Let us consider some phenomena that experimentally confirm the main provisions and conclusions of the molecular kinetic theory.
1. Brownian motion. The Scottish botanist R. Brown (1773-1858), observing a suspension of flower pollen in water under a microscope, discovered that the pollen particles moved animatedly and randomly, sometimes rotating, sometimes moving from place to place, like specks of dust in a sunbeam. Subsequently, it turned out that such a complex zigzag movement is characteristic of any small particles (1 µm) suspended in a gas or liquid. The intensity of this movement, called Brownian, increases with increasing temperature of the medium, with decreasing viscosity and particle size (regardless of their chemical nature). The cause of Brownian motion remained unclear for a long time. Only 80 years after the discovery of this effect was an explanation given: Brownian motion suspended particles are caused by impacts of molecules of the medium in which the particles are suspended. Since molecules move chaotically, Brownian particles receive shocks from different directions, which is why they move in such a bizarre shape. Thus, Brownian motion is a confirmation of the conclusions of the molecular kinetic theory about the chaotic thermal motion of atoms and molecules.
2. Stern's experiment. The first experimental determination of molecular speeds was made by the German physicist O. Stern (1888-1970). His experiments also made it possible to estimate the velocity distribution of molecules. The Stern installation diagram is shown in Fig. 70. A platinum wire coated with a layer of silver is stretched along the axis of the inner cylinder with a slot, which is heated by current while the air is evacuated. When heated, silver evaporates. Silver atoms, flying through the slit, fall on the inner surface of the second cylinder, giving an image of the slit ABOUT.
If the device is rotated around the common axis of the cylinders, then the silver atoms will not settle against the slit, but will move away from the point ABOUT to some distance s. The image of the slit appears blurry. By examining the thickness of the deposited layer, it is possible to estimate the velocity distribution of molecules, which corresponds to the Maxwellian distribution.
Knowing the radii of the cylinders, their angular velocity of rotation, and also measuring s, it is possible to calculate the speed of movement of silver atoms at a given temperature of the wire. The experimental results showed that the average speed of silver atoms is close to that which follows from the Maxwellian speed distribution of molecules.
3. Lammert experience. This experiment allows us to more accurately determine the law of molecular velocity distribution. The diagram of the vacuum installation is shown in Fig. 71. A molecular beam formed by a source, passing through a slit, enters the receiver. Two discs with slots, mounted on a common axis, are placed between the source and receiver. With stationary disks, molecules reach the receiver by passing through slits in both
disks. If the axis is rotated, then the receiver will be reached only by those molecules that have passed through the slot in the first disk and spend a time equal to or a multiple of the time of rotation of the disk to travel between the disks. Other molecules are retained by the second disk. By changing the angular velocity of rotation of the disks and measuring the number of molecules entering the receiver, it is possible to identify the distribution law of molecular velocities. This experiment also confirmed the validity of the Maxwellian velocity distribution of molecules.
4. Experimental determination of Avogadro's constant. Using the idea of the distribution of molecules by height (see formula (45.4)), the French scientist J. Perrin (1870-1942) experimentally determined Avogadro’s constant. Studying Brownian motion under a microscope, he became convinced that Brownian particles are distributed in height like gas molecules in a gravitational field. Applying the Boltzmann distribution to them, we can write
Where m- particle mass, m 1 - mass of liquid displaced by it: m= 4 / 3 r 3 , m 1 = 4 / 3 r 3 1 (r - particle radius, - particle density, 1 - liquid density).
If n 1 and n 2 are the concentrations of particles at levels h 1 And h 2,a k=R/N A , That
Meaning N a obtained from the works of J. Perrin corresponded to the values obtained in other experiments, which confirms the applicability of distribution (45.4) to Brownian particles.
The molecular kinetic theory is justified. Let us present some of the evidence of the random chaotic movement of molecules: and the desire of gas to occupy the entire volume provided to it, the spread of odorous gas throughout the room; b Brownian motion is the random movement of the smallest particles of a substance visible through a microscope that are suspended and insoluble in it. Diffusion manifests itself in all bodies in gases, liquids and solids but in varying degrees. Diffusion in gases can be observed if a vessel with an odorous...
