What provisions of the molecular kinetic theory are used. Molecular kinetic theory

Molecular kinetic theory (MKT) is a doctrine that explains thermal phenomena in macroscopic bodies and the internal properties of these bodies by the movement and interaction of atoms, molecules and ions that make up the bodies. The MCT structure of matter is based on three principles:

1. Matter consists of particles - molecules, atoms and ions. The composition of these particles includes smaller elementary particles. A molecule is the smallest stable particle of a given substance. The molecule has basic chemical properties substances. A molecule is the limit of division of a substance, that is, the smallest part of a substance that is capable of maintaining the properties of this substance. An atom is the smallest particle of a given chemical element.
2. The particles that make up matter are in continuous chaotic (disorderly) motion.
3. Particles of matter interact with each other - they attract and repel.

These basic provisions are confirmed experimentally and theoretically.

Composition of the substance

Modern instruments make it possible to observe images of individual atoms and molecules. Using an electron microscope or an ion projector (microscope), you can image individual atoms and estimate their sizes. The diameter of any atom is of the order of d = 10 -8 cm (10 -10 m). Molecular sizes more sizes 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).

Chaotic particle movement

The continuous chaotic movement of particles is confirmed by Brownian motion and diffusion. Random motion means that molecules do not have any preferred paths and their movements have random directions. This means that all directions are equally probable.

Diffusion(from 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 come into contact).

Mutual mixing of substances occurs due to the continuous and random movement of atoms or molecules (or other particles) of the substance. Over time, the depth of penetration of molecules of one substance into another increases. The depth of penetration depends on temperature: the higher the temperature, the greater the speed of movement of the particles of the substance and the faster the diffusion occurs.

Diffusion is observed in all states of matter - in gases, liquids and solids. An example of diffusion in gases is the spread of odors in the air in the absence of direct mixing. Diffusion in solids ensures the connection of metals during welding, soldering, chrome plating, etc. Diffusion occurs much faster in gases and liquids than in solids.

The existence of stable liquid and solid bodies is explained by the presence of intermolecular interaction forces (forces of mutual attraction and repulsion). 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 of an electromagnetic nature—they are forces of electrical origin. The reason for this is that molecules and atoms consist of charged particles with opposite signs of charges - electrons and positively charged atomic nuclei. In general, molecules are electrically neutral. In terms of its electrical properties, a molecule can be approximately considered as an electric dipole.

The force of interaction between molecules has a certain dependence on the distance between the molecules. This dependence is shown in Fig. 1.1. Shown here are the projections of interaction forces onto a straight line that passes through the centers of the molecules.

Rice. 1.1. Dependence of intermolecular forces on the distance between interacting atoms.

As we see, as the distance between the molecules r decreases, the force of attraction F r pr increases (red line in the figure). As already mentioned, the forces of attraction are considered to be negative, therefore, as the distance decreases, the curve goes down, that is, into the negative zone of the graph.

Attractive forces act as two atoms or molecules approach each other, as long as the distance r between the centers of the molecules is in the region of 10 -9 m (2-3 molecular diameters). As this distance increases, the attractive forces weaken. Attractive forces are short-range forces.

Where a– coefficient depending on the type of attractive forces and the structure of interacting molecules.

With further approach of atoms or molecules at distances between the centers of the molecules of the order of 10 -10 m (this distance is comparable to the linear dimensions of inorganic molecules), repulsive forces F r from (blue line in Fig. 1.1) appear. These forces appear due to the mutual repulsion of positively charged atoms in the molecule and decrease with increasing distance r even faster than the attractive forces (as can be seen on the graph - the blue line tends to zero more “steeply” than the red one).

Where b– coefficient depending on the type of repulsive forces and the structure of interacting molecules.

At a distance r = r 0 (this distance is approximately equal to the sum of the radii of the molecules), the attractive forces balance the repulsive forces, and the projection of the resulting force F r = 0. This state corresponds to the most stable arrangement of interacting molecules.

