Molecular physics – branch of physics that studies physical properties bodies in various states of aggregation based on consideration of their molecular structure, the force of interaction between the particles forming the bodies and the nature of the thermal motion of these particles.
Numerous studies conducted by these scientists made it possible to formulate basic principles of molecular kinetic theory - MKT.
MCT explains the structure and properties of bodies based on the patterns of movement and interaction of the molecules that make up the bodies .
MCT is based on three important principles, confirmed experimentally and theoretically.
- All bodies consist of tiny particles - atoms, molecules, which include even smaller ones. elementary particles(electrons, protons, neutrons). The structure of any substance is discrete (discontinuous).
- Atoms and molecules of matter are always in continuous chaotic motion.
- Between particles of any substance there are forces of interaction - attraction and repulsion. The nature of these forces is electromagnetic.
These provisions are confirmed experimentally.
Experimental substantiation of position 1.
All bodies are made up of tiny particles. Firstly, this is evidenced by the possibility of dividing matter (all bodies can be divided into parts).
The most striking experimental confirmation of the concepts of molecular kinetic theory about the random movement of atoms and molecules is Brownian motion.
It was discovered by the English botanist R. Brown (1827). In 1827 the English. botanist Brown studying internal structure plants, using a microscope, discovered that particles of solid matter in a liquid medium undergo continuous chaotic movement.
The thermal movement of particles suspended in a liquid (or gas) is calledBrownian motion.
Brownian particles move under the influence of random collisions of molecules. Due to the chaotic thermal motion of molecules, these impacts never balance each other out. As a result, the speed of a Brownian particle changes randomly in magnitude and direction, and its trajectory is a complex zigzag curve. The theory of Brownian motion was created by A. Einstein (1905). Einstein's theory was experimentally confirmed in the experiments of the French physicist J. Perrin (1908–1911).
The cause of Brownian motion is the continuous chaotic movement of molecules of a liquid or gas, which, randomly hitting a particle from all sides, set it in motion. The reason for the Brownian motion of a particle is that the impacts of molecules on it are not compensated. This means that Brownian motion is also an experimental substantiation of the 2nd position of MKT.
The continuous movement of molecules of any substance (solid, liquid, gaseous) is confirmed by numerous experiments on diffusion.
Diffusioncalled the phenomenon of spontaneous penetration of molecules of one substance into the spaces between the molecules of another. Those. This is the spontaneous mixing of substances.
If an odorous substance (perfume) is brought into a room, then after some time the smell of this substance will spread throughout the room. This indicates that molecules of one substance, without influence external forces penetrate into another. Diffusion is observed in both liquids and solids Oh.
When studying the structure of matter, it was found that forces of attraction and repulsion, called molecular forces, act simultaneously between molecules. These are forces of electromagnetic nature.
The ability of solids to resist stretching and the special properties of the surface of a liquid lead to the conclusion that there are forces between molecules gravity.
The low compressibility of very dense gases and especially liquids and solids means that between the molecules there are repulsive forces.
These forces act simultaneously. If this were not the case, then the bodies would not be stable: they would either scatter into particles or stick together.
Intermolecular interaction is the interaction of electrically neutral molecules and atoms.
The forces acting between two molecules depend on the distance between them. Molecules are complex spatial structures containing both positive and negative charges. If the distance between the molecules is sufficiently large, then the forces of intermolecular attraction predominate. At short distances, repulsive forces predominate. Resultant force dependencies F and potential energy E p interactions between molecules depending on the distance between their centers are qualitatively depicted in the figure. At some distance r = r 0 the interaction force becomes zero. This distance can be conventionally taken as the diameter of the molecule. Potential energy of interaction at r = r 0 is minimal. To remove two molecules that are at a distance from each other r 0 , we need to give them extra energy E 0 . Magnitude E 0 is called depth of potential well or binding energy .
