Arrangement of molecules in solids. Liquids. Movement of molecules in liquids What is the arrangement of molecules in solids

This material not only talks about how particles are arranged in solids, but also how they move in gases or liquids. The types of crystal lattices in various substances will also be described.

State of aggregation

There are certain standards indicating the presence of three typical states of aggregation, namely: liquid and gas.

Let us define the components for each state of aggregation.

  1. Solids are practically stable in volume and shape. Changing the latter is extremely problematic without additional energy costs.
  2. The liquid can easily change shape, but at the same time retains its volume.
  3. Gaseous substances retain neither shape nor volume.

The main criterion by which the state of aggregation is determined is the arrangement of molecules and the methods of their movement. In a gaseous substance, the minimum distance between individual molecules is much greater than themselves. In turn, the molecules do not disperse over long distances under normal conditions and retain their volume. The active particles in solids are arranged in a strictly defined order, each of them, like the pendulum of a clock, moves around a certain point in the crystal lattice. This gives the solids particular strength and rigidity.

Therefore, in this case, the most pressing question is how the active particles are located in solids. In all other cases, atoms (molecules) do not have such an ordered structure.

Features of the liquid

It is necessary to pay special attention to the fact that liquids are a kind of intermediate link between the solid state of the body and its gaseous phase. Thus, when the temperature decreases, the liquid solidifies, and when it increases above the boiling point of the substance, it turns into a gaseous state. However, liquid has common features with both solid and gaseous substances. Thus, in 1860, the outstanding domestic scientist D.I. Mendeleev established the existence of the so-called critical temperature - absolute boiling. This is the value at which the thin boundary between a gas and a substance in the solid state disappears.

The next criterion, combining two neighboring states of aggregation, is isotropy. In this case, their properties are the same in all directions. Crystals, in turn, are anisotropic. Like gases, liquids do not have a fixed shape and occupy the entire volume of the container in which they are located. That is, they have low viscosity and high fluidity. Colliding with each other, microparticles of liquid or gas move freely. Previously, it was believed that in the volume occupied by a liquid there was no ordered movement of molecules. Thus, liquid and gas were opposed to crystals. But as a result of subsequent research, the similarities between solids and liquids were proven.

In the liquid phase at a temperature close to solidification, thermal motion resembles that in solids. In this case, the liquid may still have a certain structure. Therefore, giving an answer to the question of how particles are located in solids in liquids and gases, we can say that in the latter the movement of molecules is chaotic and disordered. But in solids, molecules occupy in most cases a certain, fixed position.

In this case, the liquid is a kind of intermediate link. Moreover, the closer its temperature is to boiling, the more the molecules move as if in gases. If the temperature is closer to the transition to the solid phase, then the microparticles begin to move in more and more orderly fashion.

Change in the state of substances

Let's look at the simplest example of a change in the state of water. Ice is the solid phase of water. Its temperature is below zero. At a temperature of zero, ice begins to melt and turns into water. This is explained by the destruction of the crystal lattice: when heated, the particles begin to move. The temperature at which a substance changes its state of aggregation is called the melting point (in our case, for water it is 0). Note that the temperature of the ice will remain at the same level until it completely melts. In this case, the atoms or molecules of the liquid will move in the same way as in solids.

After this, we will continue to heat the water. At the same time, the particles begin to move more intensely until our substance reaches the next point of change in the state of aggregation - the boiling point. This moment occurs when the bonds between the molecules that form it are broken due to the acceleration of movement - then it acquires a free character, and the liquid in question passes into the gaseous phase. The process of transforming a substance (water) from a liquid phase into a gaseous phase is called boiling.

The temperature at which water boils is called the boiling point. In our case, this value is 100 degrees Celsius (temperature depends on pressure, normal pressure is one atmosphere). Note: until the existing liquid completely turns into vapor, its temperature remains constant.

The reverse process of water transition from a gaseous state (steam) to a liquid, which is called condensation, is also possible.

