Avogadro Scientist

Avogadro’s number, number of units in one mole of any substance (defined as its molecular weight in grams), equal to 6.02214076 × 10 23. The units may be electrons, atoms, ions, or molecules, depending on the nature of the substance and the character of the reaction (if any).See alsoAvogadro’s law. Most noted for his contributions to molecular theory, including what is known as Avogadro's law. In tribute to him, the number of elementary entities in 1 mole of a substance, 6.02214076×10^23 mol−1, is known as the Avogadro constant. Avogadro's Life Amedeo Avagadro was born in 1776 in Turin, a city in northwestern Italy. Avogadro spent his entire life within 80 kilometers (50 miles) of Turin, far from the cultural centers where chemistry was becoming a science. Eventually proven correct, this hypothesis became known as Avogadro’s law, a fundamental law of gases. The contributions of the Italian chemist Amedeo Avogadro (1776–1856) relate to the work of two of his contemporaries, Joseph Louis Gay-Lussac and John Dalton.

07th May 2019 @ 12 min read

Amedeo Avogadro, in full Lorenzo Romano Amedeo Carlo Avogadro, conte di Quaregna e Cerreto, (born August 9, 1776, Turin, in the Kingdom of Sardinia and Piedmont Italy—died July 9, 1856, Turin), Italian mathematical physicist who showed in what became known as Avogadro’s law that, under controlled conditions of temperature and pressure, equal volumes of gases contain an equal number of molecules.

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 N_A. It has the dimension of the reciprocal amount of substance (mol⁻¹). The approximate value of N_A 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.

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 (M_u) 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.

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 N_A = 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 m_i is the mass of atom i and M_i 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 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 k_B 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 (M_u) and the Avogadro constant.

where m_u is the atomic mass constant.

The value precise value of M_u is 0.999 999 999 65(30) g mol⁻¹. But for practical purposes, we can say M_u ≈ 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

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.

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?

Solution: Let m_Na and M_Na be the atomic mass and molar mass of sodium-23. Thus, M_Na = 22.989 g mol⁻¹.

Now, m_Na 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, m_I2 can be determined as:

Therefore, the mass of a iodine molecule is 4.208 × 10⁻²² g.

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ITALIAN CHEMIST
1776–1856

In 1811, just three years after John Dalton published his atomic theory , a brilliant theoretician named Amedeo Avogadro proposed his molecular theory. Avogadro's molecular theory related gas densities to molecular weights, explained reacting proportions by volume in terms of molecular ratios and compositions, and suggested methods for determining both molecular weights and compositions. His 1811 publication was a tour de force. Nonetheless, it was ignored for over half a century. Historians have sought reasons for the neglect of Avogadro's work in his life, his theory, and the state of chemistry at the time.

Avogadro's Life

Amedeo Avagadro was born in 1776 in Turin, a city in northwestern Italy. Avogadro spent his entire life within 80 kilometers (50 miles) of Turin, far from the cultural centers where chemistry was becoming a science. He received a classical education in the humanities, earned a doctorate in law in 1796 at the age of twenty, and practiced law for the next ten years. After auditing some courses and studying science on his own, Avogadro made a radical career change. In 1806 he became a secondary school science teacher, and in 1820 a university physics professor. He married in 1815, had seven children, and by all accounts, led a very happy family life.

During his academic career, Avogadro's publications revealed an intense curiosity, sharp intuition, vivid imagination, rigorous logic, and independent judgment—traits of an outstanding scientist. His obituary in an Italian scientific journal remarked on his retiring disposition and on the simplicity of his life, and it noted his other researches, but it did not mention the 1811 paper on his molecular theory.

Avogadro's Molecular Theory

Avogadro made two assumptions about molecules in his 1811 publication. The first assumption is now known as Avogadro's hypothesis, sometimes also called the EVEN hypothesis. It stated that equal volumes of gases contain equal numbers (thus, even) of molecules at the same temperature and pressure. The hypothesis was based on a model of the gas state in which molecules are far apart and equally spaced so that each molecule occupies the same volume. The second assumption was that gas molecules can divide during chemical reactions.

