Atomic mass unit. Avogadro's number
Matter consists of molecules. By molecule we will mean smallest particle of a given substance, preserving the chemical properties of that substance.
Reader: In what units is the mass of molecules measured?
Author: The mass of a molecule can be measured in any units of mass, for example in tons, but since the masses of molecules are very small: ~10–23 g, then for convenience introduced a special unit - atomic mass unit(a.e.m.).
Atomic mass unitis called a value equal to the th mass of the carbon atom 6 C 12.
The notation 6 C 12 means: a carbon atom having a mass of 12 amu. and nuclear charge – 6 elementary charges. Similarly, 92 U 235 is a uranium atom with a mass of 235 amu. and the charge of the nucleus is 92 elementary charges, 8 O 16 is an oxygen atom with a mass of 16 amu and the charge of the nucleus is 8 elementary charges, etc.
Reader: Why was it chosen as the atomic unit of mass? (not or ) part of the mass of an atom and specifically carbon, and not oxygen or plutonium?
It has been experimentally established that 1 g » 6.02×10 23 amu.
The number showing how many times the mass of 1 g is greater than 1 amu is called Avogadro's number: N A = 6.02×10 23.
From here
N A × (1 amu) = 1 g (5.1)
Neglecting the mass of electrons and the difference in the masses of a proton and a neutron, we can say that Avogadro’s number approximately shows how many protons (or, which is almost the same thing, hydrogen atoms) must be taken to form a mass of 1 g (Fig. 5.1).
Mole
The mass of the molecule, expressed in atomic units mass is called relative molecular weight .
Designated M r(r– from relative – relative), for example:
12 a.m.u. = 235 a.m.u.
A portion of a substance that contains the same number of grams of a given substance as the number of atomic mass units contained in a molecule of a given substance is called pray(1 mol).
For example: 1) relative molecular weight hydrogen H 2: therefore, 1 mole of hydrogen has a mass of 2 g;
2) relative molecular weight carbon dioxide CO 2:
12 amu + 2×16 a.m.u. = 44 amu
therefore, 1 mole of CO 2 has a mass of 44 g.
Statement. One mole of any substance contains the same number of molecules: N A = 6.02×10 23 pcs.
Proof. Let the relative molecular mass of a substance M r(a.m.) = M r× (1 amu). Then, according to the definition, 1 mole of a given substance has a mass M r(d) = M r×(1 g). Let N is the number of molecules in one mole, then
N×(mass of one molecule) = (mass of one mole),
The mole is the SI base unit of measurement.
Comment. A mole can be defined differently: 1 mole is N A = = 6.02×10 23 molecules of this substance. Then it is easy to understand that the mass of 1 mole is equal to M r(G). Indeed, one molecule has a mass M r(a.u.m.), i.e.
(mass of one molecule) = M r× (1 amu),
(mass of one mole) = N A ×(mass of one molecule) =
= N A × M r× (1 amu) = 
.
The mass of 1 mole is called molar mass of this substance.
Reader: If you take the mass T some substance molar mass which is equal to m, then how many moles will it be?
Let's remember:
Reader: In what SI units should m be measured?
, [m] = kg/mol.
For example, the molar mass of hydrogen
Yesterday I promised to explain this accessible language. This is important for understanding chemistry. If you understand it once, you won’t forget it later.
Chemistry has its own language, like any science. 2H 2 + O 2 → 2H 2 O - in chemical language, a recording of the reaction of the formation of water from simple substances, hydrogen (H) and oxygen (O). Small numbers refer to the number of atoms (They come after the symbol chemical element), large ones - to the number of molecules. From the equation it is clear that two hydrogen molecules combine with one oxygen molecule and as a result comes out two water molecules. Attention - this is very important to understand! It is precisely molecules that connect with molecules, not “gram with gram,” but molecule with molecule.
This proportion will always remain:
Everything would be fine, but there are two problems. The first one is in real life we cannot measure one million molecules of oxygen or hydrogen. We will be able to measure one gram or one ton of reagents. Second, the molecules are very small. There are 6.7 x 10 24 of them in one glass of water. Or, in the usual notation, 6.7 trillion trillion (that’s right - almost seven trillion times a trillion molecules). It is inconvenient to operate with such numbers.