Next, you can observe the freezing process - the process of transition of liquid (water) into solid form (the initial state is described above - this is ice). The processes described earlier provide a direct answer to how particles are arranged in solids, liquids and gases. The location and state of the molecules of a substance depend on its state of aggregation.

What is a solid? How do microparticles behave in it?

A solid body is a state of a material environment, the distinctive feature of which is the preservation of a constant shape and the constant nature of the thermal movement of microparticles that perform minor vibrations. Bodies can be in solid, liquid and gaseous states. There is also a fourth state, which modern scientists tend to classify as aggregate - this is the so-called plasma.

So, in the first case, any substance, as a rule, has a constant, unchanging shape, and the key influence on this is how the particles are arranged in solids. At the microscopic level, it is clear that the atoms that make up a solid are connected to each other by chemical bonds and are located at the nodes of the crystal lattice.

But there is an exception - amorphous substances, which are in a solid state, but cannot boast of the presence of a crystal lattice. It is from this that we can give an answer to how particles are arranged in solids. In the first case, physics indicates that atoms or molecules are located at lattice sites. But in the second case, there is certainly no such ordering, and such a substance is more similar to a liquid.

Physics and possible structure of a solid body

In this case, the substance tends to maintain its volume and, of course, shape. That is, in order to change the latter, effort must be made, and it does not matter whether it is a metal object, a piece of plastic or clay. The reason lies in its molecular structure. Or to be more precise, in the interaction of the molecules that make up the body. In this case they are located closest. This arrangement of molecules is repetitive in nature. That is why the forces of mutual attraction between each of these components are very strong.

The interaction of microparticles explains the nature of their movement. It is very difficult to adjust the shape or volume of such a solid body in one direction or another. Particles of a solid body are unable to move chaotically throughout the entire volume of the solid body, but can only oscillate around a certain point in space. The molecules of a solid oscillate chaotically in different directions, but they bump into similar ones, which return them to their original state. That is why particles in solids are, as a rule, arranged in a strictly defined order.

Particles and their arrangement in a solid

Solids can be of three types: crystalline, amorphous and composites. It is the chemical composition that influences the arrangement of particles in solids.

Crystalline solids have an ordered structure. Their molecules or atoms form a crystalline spatial lattice of regular shape. Thus, a solid in a crystalline state has a certain crystal lattice, which, in turn, sets certain physical properties. This is the answer to how particles are arranged in a solid.

Let's give an example: many years ago in St. Petersburg, a stock of white shiny tin buttons was stored in a warehouse, which, when the temperature dropped, lost their shine and turned from white to gray. The buttons crumbled into gray powder. “Tin plague” was the name given to this “disease,” but in fact it was a restructuring of the structure of crystals under the influence of low temperature. Tin, when transitioning from the white variety to the gray variety, crumbles into powder. Crystals, in turn, are divided into mono- and polycrystals.

Single crystals and polycrystals

Single crystals (table salt) are single homogeneous crystals represented by a continuous crystal lattice in the form of regular polygons. Polycrystals (sand, sugar, metals, stones) are crystalline bodies that have grown together from small, chaotically located crystals. A phenomenon called anisotropy is observed in crystals.

Amorphousness: a special case

Amorphous bodies (resin, rosin, glass, amber) do not have a clear, strict order in the arrangement of particles. This is an unusual case of the order in which particles are found in solids. In this case, the phenomenon of isotropy is observed; the physical properties of amorphous bodies are the same in all directions. At high temperatures they become like viscous liquids, and at low temperatures they become like solids. When exposed to external influence, they simultaneously exhibit elastic properties, that is, upon impact, they split into miniature particles, like solids, and fluidity: with prolonged temperature exposure, they begin to flow like liquids. They do not have specific melting and crystallization temperatures. When heated, amorphous bodies soften.

