Tunneling microscopes provide a magnification of 100 million times. This makes it possible to measure the size of atoms with very high accuracy. So, the diameter of the carbon atom turned out to be equal to 1.4 10 -8 cm. The sizes of other atoms have the same order.
The sizes of atoms and molecules found by other methods turn out to be approximately the same.
These dimensions are so small that it is impossible to imagine them. What can you say, for example, the number 2.3 10 -8 cm - the size of a hydrogen molecule? In such cases, comparisons are used. If, for example, your head is enlarged to the size middle star like the Sun, then the molecule will increase to the size of the head.
And here's another comparison. If we imagine that all sizes in the world have increased by 10 8 times, then the hydrogen molecule will look like a ball with a diameter of only 2.3 cm (average plum sizes), and a person’s height would become 170,000 km, the size of a fly would be 10,000 km, hair thickness - 10 km, size of a red blood cell (erythrocyte) - 700 m.
Number of molecules
With such small sizes of molecules, their number in any macroscopic body is extremely large. Let us calculate the approximate number of molecules in a drop of water with a mass of 1 g and, therefore, a volume of 1 cm 3 . The diameter of a water molecule is approximately 3 10 -8 cm. Assuming that each water molecule occupies a volume (3 10 -8 cm) 3 in dense packing of molecules, we can find the number of molecules in a drop by dividing the drop volume (1 cm 3) by volume per molecule:
Imagine that the surface of the globe is hard and smooth. People are standing close to each other all over the surface. The number of people in this case will be slightly less than the number of molecules in 1 cm 3 of air at normal atmospheric pressure and a temperature of 0 ° C.
We must remember the basic provisions of the molecular kinetic theory. Atoms have dimensions of the order 10 -8 cm. Images of atoms obtained using a tunneling microscope leave no doubt about their existence,
§ 2.2. Mass of molecules. Avogadro constant
The masses of molecules are very small if expressed in grams or kilograms, but the number of molecules in macroscopic bodies is enormous. It is inconvenient to deal with very small and very large numbers. Scientists have found a fairly simple way to avoid this inconvenience and characterize the masses of molecules and their number in quite observable numbers, not going far beyond a hundred. Now you will see how this is done.
Mass of a water molecule
In the previous paragraph, we found out that 1 g of water contains 3.7 10 22 molecules. Therefore, the mass of one molecule is:
Molecules of other substances have masses of the same order, excluding the huge molecules of organic compounds. For example, the mass of a hemoglobin molecule exceeds the mass of a water molecule by several tens of thousands of times.
Relative molecular weight
Since the masses of molecules are very small, it is convenient to use not the absolute values of the masses, but the relative ones. According to an international agreement adopted in 1961, the masses of all molecules are compared with 
the mass of a carbon atom* (the so-called carbon scale of atomic masses). The main reason for choosing the carbon scale of atomic masses is that carbon is included in a huge number of different organic compounds. This choice allows a very precise comparison of the masses of the heavy elements with the mass of the carbon atom. Factor 
introduced so that the relative masses of atoms are close to integers. The relative mass of a carbon atom is exactly 12, and that of a hydrogen atom is approximately one.
* More precisely, with 
the mass of an atom of the most common isotope of carbon-12.
Relative molecular (or atomic) mass of a substanceM
r
called the ratio of the mass of a molecule (or atom) given substance To
masses of a carbon atomT 0C :
(2.2.1)
Relative atomic masses of all chemical elements accurately measured. By adding the relative atomic masses, the relative molecular mass can be calculated. For example, the relative molecular weight of water H 2 O is approximately equal to 18, since the relative atomic masses of hydrogen and oxygen are approximately equal to 1 and 16:2-1 + 16=18.
Molecular-kinetic theory of ideal gases
In physics, two main methods are used to describe thermal phenomena: molecular-kinetic (statistical) and thermodynamic.
Molecular kinetic method (statistical) is based on the idea that all substances are composed of molecules in random motion. Since the number of molecules is huge, it is possible, by applying the laws of statistics, to find certain patterns for the entire substance as a whole.
Thermodynamic method proceeds from the basic experimental laws, called the laws of thermodynamics. The thermodynamic method approaches the study of phenomena like classical mechanics, which is based on Newton's experimental laws. This approach does not consider the internal structure of matter.
Basic Provisions of Molecular Kinetic Theory
And their experimental justification. Brownian motion.
Mass and size of molecules.
The theory that studies thermal phenomena in macroscopic bodies and explains the dependence of the internal properties of bodies on the nature of the movement and interaction between the particles that make up the bodies is called molecular kinetic theory ( MKT for short ) or just molecular physics.
The molecular kinetic theory is based on three major provisions:
According to the first provision of the MKT , V All bodies are made up of a huge number of particles (atoms and molecules), between which there are gaps .