There are attractive forces between the electrons of one molecule and the nuclei of another, which are conventionally considered negative (lower part of the graph). At the same time, repulsive forces act between the electrons of the molecules and their nuclei, which are conventionally considered positive (upper part of the graph). At a distance equal to the size of the molecules, the resulting force is zero, i.e. attractive forces balance repulsive forces. This is the most stable arrangement of molecules. As the distance increases, attraction exceeds the force of repulsion; as the distance between molecules decreases, vice versa.
Atoms and molecules interact and therefore have potential energy.
Atoms and molecules are in constant movement, which means they havekinetic energy.
Mass and size of molecules
Most substances consist of molecules, so to explain the properties of macroscopic objects, explain and predict phenomena, it is important to know the basic characteristics of molecules.
Moleculeis the smallest stable particle of a given substance that has its basic chemical properties.
A molecule consists of even smaller particles - atoms, which in turn consist of electrons and nuclei.
Atomcalled the smallest particle of a given chemical element.
Molecular sizes very small.
The order of magnitude of the diameter of a molecule is 1*10 - 8 cm = 1*10 - 10 m
The order of magnitude of the volume of a molecule is 1*10 - 20 m 3
The fact that the sizes of molecules are small can be judged from experience. In 1 liter (m 3) of clean water we will dilute 1 m 3 of green ink, dilute the ink 1,000,000 times. We will see that the solution is green in color and at the same time homogeneous. This suggests that even when diluted 1,000,000 times, there are a large number of dye molecules in the water. This experiment shows how small the molecules are.
1 cm 3 of water contains 3.7 * 10 -8 molecules.
The order of magnitude of the mass of molecules is 1*10 -23 g = 1*10 -26 kg
In molecular physics, it is customary to characterize the masses of atoms and molecules not by their absolute values (in kg), but by relative dimensionless quantities - relative atomic mass and relative molecular mass.
According to international agreement, as a single atomic mass m 0 is taken to be 1/12 of the mass of the carbon isotope 12 C (m 0 C):
m 0 =1/12 m 0С =1.66 *10 -27
Relative molecular weight can be determined if the absolute value of the mass of the molecule (m mol in kg) is divided by the unit atomic mass.
M 0 = m mol / 1/12 m 0С
Relative molecular (atomic) mass of a substance (from the periodic table)
7 14 N Nitrogen M 0 N = 14 M 0 N 2 = 28
The relative number of atoms or molecules contained in a substance is characterized by a physical quantity called the amount of substance.
Quantity of substanceע – is the ratio of the number of molecules (atoms)Nin a bottom macroscopic body to the number of molecules in 0.012 kg of carbonN A
The amount of substance is expressed in moles
One mole -This is the amount of a substance that has the same number of molecules (atoms) as there are atoms in 0.012 kg of carbon.
A mole of any substance contains the same number of molecules. This number is called Avogadro's constantN A=6.02 * 10 23 mol -1
The mass of one mole of a substance is called molar mass.
Number of molecules in a given mass of substance: 
Mass of substance (any amount of substance):
Determination of molar mass: 
Video resource: Mass of molecules. Amount of substance.
(youtube)bfPw9aZJVqk&list=PLhOzgnnk_5jyM6NXfLniX5sX3rZTrpoea&index=18(/youtube)
The concept of temperature is one of the most important in molecular physics.
Temperature is a physical quantity that characterizes the degree of heating of bodies.
The random chaotic movement of molecules is calledthermal movement.
The kinetic energy of thermal motion increases with increasing temperature. At low temperatures, the average kinetic energy of a molecule may be small. In this case, the molecules condense into a liquid or solid; in this case, the average distance between the molecules will be approximately equal to the diameter of the molecule. As the temperature increases, the average kinetic energy of a molecule becomes greater, the molecules fly apart, and a gaseous substance is formed.
The concept of temperature is closely related to the concept of thermal equilibrium. Bodies in contact with each other can exchange energy. The energy transferred from one body to another during thermal contact is called amount of heat.
