Atomic mass unit. Avogadro's number

Matter consists of molecules. By molecule we will mean the smallest particle of a given substance that retains the chemical properties of a given 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 comfort 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 the nuclear charge is 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? (but 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 a molecule, expressed in atomic mass units, 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 of hydrogen H2: therefore, 1 mole of hydrogen has a mass of 2 g;

2) relative molecular weight of 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(g) = 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 of some substance whose molar mass is 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

Atomic mass unit(designation A. eat.), she is dalton, - an extra-systemic unit of mass, used for the masses of molecules, atoms, atomic nuclei and elementary particles. Recommended for use by IUPAP in 1960 and IUPAC in 1961. English terms are officially recommended atomic mass unit (a.m.u.) and more accurate - unified atomic mass unit (u.a.m.u.)(a universal atomic unit of mass, but it is used less frequently in Russian-language scientific and technical sources).

The atomic mass unit is expressed in terms of the mass of the carbon nuclide 12 C. 1 a. e.m. is equal to one twelfth of the mass of this nuclide in the nuclear and atomic natural state. Established in 1997 in the 2nd edition of the IUPAC Handbook of Terms, the numerical value is 1 a. e.m. ≈ 1.6605402(10) ∙ 10 −27 kg ≈ 1.6605402(10) ∙ 10 −24 g.

On the other hand, 1 a. e.m. is the reciprocal of Avogadro's number, that is, 1/N A g. This choice of atomic mass unit is convenient in that the molar mass of a given element, expressed in grams per mole, exactly coincides with the mass of an atom of this element, expressed in A. eat.

Story

The concept of atomic mass was introduced by John Dalton in 1803; the unit of measurement of atomic mass was first the mass of the hydrogen atom (the so-called hydrogen scale). In 1818, Berzelius published a table of atomic masses relative to the atomic mass of oxygen, taken to be 103. Berzelius's system of atomic masses prevailed until the 1860s, when chemists again adopted the hydrogen scale. But in 1906 they switched to the oxygen scale, according to which 1/16 of the atomic mass of oxygen was taken as a unit of atomic mass. After the discovery of oxygen isotopes (16 O, 17 O, 18 O), atomic masses began to be indicated on two scales: chemical, which was based on 1/16 of the average mass of a natural oxygen atom, and physical, with a unit of mass equal to 1/16 of the mass of the atom nuclide 16 O. The use of two scales had a number of disadvantages, as a result of which in 1961 they switched to a single, carbon scale.

And equal to 1/12 of the mass of this nuclide.

Recommended for use by IUPAP in and IUPAC in years. English terms are officially recommended atomic mass unit (a.m.u.) and more accurate - unified atomic mass unit (u.a.m.u.)(a universal atomic unit of mass, but it is used less frequently in Russian-language scientific and technical sources).

1 a. e.m., expressed in grams, is numerically equal to the reciprocal of Avogadro's number, that is, 1/N A, expressed in mol -1. The molar mass of a given element, expressed in grams per mole, is numerically the same as the mass of the molecule of this element, expressed in a. eat.

Since the masses of elementary particles are usually expressed in electron volts, the conversion factor between eV and a is important. eat. :

1 a. e.m. ≈ 0.931 494 028(23) GeV/ c²; 1 GeV/ c² ≈ 1.073 544 188(27) a. e.m. 1 a. e.m. kg.

Story

The concept of atomic mass was introduced by John Dalton in 1995; the unit of measurement of atomic mass was first the mass of the hydrogen atom (the so-called hydrogen scale). Berzelius published a table of atomic masses referred to the atomic mass of oxygen, taken to be 103. Berzelius's system of atomic masses prevailed until the 1860s, when chemists again adopted the hydrogen scale. But they switched to the oxygen scale, according to which 1/16 of the atomic mass of oxygen was taken as a unit of atomic mass. After the discovery of oxygen isotopes (16 O, 17 O, 18 O), atomic masses began to be indicated on two scales: chemical, which was based on 1/16 of the average mass of a natural oxygen atom, and physical, with a unit of mass equal to 1/16 of the mass of the atom nuclide 16 O. The use of two scales had a number of disadvantages, as a result of which they switched to a single, carbon scale.