Examples of amorphous substances

Let's take, for example, ordinary sugar and find out the arrangement of particles in solids in various cases using its example. In this case, the same material can occur in crystalline or amorphous form. If molten sugar hardens slowly, the molecules form even rows - crystals (lump sugar, or granulated sugar). If molten sugar, for example, is poured into cold water, cooling will occur very quickly, and the particles will not have time to form the correct rows - the melt will harden without forming crystals. This is how you get sugar candy (this is non-crystalline sugar).

But after some time, such a substance can recrystallize, the particles gather in regular rows. If the sugar candy sits for several months, it will begin to become covered with a loose layer. This is how crystals appear on the surface. For sugar the lifespan will be several months, and for stone it will be millions of years. Carbon is a unique example. Graphite is crystalline carbon, its structure is layered. And diamond is the hardest mineral on earth, capable of cutting glass and sawing stones; it is used for drilling and polishing. In this case, there is only one substance - carbon, but the peculiarity lies in the ability to form different crystalline forms. This is another answer to how particles are arranged in a solid.

Results. Conclusion

The structure and arrangement of particles in solids depends on what type the substance in question belongs to. If the substance is crystalline, then the arrangement of microparticles will be ordered. Amorphous structures do not have this feature. But composites can belong to both the first and second groups.

In one case, the liquid behaves similarly to a solid (at a low temperature, which is close to the crystallization temperature), but can also behave like a gas (as it increases). Therefore, in this review, we examined how particles are located not only in solids, but also in other basic aggregate states of matter.

Kinetic energy of a molecule

In a gas, molecules move freely (isolated from other molecules), only occasionally colliding with each other or with the walls of the container. As long as a molecule moves freely, it only has kinetic energy. During a collision, the molecules also gain potential energy. Thus, the total energy of a gas is the sum of the kinetic and potential energies of its molecules. The more rarefied the gas, the more molecules at each moment of time are in a state of free movement, having only kinetic energy. Consequently, when the gas is rarefied, the proportion of potential energy decreases in comparison with kinetic energy.

The average kinetic energy of a molecule at equilibrium of an ideal gas has one very important feature: in a mixture of different gases, the average kinetic energy of a molecule for different components of the mixture is the same.

For example, air is a mixture of gases. The average energy of an air molecule for all its components under normal conditions, when air can still be considered an ideal gas, is the same. This property of ideal gases can be proven on the basis of general statistical considerations. An important corollary follows from this: if two different gases (in different vessels) are in thermal equilibrium with each other, then the average kinetic energies of their molecules are the same.

In gases, the distance between molecules and atoms is usually much greater than the size of the molecules themselves; the interaction forces between molecules are not great. As a result, the gas does not have its own shape and constant volume. Gas is easily compressed and can expand without limit. Gas molecules move freely (translationally, they can rotate), only sometimes colliding with other molecules and the walls of the vessel in which the gas is located, and they move at very high speeds.

Movement of particles in solids

The structure of solids is fundamentally different from the structure of gases. In them, the intermolecular distances are small and the potential energy of the molecules is comparable to the kinetic energy. Atoms (or ions, or whole molecules) cannot be called motionless; they perform random oscillatory motion around average positions. The higher the temperature, the greater the oscillation energy, and therefore the average amplitude of oscillations. Thermal vibrations of atoms also explain the heat capacity of solids. Let us consider in more detail the movements of particles in crystalline solids. The entire crystal as a whole is a very complex coupled oscillatory system. The deviations of atoms from their average positions are small, and therefore we can assume that the atoms are subject to the action of quasi-elastic forces that obey Hooke’s linear law. Such oscillatory systems are called linear.

There is a developed mathematical theory of systems subject to linear oscillations. It proves a very important theorem, the essence of which is as follows. If the system performs small (linear) interconnected oscillations, then by transforming the coordinates it can be formally reduced to a system of independent oscillators (whose oscillation equations do not depend on each other). A system of independent oscillators behaves like an ideal gas in the sense that the atoms of the latter can also be considered as independent.

It is by using the idea of ​​independence of gas atoms that we arrive at Boltzmann's law. This very important conclusion provides a simple and reliable basis for the entire theory of solids.