Let's look at an example. If you put heated metal on ice, the ice will begin to melt, and the metal will begin to cool until the temperatures of the bodies become the same. When two bodies of different temperatures come into contact, heat exchange occurs, as a result of which the energy of the metal decreases and the energy of the ice increases.
Energy during heat exchange is always transferred from a body with more high temperature to a body with a lower temperature. Ultimately, a state of the system of bodies occurs in which there will be no heat exchange between the bodies of the system. This condition is called thermal equilibrium.
Thermal equilibrium– This is a state of a system of bodies in thermal contact in which there is no heat transfer from one body to another, and all macroscopic parameters of the bodies remain unchanged.
Temperature– this is a physical parameter that is the same for all bodies in thermal equilibrium. The possibility of introducing the concept of temperature follows from experience and is called the zeroth law of thermodynamics.
Bodies in thermal equilibrium have the same temperatures.
To measure temperatures, the property of a liquid to change volume when heated (and cooled) is most often used.
The device with which temperature is measured is calledthermometer.
To create a thermometer, you must select a thermometric substance (for example, mercury, alcohol) and a thermometric quantity that characterizes the property of the substance (for example, the length of a mercury or alcohol column). Various thermometer designs use various physical properties of a substance (for example, changes in the linear dimensions of solids or changes electrical resistance conductors when heated). Thermometers must be calibrated. To do this, they are brought into thermal contact with bodies whose temperatures are considered given. Most often they use simple natural systems, in which the temperature remains unchanged despite heat exchange with environment is a mixture of ice and water and a mixture of water and steam when boiling at normal atmospheric pressure.
Ordinary liquid thermometer consists of a small glass reservoir to which is attached a glass tube with a narrow internal channel. The reservoir and part of the tube are filled with mercury. The temperature of the medium in which the thermometer is immersed is determined by the position of the upper level of mercury in the tube. It was agreed to mark the divisions on the scale as follows. The number 0 is placed in the place where the liquid column level is set when the thermometer is lowered into melting snow (ice), the number 100 is placed in the place where the liquid column level is set when the thermometer is immersed in water vapor boiling at normal pressure (10 5 Pa). The distance between these marks is divided by 100 equal parts, called degrees. This method of dividing the scale was introduced by Celsius. Degrees on the Celsius scale are denoted ºC.
By temperature Celsius scale The melting point of ice is assigned a temperature of 0 °C, and the boiling point of water is assigned a temperature of 100 °C. The change in the length of the liquid column in the capillaries of the thermometer by one hundredth of the length between the marks of 0 °C and 100 °C is taken equal to 1 °C.
Widely used in a number of countries (USA) Fahrenheit (T F), in which the freezing temperature of water is taken to be 32 °F and the boiling point of water is 212 °F. Hence,
Mercury thermometers used to measure temperature in the range from -30 ºС to +800 ºС. Along with liquid mercury and alcohol thermometers are used electric And gas thermometers.
Electric thermometer – resistance temperature – it uses the dependence of metal resistance on temperature.
A special place in physics is occupied by gas thermometer , in which the thermometric substance is a rarefied gas (helium, air) in a vessel of constant volume ( V= const), and the thermometric quantity is gas pressure p. Experience shows that gas pressure (at V= const) increases with increasing temperature measured on the Celsius scale.
To calibrate a gas thermometer of constant volume, you can measure pressure at two temperatures (for example, 0 °C and 100 °C), plot points p 0 and p 100 on the graph and then draw a straight line between them. Using the calibration curve thus obtained, temperatures corresponding to other pressure values can be determined.
Gas thermometers are bulky and inconvenient for practical use: they are used as a precision standard for calibrating other thermometers.
The readings of thermometers filled with different thermometric bodies usually differ slightly. To ensure that the accurate determination of temperature does not depend on the substance filling the thermometer, we introduce thermodynamic temperature scale.