In general, the resulting force is:

For r > r 0, the attraction of molecules exceeds repulsion; for r< r 0 – отталкивание молекул превосходит их притяжение.

The dependence of the interaction forces between molecules on the distance between them qualitatively explains the molecular mechanism of the appearance of elastic forces in solids.

When a solid body is stretched, the particles move away from each other at distances exceeding r 0 . In this case, attractive forces of molecules appear, which return the particles to their original position.

When a solid body is compressed, the particles approach each other at distances smaller than the distance r 0 . This leads to an increase in repulsive forces, which return the particles to their original position and prevent further compression.

If the displacement of molecules from equilibrium positions is small, then the interaction forces grow linearly with increasing displacement. On the graph, this segment is shown as a thick, light green line.

Therefore, at small deformations (millions of times greater than the size of the molecules), Hooke's law is satisfied, according to which the elastic force is proportional to the deformation. At large displacements, Hooke's law does not apply.

Basic principles of molecular kinetic theory.

Molecular kinetic theory (MKT) studies the properties of substances, based on ideas about particles of matter.

ICT is based on three main principles:

1. All substances consist of particles - molecules, atoms and ions.

2. Particles of matter move continuously and randomly.

3. Particles of matter interact with each other.

The random (chaotic) movement of atoms and molecules in a substance is called thermal motion, because the speed of movement of particles increases with increasing temperature. Experimental confirmation of the continuous movement of atoms and molecules in matter is Brownian motion and diffusion.

Particles of matter.

All substances and bodies in nature consist of atoms and molecules - groups of atoms. Such large bodies are called macroscopic. Atoms and molecules belong to microscopic bodies. Modern instruments (ion projectors, tunnel microscopes) make it possible to see images of individual atoms and molecules.
The basis of the structure of matter is atoms. Atoms also have a complex structure; they consist of elementary particles - protons, neutrons that are part of the atomic nucleus, electrons, and other elementary particles.
Atoms can combine into molecules, or there can be substances consisting only of atoms. Atoms are generally electrically neutral. Atoms that have an excess or deficiency of electrons are called ions. There are positive and negative ions.

The illustration shows examples of different substances that have a structure in the form of atoms, molecules and ions, respectively.

Interaction forces between molecules.

At very small distances between molecules, repulsive forces act. Thanks to this, molecules do not penetrate each other and pieces of matter are never compressed to the size of one molecule. The molecule is a complex system, consisting of individual charged particles: electrons and atomic nuclei. Although in general molecules are electrically neutral, significant electrical forces act between them at short distances: electrons and atomic nuclei of neighboring molecules interact. If the molecules are located at distances several times greater than their sizes, then the interaction forces have practically no effect. The forces between electrically neutral molecules are short-range. At distances exceeding 2 - 3 molecular diameters, attractive forces act. As the distance between the molecules decreases, the force of attraction first increases and then begins to decrease and decreases to zero when the distance between the two molecules becomes equal to the sum of the radii of the molecules. As the distance decreases further, the electron shells of the atoms begin to overlap, and rapidly increasing repulsive forces arise between the molecules.

Ideal gas. Basic MKT equation.

It is known that particles in gases, unlike liquids and solids, are located relative to each other at distances significantly exceeding their own sizes. In this case, the interaction between molecules is negligible and the kinetic energy of the molecules is much greater than the energy of intermolecular interaction. To clarify the most general properties inherent in all gases, a simplified model of real gases is used - an ideal gas. The main differences between an ideal gas and a real gas:

1. Particles of an ideal gas are spherical bodies of very small sizes, practically material points.
2. There are no intermolecular interaction forces between particles.
3. Particle collisions are absolutely elastic.

