The value of Avogadro number (also known as Avogadro constant) is a positive natural integer as it indicates a finite and numerable quantity of elementary objects.
No constant, as well as no quantity of physics, can be defined with infinite certainty, therefore with arbitrary precision. On the subject of the precision of measurements it is always very interesting to refer to Heisenberg’s uncertainty principle and the epistemological, historical and philosophical influence it had in the scientific world when it was formalized.
What we will do in this article will be to define a purely theoretical value of Avogadro’s number, which is the value determined in the paper “An Equivalence for Both Coulombian and Gravitational Interactions”. This theoretical value will be compared to all the values of Avogadro’s number measured over time as well as the most modern measurements.
The theoretical determination of the Avogadro’s number
As stated, the paper “An Equivalence for Both Coulombian and Gravitational Interactions” defines the value of Avogadro’s number in relation with other natural constants. This expression of avogadro number is unprecedented in the history of physics. No one before has ever managed to express Avogadro’s number in relation to other natural constants. The expression of the Avogadro number (Avogadro constant) is :
Where:
Since Avogadro's number is 6.022 × 10 23, it only makes sense that the holiday starts at 6:02 a.m. Revelers tell chemistry jokes, blow bubbles of natural gas that they set ablaze, toast with drinks chilled by dry ice and even recite the mole pledge of allegiance.
- : Is the Avogadro number
- : Is the Language constantand its value is
- : Is the reduced Planck constant
- : Is the fine structure constant
- : Is the newtonian gravitation constant
- : Is the protonmass
- : Is the electronmass
As we can see from its expression, the Avogadro number indissolubly links the world of microscopic (particles) to the world of macroscopic (large gravitational masses).
This is certainly not only an extraordinary result but unique in the history of physics because nobody until 2019 had ever been able to understand how the quantum world of physics and the gravitational world were related and connected. In this description it strongly emerges that the Avogadro number indicates the amount of critical mass beyond which the world of microscopic becomes macroscopic. Avogadro’s number is the hinge between these two connected and connected worlds.
Avogadro’s law, also known as Avogadro’s principle or Avogadro’s hypothesis, is a gas law which states that the total number of atoms/molecules of a gas (i.e. The amount of gaseous substance) is directly proportional to the volume occupied by the gas at constant temperature and pressure. Avogadro's number, or Avogadro's constant, is the number of particles found in one mole of a substance. It is the number of atoms in exactly 12 grams of carbon -12. This experimentally determined value is approximately 6.0221 x 10 23 particles per mole.
How much is the Avogadro number ?
The value officially accepted by the scientific community for the Avogadro constant is as follows:
Before continuing, it is important to define what the CODATA values are. The scientific community organizes its worldviews through a continuous and positive dialogue through all the experts of the individual branches of physics. Periodically all the experiments carried out in the world are analyzed and the results are sifted through. Following this global process of evaluating the entire world of laboratory experiments, the “most likely true” values are chosen for each of the characteristics of the observable universe. This is really beautiful work and high quality. Here you can find a direct link to CODATA 2018 value for the Avogadro number.
In 2018, the concept of kilograms, which has always been linked to the Avogadro number, was dealt with by the BIPM (Bureau International des Poids et Mesures) weights and measures commission in a special focus. Discussions on the subject can be found at this link: https://www.bipm.org/en/bipm/mass/avogadro/.
In the BIPM decision, a deterministic value is set for the Avogadro number so that all other constants in the international system are connected. This discussion and the related documents are really very interesting also to understand how the scientific community evolves.
This BIPM decision of 2018 has completely overturned the history of measurement.
For this reason for all calculations made with the proposed mathematical model we will use the CODATA 2014 values.
The experimental values of the Avogadro number
Here we propose to use the CODATA 2014 values or to take a look to all the historical measurement of the constant. The 2014 codata value is following:
In his well written article “History and progress in the accurate determination of the Avogadro constant” the scientist Peter Becker makes a beautiful historical and quantitative analysis of evolution in the measure of Avogadro number. In his list he summarizes all the most important measures up to 2001.
Below we report a longer and more detailed research work summarized in a table produced by us for all measurements of the most important experiments.
We can observe how the more time passes the more the value of Avogadro’s number converges with the CODATA 2014 value we indicated.
In conclusion, we can say that we have explored the theme of Avogadro’s number and that we can observe that the value proposed for the constant is extremely accurate and in line with the experimental measurements, less an error of two parts per billion.