Atom is an electrically neutral microparticle consisting of a positively charged nucleus and an electron shell surrounding it. A group of atoms of the same type is called chemical element . In the natural state, atoms of 90 chemical elements are found in nature, the heaviest of which is uranium. When approaching, atoms can combine into stable groups. Systems of a small number of atoms connected to each other are called molecule . For example, a water molecule consists of three atoms (Fig.): two hydrogen atoms (H) and one oxygen atom (O), so it is designated H 2 O. Molecules are the smallest stable particles of a given substance that have its main chemical properties. For example, the smallest particle of water is a water molecule, the smallest particle of sugar is a sugar molecule.
About substances consisting of atoms that are not united into molecules, they say that they are in atomic state; otherwise, talk about molecular state. In the first case, the smallest particle of a substance is an atom (for example, He), in the second case, a molecule (for example, H 2 O).
If two bodies consist of the same number of particles, then these bodies are said to contain the same amount of substance . The amount of a substance is denoted by the Greek letter ν (nu) and is measured in moles. For 1 mole take the amount of substance in 12 g of carbon. Since 12 g of carbon contains approximately 6∙10 23 atoms, then for the amount of substance (i.e., the number of moles) in a body consisting of N particles, we can write
If you enter the notation N A = 6∙10 23 mol -1.
then relation (1) will take the form of the following simple formula:
Thus, amount of substance
is the ratio of the number N of molecules (atoms) in a given macroscopic body to the number N A of atoms in 0.012 kg of carbon atoms:
1 mole of any substance contains N A = 6.02 10 23 molecules. The number N A is called constant Avogadro. The physical meaning of the Avogadro constant lies in the fact that its value shows the number of particles (atoms in an atomic substance, molecules in a molecular substance) contained in 1 mole of any substance.
The mass of one mole of a substance is called molar mass . If the molar mass is denoted by the letter μ, then for the amount of substance in a body of mass m, we can write:
From formulas (2) and (3) it follows that the number of particles in any body can be determined by the formula:
The molar mass is determined by the formula
M=M g 10 -3 kg/mol
Here M r denotes relative molecular (atomic) mass of a substance, measured in a.u.m. (atomic mass units), which in molecular physics it is customary to characterize the mass of molecules (atoms). The relative molecular mass M g can be determined if the average mass of a molecule (m m) of a given substance is divided by 1/12 of the mass of the carbon isotope 12 C:
1/12 m 12 C \u003d 1a.u.m \u003d 1.66 10 -27 kg.
When solving problems, this value is found using the periodic table. This table lists the relative atomic masses of the elements. Adding them in accordance with the chemical formula of the molecule of a given substance, and get the relative molecular M g .
For example, for
carbon (C) M g \u003d 12 10 -3 kg / mol
water (H 2 O) M g \u003d (1 2 + 16) \u003d 18 10 -3 kg / mol.
Similarly, it is defined relative atomic mass.
A mole of gas under normal conditions occupies a volume V 0 = 22.4 10 23 m 3
Therefore, in 1 m 3 of any gas at normal conditions (determined by pressure P \u003d 101325 Pa \u003d 10 5 Pa \u003d 1 atm; temperature 273ºK (0ºС), volume of 1 mole of ideal gas V 0 \u003d 22.4 10 -3 m 3) contains the same number of molecules:
This number is called a constant. Loshmidt.
Molecules (like atoms) do not have clear boundaries. The dimensions of the molecules of solids can be approximately estimated as follows:
where is the volume per 1 molecule, is the volume of the whole body,
m and ρ are its mass and density, N is the number of molecules in it.
Atoms and molecules cannot be seen naked eye or with an optical microscope. Therefore, the doubts of many scientists late XIX V. in the reality of their existence can be understood. However, in the XX century. the situation has changed. Now, with the help of an electron microscope, as well as holographic microscopy, it is possible to observe images not only of molecules, but even of individual atoms.
X-ray diffraction data show that the diameter of any atom is of the order of d = 10 -8 cm (10 -10 m). Molecules are larger than atoms. Since molecules are made up of several atoms, what more quantity atoms in a molecule, the larger its size. The sizes of molecules range from 10 -8 cm (10 -10 m) to 10 -5 cm (10 -7 m).
The masses of individual molecules and atoms are very small, for example, the absolute value of the mass of a water molecule is about 3·10 -26 kg. The mass of individual molecules is experimentally determined using a special device - a mass spectrometer.
In addition to direct experiments that make it possible to observe atoms and molecules, many other indirect data speak in favor of their existence. Such, for example, are the facts concerning the thermal expansion of bodies, their compressibility, the dissolution of certain substances in others, and so on.
According to the second position of the molecular kinetic theory, particles move continuously and chaotically (randomly).
This position is confirmed by the existence of diffusion, evaporation, gas pressure on the walls of the vessel, as well as the phenomenon brownian motion.
The randomness of motion means that the molecules do not have any preferred paths and their movements have random directions.