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• Fundamental Physical Constants --- Complete Listing

Notes

The composition of substances is complex, although they are formed by tiny particles - atoms, molecules, ions. many liquids and gases, as well as some solids. Metals and many salts are made up of atoms and charged ions. All particles have mass, even the smallest one, if expressed in kilograms, receives a very small value. For example, m (H 2 O) = 30. 10 -27 kg. Physicists and chemists have long studied the most important characteristics of a substance, such as the mass and size of microparticles. The foundations were laid in the works of Mikhail Lomonosov and Let us consider how views on the microworld have changed since then.

Lomonosov's ideas about “corpuscles”

The assumption of discreteness was expressed by scientists of Ancient Greece. At the same time, the name “atom” was given to the smallest indivisible particle of bodies, the “brick” of the universe. The great Russian researcher M.V. Lomonosov wrote about an insignificantly small particle of the structure of matter, indivisible by physical means - a corpuscle. Later, in the works of other scientists, it was called a “molecule.”

The mass of a molecule, as well as its dimensions, are determined by the properties of its constituent atoms. For a long time, scientists were unable to look deep into the microworld, which hampered the development of chemistry and physics. Lomonosov repeatedly urged his colleagues to study and in their work rely on accurate quantitative data - “measure and weight”. Thanks to the work of the Russian chemist and physicist, the foundations of the doctrine of the structure of matter were laid, which became an integral part of the harmonious atomic-molecular theory.

Atoms and molecules are the “building blocks of the universe”

Even microscopically small bodies are complex and have different properties. Particles such as atoms, formed by a nucleus and electron layers, differ in the number of positive and negative charges, radius, and mass. Atoms and molecules do not exist in isolation within substances; they attract with different strengths. The effect of attractive forces is more noticeable in solids, weaker in liquids, and almost not felt in gaseous substances.

Chemical reactions are not accompanied by the destruction of atoms. Most often, they rearrange and another molecule appears. The mass of a molecule depends on what atoms it is formed from. But despite all the changes, the atoms remain chemically indivisible. But they can be part of different molecules. In this case, the atoms retain the properties of the element to which they belong. Before its disintegration into atoms, a molecule retains all the characteristics of a substance.

A microparticle of a body's structure is a molecule. Molecule mass

To measure the mass of macroscopic bodies, instruments are used, the oldest of which is scales. It is convenient to obtain the measurement result in kilograms, because this is the basic unit of the International System of Physical Quantities (SI). To determine the mass of a molecule in kilograms, one must add up the atomic masses, taking into account the number of particles. For convenience, a special unit of mass was introduced - the atomic one. You can write it as a letter abbreviation (a.u.m.). This unit corresponds to one-twelfth of the mass of the 12 C carbon nuclide.

If we express the found value in standard units, we get 1.66. 10 -27 kg. It is mainly physicists who operate with such small indicators for the mass of bodies. The article provides a table from which you can find out what the atomic masses of some chemical elements are. To find out what the mass of one is in kilograms, multiply by two the atomic mass of this chemical element given in the table. As a result, we obtain the mass of a molecule consisting of two atoms.

Relative molecular weight

It is difficult to operate in calculations with very small quantities, it is inconvenient, leads to time consumption and errors. As for the mass of microparticles, the way out of the difficult situation was to use a term familiar to chemists consisting of two words - “atomic mass”, its designation is Ar. An identical concept was introduced for molecular mass (the same as the mass of a molecule). Formula connecting two quantities: Mr = m(in-va)/1/12 m(12 C).

It is not uncommon to hear people say “molecular weight.” This outdated term is still used in relation to the mass of a molecule, but less and less often. The fact is that weight is another physical quantity - a force that depends on the body. On the contrary, mass serves as a constant characteristic of particles that participate in chemical processes and move at normal speed.

How to determine the mass of a molecule

An accurate determination of the weight of a molecule is carried out using a device - a mass spectrometer. To solve problems, you can use information from the periodic table. For example, the mass of an oxygen molecule is 16. 2 = 32. Let’s perform simple calculations and find the value of Mr(H 2 O) - the relative molecular weight of water. Using the periodic table, we determine that the mass of an oxygen atom is 16, and that of a hydrogen atom is 1. Let’s carry out simple calculations: M r (H 2 O) = 1. 2 + 16 = 18, where M r is the molecular weight, H 2 O is the water molecule, H is the symbol of the element hydrogen, O is the chemical symbol of oxygen.