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EXPERIMENTAL JUSTIFICATION OF THE MOLECULAR KINETIC THEORY
According to the molecular kinetic theory, all substances consist of tiny particles - molecules. Molecules are in continuous motion and interact with each other. A molecule is the smallest particle of a substance that has its chemical properties. Molecules consist of simpler particles - atoms of chemical elements. Molecules various substances have different atomic compositions.
Molecules have kinetic energy E kin and at the same time the potential energy of interaction E sweat . In gaseous state E kin > E sweat . In liquid and solid states, the kinetic energy of particles is comparable to the energy of their interaction.
Three main points molecular kinetic theory:
1. All substances consist of molecules, i.e. have a discrete structure, the molecules are separated by spaces.
2. Molecules are in continuous random (chaotic) motion.
3. There are interaction forces between the molecules of the body.
The molecular kinetic theory is justified
Here are some of the proofs of the random (chaotic) movement of molecules:
a) the desire of gas to occupy the entire volume provided to it (the spread of odorous gas throughout the room);
b) Brownian motion - the random movement of the smallest particles of a substance visible through a microscope, suspended and insoluble in it. This movement occurs under the influence of random impacts of molecules surrounding the liquid, which are in constant chaotic motion;
c) diffusion - mutual penetration of molecules of contacting substances. During diffusion, the molecules of one body, being in continuous motion, penetrate into the gaps between the molecules of another body in contact with it and spread between them. Diffusion occurs in all bodies - gases, liquids and solids - but to varying degrees.
1. Diffusion.
Diffusion in gases can be observed if a container with an odorous gas is opened indoors. After some time, the gas will spread throughout the room.
Diffusion in liquids occurs much slower than in gases. For example, pour a solution of copper sulfate into a glass, and then very carefully add a layer of water and leave the glass in a room with a constant temperature and where it is not subject to shock. After some time, we will observe the disappearance of the sharp boundary between vitriol and water, and after a few days the liquids will mix, despite the fact that the density of vitriol is greater than the density of water. Water with alcohol and other liquids also diffuse.
Diffusion in solids occurs even more slowly than in liquids (from several hours to several years). It can only be observed in well-polished bodies, when the distances between the surfaces of polished bodies are close to the distances between molecules (10-8 cm). In this case, the rate of diffusion increases with increasing temperature and pressure.
Evidence of the force interaction of molecules:
a) deformation of bodies under the influence of force;
b) preservation of shape by solids;
c) surface tension of liquids and, as a consequence, the phenomenon of wetting and capillarity.
Between molecules there are simultaneously attractive and repulsive forces (Fig. 1). At small distances between molecules, repulsive forces predominate. As the distance r between molecules increases, both the attractive and repulsive forces decrease, and the repulsive forces decrease faster. Therefore, for a certain value of r 0 (distance between molecules) attractive and repulsive forces are mutually balanced.
Rice. 1. Attractive and repulsive forces.
If we agree to assign a positive sign to the repulsive forces, and a negative sign to the attractive forces, and perform the algebraic addition of the repulsive and attractive forces, we obtain the graph shown in Figure 2.
Rice. 2. Algebraic addition of repulsive and attractive forces.
Rice. 3. Dependence of the potential energy of interaction of molecules on the distance between them.
Figure 3 shows a graph of the potential energy of interaction between molecules versus the distance between them. Distance r 0 between molecules corresponds to the minimum of their potential energy (Fig. 3). To change the distance between molecules in one direction or another, work must be expended against the prevailing forces of attraction or repulsion. At shorter distances (Fig. 2), the curve rises steeply; this region corresponds to the strong repulsion of molecules (caused mainly by the Coulomb repulsion of approaching nuclei). Over large distances, molecules attract each other.
Distance r 0 corresponds to a stable equilibrium mutual position of molecules. From Figure 2 it is clear that as the distance between molecules increases, the prevailing forces of attraction restore the equilibrium position, and as the distance between them decreases, equilibrium is restored by the prevailing forces of repulsion.
