- History
- Inspirations of Amedeo Avogadro
- Molecular hypothesis
- Fifty years later
- The birth of the term
- What it consists of and units
- Atom-gram and molecule-gram
- Molar masses and mole
- How Avogadro's number is calculated
- More accurate measurement methods
- Applications
- Solved exercises
- Exercise 1
- Exercise 2
- References
The Avogadro number is one that indicates how many particles comprise one mole of matter. It is normally designated by the symbol N A or L, and has an extraordinary magnitude: 6.02 · 10 23, written in scientific notation; if not used, it would have to be written in full: 602000000000000000000000.
To avoid and facilitate its use, it is convenient to refer to Avogadro's number calling it mole; this is the name given to the unit corresponding to such quantity of particles (atoms, protons, neutrons, electrons, etc.). Thus, if a dozen corresponds to 12 units, a mole encompasses N A units, simplifying stoichiometric calculations.
Avogadro's number written in scientific notation. Source: PRHaney
Mathematically, Avogadro's number may not be the greatest of all; but outside the realm of science, using it to indicate the quantity of any object would exceed the limits of human imagination.
For example, a mole of pencils would involve the manufacture of 6.02 · 10 23 units, leaving the Earth without its plant lungs in the process. Like this hypothetical example, many others abound, which allow a glimpse of the magnificence and applicability of this number for astronomical quantities.
If N A and the mole refer to exorbitant amounts of anything, how useful are in science? As said right at the beginning: they allow you to “count” very small particles, the numbers of which are incredibly vast even in negligible amounts of matter.
The smallest drop of a liquid contains billions of particles, as well as the most ridiculous quantity of a given solid that can be weighed on any balance.
Not use scientific notation, the mole comes in support, indicating how much, more or less, it is a substance or compound to N A. For example, 1 g of silver corresponds to about 9 · 10 -3 mol; in other words, almost one hundredth of N A (5.6 · 10 21 Ag atoms, approximately) “inhabit” that gram.
History
Inspirations of Amedeo Avogadro
Some people believe that Avogadro's number was a constant determined by Lorenzo Romano Amedeo Carlo Avogadro of Quaregna and Cerreto, better known as Amedeo Avogadro; However, this scientist-lawyer, devoted to studying the properties of gases, and inspired by the work of Dalton and Gay-Lussac was not who introduced the N A.
From Dalton, Amadeo Avogadro learned that the masses of gases combine or react in constant proportions. For example, a mass of hydrogen reacts completely with an eight times greater mass of oxygen; when this proportion was not fulfilled, one of the two gases remained in excess.
From Gay-Lussac, on the other hand, he learned that the volumes of gases react in a fixed relationship. Thus, two volumes of hydrogen react with one of oxygen to produce two volumes of water (in the form of steam, given the high temperatures generated).
Molecular hypothesis
In 1811 Avogadro condensed his ideas to formulate his molecular hypothesis, in which he explained that the distance that separates gaseous molecules is constant as long as pressure and temperature do not change. This distance, then, defines the volume that a gas can occupy in a container with expandable barriers (a balloon, for example).
Thus, given a mass of gas A, m A, and a mass of gas B, m B, m A and m B will have the same volume under normal conditions (T = 0ºC, and P = 1 atm) if both ideal gases have the same number of molecules; this was the hypothesis, nowadays law, of Avogadro.
From his observations he also deduced that the relationship between the densities of gases, again A and B, is the same as that of their relative molecular masses (ρ A / ρ B = M A / M B).
His greatest success was to introduce the term 'molecule' as it is known today. Avogadro treated hydrogen, oxygen, and water as molecules and not as atoms.
Fifty years later
The idea of its diatomic molecules met with strong resistance among chemists in the 19th century. Although Amadeo Avogadro taught physics at the University of Turin, his work was not very well accepted and, under the shadow of experiments and observations by more renowned chemists, his hypothesis was buried for fifty years.
Even the contribution of the well-known scientist André Ampere, who supported Avogadro's hypothesis, was not enough for chemists to seriously consider it.
It was not until the Congress of Karlsruhe, Germany in 1860, that the young Italian chemist, Stanislao Cannizzaro, rescued Avogadro's work in response to the chaos due to the lack of reliable and solid atomic masses and chemical equations.
The birth of the term
What is known as 'Avogadro's number' was introduced by French physicist Jean Baptiste Perrin, almost a hundred years later. He determined an approximation of N A through various methods from his work on Brownian motion.
What it consists of and units
Atom-gram and molecule-gram
Avogadro's number and the mole are related; however, the second existed before the first.
Knowing the relative masses of the atoms, the atomic mass unit (amu) was introduced as one twelfth of a carbon 12 isotope atom; roughly the mass of a proton or neutron. In this way, carbon was known to be twelve times heavier than hydrogen; which is to say, 12 C weighs 12u, and 1 H weighs 1 u.