Real rarefied gases indeed behave like an ideal gas. Let's use the ideal gas model to explain the origin of gas pressure. Due to thermal movement, gas particles hit the walls of the container from time to time. With each impact, the molecules act on the wall of the vessel with some force. Adding to each other, the impact forces of individual particles form a certain pressure force that constantly acts on the wall. It is clear that the more particles are contained in a vessel, the more often they will hit the wall of the vessel, and the greater will be the pressure force, and therefore the pressure. The faster the particles move, the harder they hit the wall of the container. Let us mentally imagine a simple experiment: a rolling ball hits a wall. If the ball rolls slowly, it will hit the wall with less force than if it were moving quickly. The greater the mass of the particle, the greater the impact force. The faster the particles move, the more often they hit the walls of the container. So, the force with which molecules act on the wall of a vessel is directly proportional to the number of molecules contained in a unit volume (this number is called the concentration of molecules and is denoted by n), the mass of the molecule mo, the average square of their velocities and the area of ​​the vessel wall. As a result, we get: gas pressure is directly proportional to the concentration of particles, the mass of the particle and the square of the particle speed (or their kinetic energy). The dependence of the pressure of an ideal gas on the concentration and on the average kinetic energy of particles is expressed by the basic equation of the molecular kinetic theory of an ideal gas. We obtained the basic MKT equation for an ideal gas from general considerations, but it can be strictly derived based on the laws of classical mechanics. Here is one form of writing the basic MKT equation:
P=(1/3)· n· m o · V 2.

Basic principles of molecular kinetic theory.

Molecular kinetic theory (MKT) studies the properties of substances, based on ideas about particles of matter.

ICT is based on three main principles:

1. All substances consist of particles - molecules, atoms and ions.

2. Particles of matter move continuously and randomly.

3. Particles of matter interact with each other.

The random (chaotic) movement of atoms and molecules in a substance is called thermal motion, because the speed of movement of particles increases with increasing temperature. Experimental confirmation of the continuous movement of atoms and molecules in matter is Brownian motion and diffusion.

Particles of matter.

All substances and bodies in nature consist of atoms and molecules - groups of atoms. Such large bodies are called macroscopic. Atoms and molecules belong to microscopic bodies. Modern instruments (ion projectors, tunnel microscopes) make it possible to see images of individual atoms and molecules.
The basis of the structure of matter is atoms. Atoms also have a complex structure; they consist of elementary particles - protons, neutrons that are part of the atomic nucleus, electrons, and other elementary particles.
Atoms can combine into molecules, or there can be substances consisting only of atoms. Atoms are generally electrically neutral. Atoms that have an excess or deficiency of electrons are called ions. There are positive and negative ions.

Interaction forces between molecules.

At very small distances between molecules, repulsive forces act. Thanks to this, molecules do not penetrate each other and pieces of matter are never compressed to the size of one molecule. A molecule is a complex system consisting of individual charged particles: electrons and atomic nuclei. Although in general molecules are electrically neutral, significant electrical forces act between them at short distances: electrons and atomic nuclei of neighboring molecules interact. If the molecules are located at distances several times greater than their sizes, then the interaction forces have practically no effect. The forces between electrically neutral molecules are short-range. At distances exceeding 2 - 3 molecular diameters, attractive forces act. As the distance between the molecules decreases, the force of attraction first increases and then begins to decrease and decreases to zero when the distance between the two molecules becomes equal to the sum of the radii of the molecules. As the distance decreases further, the electron shells of the atoms begin to overlap, and rapidly increasing repulsive forces arise between the molecules.

Ideal gas. Basic MKT equation.

It is known that particles in gases, unlike liquids and solids, are located relative to each other at distances significantly exceeding their own sizes. In this case, the interaction between molecules is negligible and the kinetic energy of the molecules is much greater than the energy of intermolecular interaction. To clarify the most general properties inherent in all gases, a simplified model of real gases is used - an ideal gas. The main differences between an ideal gas and a real gas:

1. Particles of an ideal gas are spherical bodies of very small sizes, practically material points.
2. There are no intermolecular interaction forces between particles.
3. Particle collisions are absolutely elastic.