Boltzmann's law

The number of oscillators with given parameters (coordinates and velocities) is determined in the same way as the number of gas molecules in a given state, according to the formula:

Oscillator energy.

Boltzmann's law (1) in the theory of solid bodies has no restrictions, but formula (2) for the oscillator energy is taken from classical mechanics. When theoretically considering solids, one must rely on quantum mechanics, which is characterized by discrete changes in the energy of the oscillator. The discreteness of the oscillator energy becomes insignificant only at sufficiently high values ​​of its energy. This means that (2) can only be used at sufficiently high temperatures. At high temperatures of a solid, close to the melting point, the law of uniform distribution of energy over the degrees of freedom follows from Boltzmann’s law. If in gases for each degree of freedom there is on average an amount of energy equal to (1/2) kT, then the oscillator has one degree of freedom, in addition to the kinetic one, with potential energy. Therefore, per one degree of freedom in a solid at a sufficiently high temperature there is an energy equal to kT. Based on this law, it is not difficult to calculate the total internal energy of a solid body, and after it its heat capacity. A mole of a solid contains NA atoms, and each atom has three degrees of freedom. Therefore, the mole contains 3 NA oscillators. Energy of a mole of a solid

and the molar heat capacity of a solid at sufficiently high temperatures is

Experience confirms this law.

Liquids occupy an intermediate position between gases and solids. Liquid molecules do not disperse over long distances, and liquid under normal conditions retains its volume. But unlike solids, molecules not only vibrate, but also jump from place to place, that is, they perform free movements. As the temperature increases, liquids boil (there is a so-called boiling point) and turn into gas. As the temperature decreases, liquids crystallize and become solids. There is a point in the temperature field at which the boundary between gas (saturated vapor) and liquid disappears (critical point). The pattern of thermal motion of molecules in liquids near the solidification temperature is very similar to the behavior of molecules in solids. For example, the heat capacity coefficients are exactly the same. Since the heat capacity of a substance changes slightly during melting, we can conclude that the nature of the movement of particles in a liquid is close to the movement in a solid (at the melting temperature). When heated, the properties of the liquid gradually change, and it becomes more like a gas. In liquids, the average kinetic energy of particles is less than the potential energy of their intermolecular interaction. The energy of intermolecular interaction in liquids and solids differs insignificantly. If we compare the heat of fusion and the heat of evaporation, we will see that during the transition from one state of aggregation to another, the heat of fusion is significantly lower than the heat of vaporization. An adequate mathematical description of the structure of a liquid can only be given with the help of statistical physics. For example, if a liquid consists of identical spherical molecules, then its structure can be described by the radial distribution function g(r), which gives the probability of detecting any molecule at a distance r from the given one chosen as a reference point. This function can be found experimentally by studying the diffraction of x-rays or neutrons, or a computer simulation of this function can be carried out using Newtonian mechanics.

The kinetic theory of liquid was developed by Ya.I. Frenkel. In this theory, a liquid is considered, as in the case of a solid, as a dynamic system of harmonious oscillators. But unlike a solid body, the equilibrium position of molecules in a liquid is temporary. After oscillating around one position, the liquid molecule jumps to a new position located nearby. Such a jump occurs with the expenditure of energy. The average “settled life” time of a liquid molecule can be calculated as:

\[\left\langle t\right\rangle =t_0e^(\frac(W)(kT))\left(5\right),\]

where $t_0\ $ is the period of oscillations around one equilibrium position. The energy that a molecule must receive in order to move from one position to another is called the activation energy W, and the time the molecule is in the equilibrium position is called the “settled life” time t.

For a water molecule, for example, at room temperature, one molecule undergoes about 100 vibrations and jumps to a new position. The forces of attraction between the molecules of a liquid are strong so that the volume is maintained, but the limited sedentary life of the molecules leads to the emergence of such a phenomenon as fluidity. During particle oscillations near the equilibrium position, they continuously collide with each other, so even a small compression of the liquid leads to a sharp “hardening” of particle collisions. This means a sharp increase in the pressure of the liquid on the walls of the vessel in which it is compressed.