Diffusion (from the Latin diffusion - spreading, spreading) - a phenomenon when, as a result of the thermal movement of a substance, spontaneous penetration of one substance into another occurs (if these substances are in contact). According to molecular kinetic theory, such mixing occurs as a result of the fact that randomly moving molecules of one substance penetrate into the gaps between the molecules of another substance. The depth of penetration depends on the temperature: the higher the temperature, the greater the speed of movement of the particles of the substance and the faster the diffusion. Diffusion is observed in all states of matter - in gases, liquids and solids. Diffusion occurs most rapidly in gases (which is why the smell spreads so quickly in the air). Diffusion in liquids is slower than in gases. This is due to the fact that the liquid molecules are located much denser, and therefore it is much more difficult to "wade" through them. Diffusion occurs most slowly in solids. In one of the experiments, smoothly polished plates of lead and gold were placed one on top of the other and squeezed with a load. Five years later, gold and lead penetrated into each other by 1 mm. Diffusion in solids ensures the connection of metals during welding, soldering, chrome plating, etc. Diffusion has great importance in the life processes of humans, animals and plants. For example, it is thanks to diffusion that oxygen from the lungs penetrates into the human blood, and from the blood into the tissues.
Brownian motion called the random movement of small particles of another substance suspended in a liquid or gas. This movement was discovered in 1827 by the English botanist R. Brown, who observed the movement of flower pollen suspended in water under a microscope. Nowadays, small pieces of gummigut paint, which does not dissolve in water, are used for such observations. In a gas, Brownian motion is performed, for example, by particles of dust or smoke suspended in the air. The Brownian motion of a particle arises because the impulses with which the molecules of a liquid or gas act on this particle do not compensate each other. The molecules of the medium (that is, the molecules of a gas or liquid) move randomly, so their impacts lead the Brownian particle into random motion: the Brownian particle quickly changes its speed in direction and magnitude (Fig. 1).
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During the study of Brownian motion, it was found that its intensity: a) increases with increasing temperature of the medium; b) increases with a decrease in the size of the Brownian particles themselves; c) decreases in a more viscous liquid; and d) is completely independent of the material (density) of the Brownian particles. In addition, it was found that this movement is universal (since it is observed in all substances suspended in a sprayed state in a liquid), continuous (in a cuvette closed on all sides, it can be observed for weeks, months, years) and chaotic (randomly).
According to third provision of the ICT , particles of matter interact with each other: they attract at small distances and repel when these distances decrease.
The presence of forces of intermolecular interaction (forces of mutual attraction and repulsion) explains the existence of stable liquid and solid bodies.
The same reasons explain the low compressibility of liquids and the ability of solids to resist compressive and tensile deformations.
The forces of intermolecular interaction are electromagnetic in nature and are reduced to two types: attraction and repulsion. These forces manifest themselves at distances comparable to the size of molecules. The reason for these forces is that molecules and atoms are composed of charged particles with opposite signs of charge - negative electrons and positively charged atomic nuclei. In general, molecules are electrically neutral. In Figure 2.2, using arrows, it is shown that the nuclei of atoms, inside which there are positively charged protons, repel each other, and negatively charged electrons behave the same way. But between the nuclei and electrons, there are forces of attraction.
The dependence of the interaction forces of molecules on the distance between them qualitatively explains the molecular mechanism of the appearance of elastic forces in solids. Tensile solid body particles move away from each other. At the same time, attractive forces of molecules appear, which return the particles to their original position. When a solid body is compressed, the particles move closer together. This leads to an increase in repulsive forces, which return the particles to their original position and prevent further compression.
Therefore, at small deformations (millions of times greater than the size of molecules), Hooke's law is fulfilled, according to which the elastic force is proportional to the deformation. For large displacements, Hooke's law does not apply.
The validity of this provision is evidenced by the resistance of all bodies to compression, and also (with the exception of gases) to their tension.
Molecules have sizes and various shapes. For clarity, we will depict the molecule in the form of a ball, imagining that it is covered spherical surface, inside which are the electron shells of its atoms (Fig. 4, a). According to modern concepts, molecules do not have a geometrically defined diameter. Therefore, it was agreed to take the distance between the centers of two molecules (Fig. 4b) as the diameter d of a molecule, so close that the forces of attraction between them are balanced by the forces of repulsion.
From the course of chemistry "it is known that a kilogram-molecule (kilomole) of any substance, regardless of its state of aggregation, contains the same number of molecules, called Avogadro's number, namely N A \u003d 6.02 * 10 26 molecules.
Now let's estimate the diameter of a molecule, for example water. To do this, we divide the volume of a kilomole of water by the Avogadro number. A kilomole of water has a mass 18 kg. Assuming that water molecules are located close to each other and its density 1000 kg / m 3, we can say that 1 kmol water occupies a volume V \u003d 0.018 m 3. Volume per molecule of water
Taking the molecule as a ball and using the ball volume formula, we calculate the approximate diameter, otherwise the linear size of the water molecule:
Copper molecule diameter 2.25*10 -10 m. The diameters of gas molecules are of the same order. For example, the diameter of a hydrogen molecule 2.47 * 10 -10 m, carbon dioxide - 3.32*10 -10 m. So the molecule has a diameter of the order 10 -10 m. On length 1 cm 100 million molecules can be located nearby.
Let's estimate the mass of a molecule, for example sugar (C 12 H 22 O 11). To do this, you need a mass of kilomoles of sugar (μ = 342.31 kg/kmol) divided by the Avogadro number, i.e., by the number of molecules in