Modern experimental methods of physics (X-ray diffraction analysis, observations using electron microscope and others) made it possible to observe the microstructure of substances.
2. Avogadro's number.
The number of grams of a substance equal to the molecular weight of that substance is called a gram molecule or mole. For example, 2 g of hydrogen constitutes a gram molecule of hydrogen; 32 g of oxygen make up a gram molecule of oxygen. The mass of one mole of a substance is called the molar mass of that substance.
Denoted by m. For hydrogen 
; for oxygen 
; for nitrogen 
etc.
Number of molecules contained in one mole different substances is the same and is called Avogadro's number (N A).
Avogadro's number is extremely high. To feel its enormity, imagine that a number of pinheads (each about 1 mm in diameter) equal to Avogadro’s number were poured into the Black Sea. In this case, it would turn out that there is no longer any room left for water in the Black Sea: it would not only be filled to the brim, but also with a large excess of these pinheads. With the same number of pinheads, it would be possible to cover an area equal to, for example, the territory of France, with a layer about 1 km thick. And such a huge number of individual molecules are contained in just 18 g of water; in 2 g of hydrogen, etc.
It has been established that in 1 cm 3 any gas under normal conditions (i.e. at 0 0 C and pressure 760 mm. Hg Art.) contains 2.710 19 molecules.
If we take a number of bricks equal to this number, then, being tightly packed, these bricks would cover the surface of the entire landmass of the Earth with a layer 120 m high. The kinetic theory of gases allows us to calculate only the free path of a gas molecule (i.e., the average distance traveled molecule from collision to collision with other molecules) and the diameter of the molecule.
We present some results of these calculations.
|
Substance |
Free path length at 760 mmHg. |
Molecule diameter |
|
Hydrogen H 2 |
1.12310 -5 cm |
2.310 -8 cm |
|
Oxygen O 2 |
0.64710 -5 cm |
2.910 -8 cm |
|
Nitrogen N 2 |
0.59910 -5 cm |
3.110 -8 cm |
The diameters of individual molecules are small quantities. At a million times magnification, the molecules would be the size of a dot in this book. Let us denote by m the mass of the gas (any substance). Then the attitudegives the number of moles of gas.
The number of gas molecules n can be expressed:
(1).
Number of molecules per unit volume n 0 will be equal to:
(2) , where: V is the volume of gas.
Mass of one molecule m 0 can be determined by the formula:
(3) .
Relative molecular mass m rel is called the quantity equal to the ratio absolute molecular mass m 0 to 1/12 the mass of a carbon atom m oc.
(4), where m oc = 210 -26 kg.
3. Ideal gas equation and isoprocesses.
Using the equation of state of an ideal gas, you can study processes in which the mass of the gas and one of three parameters - pressure, volume or temperature - remain unchanged. Quantitative relationships between two gas parameters with a fixed value of the third parameter are called gas laws.
Processes that occur with a constant value of one of the parameters are called isoprocesses (from the Greek “isos” - equal). True, in reality, no process can occur with a strictly fixed value of any parameter. There are always some influences that violate the constancy of temperature, pressure or volume. Only in laboratory conditions is it possible to maintain the constancy of one or another parameter with good accuracy, but in existing technical devices and in nature this is practically impossible.
An isoprocess is an idealized model of a real process, which only approximately reflects reality.
The process of changing the state of a thermodynamic system of macroscopic bodies at a constant temperature is called isothermal.
To maintain a constant gas temperature, it is necessary that it can exchange heat with a large system - a thermostat. Otherwise, during compression or expansion, the temperature of the gas will change. Can serve as a thermostat atmospheric air, if its temperature does not change noticeably throughout the entire process.
According to the equation of state of an ideal gas in any state with constant temperature the product of gas pressure and its volume remains constant: pV=const at T=const. For a gas of a given mass, the product of the gas pressure and its volume is constant if the gas temperature does not change.
This law was experimentally discovered by the English scientist R. Bouler (1627 - 1691) and somewhat later by the French scientist E. Mariotte (1620 -1684). Therefore, it is called the Boyle-Mariotte law.