Real rarefied gases indeed behave like an ideal gas. Let's use the ideal gas model to explain the origin of gas pressure. Due to thermal movement, gas particles hit the walls of the container from time to time. With each impact, the molecules act on the wall of the vessel with some force. Adding to each other, the impact forces of individual particles form a certain pressure force that constantly acts on the wall. It is clear that the more particles are contained in a vessel, the more often they will hit the wall of the vessel, and the greater will be the pressure force, and therefore the pressure. The faster the particles move, the harder they hit the wall of the container. Let us mentally imagine a simple experiment: a rolling ball hits a wall. If the ball rolls slowly, it will hit the wall with less force than if it were moving quickly. The greater the mass of the particle, the greater the impact force. The faster the particles move, the more often they hit the walls of the container. So, the force with which molecules act on the wall of a vessel is directly proportional to the number of molecules contained in a unit volume (this number is called the concentration of molecules and is denoted by n), the mass of the molecule mo, the average square of their velocities and the area of ​​the vessel wall. As a result, we get: gas pressure is directly proportional to the concentration of particles, the mass of the particle and the square of the particle speed (or their kinetic energy). The dependence of the pressure of an ideal gas on the concentration and on the average kinetic energy of particles is expressed by the basic equation of the molecular kinetic theory of an ideal gas. We obtained the basic MKT equation for an ideal gas from general considerations, but it can be strictly derived based on the laws of classical mechanics. Here is one form of writing the basic MKT equation:
P=(1/3)· n· m o · V 2.

Main provisions of the ICT:

1. All substances consist of tiny particles: molecules, atoms or ions.

2. These particles are in continuous chaotic motion, the speed of which determines the temperature of the substance.

3. Between particles there are forces of attraction and repulsion, the nature of which depends on the distance between them.

An ideal gas is a gas in which the interaction between its molecules is negligible.

The main differences between an ideal gas and a real one: particles of an ideal gas are very small balls, practically material points; there are no intermolecular interaction forces between particles; particle collisions are absolutely elastic. A real gas is a gas that is not described by the Clapeyron-Mendeleev equation of state for an ideal gas. The relationships between its parameters show that molecules in a real gas interact with each other and occupy a certain volume. The state of a real gas is often described in practice by the generalized Mendeleev-Clapeyron equation.

2 Status parameters and functions. Equation of state of an ideal gas.

Options:

Pressure is caused by the interaction of the molecules of the working fluid with the surface and is numerically equal to the force acting per unit surface area of ​​the body normal to the latter.

Temperature is a physical quantity that characterizes the degree of heating of a body. From the point of view of molecular kinetic concepts, temperature is a measure of the intensity of thermal motion of molecules.

Specific volume v is the volume of a unit mass of a substance. If a homogeneous body of mass M occupies a volume v, then by definition v = V/M. In the SI system, the unit of specific volume is 1 m3/kg. There is an obvious relationship between the specific volume of a substance and its density:

If all thermodynamic parameters are constant in time and the same at all points of the system, then this state of the system is called equilibrium.

For an equilibrium thermodynamic system, there is a functional relationship between the state parameters, which is called the equation of state

Clapeyron-Mendeleev equation

3 Gas mixtures. Apparent molecular weight. Gas constant of a mixture of gases.

A mixture of gases is a mechanical combination of gases that do not interact with each other. chemical reaction gases The basic law that determines the behavior of a gas mixture is Dalton’s law: the total pressure of a mixture of ideal gases is equal to the sum of the partial pressures of all its components: Partial pressure pi is the pressure that a gas would have if it alone, at the same temperature, occupied the entire volume of the mixture . The gas constant of the mixture is determined as: - apparent (average) molecular mass mixtures. With volumetric composition, with mass composition: - universal gas constant.