Avogadro used the EVEN hypothesis to interpret gas densities and assign molecular weights. EVEN implies that the density of a gas at a given temperature and pressure depends only on the weight of its molecules. Avogadro supposed that since the reported gas density of oxygen was 15 times that of hydrogen, the molecular weight of oxygen was 15 times that of hydrogen (the modern calculation of the ratio of the densities and molecular weights is actually sixteen). Consequently, he assigned oxygen a molecular weight of 15, relative to 1 for hydrogen. By this method Avogadro could determine a molecular weight for any gas, given its density.

Avogadro needed both assumptions to explain reacting proportions and molecular compositions. For example, when water forms, the reacting proportions of hydrogen, oxygen, and water are 2:1:2 by volume. On the basis of the EVEN hypothesis, a 2:1:2 volumetric ratio should correspond to a 2:1:2 molecular ratio. Thus, two molecules of hydrogen (h) should combine with one molecule of oxygen (o) to give two molecules of water. Direct combination, however, would give only one molecule of h ₂ o. To fit the volumetric data, Avogadro split the h ₂ o water molecule into two ho _1/2 molecules. This in turn forced him to assume that oxygen molecules could divide into two 'half molecules' during the reaction: 2h + o → [h ₂ o] → 2ho _1/2 . He expressed the composition of water as one 'half molecule' of oxygen combined with one molecule of hydrogen (ho _1/2 ). With the aid of his two assumptions—EVEN and divisible molecules—Avogadro determined compositions for water, ammonia, hydrogen chloride, and gaseous oxides of nitrogen, carbon, and sulfur.

Early Nineteenth-Century Chemistry

The state of chemical theory and practice in 1811 was primitive by modern standards and not yet ready for Avogadro's molecular theory. Dalton's model of the gas state (atoms of different size in contact) precluded EVEN. Jöns Jakob Berzelius, another very influential chemist, believed gaseous elements like oxygen contained only indivisible atoms, not divisible molecules. Gas density and combining ratios data were limited and inaccurate. Atomic weights depended on unknown formulas and vice versa—a vicious cycle.

Conclusion

In retrospect the neglect of Avogadro's theory seems quite understandable. In 1811 he was a secondary school teacher living in a remote province. Furthermore, he was a theoretical physicist writing for practical chemists in legal language. His molecular theory was based on speculative assumptions, lacked independent experimental evidence or theoretical justification, and could only explain but not predict volumetric ratios. His molecular ratios (2h + o → 2ho _1/2 ) were far removed from modern atomic ratios (2H ₂ + O ₂ → 2H ₂ O) and did not solve the atomic weight –formula problem. Chemists in the early nineteenth century, however, needed more immediately productive theories and much more experimental information before Avogadro's theory could be truly useful. It took half a century of effort, the development of organic chemistry, and the ingenuity of another Italian, Stanislao Cannizzaro, to build a modern chemistry on the foundations laid by Avogadro. Nonetheless, as Nobel Prize winner Linus Pauling observed in a 1956 article in Science , Avogadro's work 'forms the basis of the whole of theoretical chemistry' and is 'one of the greatest contributions to chemistry that has ever been made.'

SEE ALSO Berzelius, JÖns Jakob ; Cannizzaro, Stanislao ; Dalton, John ; Pauling, Linus .

John D. Hostettler

Bibliography

Causey, Robert L. (1971). 'Avogadro's Hypothesis and the Duhemian Pitfall.' Journal of Chemical Education 48(6):365–367.

Avogadro Scientist

Ihde, Aaron (1964). The Development of Modern Chemistry. New York: Harper & Row.

Lipeles, Enid S. (1983). 'The Chemical Contributions of Amedeo Avogadro.' Journal of Chemical Education 60(2):127–128.

Nash, Leonard K. (1957). 'The Atomic-Molecular Theory.' In Harvard Case Histories in Experimental Science , Vol. 1, ed. James Bryant Conant. Cambridge, MA: Harvard University Press.

Italian Scientist Avogadro

Pauling, Linus (1956). 'Amedeo Avogadro.' Science 124:708–713.