The Boyle-Mariotte law is valid for any gases, as well as their mixtures, for example for air. Only at pressures several hundred times greater than atmospheric pressure does the deviation from this law become significant.
The dependence of gas pressure on volume at a constant temperature is graphically depicted by a curve called an isotherm. The gas isotherm depicts the inverse relationship between pressure and volume. In mathematics, a curve of this kind is called a hyperbola.
Different constant temperatures correspond to different isotherms. As the temperature increases, the pressure according to the equation of state increases if V=const. Therefore, the isotherm corresponding to a higher temperature T 2 , lies above the isotherm corresponding to the lower temperature T 1 .
An isothermal process can be approximately considered the process of slow compression of air during the expansion of gas under the pump piston when pumping it out of the vessel. True, the temperature of the gas changes, but to a first approximation this change can be neglected
The process of changing the state of a thermodynamic system at constant pressure is called isobaric (from the Greek “baros” - weight, heaviness).
According to the equation, in any state of a gas with constant pressure, the ratio of the gas volume to its temperature remains constant: =const at p=const.
For a gas of a given mass, the ratio of volume to temperature is constant if the gas pressure does not change.
This law was established experimentally in 1802 by the French scientist J. Gay-Lussac (1778 - 1850) and is called Gay-Lussac's law.
According to the equation, the volume of gas depends linearly on temperature at constant pressure: V=const T.
This relationship is graphically represented by a straight line called an isobar. Different pressures correspond to different isobars. With increasing pressure, the volume of gas at a constant temperature decreases according to the Boyle-Mariotte law. Therefore, the isobar corresponding to a higher pressure p 2 , lies below the isobar corresponding to the lower pressure p 1 .
In the area low temperatures all isobars of an ideal gas converge at the point T=0. But this does not mean that the volume of real gas actually vanishes. All gases turn into liquid when strongly cooled, and the equations of state are not applicable to liquids.
The process of changing the state of a thermodynamic system at a constant volume is called isochoric (from the Greek “horema” - capacity).
It follows from the equation of state that in any state of a gas with a constant volume, the ratio of gas pressure to its temperature remains unchanged: =const at V=const.
For a gas of a given mass, the ratio of pressure to temperature is constant if the volume does not change.
This gas law was established in 1787 by the French physicist J. Charles (1746 - 1823) and is called Charles's law. According to the equation:
Const at V=const gas pressure linearly depends on temperature at constant volume: p=const T.
This dependence is depicted by a straight line called an isochore.
Different isochores correspond to different volumes. As the volume of a gas increases at a constant temperature, its pressure decreases according to the Boyle-Mariotte law. Therefore, the isochore corresponding to the larger volume V 2 , lies below the isochore corresponding to the smaller volume V 1 .
According to the equation, all isochores begin at the point T=0.
This means that the pressure of an ideal gas at absolute zero is zero.
An increase in gas pressure in any container or light bulb when heated is an isochoric process. The isochoric process is used in constant-volume gas thermostats.
4. Temperature.
Any macroscopic body or group of macroscopic bodies is called a thermodynamic system.
Thermal or thermodynamic equilibrium is a state of a thermodynamic system in which all its macroscopic parameters remain unchanged: volume, pressure do not change, heat exchange does not occur, there are no transitions from one state of aggregation to another, etc. Under constant external conditions, any thermodynamic system spontaneously goes into a state of thermal equilibrium.
Temperature - physical quantity, characterizing the state of thermal equilibrium of a system of bodies: all bodies of the system that are in thermal equilibrium with each other have the same temperature.
Absolute zero temperature is the limiting temperature at which the pressure of an ideal gas at constant volume must be equal to zero or the volume of an ideal gas at constant pressure must be equal to zero.
Thermometer is a device for measuring temperature. Typically, thermometers are calibrated on the Celsius scale: the crystallization temperature of water (ice melting) corresponds to 0°C, its boiling point - 100°C.
Kelvin introduced the absolute temperature scale, according to which zero temperature corresponds to absolute zero, the unit of temperature on the Kelvin scale is equal to the degree Celsius: [T] = 1 K (Kelvin).