To introduce it, let us consider how gas pressure depends on temperature when its mass and volume remain constant.
Thermodynamic temperature scale. Absolute zero.
Let's take a closed vessel with gas and heat it, initially placing it in melting ice. We determine the gas temperature t using a thermometer, and the pressure p using a manometer. As the temperature of the gas increases, its pressure will increase. The French physicist Charles found such a relationship. A graph of p versus t, constructed on the basis of such an experiment, looks like a straight line.
If we continue the graph into the region of low pressures, we can determine some “hypothetical” temperature at which the gas pressure would become zero. Experience shows that this temperature is –273.15 °C and does not depend on the properties of the gas. It is impossible to experimentally obtain a gas in a state with zero pressure by cooling, since at very low temperatures all gases turn into liquid or solid states. Pressure ideal gas determined by the impacts of chaotically moving molecules on the walls of the vessel. This means that the decrease in pressure when the gas is cooled is explained by a decrease in the average energy forward motion gas molecules E; The gas pressure will be zero when the energy of translational motion of the molecules becomes zero.
The English physicist W. Kelvin (Thomson) put forward the idea that the resulting value absolute zero corresponds to the cessation of the translational movement of molecules of all substances. Temperatures below absolute zero cannot exist in nature. This is the limiting temperature at which the pressure of an ideal gas is zero.
The temperature at which the forward motion of molecules should stop is calledabsolute zero ( or zero Kelvin).
Kelvin in 1848 proposed using the point of zero gas pressure to build a new temperature scale – thermodynamic temperature scale(Kelvin scale). The temperature of absolute zero is taken as the starting point for this scale.
In the SI system, the unit of temperature measured on the Kelvin scale is called kelvin and denoted by the letter K.
The size of the Kelvin degree is determined so that it coincides with the Celsius degree, i.e. 1K corresponds to 1ºС.
Temperature measured by thermodynamic scale temperatures, denoted by T. It is called absolute temperature or thermodynamic temperature.
The Kelvin temperature scale is called absolute temperature scale . It turns out to be most convenient when constructing physical theories.
In addition to the point of zero gas pressure, which is called absolute zero temperature , it is enough to take another fixed reference point. In the Kelvin scale, this point is used triple point temperature of water(0.01 °C), in which all three phases - ice, water and steam - are in thermal equilibrium. On the Kelvin scale, the temperature of the triple point is taken to be 273.16 K.
Relationship between absolute temperature and scale temperature Celsius expressed by the formula T = 273.16 +t, where t is the temperature in degrees Celsius.
More often they use the approximate formula T = 273 + t and t = T – 273
Absolute temperature cannot be negative.
Gas temperature is a measure of the average kinetic energy of molecular motion.
In experiments, Charles found the dependence of p on t. The same relationship will exist between p and T: i.e. there is a directly proportional relationship between p and T.
On the one hand, the gas pressure is directly proportional to its temperature, on the other hand, we already know that the gas pressure is directly proportional to the average kinetic energy of the translational motion of molecules E (p = 2/3*E*n). This means E is directly proportional to T.
The German scientist Boltzmann proposed introducing a proportionality coefficient (3/2)k into the dependence of E on T
E = (3/2)kT
From this formula it follows that the average value of the kinetic energy of the translational motion of molecules does not depend on the nature of the gas, but is determined only by its temperature.
Since E = m*v 2 /2, then m*v 2 /2 = (3/2)kT
where does the root mean square speed of gas molecules come from?
The constant value k is called Boltzmann's constant.
In SI it has the value k = 1.38*10 -23 J/K
If we substitute the value of E into the formula p = 2/3*E*n, we get p = 2/3*(3/2)kT* n, reducing, we get p = n* k*T
The pressure of a gas does not depend on its nature, but is determined only by the concentration of moleculesnand gas temperature T.