Example 1

Task: Determine the specific heat capacity of copper. Assume that the temperature of copper is close to the melting point. (Molar mass of copper $\mu =63\cdot 10^(-3)\frac(kg)(mol))$

According to Dulong and Petit's law, a mole of chemically simple substances at temperatures close to the melting point has a heat capacity:

Specific heat capacity of copper:

\[С=\frac(с)(\mu )\to С=\frac(3R)(\mu )\left(1.2\right),\] \[С=\frac(3\cdot 8.31) (63\cdot 10^(-3))=0.39\ \cdot 10^3(\frac(J)(kgK))\]

Answer: Specific heat capacity of copper $0.39\ \cdot 10^3\left(\frac(J)(kgK)\right).$

Assignment: Explain in a simplified way from a physics point of view the process of dissolving salt (NaCl) in water.

The basis of the modern theory of solutions was created by D.I. Mendeleev. He established that during dissolution, two processes occur simultaneously: physical - the uniform distribution of particles of the solute throughout the entire volume of the solution, and chemical - the interaction of the solvent with the solute. We are interested in the physical process. Salt molecules do not destroy water molecules. In this case, it would be impossible to evaporate the water. If salt molecules joined water molecules, we would get some new substance. And salt molecules cannot penetrate inside the molecules.

An ion-dipole bond occurs between the Na+ and Cl- ions of chlorine and polar water molecules. It turns out to be stronger than the ionic bonds in the molecules of table salt. As a result of this process, the bond between the ions located on the surface of NaCl crystals is weakened, sodium and chlorine ions are detached from the crystal, and water molecules form so-called hydration shells around them. The separated hydrated ions, under the influence of thermal motion, are evenly distributed between the solvent molecules.

The molecules and atoms of a solid are arranged in a certain order and form crystal lattice. Such solids are called crystalline. Atoms perform vibrational movements around the equilibrium position, and the attraction between them is very strong. Therefore, solids under normal conditions retain their volume and have their own shape.

Thermal equilibrium is the state of a thermodynamic system into which it spontaneously passes after a sufficiently long period of time under conditions of isolation from the environment.

Temperature is a physical quantity that characterizes the average kinetic energy of particles of a macroscopic system in a state of thermodynamic equilibrium. In an equilibrium state, the temperature has the same value for all macroscopic parts of the system.

Degree Celsius(designation: °C) is a widely used unit of temperature, used in the International System of Units (SI) along with the kelvin.

Mercury medical thermometer

Mechanical thermometer

The degree Celsius is named after the Swedish scientist Anders Celsius, who proposed a new scale for measuring temperature in 1742. The melting point of ice was taken as zero on the Celsius scale, and the boiling point of water at standard atmospheric pressure as 100°. (Initially, Celsius took the melting temperature of ice as 100°, and the boiling temperature of water as 0°. And only later his contemporary Carl Linnaeus “turned” this scale). This scale is linear in the range 0-100° and also continues linearly in the region below 0° and above 100°. Linearity is a major issue in accurate temperature measurements. Suffice it to mention that a classic thermometer filled with water cannot be marked for temperatures below 4 degrees Celsius, since in this range the water begins to expand again.

The original definition of degrees Celsius depended on the definition of standard atmospheric pressure because both the boiling point of water and the melting point of ice depend on pressure. This is not very convenient for standardizing the unit of measurement. Therefore, after the adoption of the Kelvin K as the basic unit of temperature, the definition of the degree Celsius was revised.

