The Avogadro's number It is the one that indicates how many particles make up a mole of matter. It is normally designated by the symbol NTO or L, and has an extraordinary magnitude: 6.02 · 102. 3, 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 a 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 NTO units, simplifying stoichiometric calculations.
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 imply the manufacture of 6.02 · 102. 3 units, leaving the Earth without its plant lungs in the attempt. Like this hypothetical example, many others abound, which allow us to glimpse the magnificence and applicability of this number for astronomical quantities.
WithoutTO and the mole allude to exorbitant amounts of anything, what use are they 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.
In order not to resort to scientific notations, the mole comes to the aid, indicating how much, more or less, one has of a substance or compound with respect to NTO. For example, 1 g of silver corresponds to about 9 · 10-3 mole; in other words, that gram "inhabits" almost one hundredth of NTO (5,6 10twenty-one Ag atoms, approximately).
Article index
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, dedicated to studying the properties of gases, and inspired by the work of Dalton and Gay-Lussac, was not the one who introduced the NTO.
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).
In 1811 Avogadro condensed his ideas to formulate his molecular hypothesis, in which he explained that the distance that separates the gaseous molecules is constant as long as the 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, mTO, and a mass of gas B, mB, mTO and mB they 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 the gases, again A and B, is the same as that of their relative molecular masses (ρTO/ ρB = MTO/ MB).
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.
The idea of its diatomic molecules met 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 of 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..
What is known as 'Avogadro's number' was introduced by the French physicist Jean Baptiste Perrin, almost a hundred years later. He determined an approximate of NTO through different methods from his work on Brownian motion.
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; what is equivalent to say, 12C weighs 12u, and 1H 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 12C = N ma
A number of N atoms of 12C, multiplied by its atomic mass, gives a value numerically identical to the relative atomic mass (12 amu). Therefore, 12 g of 12C equaled one gram atom; 16 g of 16Or, to a gram-atom of oxygen; 16 g CH4, a gram-molecule for methane, and so on with other elements or compounds.
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 for its part, N happened to be denoted as NTO.
So, 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 Otwo is 32g / mol; that is, one mole of oxygen molecules has a mass of 32 g, and one molecule of Otwo it 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 much is a mole? What is the value of NTO 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 12C = NTOMa
But ma is 12 uma.
12 g 12C = NTO12uma
If it is known how much an amu is worth (1,667 10-24 g), you can directly calculate NTO:
NTO = (12g / 2 10-2. 3g)
= 5,998 102. 3 atoms of 12C
Is this number identical to the one presented at the beginning of the article? No. Although decimals play against, there are much more precise calculations to determine NTO.
If the definition of a mole is previously known, especially a mole of electrons and the electric charge they carry (approximately 96,500 C / mol), knowing the charge of an individual electron (1.602 × 10−19C), you can calculate NTO also in this way:
NTO = (96500 C / 1.602 × 10−19C)
= 6.0237203 102. 3 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:
NTO = n(Vor/ Vm)
Where n is the number of atoms present in the unit cell of a silicon crystal (n= 8), and Vor and Vm are the unit cell and molar volumes, respectively. Knowing the variables for the silicon crystal, the Avogadro number can be calculated by this method.
Avogadro's number allows in essence to express the abysmal quantities of elementary particles in simple grams, which can be measured in analytical or rudimentary balances. Not only this: if an atomic property is multiplied by NTO, 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).
In the calculations section, two examples of exercises were addressed using NTO. Then we will proceed to solve another two.
What is the mass of a molecule of HtwoOR?
If its molar mass is known to be 18 g / mol, then one mole of H moleculestwoOr it 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 HtwoO) · (mol HtwoO / 6.02 · 102. 3 H moleculestwoO) = 2.99 · 10-2. 3 g / molecule HtwoOR
That is, a molecule of HtwoOr it has a mass of 2.99 · 10-2. 3 g.
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 · 102. 3 atoms Dy / mol Dy) = 9.63 · 1022 Dy atoms
This value is 0.16 times smaller than NTO (9.63 · 1022/ 6.02 102. 3), and therefore, said piece has 0.16 moles of dysprosium (also being able to calculate with 26 / 162.5).
Yet No Comments