The relation p = 2/3*E*n establishes a connection between microscopic (values are determined using calculations) and macroscopic (values can be determined from instrument readings) gas parameters, so it is usually called the basic equation of the molecular kinetic theory of gases.
Contents 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 tiny indivisible particles, atoms, goes back to 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 not classical laws, but quantum mechanics. This gave a powerful impetus to the development of statistical physics and made it possible to describe a number of physical phenomena that previously could not be explained within the framework of the usual 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 the molecule at elastic collision with the wall varies depending on the size v to – 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 the average 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 the well-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 the pressure of a mixture of ideal gases is 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 ones he received were unusual large values These speeds immediately raised 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 very large number 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 at 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.
We begin our study of molecular physics by studying the molecular kinetic theory of gases.
Molecular kinetic theory of gases - a branch of physics that studies their properties using statistical methods based on an idea of their molecular structure and a certain law of interaction between molecules.
Gas (from the Greek chaoc - chaos) - physical state a substance in which its constituent atoms and molecules weakly interact and move chaotically as a result of collisions with each other, occupying the entire volume provided to them.
The kinetic theory of gases is based on some general concepts and experimental facts. Let's first consider a model called an ideal gas.
Ideal gas - it is a gas of molecules, which can be considered as material points and for which the potential energy of interaction of molecules can be neglected in comparison with their kinetic energy. Collisions of gas molecules with each other and with the walls of the container are considered absolutely elastic.
Some real gases are close in their properties to an ideal gas under conditions close to normal (oxygen, helium), as well as at low pressures and high temperatures.
Macroscopic The state of a gas is determined by pressure, temperature and volume. In turn, pressure, temperature and volume are parameters characterizing the macroscopic state of the system. Microscopic The state of a gas is determined by the position and velocities of all its molecules.
System status settings may change. A change in any thermodynamic parameter is called thermodynamic process. If the state of the system does not change over time, then it is steady state. The stationary state of the system, not caused by external processes, is called equilibrium state of the system. The equation that describes the equilibrium state of a thermodynamic system is called equation of state.
Basic principles of the molecular kinetic theory of gases
The first position of the molecular kinetic theory is the complete randomness of the movement of molecules. In a gas, all directions of molecular motion are equal. There is no one direction in which molecules move in greater numbers or in which faster molecules predominate than in any other direction.
The second main position is the proportionality of the average speed of molecules to the square root of their absolute temperature. This position is the result of experiments.
The third position is that the average kinetic energies of molecules of different gases at the same temperature are equal to each other. This position is also the result of experiments.
1.1. Basic equation of the kinetic theory of gases
To derive this equation, assume that the container contains an ideal gas. Gas molecules collide with each other and with the walls of the container. Collisions of molecules with each other only lead to a redistribution of energy between the molecules. Let's select some elementary area on the wall of the vessel and calculate the gas pressure on it (Fig. 1). With each collision, a molecule moving perpendicular to the platform transfers momentum to it 
, where m is the mass of the molecule, v is its speed. During the time t of the platform S, only those molecules are reached that are enclosed in the volume of a cylinder with a base S and height vt. If n is the concentration of molecules, then the number of these molecules is nSvt. However, it should be taken into account that the molecules move towards the area S at different angles and at different speeds. Since the movement of molecules is chaotic, it can be replaced by movement along three mutually perpendicular directions. In addition, since none of the directions has advantages over the others, at any moment of time 1/3 of all molecules move along each of them, and half of them, i.e. 1/6 in one direction, the other half in the opposite direction. Then, during the time t, the number of molecules equal to the area S will reach 
. When colliding with the platformS, these molecules will transfer momentum to it
Then the pressure exerted by the gas on the wall of the vessel is equal to
.
(1.1.1)
As noted above, molecules move at different speeds v 1, v 2 , ..., v n , if the volume V of a gas contains N molecules, then instead of the speed v it is necessary to take into account root mean square speed
Then equation (1.1.1) will be written in the form
(1.1.2)
Equation (1.1.2) is called the basic equation of the kinetic theory of ideal gases .