What is the way out? Molecules also have mass, albeit very small. We just take mass of one molecule, multiply by number of molecules and we get the mass we need. We agreed so - we take it very much large number molecules (600 billion trillion pieces) and invent for this amount special unit of measurement mole. How do you eat 12 pieces of something? special name "dozen", and when they talk about “ten dozen,” they mean 120 pieces. 5 dozen eggs = 60 pieces. Same with moles. 1 mole is 600 billion trillion molecules or, in mathematical notation, 6.02 10 23 molecules. That is, when we are told “1 mole” of hydrogen, we know that we are talking about 600 billion trillion molecules of hydrogen. When they talk about 0.2 moles of water, we understand that we are talking about 120 billion trillion water molecules.
Once again - the moth is just like that counting unit, only specifically for molecules. Like “ten”, “dozen” or “million”, only much more.
Continuing the table above, you can write:
We solved the first problem; writing 1 mole or 2 moles is much more convenient than 600 billion trillion molecules or 1.2 trillion trillion molecules. But for convenience alone, there was no need to fence the garden. The second problem, as we remember, is the transition from number of molecules(don’t count them individually!) to mass of matter, to the fact that we can measure on scales. This number of molecules in one mole (it is a little strange, non-round - 6.02·10 23 molecules) was chosen for a reason. One mole of carbon molecules weighs exactly 12 grams.
It is clear that all molecules are different. There are large and heavy ones - they may contain many atoms, or not very many, but the atoms themselves are heavy. And there are small and light molecules. For each atom and for many molecules there are tables with their molar mass. That is, with the weight of one mole of such molecules (if not, you can easily calculate it yourself by adding up the molar masses of all the atoms that make up the molecule). Molar mass is measured in grams/mol (how many grams one mole weighs, that is, how many grams 6.02·10 23 molecules weigh). We remember that a mole is just a counting unit. Well, as if the directory wrote - 1 dozen chicken eggs weighs 600 grams, and 1 dozen ostriches weighs 19 kilograms. A dozen is just a quantity (12 pieces), and the eggs themselves, chicken or ostrich, weigh differently. And a dozen of these or other eggs also weigh differently.
Same with molecules. 1 mole of small and light hydrogen molecules weighs 2 grams, and 1 mole of large sulfuric acid molecules weighs 98 grams. 1 mole of oxygen weighs 32 grams, 1 mole of water weighs 18 grams. Here is a picture as an example, where small hydrogen molecules and large molecules oxygen. This picture is a graphical representation of the reaction 2H 2 + O 2 → 2H 2 O.
We continue to fill out the table:
Do you see the transition from number of molecules to their mass? Do you see that the law of conservation of matter is fulfilled? 4 grams + 32 grams gives 36 grams.
Now we can decide simple tasks in chemistry. Here is the most primitive one: There were 100 oxygen molecules and 100 hydrogen molecules. What will happen as a result of the reaction? We know that for 1 molecule of oxygen you need 2 molecules of hydrogen. Therefore, all 100 hydrogen molecules will react (and 100 water molecules will be formed), but not all oxygen will react, another 50 molecules will remain. Oxygen is in excess.
As I said above, no one counts molecules as pieces. Substances are usually measured in grams. Now the task from school textbook: There are 10 g of hydrogen and 64 g of oxygen, what happens if you mix them? First, we must convert the masses into moles (that is, into the number of molecules or the amount of substance, as chemists say). 10 g of hydrogen is 5 moles of hydrogen (1 mole of hydrogen weighs 2 grams). 64 g of oxygen is 2 moles (1 mole weighs 32 grams). We know that for 1 mole of oxygen, 2 moles of hydrogen are lost during the reaction. This means that in our case, all the oxygen (2 moles) and 4 moles of hydrogen out of five will react. This results in 4 moles of water and one mole of hydrogen remaining.
Let's convert the answer back into grams. All oxygen (64 grams) and 8 grams of hydrogen (4 mol * 2 g/mol) will react. 1 mole of hydrogen will remain unreacted (that's 2 grams) and you'll get 72 grams of water (4 moles * 18 g/mol). The law of conservation of matter is again fulfilled - 64 + 10 = 72 + 2.
I think that by now it should be clear to everyone. 1 mole is simply the number of molecules. Molar mass is the mass of one mole. It is needed in order to move from the mass of matter (with which we work in real world) to the number of molecules, or the amount of substance needed for reactions.
