Avogadro’s number, also known as the Avogadro’s constant, refers to the number of particles that exist in one mole of any substance. Furthermore, it is the number of atoms that are found to be existing in exactly 12 grams of carbon-12. Moreover, this value is experimentally determined and it turns out to be approximately 6.0221 x 10^{23} particles per mole.

**Introduction to Avogadro’s Number**

In the field of chemistry and physics, Avogadro’s number usually gives us the number of ions, molecules, or atoms. However, its application can take place to any particle.

Take for example; 6.02 x 10^{23} elephants are the number of elephants existing in one mole of them. Obviously, ions, molecules, and atoms are extremely smaller in size than elephants. Consequently, there is a requirement of a large number to properly express the uniform quantity of them so as to facilitate their comparison relative to each other in chemical reactions and equations.

**How Do We Measure Avogadro’s Number?**

Obtain two copper electrodes and immerse it in 6 M HNO3 in a fume hood for 2-3 seconds. Rinse the electrode and then dip the electrode into an alcohol beaker of alcohol. Afterwards, put the electrode onto a paper towel weigh it the nearest 0.0001 gram on an analytical balance.

Below is an explanation of the way to measure the Avogadro’s formula on the basis of the above experiment.

Consider the Anode mass lost to be 0.3554 grams (g)

Furthermore, the Current(average) is 0.601 amperes (amp)

Time of electrolysis is 1802 seconds (s)

Remember the following points;

One ampere = 1 coulomb/second or one amp.s = 1 coulomb

The charge of one electron turns out to be 1.602 x 10-19 coulomb

Calculate the total charge, that passes via the circuit.(0.601 amp)(1 coul/1amp-s)(1802 s) = 1083 coul

Find out the number of electrons involved in the process of electrolysis.(1083 coul)(1 electron/1.6022 x 1019coul) = 6.759 x 1021 electrons

Determine the number of copper atoms that are lost via the anode.

Students must understand that the electrolysis process consumes two electrons per copper ion formed. Therefore, the formation of the number of copper (II) ions that takes place is half the number of electrons.

Number of Cu2+ ions = ½ number of electrons measured

Number of Cu2+ ions = (6.752 x 1021 electrons)(1 Cu2+ / 2 electrons)Number of Cu2+ ions = 3.380 x 1021 Cu2+ ions

Find out the number of copper ions per every gram of copper. This should take place from the number of copper ions that are above as well as the mass of copper ions formed.

The production of the mass of the copper ions takes place, which happens to be equal to the anode’s mass loss. Moreover, the mass of the electrons is negligible due to being extremely small. Moreover, the mass of copper atoms is the same as the mass of the copper (II) ions.)

mass loss of electrode = mass of Cu2+ ions = 0.3554 g3.380 x 1021 Cu2+ ions / 0.3544g = 9.510 x 1021 Cu2+ ions/g = 9.510 x 1021 Cu atoms/g

Find out the number of copper atoms that exist in a mole of copper, 63.546 grams.Cu atoms/mole of Cu = (9.510 x 1021 copper atoms/g copper)(63.546 g/mole copper)Cu atoms/mole of Cu = 6.040 x 1023 copper atoms/mole of copper. Most noteworthy, This is the value of the Avogadro’s number.

Finally, the Absolute error is calculated as: |6.02 x 1023 – 6.04 x 1023 | = 2 x 1021, while the percent error is calculated as : (2 x 10 21 / 6.02 x 10 23)(100) = 0.3 %

**Formula of Avogadro’s Number**

The numbers of atoms required are such that the number of grams of a substance turns out to be equal to the substance’s atomic mass.

N_{A} = 6.0220 x 10^{23} mol^{-1}.

The word mole refers to the Avogadro’s number of a substance. For example, a mole of carbon-12 atoms happens to be 12 grams. Moreover, a mole of hydrogen molecules is 2 grams while a mole of hydrogen atoms happens to be 1 gram.

**Derivation of The Formula of Avogadro’s Number**

The main question is- how was Avogadro’s number determined or derived? Accurate determinations of Avogadro’s number require the measurement of a single quantity on the two scales- the macroscopic and atomic. Moreover, this measurement will take place by using the same unit of measurement.

For the first time, this became possible when American physicist Robert Millikan carried out the measurement of the charge on an electron. Furthermore, the charge on a mole of electrons is referred to as the Faraday and it has been known for some time.

According to the National Institute of Standards and Technology (NIST), the best estimate of the value of a Faraday is 96,485.3383 coulombs per mole of electrons. Moreover, the best estimate of an electron’s charge on the basis of modern experiments is 1.60217653 x 10-19 coulombs per electron. In case the division of the charge on a mole of electrons takes place by the charge on a single electron, the result would be the value of Avogadro’s number of 6.02214154 x 1023 particles per mole.

There is another approach to determining Avogadro’s number. This approach starts with careful measurements, on the macroscopic scale, of the density of an ultrapure sample of a material.

On the atomic scale, the measurement of the density of this material takes place by using x-ray diffraction techniques. This would determine the number of atoms per unit cell that exist in the crystal. It would also determine the distance between the equivalent points, which play a vital role in defining the unit cell.

**FAQs on Avogadro’s Number**

**Questions 1: Write the full Avogadro’s number and explain what is meant by it?**

**Answer 1:** The Avogadro’s number full is equal to 6.02214076 × 10^{23}. Furthermore, Avogadro’s number refers to the number of particles that exist in one mole of any substance. Moreover, this number is also known as the Avogadro’s constant and is the number of atoms that are found to be existing in exactly 12 grams of carbon-12.

**Question 2: Explain what is meant by a mole?**

**Answer 2:** A mole refers to an Avogadro’s number of a substance. For example, a mole of carbon-12 atoms happens to be 12 grams.

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