Relationship between temperature in energy units and temperature in Kelvin:
where k = 1.38*10 -23 J/K - Boltzmann's constant.
Relationship between the absolute scale and the Celsius scale:
T = t + 273, where t - temperature in degrees Celsius.
The average kinetic energy of the chaotic movement of gas molecules is proportional to the absolute temperature:
Taking into account equality (1), the basic equation of molecular kinetic theory can be written as follows: p = nkT.
Basic equations of the molecular kinetic theory of an ideal gas for pressure.
A gas is called ideal if:
1) the intrinsic volume of gas molecules is negligible compared to the volume of the container;
2) there are no interaction forces between gas molecules;
3) collisions of gas molecules with the walls of the vessel are absolutely elastic.
Real gases (for example, oxygen and helium) under conditions close to normal, as well as at low pressures and high temperatures, are close to ideal gases. Particles of an ideal gas move uniformly and rectilinearly in the intervals between collisions. The gas pressure on the walls of a vessel can be considered as a series of rapidly successive impacts of gas molecules on the wall. Let's look at how to calculate the pressure caused by individual impacts. Let us imagine that a series of separate and frequent impacts occur on a certain surface. Let's find such an average constant force
Where t 1, t 2, t 3 ... t n - interaction time of the first, second, ..., nth molecules with a wall (i.e. duration of impact); f 1, f 2, f 3 ... f n - the force of impact of molecules on the wall. From this formula it follows:
(7).
The average pressure force caused by a series of individual impacts on a certain surface is numerically equal to the sum of the impulses of all impacts received by this surface per unit time is called an isochore.
5. Velocities of gas molecules.
Formula (12) can be written as:
(15), where (gas mass).
From expression (15) we calculate the root mean square speed of gas molecules:
(16) .
Knowing that (R-universal gas constant; R=8.31), we obtain new expressions for determining
(17) .
An experimental determination of the speed of movement of silver vapor molecules was first carried out in 1920 by Stern.
Rice. 5. Stern's experience.
Air was pumped out of glass cylinder E (Fig. 5). Inside this cylinder was placed a second cylinder D, which had a common axis O with it. Along the generatrix of the cylinder D there was a slot in the form of a narrow slit C. A silver-plated platinum wire was stretched along the axis, through which current could be passed. At the same time, the wire became heated, and the silver from its surface turned into steam. The molecules of silver vapor scattered in different directions, some of them passed through the slot C of cylinder D and a silver coating in the form of a narrow strip was obtained on the inner surface of cylinder E. In Fig. 5, the position of the silver strip is marked with the letter A.
When the entire system was set into very rapid motion in such a way that the wire was the axis of rotation, then strip A on cylinder E turned out to be shifted to the side, i.e. for example, not at point A, but at point B. This happened because while the silver molecules were flying along the path CA, point A of cylinder E had time to rotate by a distance AB and the silver molecules ended up not at point A, but at point B.
Let us denote the displacement value of the silver strip AB = d; the radius of the cylinder E through R, the radius of the cylinder D through r, and the number of revolutions of the entire system per second through n.
For one revolution of the system, point A on the surface of cylinder E will go the way, equal to the circumference of the circle 2πR, and in 1 second it will cover the distance. The time t during which point A moved to a distance AB = d will be equal to:. During time t, the silver vapor molecules flew a distance CA = R - r . The speed of their movement v can be found as the distance traveled divided by the time:or, replacing t, we get:
.
The silver deposit on the wall of cylinder D turned out to be blurry, which confirmed the presence of different speeds of molecular movement. From experience, it was possible to determine the most probable speed v ver which corresponded to the greatest thickness of silver plaque.
The most probable speed can be calculated using the formula given by Maxwell:(18). According to Maxwell's calculations, the arithmetic average speed of movement of molecules is equal to:
(19).
6. The equation of state of an ideal gas is the Mendeleev-Clapeyron equation.
From the basic equation of molecular kinetic theory (formula (14)) follows Avogadro’s law: equal volumes of dissimilar gases under the same conditions (same temperature and same pressure) contain the same number of molecules:(for one gas),(for other gas).