P 
since concentrationn=N/V, therefore
or 
,
where E is the average kinetic energy of one molecule, E is the kinetic energy of the gas.
Pressure is proportional to the number of molecules per unit volume and the average kinetic energy of the molecules.
From the basic equation we can derive all the gas laws established experimentally back in the 18th century; for a given mass of gas the following laws are valid:
Boyle-Mariotte PV=const, with T=const;
Gay Lussac 
with p=const and 
whenV=const;
Dalton p=p 1 +p 2 +…+p n ;
For 1 kilomole of an ideal gas, the Clapeyron-Mendeleev formula is valid
,
(1.1.4)
where R=8.314 J/(molK) is the universal gas constant. For one mole of gas N=N A =6.0210 23 - Avagadro's number. Therefore, Avogadro's number is the number of molecules in a mole of any substance. The number of gas molecules under normal conditions (p = 1.01310 -5 Pa, T = 273K) located in a unit volume (1m 2) is called the Loschmidt number N L = 2.68710 25 m -3. It is equal to Avogadro’s number divided by the volume of a mole of gas under normal conditions V m = 22.4110 -3 m 3 mol -1
Comparing expressions (1.1.3) and (1.1.4), we obtain
Taking into account the Boltzmann constant (k=R/N A =1.3810 -23 J/K):
(1.1.5)
We have obtained a relation relating the average kinetic energy of one molecule to temperature.
Temperature - a physical quantity that characterizes the state of equilibrium of a thermodynamic system and is proportional to the average kinetic energy of the chaotic movement of the particles that make up the system.
When bringing substances into contact with different temperatures, i.e. kinetic energies of particles, heat exchange takes place - temperature equalization.
To measure temperature, the dependence of the physical properties of substances on temperature is used (contact potential difference, thermal expansion, dependence of electrical resistance, emissivity, etc.).
From equation (1.1.4) we can consider the relationship between temperature, pressure and volume for a given mass of an ideal gas
where m is the gas mass,
- molar mass of gas,
- number of moles,
N is the number of molecules in a given volume of gas.
Since for two different states of the same mass of gas p 1 V 1 =NkT 1 and p 2 V 2 =NkT 2, we have 
those. 
(1.1.6)
Thermodynamic temperature is directly proportional to the product of volume and pressure (for a given mass of gas).
As an example of the application of the Mendeleev-Clapeyron equation, consider the process of changing temperature and pressure at a constant volume V=const (isochoric process). In this case, it is convenient to use the dependence of pressure on density and temperature
,
(1.1.7)
where =m/ is gas density (kg/m3).
The graph of an isochoric process in p, T coordinates (Fig. 1.1.2) represents straight lines passing through the origin of coordinates. From dependence (1.1.7) and the graph it follows that higher density (or concentration n) corresponds to higher pressure. On the other hand, a larger volume V (at a constant mass m) corresponds to a smaller angle of inclination of the straight line to the abscissa axis - an inverse relationship.
Example 1. Determine the temperature at which 4 m 2 of gas creates a pressure of 1.510 5 Pa, if under normal conditions the gas occupies a volume of 5 m 3.
Solution. Under normal conditions, V 1 =5 m 3, p 1 =1 atm=101325 Pa, T 1 =273K, it is necessary to find T 2 at V 2 =4m 3, p 2 =1.510 5 Pa. According to (5) we have
where 
Example 2. How many molecules do you inhale if you get 1 liter of air in one breath?
Solution. The volume of one kilomole is equal to 22.4 m 3, which means 1 liter of air is equal to 110 -3 /22.4 = 4.510 -5 kmol. Thus, 1 liter of air contains 4.510 -5 6.0210 26 =2.710 22 molecules.
Example 3. What is heavier than 1 m 3 of dry air or 1 m 3 of humid air at the same temperatures and pressures? air =29 kg/kmol, water =18 kg/kmol.