According to modern definition, a degree Celsius is equal to one kelvin K, and the zero of the Celsius scale is set so that the temperature of the triple point of water is 0.01 °C. As a result, the Celsius and Kelvin scales are shifted by 273.15:

26)Ideal gas- a mathematical model of a gas, in which it is assumed that the potential interaction energy of molecules can be neglected in comparison with their kinetic energy. There are no forces of attraction or repulsion between molecules, collisions of particles with each other and with the walls of the vessel are absolutely elastic, and the interaction time between molecules is negligible compared to the average time between collisions.



Where k is the Boltzmann constant (the ratio of the universal gas constant R to Avogadro's number N A), i- the number of degrees of freedom of molecules (in most problems about ideal gases, where molecules are assumed to be spheres of small radius, the physical analogue of which can be inert gases), and T- absolute temperature.

The basic MKT equation connects macroscopic parameters (pressure, volume, temperature) of a gas system with microscopic ones (mass of molecules, average speed of their movement).

Physics. Molecules. Arrangement of molecules in gaseous, liquid and solid distances.



  1. In the gaseous state, the molecules are not connected to each other and are located at a great distance from each other. Brownian movement. The gas can be compressed relatively easily.
    In a liquid, the molecules are close to each other and vibrate together. Almost impossible to compress.
    In a solid, the molecules are arranged in a strict order (in crystal lattices), and there is no molecular movement. Can't be compressed.
  2. The structure of matter and the beginnings of chemistry:
    http://samlib.ru/a/anemow_e_m/aa0.shtml
    (without registration and SMS messages, in a convenient text format: you can use Ctrl+C)
  3. It is impossible to agree that in the solid state molecules do not move.

    Movement of molecules in gases

    In gases, the distance between molecules and atoms is usually much greater than the size of the molecules, and the attractive forces are very small. Therefore, gases do not have their own shape and constant volume. Gases are easily compressed because repulsive forces over large distances are also small. Gases have the property of expanding indefinitely, filling the entire volume provided to them. Gas molecules move at very high speeds, collide with each other, and bounce off each other in different directions. Numerous impacts of molecules on the walls of the vessel create gas pressure.

    Movement of molecules in liquids

    In liquids, molecules not only oscillate around the equilibrium position, but also make jumps from one equilibrium position to the next. These jumps occur periodically. The time period between such jumps is called the average time of sedentary life (or average relaxation time) and is denoted by the letter ?. In other words, relaxation time is the time of oscillations around one specific equilibrium position. At room temperature, this time averages 10-11 s. The time of one oscillation is 10-1210-13 s.

    The time of sedentary life decreases with increasing temperature. The distance between the molecules of a liquid is smaller than the size of the molecules, the particles are located close to each other, and the intermolecular attraction is strong. However, the arrangement of liquid molecules is not strictly ordered throughout the volume.

    Liquids, like solids, retain their volume, but do not have their own shape. Therefore, they take the shape of the vessel in which they are located. Liquid has the property of fluidity. Thanks to this property, the liquid does not resist changing shape, is slightly compressed, and its physical properties are the same in all directions inside the liquid (isotropy of liquids). The nature of molecular motion in liquids was first established by the Soviet physicist Yakov Ilyich Frenkel (1894 1952).

    Movement of molecules in solids

    The molecules and atoms of a solid are arranged in a certain order and form a crystal lattice. Such solids are called crystalline. Atoms perform vibrational movements around the equilibrium position, and the attraction between them is very strong. Therefore, solids under normal conditions retain their volume and have their own shape.

  4. In the gaseous - they move randomly, they turn on
    In liquid - move in accordance with each other
    In solids they do not move.

Kinetic energy of a molecule

In a gas, molecules move freely (isolated from other molecules), only occasionally colliding with each other or with the walls of the container. As long as a molecule moves freely, it only has kinetic energy. During a collision, the molecules also gain potential energy. Thus, the total energy of a gas is the sum of the kinetic and potential energies of its molecules. The more rarefied the gas, the more molecules at each moment of time are in a state of free movement, having only kinetic energy. Consequently, when the gas is rarefied, the proportion of potential energy decreases in comparison with kinetic energy.