4 First law of thermodynamics.

The first law of thermodynamics is the law of conservation of energy, written using thermodynamic concepts (analytical formulation: a perpetual motion machine of the 1st kind is impossible):

Energy. Internal energy in thermodynamics is understood as the kinetic energy of the movement of molecules, the potential energy of their interaction, and zero energy (the energy of movement of particles inside a molecule at T = 0K). Kinetic energy molecules is a function of temperature, the value of potential energy depends on the average distance between the molecules and, therefore, on the volume V occupied by the gas, i.e., it is a function of V. Therefore, the internal energy U is a function of the state of the body.

Heat. Energy transferred from one body to another due to temperature differences is called heat. Heat can be transferred either through direct contact between bodies (conduction, convection) or over a distance (radiation), and in all cases this process is possible only if there is a temperature difference between the bodies.

Job. Energy transferred from one body to another when the volume of these bodies changes or moves in space is called work. For a finite change in volume, the work done against external pressure forces, called the work of expansion, is equal to The work of change in volume is equivalent to the area under the process curve in the p, v diagram.

Internal energy is a property of the system itself; it characterizes the state of the system. Heat and work are the energy characteristics of the processes of mechanical and thermal interactions of the system with environment. They characterize those amounts of energy that are transferred to the system or given away by it across its boundaries in a certain process.

The content of the article

MOLECULAR KINETIC THEORY– a branch of molecular physics that studies the properties of matter based on ideas about their molecular structure and certain laws of interaction between the atoms (molecules) that make up the substance. It is believed that particles of matter are in continuous, random motion and this movement is perceived as heat.

Until the 19th century A very popular basis for the doctrine of heat was the theory of caloric or some liquid substance flowing from one body to another. Heating of bodies was explained by an increase, and cooling by a decrease in the caloric content contained within them. The concept of atoms for a long time seemed unnecessary for the theory of heat, but many scientists even then intuitively connected heat with the movement of molecules. So, in particular, thought the Russian scientist M.V. Lomonosov. A lot of time passed before the molecular kinetic theory finally won in the minds of scientists and became an integral property of physics.

Many phenomena in gases, liquids and solids find a simple and convincing explanation within the framework of molecular kinetic theory. So pressure, exerted by a gas on the walls of the vessel in which it is enclosed, is considered as the total result of numerous collisions of rapidly moving molecules with the wall, as a result of which they transfer their momentum to the wall. (Recall that it is the change in momentum per unit time that, according to the laws of mechanics, leads to the appearance of force, and the force per unit surface of the wall is pressure). The kinetic energy of particle motion, averaged over their huge number, determines what is commonly called temperature substances.

The origins of the atomistic idea, i.e. The idea that all bodies in nature consist of the smallest indivisible particles, atoms, goes back to the ancient Greek philosophers - Leucippus and Democritus. More than two thousand years ago, Democritus wrote: “... atoms are countless in size and number, but they rush around the universe, whirling in a whirlwind, and thus everything complex is born: fire, water, air, earth.” A decisive contribution to the development of molecular kinetic theory was made in the second half of the 19th century. the works of remarkable scientists J.C. Maxwell and L. Boltzmann, who laid the foundations for a statistical (probabilistic) description of the properties of substances (mainly gases) consisting of a huge number of chaotically moving molecules. The statistical approach was generalized (in relation to any state of matter) at the beginning of the 20th century. in the works of the American scientist J. Gibbs, who is considered one of the founders of statistical mechanics or statistical physics. Finally, in the first decades of the 20th century. physicists realized that the behavior of atoms and molecules obeys the laws not of classical, but of quantum mechanics. This gave a powerful impetus to the development of statistical physics and made it possible to describe a whole series physical phenomena, which previously could not be explained within the framework of conventional concepts of classical mechanics.

Molecular kinetic theory of gases.