We repeat again:
a) substances react in the ratio of n molecules of one to m molecules of the other. This proportion will be the same for 100 molecules starting material, and for a hundred trillion, or for a hundred trillion trillion.
b) for convenience, in order not to count molecules as pieces, they came up with a special counting unit - the mole, that is, 6.02·10 23 molecules at once. The number of these moles is called the usual “amount of substance”
c) a mole of each substance weighs differently, because The molecules and atoms that make up a substance themselves weigh differently. The mass of one mole of a substance is called its molar mass. Another example - ordinary and sand-lime bricks weigh differently. If we draw an analogy, then “the weight of a thousand bricks” is “molar mass” (with the difference that there are not 1000 molecules, but more). The mass of this “thousand bricks” is different for sand-lime bricks and ordinary bricks.
d) we fence this whole garden so that it is easy to move from the mass of reagents to the amount of substance (number of molecules, number of moles) and back. And you need to go back and forth because in the real world we measure reagents in grams, and chemical reactions are proportional not to mass, but to the number of molecules.
P.S. For chemists and others, I have intentionally simplified a lot here. I don’t need to explain that 12 grams weighs not 1 mole of carbon, but 1 mole of molecules of the C12 isotope, or that instead of “molecules” one should write “ structural units"(molecules, ions, atoms...), did not specifically mention that 1 mole of gas occupies the same volume under the same conditions and much more
What I didn’t like about the textbooks was just formal definition praying, without indicating the meaning of this concept and why it is needed.
Every schoolchild who begins to study chemistry encounters the concept of “mole.” With more complex concepts, such as concentration, molarity of the solvent, are difficult to figure out without knowing what a mole is. It can be concluded that the moth is one of the the most important concepts in chemistry. Many problems cannot be solved without determining the number of moles.
Definition
So what is a mole in chemistry? The explanation is quite simple: this is a unit in which the amount of a substance is expressed, one of the SI units. The definition of what a mole is in chemistry can be formulated this way: 1 mole is equivalent to the structural particles contained in 12 g of carbon-12.
It was found that 12 g of this isotope contains a number of atoms numerically equal to Avogadro’s constant.
Origin of the concept
Having understood a little about what a mole is in chemistry with the help of definitions, let’s turn to the history of this concept. As is commonly believed, the term "mole" was introduced by the German chemist Wilhelm Oswald, who received Nobel Prize in 1909. The word "mole" obviously comes from the word "molecule".
An interesting fact is that Avogadro’s hypothesis that under the same conditions the same volumes of different gases contain the same amount of substance was put forward long before Oswald, and the constant itself was calculated by Avogadro back in early XIX century. That is, although the concept of “mole” did not exist, the very idea of the amount of substance already existed.
Basic formulas
The amount of substance is found differently, depending on the data of the problem. This is the most common formula, in which this quantity is expressed as the ratio of mass to molar mass:
It is worth saying that the amount of a substance is an additive quantity. That is, in order to calculate the value of this quantity for a mixture, you must first determine the amount of substance for each of its elements and add them up.
Another formula is applied if the number of particles is known:
If the problem specifies that the process occurs when normal conditions, you can use the following rule: under normal conditions, any gas occupies an invariant volume - 22.4 liters. Then you can use the following expression:
The amount of substance is expressed from the Clapeyron equation:
Knowledge of what a mole is in chemistry and basic formulas to determine the number of moles of a substance, makes it possible to solve many problems much faster. If the amount of a substance is known, mass, volume, density and other parameters can be found.
The unit of quantity of a substance is taken mole - the amount of a substance containing the same number of structural units (atoms, ions, molecules, etc.) as there are atoms contained in 0.012 kg of the carbon isotope 12 C. The number of particles contained in one mole of a substance is called Avogadro's number (Avagadro's constant) N A . This is one of the universal constants, which does not depend on the nature of the substance and external conditions.
N A ≈ 6.022. 10 23 mol -1 (60 methods of determination).
The amount of a substance, expressed in moles, is related to its mass, a quantity called the molar mass of the substance.
Molar mass is numerically equal to molecular mass:
Oxygen (O 2) – relative molecular weight 32 c.u. and molar mass – 32 g/mol. Knowing Avogadro's constant, we can find absolute value mass of any atom (molecule) and estimate the sizes of atoms.