The average kinetic energy of a molecule at equilibrium of an ideal gas has one very important feature: in a mixture of different gases, the average kinetic energy of a molecule for different components of the mixture is the same.

For example, air is a mixture of gases. The average energy of an air molecule for all its components under normal conditions, when air can still be considered an ideal gas, is the same. This property of ideal gases can be proven on the basis of general statistical considerations. An important corollary follows from this: if two different gases (in different vessels) are in thermal equilibrium with each other, then the average kinetic energies of their molecules are the same.

In gases, the distance between molecules and atoms is usually much greater than the size of the molecules themselves; the interaction forces between molecules are not great. As a result, the gas does not have its own shape and constant volume. Gas is easily compressed and can expand without limit. Gas molecules move freely (translationally, they can rotate), only sometimes colliding with other molecules and the walls of the vessel in which the gas is located, and they move at very high speeds.

Movement of particles in solids

The structure of solids is fundamentally different from the structure of gases. In them, the intermolecular distances are small and the potential energy of the molecules is comparable to the kinetic energy. Atoms (or ions, or whole molecules) cannot be called motionless; they perform random oscillatory motion around average positions. The higher the temperature, the greater the oscillation energy, and therefore the average amplitude of oscillations. Thermal vibrations of atoms also explain the heat capacity of solids. Let us consider in more detail the movements of particles in crystalline solids. The entire crystal as a whole is a very complex coupled oscillatory system. The deviations of atoms from their average positions are small, and therefore we can assume that the atoms are subject to the action of quasi-elastic forces that obey Hooke’s linear law. Such oscillatory systems are called linear.

There is a developed mathematical theory of systems subject to linear oscillations. It proves a very important theorem, the essence of which is as follows. If the system performs small (linear) interconnected oscillations, then by transforming the coordinates it can be formally reduced to a system of independent oscillators (whose oscillation equations do not depend on each other). A system of independent oscillators behaves like an ideal gas in the sense that the atoms of the latter can also be considered as independent.

It is by using the idea of ​​independence of gas atoms that we arrive at Boltzmann's law. This very important conclusion provides a simple and reliable basis for the entire theory of solids.

Boltzmann's law

The number of oscillators with given parameters (coordinates and velocities) is determined in the same way as the number of gas molecules in a given state, according to the formula:

Oscillator energy.

Boltzmann's law (1) in the theory of solid bodies has no restrictions, but formula (2) for the oscillator energy is taken from classical mechanics. When theoretically considering solids, one must rely on quantum mechanics, which is characterized by discrete changes in the energy of the oscillator. The discreteness of the oscillator energy becomes insignificant only at sufficiently high values ​​of its energy. This means that (2) can only be used at sufficiently high temperatures. At high temperatures of a solid, close to the melting point, the law of uniform distribution of energy over the degrees of freedom follows from Boltzmann’s law. If in gases for each degree of freedom there is on average an amount of energy equal to (1/2) kT, then the oscillator has one degree of freedom, in addition to the kinetic one, with potential energy. Therefore, per one degree of freedom in a solid at a sufficiently high temperature there is an energy equal to kT. Based on this law, it is not difficult to calculate the total internal energy of a solid body, and after it its heat capacity. A mole of a solid contains NA atoms, and each atom has three degrees of freedom. Therefore, the mole contains 3 NA oscillators. Energy of a mole of a solid

and the molar heat capacity of a solid at sufficiently high temperatures is

Experience confirms this law.