07th May 2019 @ 12 min read
The Avogadro constant or (the Avogadro number earlier) is the number of elementary units in one mole of any substance. The Avogadro constant is denoted as NA. It has the dimension of the reciprocal amount of substance (mol−1). The approximate value of NA is 6.022 × 1023 mol−1. This means one mole of any substance contains 6.022 × 1023 elementary particles. The Avogadro constant is named after Italian scientist Amedeo Avogadro.
These elementary units in one mole can be anything like atoms, molecules, ions, electrons, protons, neutrons, particles of sand. So, when we say one mole of sodium chloride, it means 6.022 × 1023 molecules of sodium chloride.
Values of Avogadro's Constant
The value of the Avogadro constant is revised over a period of time. As of the 2019 redefinition of the SI base units, the value of the Avogadro constant is fixed to 6.02214076×1023mol−1. This is the exact value of the constant. The table below mentions the value of the constant in different units.
| Value | Unit |
|---|---|
| 6.022 140 76 × 1023 | mol−1 |
| 6.022 140 76 × 1026 | kmol−1 |
| 2.731 597 099 802 001 2 × 1026 | lb-mol−1 |
| 1.707 248 187 376 250 75 × 1025 | oz-mol−1 |
| 0.602 214 076 | mL mol−1 Å |
History of Avogadro's Constant
The Avogadro constant has a long history. The constant is named in honour of Avogadro, but he did not discover it. In 1811, Avogadro discovered the relationship between the volume of gas and the amount of gas through his experiments. He was the first to proposed the volume of a gas is directly proportional to the amount of the gas at constant pressure and temperature. This is today we call Avogadro's law or Avogadro's hypothesis. His work does not mention Avogadro's constant.
Perrin's Work
French Nobel Laureate Jean Baptiste Perrin estimated the Avogadro number with several methods. And he credited the naming of the number to Avogadro in 1909. Perrin named the number Avogadro's number, not Avogadro's constant. This name had continued till 1971. In 1971, the International System of Unit (SI) introduced a new quantity called Avogadro's constant. The Avogadro constant has the same numerical value as the Avogadro number, but they differ in the unit which will be explained later in this article.
Perrin defined the Avogadro number as the number of atoms in one gram of hydrogen (one gram-molecule). This definition was later revised to the number of atoms in 12 grams of carbon-12 (12C).
Loschmidt's Estimation
Before Perrin, Loschmidt also made a significant contribution to the number. Josef Loschmidt was an Austrian scientist who is notable for his work on estimation of the diameter of the molecules in the air. Through his method, it is possible to calculate the number density (the number of molecules or atoms per unit volume). This quantity is closely relative to the Avogadro constant. The relationship between them is discussed later in this article. The number density of an ideal gas is called as the Loschmidt constant. In many of German literature, these two constants are interchangeable. They can easily be distinguished from their units. The Avogadro constant is also denotated as L in honour of Loschmidt.
Other Efforts
Robert Millikan was an American physicist and Nobel Laureate. He successfully measured the charge on an electron in 1910. The electric charge per mole (the Faraday constant) of electrons had already known at that time. With the help of these two quantities, the electric charge on an electron and the Faraday constant, it is possible to calculate the number of electrons per mole. The value of this number of electrons per mole is the same as Avogadro's constant.
One of a modern method to estimate the value of the constant is X-ray crystallography. This method estimates the constant by determining the number of silicon atoms in a crystal cell, the volume per unit cell, and the molar volume.
The measurement of the accurate value of the Avogadro's constant is always troublesome. Over the period, the new methods were developed, and the Avogadro constant has continuously been improvised. From 2019, the international committee fixed the value of the Avogadro's constant exactly to 6.022 140 76 × 1023 mol−1.
2019 Redefinition and Prior Definition of Avogadro's Constant
As discussed above, the 2019 redefinition of the Avogadro constant is 6.022 140 76 × 1023 mol−1. The consequence of this redefinition is the prior definition of the constant is no longer valid. Before the 2019 redefinition, the value of the constant was defined as the amount of atoms presents in 12g of carbon-12 (12C). Also, because of the definition the molar mass constant (Mu) is no longer exactly equal to 1 g mol−1. Instead, it is approximately equal to 1 g mol−1. This is summarised in the table below.
| 2019 Redefinition | Prior to 2019 Redefinition |
|---|---|
| NA = 6.022 140 76 × 1023 mol−1 | The value of NA is the number of 12C atoms in 12 g of carbon-12. |
| The molar mass constant is approximately equal to 1 g mol−1 (Mu ≈ 1 g mol−1). | Mu is exactly equal to 1 g mol−1 (Mu = 1 g mol−1). |
Note: The difference in the value of the Avogadro constant before and after the 2019 definition is very small. The redefinition would not affect most of the calculations unless the high degree of precision is needed. For practical calculations, we can take NA = 6.022 × 1023 mol−1.
