as “molecule” to explain his theory, and his ideas met opposition from John Dalton, among others. It took another chemist Stanislao Cannizzaro to bring Avogadro’s ideas the attention that it deserved. By the time those ideas gained traction, Avogadro had already passed away.

Because Avogadro’s law was so critical to the advancement of chemistry, chemist Jean Baptiste Perrin named the number in his honour.

• In the atomic level substances are measured as per atomic mass unit. The Atomic mass unit is defined as the 1/12th weight of the mass of one carbon atom.
• For example, the atomic mass unit of Hydrogen is 1.00794 amu. Now to calculate the ability of a single particle (atom, electron, molecule) to say, carry out a reaction isn’t possible.

So instead, chemists came up with a way to link the atomic mass unit and the gram.

1 amu = 1.66 x 10-24 grams

Using this, we are able to convert between measurement in grams and the invisible unit of measurement of the atomic mass unit. And hence, this is the significance of Avogadro’s number.

### Brainstorm:

 Try applying your knowledge of Avogadro’s constant to the following question. You have a litre of water and are told that the mass of water is 18 amu. So, how many particles are there in this 1 litre of water? (Hint: 1kg = 1000g)

## Frequently Asked Questions – FAQs

### What is the symbol for Avogadro’s constant?

The symbol for Avogadro’s constant is either NA or L.

### Which among 4 mol of H2O and 5 mol of CH3COOCH contains the greatest number of hydrogen atoms?

Among 4 mol of H2O and 5 mol of CH3COOCH, 5 mol of CH3COOH contains the greatest number of hydrogen atoms. This is because in 4 mol of H2O there are 4N molecules where N is equal to Avogadro’s number. In 5 mol of CH3COOH, there are 5N molecules where N is equal to Avogardro’s number. Also, the number of hydrogen atoms in the formula is the same as the total number of hydrogen atoms in the sample. Therefore, in 4 mol of H2O there are 8N hydrogen atoms while in 5 mol of CH3COOH there are 20N hydrogen atoms. Therefore, 5 mol of CH3COOH contains the greatest number of hydrogen atoms.

### Based on the periodic table, what is the molar mass of Cs and Fe?

Based on the periodic table, the molar mass of Cs and Fe are 132.91 g/mol and 55.85 g/mol respectively.

### What is 7.1 mol of Al in grams?

7.1 mol of Al is 26.98g/1mol = 191.56 grams of Al.

### What is 0.134 kg of Li in moles, and what is the total number of atoms?

0.134 kg of Li is 1000g/1kg = 134 g of Li (1 mol/6.941g) = 19.3 mol of Li. The total number of atoms is 1.16 x 1025 atoms of Li.