If V 1 = V 2 ; T 1 = T 2; r 1 = r 2, then n 01 = n 02.
Recall that the SI unit of quantity of a substance is the mole (gram molecule) mass m One mole of a substance is called the molar mass of that substance. The number of molecules contained in one mole of different substances is the same and is called Avogadro's number (N A = 6.0210 23 1/mol).
Let us write the equation of state of an ideal gas for one mole:, where V m - volume of one mole of gas;, where V m - volume of one mole of gas; (universal gas constant).
Finally we have: (26).
Equation (26) is called the Clapeyron equation (for one mole of gas). Under normal conditions (p = 1.01310 5 Pa and T = 273.15 0 K) molar volume of any gas V m = 22.410 -3 . From formula (26) we determine;
.
From equation (26) for a mole of gas one can go to the Mendeleev-Clapeyron equation for any gas mass m.
Attitude gives the number of moles of gas. We multiply the left and right sides of inequality (26) by.
We have 
, where is the volume of gas.
Let's finally write: (27 ) . Equation (27) is the Mendeleev-Clapeyron equation. The gas density can be entered into this equation And .
In formula (27) we replace V and get or .
7. Experimental gas laws. Pressure of a mixture of ideal gases (Dalton's law).
Experimentally, long before the advent of molecular kinetic theory, it was discovered a whole series laws describing equilibrium isoprocesses in an ideal gas. An isoprocess is an equilibrium process in which one of the state parameters does not change (constant). There are isothermal (T = const), isobaric (p = const), isochoric (V = const) isoprocesses. An isothermal process is described by the Boyle-Marriott law: “if during the process the mass and temperature of an ideal gas do not change, then the product of the gas pressure and its volume is a constant PV = const (29). Graphic image equations of state are called state diagrams. In the case of isoprocesses, phase diagrams are depicted as two-dimensional (flat) curves and are called isotherms, isobars and isochores, respectively.
Isotherms corresponding to two different temperatures are shown in Fig. 6.
Rice. 6. Isotherms corresponding to two different temperatures.
An isobaric process is described by the Gay-Lussac law: “if during the process the pressure and mass of an ideal gas do not change, then the ratio of the volume of the gas to its absolute temperature is a constant:(30).
Isobars corresponding to two different pressures are shown in Fig. 7.
Rice. 7. Isobars corresponding to two different pressures.
The equation of the isobaric process can be written differently:
31), where V 0 - volume of gas at 0 0 C; V t - volume of gas at t 0
C; t is the gas temperature in degrees Celsius;α
- coefficient of volumetric expansion. From formula (31) it follows that. The experiments of the French physicist Gay-Lussac (1802) showed that the coefficients of volumetric expansion of all types of gases are the same and, i.e. when heated by 1 0
C gas increases its volume by a fraction of the volume it occupied at 0 0
C. In Fig. Figure 8 shows a graph of gas volume V t on temperature t 0 C.
Rice. 8. Graph of gas volume V t on temperature t 0 C.
An isochoric process is described by Charles’ law: “if during the process the volume and mass of an ideal gas do not change, then the ratio of the gas pressure to its absolute temperature is a constant:
(32).
Isochores corresponding to two different volumes are shown in Fig. 9.
Rice. 9. Isochores corresponding to two different volumes.
The equation of the isochoric process can be written differently:
(33), where - gas pressure at WITH; - gas pressure at t; t is the gas temperature in degrees Celsius;- temperature coefficient pressure. From formula (33) it follows that. For all gases and 
. If the gas is heated toC (at V=const), then the gas pressure will increase bypart of the pressure he had whenC. Figure 10 shows a graph of gas pressure versus temperature t.
Rice. 10. Graph of gas pressure versus temperature t.
If we continue line AB until it intersects the x axis (point), then the value of this abscissa is determined from formula (33), ifequate to zero.
;
Therefore, at temperaturethe pressure of the gas should have gone to zero, however, with such cooling the gas will not retain its gaseous state, but will turn into a liquid and even into a solid. Temperatureis called absolute zero.