Avogadro's Constant and Mole
The Avogadro constant and the mole are related quantities. In fact, the Avogadro constant is defined in terms of the mole. The value of Avogadro's constant is the number of elementary units in one mole of any substance. The definition is universally true. The below equation establishes the relation between both.
Avogadro's Constant and Molar Mass
We can use the Avogadro constant to determine the mass of any atom if we know the molar mass of that atom. This statement is also true for molecules. The molar mass is the mass of one mole of a given sample. It is expressed in g mol−1. The relation between both is as follows:
where mi is the mass of atom i and Mi is molar mass of atom i.
Avogadro's Constant and Avogadro's Number
The Avogadro constant and the Avogadro number have the same numerical value. They only differ in the unit. The Avogadro number is a dimensionless quantity, but the Avogadro constant has the dimension of the reciprocal amount of substance (mol−1). The below table describes the same.
| Avogadro's Constant | Avogadro's Number |
|---|---|
| The constant has the unit of mol−1. | It is a dimensionless quantity. |
| It is denoted as NA. | We use N to denote the Avogadro number. |
| NA = 6.022 × 1023 mol−1 | NA = 6.022 × 1023 |
Avogadro's Constant and Boltzmann's constant
The Boltzmann constant is an important physical constant which plays a vital role in classical statistical mechanics. It is denoted as kB or simply k. The Avogadro constant is related to the Boltzmann constant by the gas constant R.
Avogadro's Constant and Loschmidt's Constant
The Loschmidt constant is the number density (the number of molecules per unit volume). For an ideal gas, the relationship between the Loschmidt constant and the Avogadro constant at STP (P0 = 1 atm, T0 = 273.15 K) is described in the equation below.
Avogadro's Constant and Faraday's Constant
The Faraday constant (F) is the Avogadro constant times the elementary charge (e).
Avogadro's Constant and Unified Mass Unit
The unified mass unit or the dalton (u) is the ratio of the molar mass constant (Mu) and the Avogadro constant.
where mu is the atomic mass constant.
The value precise value of Mu is 0.999 999 999 65(30) g mol−1. But for practical purposes, we can say Mu ≈ 1 g mol−1.
Examples
Example 1: To Determine Calcium Atoms
Statement: For 100 g of calcium in a beaker, calculate the number of calcium atoms in the beaker?
Solution: The molecular weight of calcium is 40.1 g mol−1. The number of moles of calcium in the beaker is
The number of calcium atoms in the beaker is calculated as:
Therefore, the number of calcium atoms is 1.50 × 1024.
Example 2: To Determine Total Molecules in Sodium Chlorine Solution
The Value Of Avogadro Number Is
Statement: Consider 50.0 g of NaCl is dissolved in 200 g of water. Estimate the total molecules in the solution?
Solution: The molecular weight of NaCl and water is 58.44 g mol−1 and 18.01 g mol−1.
The moles of NaCl in 50.0 g:
The moles of H2O in 100 g:
When 1 mol of NaCl dissociates, 1 mol of Na+ and 1 mol of Cl− are formed. So, when 0.855 5 mol of NaCl dissociates, 0.855 5 mol of Na+ and 0.855 5 mol of Cl− are formed.
$underset{1,text{mol}}{ce{Na+}}$ + $underset{1,text{mol}}{ce{Cl-}}$}' alt='>Thus, the total number of moles after the dissociation is the sum of the moles of Na+, Cl−, and H2O.
The total number of molecules in the solution is
Therefore, the total number of moles in NaCl solution is 4.374 × 1024 mol.
Example 3: To Determine Mass of Sodium Atom
Statement: The molar mass of sodium-23 is 22.989 g mol−1. Calculates the mass of a sodium atom?
Avogadro's Full Number
Solution: Let mNa and MNa be the atomic mass and molar mass of sodium-23. Thus, MNa = 22.989 g mol−1.
Now, mNa can be determined using the formula below.
Therefore, the mass of a sodium-23 atom is 3.817 × 10−23 g.
Example 4: To Determine Molecular Mass of Iodine gas
Statement: The atomic mass of iodine is 126.9 g mol−1. Determine the molecular mass of iodine gas?
Solution: The iodine gas is a diatomic gas. The molecular formula is I2. So, the molar mass of I2 is twice the molar mass of I.
Now, mI2 can be determined as:
Therefore, the mass of a iodine molecule is 4.208 × 10−22 g.
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29th Oct 2019