Isotopic masses

Chemical elements in nature and technology exist in the form of several varieties of atoms - isotopes. Each of them has an individual mass; its value cannot have a fractional value. But the atomic mass of a chemical element is most often a number with several decimal places. The calculations take into account the prevalence of each variety in the earth's crust. Therefore, the masses of atoms in the periodic table are not always whole numbers. Using such quantities for calculations, we obtain the masses of molecules, which are also not integers. In some cases, values ​​may be rounded.

Molecular mass of substances of non-molecular structure

Dimensions and mass of molecules

In electron micrographs of large molecules, individual atoms can be seen, but they are so small that they are not visible with a regular microscope. The linear size of a particle of any substance, like mass, is a constant characteristic. The diameter of a molecule depends on the radii of the atoms forming it and their mutual attraction. Particle sizes change with increasing number of protons and energy levels. The hydrogen atom is the smallest in size, its radius is only 0.5. 10 -8 cm. A uranium atom is three times larger than a hydrogen atom. The real “giants” of the microcosm are molecules of organic substances. Thus, the linear size of one of the protein particles is 44 . 10 -8 cm.

To summarize: the mass of molecules is the sum of the masses of the atoms that make up their composition. The absolute value in kilograms can be obtained by multiplying the molecular weight value found in the periodic table by the value 1.66. 10 -27 kg.

Molecules are negligible compared to macrobodies. For example, in size, a water molecule H 2 O is smaller than an apple by the same amount as this fruit is smaller than our planet.

As you already know, all bodies are made of molecules. If we talk about the mass of molecules and express it in grams or kilograms, then we will see that the mass is very small, but if we talk about the number of molecules, for example, in one cubic centimeter of the space surrounding us, then the number of these molecules will be huge. Working with very small or very large numbers is not very convenient, however, scientists were able to figure out how to express the mass or size of molecules in not very large observable numbers, no more than a hundred. Today we will show you how they managed to do this.

We see that one weight significantly outweighs seven plastic balls. Experience with scales gives us the answer - there is more substance in an iron weight, this is if we compare masses - measures of inertia of iron and plastic.

But what if we compare not the masses, but the amount of substance that went into making the balls and weights, in fact, the number of particles of which they are composed? Taking the balls and the weight in our hands, we will see that the weight is actually lost against the background of these balls. If we could count the number of particles that are included in iron and plastic, then we would see that the number of iron atoms would be significantly less than the number of molecules in all plastic balls. This means there is more substance in plastic.

Both answers are correct.

The thing is that in the first case we compared mass, that is, a measure of the inertia of bodies, and in the second case we compared the number of molecules, the amount of substance.

We can draw a simple analogy with sugar in a measuring cup. The question of how much sugar there is can be answered by looking at the division of the glass and approximately telling how many grams of sugar there are. You can count each grain in the glass and answer how many of them the glass contains. Both the first and second answers will be correct. When is it more convenient to talk about the mass of molecules, and when is it more convenient to talk about the amount of substance? This is precisely the topic of the lesson: “Mass of molecules, Amount of substance.”

In the 19th century, the Italian scientist Avogadro established an interesting fact: if two different gases, for example hydrogen and oxygen, are in the same vessels, at the same pressures and temperatures, then in each vessel there will be the same number of molecules, although the masses of the gases can differ very much, in our example - 16 times (Fig. 2).

Rice. 2. Avogadro's experiment ()

All this means that some properties of a body are determined precisely by the number of molecules, and not just by mass.

What do we mean by the term “amount of substance”? Any substance consists of molecules, atoms, ions - which means that by the amount of a substance we understand the number of molecules.

The physical quantity that determines the number of molecules in a given body is called amount of substance. Denoted by the Greek letter ν - nu.

We agreed to take as a unit amount of a substance the quantity that contains as many particles (atoms, molecules) as there are atoms in 0.012 kg (12 grams) of a carbon isotope with atomic mass 12.

This unit is called mole.

From this definition it follows that in one mole of any substance there will be the same number of molecules. One mole of any substance contains 6.02 10 23 molecules or particles. This quantity is called Avogadro's constant.

Rice. 3. Determination of the total number of molecules ()

This formula allows you to find out the total number of molecules for a known amount of substance.

The mass of the molecule is extremely small. Physicists determined this using a so-called mass spectrograph. For example, the value of the mass of a water molecule (Fig. 4):

Rice. 4. Determination of the mass of a water molecule ()

As we see, just as in cases with the amount of a substance, comparing the mass of one molecule with a mass standard, a kilogram, is not very convenient. If in cases with the amount of substance the numbers are huge, then in cases with the mass of molecules the numbers are very small. That is why a special extra-systemic unit was chosen as a unit of measurement for the mass of a molecule or atom - atomic mass unit. We will compare a unit of mass not with a standard, but with the mass of a molecule of some substance.