Each molecule flying towards the wall, when colliding with it, transfers its momentum to the wall. Since the speed of a molecule during an elastic collision with a wall varies from the value v before - v, the magnitude of the transmitted pulse is 2 mv. Force acting on the wall surface D S in time D t, is determined by the magnitude of the total momentum transmitted by all molecules reaching the wall during this period of time, i.e. F= 2mv n c D S/D t, where n c defined by expression (1). For pressure value p = F/D S in this case we find: p = (1/3)nmv 2.

To obtain the final result, you can abandon the assumption of the same speed of molecules by identifying independent groups of molecules, each of which has its own approximately the same speed. Then average value pressure is found by averaging the square of the velocity over all groups of molecules or

This expression can also be represented in the form

It is convenient to give this formula a different form by multiplying the numerator and denominator under the sign square root by Avogadro's number

N a= 6.023·10 23.

Here M = mN A– atomic or molecular mass, value R = kN A= 8.318·10 7 erg is called the gas constant.

The average speed of molecules in a gas, even at moderate temperatures, turns out to be very high. So, for hydrogen molecules (H2) at room temperature ( T= 293K) this speed is about 1900 m/s, for nitrogen molecules in the air - about 500 m/s. The speed of sound in air under the same conditions is 340 m/s.

Considering that n = N/V, Where V– volume occupied by gas, N is the total number of molecules in this volume, it is easy to obtain consequences from (5) in the form of known gas laws. To do this, the total number of molecules is represented as N = vN A, Where v is the number of moles of gas, and equation (5) takes the form

(8) pV = vRT,

which is called the Clapeyron–Mendeleev equation.

Given that T= const the gas pressure changes in inverse proportion to the volume it occupies (Boyle–Mariotte law).

In a closed vessel of a fixed volume V= const pressure changes directly proportional to the change in absolute gas temperature T. If the gas is in conditions where its pressure remains constant p= const, but the temperature changes (such conditions can be achieved, for example, if a gas is placed in a cylinder closed with a movable piston), then the volume occupied by the gas will change in proportion to the change in its temperature (Gay-Lussac's law).

Let there be a mixture of gases in the vessel, i.e. There are several different kinds of molecules. In this case, the magnitude of the momentum transferred to the wall by molecules of each type does not depend on the presence of molecules of other types. It follows that mixture pressure ideal gases equal to the sum of the partial pressures that each gas would create separately if it occupied the entire volume. This is another of the gas laws - the famous Dalton's law.

Molecular mean free path . One of the first who, back in the 1850s, gave reasonable estimates of the average thermal velocity of molecules of various gases was the Austrian physicist Clausius. The unusually large values ​​of these velocities he obtained immediately aroused objections. If the speeds of molecules are really so high, then the smell of any odorous substance should spread almost instantly from one end of a closed room to the other. In fact, the spread of odor occurs very slowly and occurs, as is now known, through a process called gas diffusion. Clausius, and later others, were able to provide a convincing explanation for this and other gas transport processes (such as thermal conductivity and viscosity) using the concept of mean free path molecules , those. the average distance a molecule travels from one collision to another.

Each molecule in a gas experiences a very large number of collisions with other molecules. In the interval between collisions, the molecules move almost in a straight line, experiencing sharp changes in speed only at the moment of the collision itself. Naturally, the lengths of straight sections along the path of a molecule can be different, so it makes sense to talk only about a certain average free path of molecules.

During time D t the molecule goes through a complex zigzag path equal to v D t. There are as many kinks in the trajectory along this path as there are collisions. Let Z means the number of collisions that a molecule experiences per unit time Average length the free path is then equal to the ratio of the path length N 2, for example, a» 2.0·10 –10 m. Table 1 shows the values ​​of l 0 in µm (1 µm = 10 –6 m) calculated using formula (10) for some gases under normal conditions ( p= 1 atm, T=273K). These values ​​turn out to be approximately 100–300 times greater than the intrinsic diameter of the molecules.