Solution. The average mass of a molecule of dry air is greater than that of water vapor. The number of molecules in both cases is the same, but in humid air some of the molecules are replaced by lighter water molecules, therefore, 1 m 3 of dry air is heavier than 1 m 3 of humid air.
Example 4. How will the pressure of a given mass of gas change at a constant volume if the temperature of the gas is doubled and each molecule disintegrates into two atoms?
Solution.
, since N and T increase by 2 times, the pressure will increase by 4 times.
Example 5.
Show that 
.
Solution. Let's consider four molecules whose speeds are different and equal to 1, 2, 3 and 4 m/s. Square of the mean 
equals
,
and the root mean square speed is
If the speeds of individual molecules are +1, -2, -3, +4 m/s, then 
, A 
DEFINITION
Atom - the smallest particle of a given chemical element. All atoms existing in nature are represented in periodic table Mendeleev's elements.
Atoms are combined into a molecule by chemical bonds, based on electrical interaction. The number of atoms in a molecule can vary. A molecule can consist of one, two, three, or even several hundred atoms.
DEFINITION
Molecule- the smallest particle of a given substance that has its chemical properties.
Molecular kinetic theory- the doctrine of the structure and properties of matter based on ideas about the existence of atoms and molecules.
The founder of the molecular kinetic theory is M.V. Lomonosov (1711-1765), who formulated its main principles and applied them to explain various thermal phenomena.
Basic principles of molecular kinetic theory
Main provisions of the ICT:
- all bodies in nature consist of tiny particles (atoms and molecules);
- particles are in continuous chaotic motion, which is called thermal;
- particles interact with each other: forces of attraction and repulsion act between particles, which depend on the distance between the particles.
The molecular kinetic theory is confirmed by many phenomena.
The mixing of various liquids and the dissolution of solids in liquids is explained by the mixing of molecules of various kinds. In this case, the volume of the mixture may differ from the total volume of its components. which indicates different sizes of molecular compounds.
DEFINITION
Diffusion- the phenomenon of penetration of two or more contacting substances into each other.
Diffusion occurs most intensely in gases. The spread of odors is due to diffusion. Diffusion indicates that molecules are in constant chaotic motion. Also, the phenomenon of diffusion indicates that there are gaps between molecules, i.e. matter is discrete.
DEFINITION
Brownian motion - thermal movement tiny microscopic particles suspended in a liquid or gas.
This phenomenon was first observed by the English botanist R. Brown in 1827. Observing flower pollen suspended in water through a microscope, he saw that each pollen particle made rapid, random movements, moving over a certain distance. As a result of individual movements, each pollen particle moved along a zigzag trajectory (Fig. 1, a).
Fig.1. Brownian motion: a) trajectories of movement of individual particles suspended in a liquid; b) transfer of momentum from liquid molecules to a suspended particle.
Further studies of Brownian motion in various liquids and with various solid particles showed that this motion becomes more intense the smaller the particle sizes and the higher the temperature of the experiment. This movement never stops and does not depend on any external reasons.
R. Brown was unable to provide an explanation for the observed phenomenon. The theory of Brownian motion was constructed by A. Einstein in 1905 and received experimental confirmation in the experiments of the French physicist J. Perrin (1900-1911).
Liquid molecules, which are in constant chaotic motion when colliding with a suspended particle, transfer some momentum to it (Fig. 1, b). In the case of a large particle, the number of molecules incident on it from all sides is large, their impacts are compensated at each moment of time, and the particle remains practically motionless. If the particle size is very small, then the impacts of the molecules are not compensated - more molecules can hit it on one side than on the other, as a result of which the particle begins to move. It is precisely this kind of movement that Brownian particles perform under the influence of random impacts of molecules. Although Brownian particles have a mass billions of times greater than the mass of individual molecules and move at very low speeds (compared to the speeds of molecules), their movement can still be observed through a microscope.