However, how much mass does one amu really equal? Also, how would it be possible to measure the mass of such small particles? Then came the idea of the gram-atom and gram-molecule, which were later replaced by the mole. These units conveniently connected the gram with the amu as follows:
12 g 12 C = N ma
A number of 12 C N atoms, multiplied by their atomic mass, gives a value numerically identical to the relative atomic mass (12 amu). Therefore, 12 g of 12 C equaled one gram atom; 16 g of 16 O, to one gram atom of oxygen; 16 g of CH 4, one gram molecule for methane, and so on with other elements or compounds.
Molar masses and mole
The gram-atom and gram-molecule, rather than units, consisted of the molar masses of the atoms and molecules, respectively.
Thus, the definition of a mole becomes: the unit designated for the number of atoms present in 12 g of pure carbon 12 (or 0.012 Kg). And meanwhile, he became denoted N N A.
Thus, Avogadro's number consists formally of the number of atoms that make up such 12 g of carbon 12; and its unit is the mole and its derivatives (kmol, mmol, lb-mole, etc.).
Molar masses are molecular (or atomic) masses expressed as a function of moles.
For example, the molar mass of O 2 is 32g / mol; that is, a mole of oxygen molecules has a mass of 32 g, and a molecule of O 2 has a molecular mass of 32 u. Similarly, the molar mass of H is 1g / mol: one mole of H atoms has a mass of 1 g, and one H atom has an atomic mass of 1 u.
How Avogadro's number is calculated
How much is a mole? What is the value of N A so that the atomic and molecular masses have the same numerical value as the molar masses? To find out, the following equation must be solved:
12 g 12 C = N A ma
But ma is 12 amu.
12 g 12 C = N A 12uma
If you know how much an amu is worth (1,667 10 -24 g), you can directly calculate N A:
N A = (12g / 2 · 10 -23 g)
= 5,998 10 23 atoms of 12 C
Is this number identical to the one presented at the beginning of the article? No. While decimals play against, there are many more accurate calculations to determine N A.
More accurate measurement methods
If you already know the definition of a mole, especially a mole of electrons and the electric charge they carry (approximately 96,500 C / mole), knowing the charge of an individual electron (1,602 × 10 −19 C), you can calculate N A also in this way:
N A = (96500 C / 1.602 × 10 −19 C)
= 6.0237203 10 23 electrons
This value looks even better.
Another way to calculate it consists of X-ray crystallographic techniques, using a 1 kg ultra-pure silicon sphere. For this, the formula is used:
N A = n (V u / V m)
Where n is the number of atoms present in the unit cell of a silicon crystal (n = 8), and V u and V m are the volumes of the unit and molar cell, respectively. Knowing the variables for the silicon crystal, Avogadro's number can be calculated by this method.
Applications
Avogadro's number allows in essence to express the abysmal quantities of elementary particles in simple grams, which can be measured on analytical or rudimentary balances. Not only this: if an atomic property is multiplied by N A, its manifestation will be obtained at macroscopic scales, visible in the world and with the naked eye.
Therefore, and with good reason, this number is said to function as a bridge between the microscopic and the macroscopic. It is often found especially in physicochemistry, when trying to link the behavior of molecules or ions with that of their physical phases (liquid, gas or solid).
Solved exercises
Calculations in section two examples of exercises using N were addressed to. Then we will proceed to solve another two.
Exercise 1
What is the mass of a molecule of H 2 O?
If its molar mass is known to be 18 g / mol, then one mole of H 2 O molecules has a mass of 18 grams; but the question refers to an individual molecule, alone. To then calculate its mass, the conversion factors are used:
(18g / mol H 2 O) · (mol H 2 O / 6.02 · 10 23 molecules H 2 O) = 2.99 · 10 -23 g / molecule H 2 O
That is, a molecule of H 2 O has a mass of 2.99 · 10 -23 g.
Exercise 2
How many atoms of dysprosium metal (Dy) will contain a piece of it whose mass is 26 g?
The atomic mass of dysprosium is 162.5 u, equal to 162.5 g / mol using Avogadro's number. Again, we proceed with the conversion factors:
(26 g) · (mol Dy / 162.5g) · (6.02 · 10 23 Dy atoms / mol Dy) = 9.63 · 10 22 Dy atoms
This value is 0.16 times smaller than N A (9.63 · 10 22 / 6.02 · 10 23), and therefore, said piece has 0.16 moles of dysprosium (it can also be calculated with 26/162,5).
References
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- Mole Day. (sf). The History of Avogadro's Number: 6.02 times 10 to the 23 rd. Recovered from: moleday.org
- Helmenstine, Anne Marie, Ph.D. (January 06, 2019). Experimental Determination of Avogadro's Number. Recovered from: thoughtco.com
- Tomás Germán. (sf). Avogadro's number. IES Domingo Miral. Recovered from: iesdmjac.educa.aragon.es
- Joaquín San Frutos Fernández. (sf). Avogadro's number and mole concept. Recovered from: encina.pntic.mec.es
- Bernardo Herradón. (September 3, 2010). Karlsruhe Congress: 150 years. Recovered from: madrimasd.org
- George M. Bodner. (February 16, 2004). How Was Avogadro's Number Determined? Scientific American. Recovered from: scientificamerican.com