The mass of an atom (molecule) m is found by dividing the molar mass M by Avagadro’s constant:
Molar volume is the volume of 1 mole of a substance, expressed in l/mol.
To determine the molar volume of gases, Avagadro's law is used: equal volumes of all gases under the same conditions (temperature and pressure) contain same number molecules.
Consequences of Avagadro's law:
1) At the same temperature and pressure, 1 mole of any substance in gaseous state occupies the same volume.
2) 1 mole of any gas under normal conditions occupies a volume of 22.4 liters.
normal conditions: no. 1 atm = 101325 Pa = 760 mm Hg. and 0 0 C.
To determine molar (molecular) mass gaseous substances can be used combined gas law(Mendeleev-Clapeyron law):
,Where
R- pressure, Pa;
V- volume, m 3;
m- mass, g;
T- temperature, K;
M- molar mass, g/mol;
R- universal gas constant, J/mol∙K
To determine the molecular weight of gaseous substances, you can also use data on the relative density of the gas.
Relative density one gas to another ( D) is the ratio of the mass of a given gas to the mass of the same volume of another gas taken at the same temperature and the same pressure.
For example, the mass of 1 liter of carbon dioxide (CO 2) is equal to 1.98 g, under the same conditions the mass of 1 liter of hydrogen (H 2) is equal to 0.09 g. Therefore, the density of carbon dioxide by hydrogen is: 1.98: 0.09 = 22
, Where
m 1, m 2- masses of 1st and 2nd gases, g;
M 1, M 2- molar (molecular) masses of the 1st and 2nd gases.
It is more difficult to determine the size of atoms. The size of an atom can only be determined conditionally. For crystalline simple substances, the atomic radius is taken to be half the distance between the centers of neighboring atoms. This value can be found by knowing the density of the substance and Avagadro's constant. If we divide the volume occupied by one mole of a simple solid V m(molar volume) by Avagadro’s constant, then we find the volume V, per one atom. This atom can be approximately considered as a sphere inscribed in a cube of volume V, then the atomic radius r is expressed by the equation
The radius of a molecule is expressed similarly.
To accurately calculate the sizes of atoms, it is necessary to know their location in crystals solids. It has been established that many simple substances have a structure similar to the densest packing of spheres. In such packaging, the balls themselves account for 74.05% of the occupied volume.
Exact value atomic radius:
The atomic radii are on the order of 100 pm.
Instructions
Knowing the quantity ν, find the number molecules in it. To do this, multiply the amount of substance measured in moles by Avogadro’s constant (NA=6.022∙10^23 1/mol), which is equal to the number molecules in 1 mole of substance N=ν/NA. For example, if there are 1.2 mol table salt, then it contains N=1.2∙6.022∙10^23 ≈7.2∙10^23 molecules.
If the substance is known, using periodic table elements, find its molar mass. To do this, use the table to find the relative atomic masses of the atoms that make up the molecules oh, and fold them. As a result, you will get the relative molecules the apparent mass of a substance, which is numerically equal to its molar mass per mole. Then, on a scale, measure the mass of the test substance in . To find the quantity molecules V substance, multiply the mass of the substance m by Avogadro’s constant (NA=6.022∙10^23 1/mol) and divide the result by the molar mass M (N=m∙NA/M).
Example Determine the quantity molecules, which is contained in 147 g. Find the molar mass. Her molecules a consists of 2 hydrogen atoms, one sulfur and 4 oxygen atoms. Their atomic masses are 1, 32 and 16. Relative molecules the apparent mass is 2∙1+32+4∙16=98. It is equal to the molar mass, so M = 98 g/mol. Then quantity molecules contained in 147 g of sulfuric acid will be equal to N=147∙6.022∙10^23/98≈9∙10^23 molecules.
To find the quantity molecules gas under normal conditions at a temperature of 0ºС 760 mm Hg. column, find its volume. To do this, measure or calculate the V in which it is located in liters. To find the quantity molecules gas, divide this volume by 22.4 liters (the volume of one mole of gas under normal conditions), and multiply by Avogadro's number (NA=6.022∙10^23 1/mol) N= V∙NA/22.4.