Examples of problem solving
EXAMPLE 1
EXAMPLE 2
DEFINITION
The equation underlying the molecular kinetic theory connects macroscopic quantities that describe (for example, pressure) with the parameters of its molecules (their velocities). This equation looks like:
Here is the mass of a gas molecule, is the concentration of such particles per unit volume, and is the average square of the speed of the molecules.
The basic MKT equation clearly explains how an ideal gas creates pressure on the surrounding walls of the vessel. Molecules hit the wall all the time, acting on it with a certain force F. Here you should remember: when a molecule hits an object, a force -F acts on it, as a result of which the molecule “bounces” off the wall. In this case, we consider the collisions of molecules with the wall to be absolutely elastic: mechanical energy molecules and walls are completely preserved, without turning into . This means that during collisions only molecules change, and heating of the molecules and the wall does not occur.
Knowing that the collision with the wall was elastic, we can predict how the speed of the molecule will change after the collision. The velocity module will remain the same as before the collision, and the direction of movement will change to the opposite relative to the Ox axis (we assume that Ox is the axis that is perpendicular to the wall).
There are a lot of gas molecules, they move chaotically and often hit the wall. Having found geometric sum the force with which each molecule acts on the wall, we recognize the force of gas pressure. To average the speeds of molecules, it is necessary to use statistical methods. That is why in the basic MKT equation they use the average squared speed of molecules, and not the square of average speed: the average speed of chaotically moving molecules is zero, and in this case we would not get any pressure.
Now it's clear physical meaning equations: the more molecules are contained in a volume, the heavier they are and the faster they move, the more pressure they create on the walls of the vessel.
Basic MKT equation for the ideal gas model
It should be noted that the basic MKT equation was derived for the ideal gas model with the appropriate assumptions:
- Collisions of molecules with surrounding objects are absolutely elastic. For real gases this is not entirely true; some molecules still pass into internal energy molecules and walls.
- The forces of interaction between molecules can be neglected. If the real gas is at high blood pressure and relatively low temperatures, these forces become quite significant.
- We count molecules material points, neglecting their size. However, the molecular sizes real gases affect the distance between the molecules themselves and the wall.
- And finally, the basic MKT equation considers a homogeneous gas - but in reality we often deal with mixtures of gases. Like, for example, .
However, for rarefied gases this equation gives very accurate results. In addition, many real gases at room temperature and at pressures close to atmospheric are very similar in properties to an ideal gas.
As is known from the laws, the kinetic energy of any body or particle. Replacing the product of the mass of each particle and the square of their speed in the equation we wrote down, we can present it in the form:
Also, the kinetic energy of gas molecules is expressed by the formula, which is often used in problems. Here k is Boltzmann's constant, which establishes the relationship between temperature and energy. k=1.38 10 -23 J/K.
The basic MKT equation is the basis of thermodynamics. It is also used in practice in astronautics, cryogenics and neutron physics.
Examples of problem solving
EXAMPLE 1
| Exercise | Determine the speed of movement of air particles under normal conditions. |
| Solution | We use the basic MKT equation, considering air to be a homogeneous gas. Since air is actually a mixture of gases, the solution to the problem will not be absolutely accurate. Gas pressure:
We can note that the product is a gas, since n is the concentration of air molecules (the reciprocal of volume), and m is the mass of the molecule. Then the previous equation will take the form: Under normal conditions, the pressure is 10 5 Pa, the air density is 1.29 kg/m 3 - these data can be taken from reference literature. From the previous expression we obtain air molecules:
|
| Answer | m/s |
EXAMPLE 2
| Exercise | Determine the concentration of molecules of a homogeneous gas at a temperature of 300 K and 1 MPa. Gas is considered ideal. |
| Solution | Let's start solving the problem with the basic MKT equation:  , as well as any material particles: . Then our calculation formula will take a slightly different form: |