Liquids occupy an intermediate position between gases and solids. Liquid molecules do not disperse over long distances, and liquid under normal conditions retains its volume. But unlike solids, molecules not only vibrate, but also jump from place to place, that is, they perform free movements. As the temperature increases, liquids boil (there is a so-called boiling point) and turn into gas. As the temperature decreases, liquids crystallize and become solids. There is a point in the temperature field at which the boundary between gas (saturated vapor) and liquid disappears (critical point). The pattern of thermal motion of molecules in liquids near the solidification temperature is very similar to the behavior of molecules in solids. For example, the heat capacity coefficients are exactly the same. Since the heat capacity of a substance changes slightly during melting, we can conclude that the nature of the movement of particles in a liquid is close to the movement in a solid (at the melting temperature). When heated, the properties of the liquid gradually change, and it becomes more like a gas. In liquids, the average kinetic energy of particles is less than the potential energy of their intermolecular interaction. The energy of intermolecular interaction in liquids and solids differs insignificantly. If we compare the heat of fusion and the heat of evaporation, we will see that during the transition from one state of aggregation to another, the heat of fusion is significantly lower than the heat of vaporization. An adequate mathematical description of the structure of a liquid can only be given with the help of statistical physics. For example, if a liquid consists of identical spherical molecules, then its structure can be described by the radial distribution function g(r), which gives the probability of detecting any molecule at a distance r from the given one chosen as a reference point. This function can be found experimentally by studying the diffraction of x-rays or neutrons, or a computer simulation of this function can be carried out using Newtonian mechanics.

The kinetic theory of liquid was developed by Ya.I. Frenkel. In this theory, a liquid is considered, as in the case of a solid, as a dynamic system of harmonious oscillators. But unlike a solid body, the equilibrium position of molecules in a liquid is temporary. After oscillating around one position, the liquid molecule jumps to a new position located nearby. Such a jump occurs with the expenditure of energy. The average “settled life” time of a liquid molecule can be calculated as:

\[\left\langle t\right\rangle =t_0e^(\frac(W)(kT))\left(5\right),\]

where $t_0\ $ is the period of oscillations around one equilibrium position. The energy that a molecule must receive in order to move from one position to another is called the activation energy W, and the time the molecule is in the equilibrium position is called the “settled life” time t.

For a water molecule, for example, at room temperature, one molecule undergoes about 100 vibrations and jumps to a new position. The forces of attraction between the molecules of a liquid are strong so that the volume is maintained, but the limited sedentary life of the molecules leads to the emergence of such a phenomenon as fluidity. During particle oscillations near the equilibrium position, they continuously collide with each other, so even a small compression of the liquid leads to a sharp “hardening” of particle collisions. This means a sharp increase in the pressure of the liquid on the walls of the vessel in which it is compressed.

Example 1

Task: Determine the specific heat capacity of copper. Assume that the temperature of copper is close to the melting point. (Molar mass of copper $\mu =63\cdot 10^(-3)\frac(kg)(mol))$

According to Dulong and Petit's law, a mole of chemically simple substances at temperatures close to the melting point has a heat capacity:

Specific heat capacity of copper:

\[С=\frac(с)(\mu )\to С=\frac(3R)(\mu )\left(1.2\right),\] \[С=\frac(3\cdot 8.31) (63\cdot 10^(-3))=0.39\ \cdot 10^3(\frac(J)(kgK))\]

Answer: Specific heat capacity of copper $0.39\ \cdot 10^3\left(\frac(J)(kgK)\right).$

Assignment: Explain in a simplified way from a physics point of view the process of dissolving salt (NaCl) in water.

The basis of the modern theory of solutions was created by D.I. Mendeleev. He established that during dissolution, two processes occur simultaneously: physical - the uniform distribution of particles of the solute throughout the entire volume of the solution, and chemical - the interaction of the solvent with the solute. We are interested in the physical process. Salt molecules do not destroy water molecules. In this case, it would be impossible to evaporate the water. If salt molecules joined water molecules, we would get some new substance. And salt molecules cannot penetrate inside the molecules.

An ion-dipole bond occurs between the Na+ and Cl- ions of chlorine and polar water molecules. It turns out to be stronger than the ionic bonds in the molecules of table salt. As a result of this process, the bond between the ions located on the surface of NaCl crystals is weakened, sodium and chlorine ions are detached from the crystal, and water molecules form so-called hydration shells around them. The separated hydrated ions, under the influence of thermal motion, are evenly distributed between the solvent molecules.