This substance became the most common element in nature - carbon, which is included in all organic compounds. The atomic mass unit is equal to:

1 amu = 1/12 mass of carbon - 12 (isotope with 12 nucleons)

1 amu = 1.66·10 -27 kg

Since we will measure the mass of molecules in atomic mass units, we arrive at a new physical quantity - relative molecular mass.

The ratio of the mass of a molecule (atom) of a given substance to 1/12 of the mass of a carbon atom is called relative molecular weight(or relative atomic mass) in the case of the atomic structure of a substance.

Formulas expressing this definition:

Relative molecular weight is a dimensionless quantity; it is not measured in anything. Nothing prevents us from continuing to measure the masses of atoms and molecules in kilograms whenever it is convenient for us. From the chemistry course we know that: the relative molecular mass of a substance is equal to the sum of the relative atomic masses of the elements included in it. For example, for water H2O the relative molecular weight will be:

Mr = 1 2 + 16 = 18

The sum of the relative molecular weights of oxygen (16) and two hydrogens (2.1) will give 18

How to find the commonality between the mass in kilograms and the amount of substance in moles? This quantity is molar mass.

Molar mass is the mass of one mole of a substance.

Designated [M], measured in kg/mol.

Molar mass is equal to the ratio of mass to amount of substance:

We obtain formulas that relate various characteristics of molecules.

To determine the molar mass of a chemical element, let's turn to Mendeleev's periodic table of chemical elements - we simply take atomic mass A (the number of nucleons of the required element) - this will be its molar mass, expressed in g/mol.

For example, for aluminum (Fig. 5):

Rice. 5. Determination of the molar mass of a substance ( )

The atomic mass of aluminum will be 27 and the molar mass will be 0.027 kg/mol.

This is explained by the fact that the molar mass of carbon is 12 g/mol by definition, while the nucleus of a carbon atom contains 12 nucleons - 6 protons and 6 neutrons, it turns out that each nucleon contributes 1 g/mol to the molar mass, so the molar mass of a chemical element with atomic mass A will be equal to A g/mol.

The molar mass of a substance whose molecule consists of several atoms is obtained by simply summing the molar masses, for example (Fig. 6):

Rice. 6. Molar mass of carbon dioxide ()

You need to be especially careful with the molar masses of some gases, such as hydrogen gas, nitrogen, oxygen - their molecule consists of two atoms - H 2, N 2, O 2, and helium, often found in problems, is monatomic and has a molecular weight of 4 g/mol prescribed by the periodic table (Fig. 7).

Rice. 7. Molar masses of some gases ()

One mole of any substance contains the Avogadro number of molecules, which means that if we multiply the Avogadro number (the number of molecules in one mole) by the mass of one molecule m0, then we get the molar mass of the substance, that is, the mass of one mole of the substance:

M = m 0 N A

If 25 students are studying in a classroom with an area of ​​50 m2, then for each student there is 2 m2. When they go to a gym with an area of ​​500 m2, each student will already have 20 m2. The number of students has not changed, but they have become less distributed, in this case they say: the concentration of people has decreased. In the same way, the concept of concentration is introduced for molecules in molecular kinetic theory.

Concentration(n) is the number of molecules per unit volume of a substance. It is equal to the ratio of the number of molecules to volume:

Formulas relating concentration to other characteristics of molecules:

Using these formulas, we can compare substances both by the number of molecules and by mass.

We have received everything we need to build a molecular kinetic theory, which we will do in the next lessons.

Bibliography

1. Tikhomirova S.A., Yavorsky B.M. Physics (basic level) - M.: Mnemosyne, 2012.
2. Gendenshtein L.E., Dick Yu.I. Physics 10th grade. - M.: Mnemosyne, 2014.
3. Kikoin I.K., Kikoin A.K. Physics - 9, Moscow, Education, 1990.

1. Lib.podelise.ru ().
2. Class-fizika.spb.ru ().
3. Bolshoyvopros.ru ().

Homework

1. Define the amount of a substance.
2. Name the unit of measurement for the mass of a molecule or atom.
3. Define relative molecular weight.