Sources:
- how to determine the number of molecules
A. Avogadro in 1811, at the very beginning of development atomic theory made the assumption that in equal quantities ideal gases at the same pressure and temperature there are the same number of molecules. Later this assumption was confirmed and became a necessary consequence for kinetic theory. Now this theory is called Avogadro.
Instructions
Video on the topic
A molecule is an electrically neutral particle that has all chemical properties inherent in this particular substance. Including gases: oxygen, nitrogen, chlorine, etc. How can you determine the number of gas molecules?
Instructions
If you need to calculate how much oxygen is contained in 320 of this gas under normal conditions, first of all, determine how many moles of oxygen are contained in this amount. According to the periodic table, you can see that the rounded atomic mass oxygen - 16 atomic units. Since the oxygen molecule is diatomic, the mass of the molecule will be 32 atomic units. Therefore, the number of moles is 320/32 = 10.
It will help you further universal number Avogadro, named in, who proposed that equal volumes of ideal molecules under constant conditions contain equal numbers of molecules. It is denoted by the symbol N(A) and is very large - 6.022*10(23). Multiply this number by the calculated number of moles of oxygen and you will find out that the required number of molecules in 320 grams of oxygen is 6.022*10(24).
What if you need oxygen, as well as the volume occupied by it and the temperature? How to calculate the number of its molecules with such data? And there is nothing complicated here. You just need to write down the universal Mendeleev-Clapeyron equation for ideal gases:
Where P is the gas pressure in pascals, V is its volume in cubic meters, R is the universal gas constant, M is the mass of the gas, and m is its molar mass.
Rearranging this equation slightly, you get:
Since you have all the necessary data (pressure, volume, temperature are initially set, R = 8.31, and the molar mass of oxygen = 32 grams/mol), you can easily find the mass of the gas at a given volume, pressure and . And then the problem is solved in exactly the same way as in the example described above: N(A)M/m. After making calculations, you will find out how many oxygen molecules are contained in given conditions.
Video on the topic
None real gas(including oxygen), of course, is not ideal, so the Mendeleev-Clapeyron equation can be used for calculations only under conditions that do not differ very much from normal.
The molecule has such tiny dimensions that the number of molecules even in a tiny grain or drop of any substance will be simply enormous. It cannot be measured using conventional methods calculus.
What is a “mole” and how to use it to find the number of molecules in a substance
To determine how many molecules are in a given amount of a substance, the concept of “mole” is used. A mole is the amount of a substance that contains 6.022*10^23 of its molecules (or atoms, or ions). This huge value is called “Avogadro’s constant”, it is named after the famous Italian scientist. The value is designated NA. Using Avogadro's constant, you can very easily determine how many molecules are contained in any number of moles of any substance. For example, 1.5 moles contains 1.5*NA = 9.033*10^23 molecules. In cases where very high measurement accuracy is required, it is necessary to use the value of Avogadro's number with a large number decimal places. Its most complete value is: 6.022 141 29(27)*10^23.
How can you find the number of moles of a substance?
Determining how many moles are contained in a certain amount of a substance is very simple. To do this, you only need to have the exact formula of the substance and the periodic table at hand. Let's say you have 116 grams of regular table salt. Do you need to determine how many moles are contained in such a quantity (and, accordingly, how many molecules are there)?
First of all, remember chemical formula table salt. It looks like this: NaCl. The molecule of this substance consists of two atoms (more precisely, ions): sodium and chlorine. What is its molecular weight? It is made up of the atomic masses of elements. Using the periodic table, you know that the atomic mass of sodium is approximately 23, and the atomic mass of chlorine is 35. Therefore, the molecular mass of this substance is 23 + 35 = 58. Mass is measured in atomic mass units, where the lightest atom is taken as the standard - hydrogen.
And knowing the molecular mass of a substance, you can immediately determine its molar mass (that is, the mass of one mole). The fact is that numerically the molecular and molar mass are completely the same, they only have different units of measurement. If molecular mass is measured in atomic units, then molar mass is measured in grams. Therefore, 1 mole of table salt weighs approximately 58 grams. And according to the conditions of the problem, you have 116 grams of table salt, that is, 116/58 = 2 moles. Multiplying 2 by Avogadro's constant determines that there are approximately 12.044*10^23 molecules in 116 grams of sodium, or approximately 1.2044*10^24.