In the case of a mechanical mixture of gases that do not enter into chemical reactions, the mixture pressure is also determined by the formula
, Where (mixture concentrationequal to the sum of the concentrations of the components of a mixture of only n - components).
Dalton's law states: Mixture pressureequal to the sum of the partial pressures of the gases forming the mixture.. Pressure 
called partial. Partial pressure is the pressure that a given gas would create if it alone occupied the vessel in which the mixture is located (in the same amount as it is contained in the mixture).
REFERENCES
1. Brychkov Yu.A., Marichev O.I., Prudnikov A.P. Tables indefinite integrals: Directory. - M.: Nauka, 1986.
2. Kogan M.N. Dynamics of rarefied gas. M., Fizmatlit, 1999.
3. Kikoin A.K., Molecular physics. M., Fizmatlit, 1976.
4. Sivukhin D.V. General course physics, vol. 2. Thermodynamics and molecular physics. M., Fizmatlit, 1989.
5. Kiryanov A.P., Korshunov S.M. Thermodynamics and molecular physics. A manual for students. Ed. prof. HELL. Gladuna. - M., “Enlightenment”, 1977.
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We are surrounded by various objects. We can see that they are either solids, liquids or gases. A lot of questions arise about everything that surrounds us. Provides answers to many questions molecular kinetic theory.
Molecular kinetic theory is a set of views used to describe the observable and measurable properties of a substance based on the study of the properties of atoms and molecules of a given substance, their interaction and movement.
Basic principles of molecular kinetic theory
All bodies consist of particles - atoms, molecules, ions.
All particles are in continuous chaotic thermal motion.
Between the particles of any body there are forces of interaction - attraction and repulsion.
Thus, in molecular kinetic theory, the object of study is a system consisting of a large number of particles - macrosystem. The laws of mechanics are not applicable to explain the behavior of such a system. Therefore, the main research method is statistical method studying the properties of matter.
To explain and predict phenomena it is important to know main characteristics of molecules:
- Dimensions
An estimate of the size of a molecule can be made as the size of a cube a containing one molecule, based on the density of solids or liquid substances and the mass of one molecule:
- Mass of molecules
Substance mass ratio m to the number of molecules N in this substance:
- Relative molecular weight
The ratio of the mass of a molecule (or atom) of a given substance to 1/12 of the mass of a carbon atom:
- Quantity of substance
The amount of substance is equal to the ratio of the number of particles N in a body (atoms - in an atomic substance, molecules - in a molecular substance) to the number of molecules in one mole of a substance NA:
- Avogadro's constant
The number of molecules contained in 1 mole of a substance.
- Molar mass
The molar mass of a substance is the mass of a substance taken in an amount of 1 mole.
IN International system units the molar mass of a substance is expressed in kg/mol.
- Interaction (quantitatively based on experiments)
The interaction of molecules is characterized by both attraction and repulsion: at distances r
The molecular kinetic theory makes it possible to understand why a substance can exist in gaseous, liquid and solid states. From the point of view of MKT states of aggregation vary in the value of the average distance between molecules and the nature of the movement of molecules relative to each other.
The basic provisions of the molecular kinetic theory have been repeatedly confirmed by various physical experiments. For example, research:
A) Diffusion
B) Brownian motion
Brief summary
Molecular kinetic theory explains the structure and properties of bodies based on the movement and interaction of atoms, molecules and ions. MCT is based on three positions, which are fully confirmed experimentally and theoretically:
1) all bodies consist of particles - molecules, atoms, ions;
2) particles are in continuous chaotic thermal motion;
3) between particles of any body there are forces of interaction - attraction and repulsion.
The molecular structure of a substance is confirmed by direct observation of molecules in electron microscopes, as well as by the dissolution of solids in liquids, the compressibility and permeability of the substance. Thermal motion – Brownian motion and diffusion. The presence of intermolecular interaction with the strength and elasticity of solids, surface tension liquids.
Basic notes for the lesson:
Questions for self-control in the block “Basic principles of molecular kinetic theory and their experimental justification”
- Formulate the main provisions of the molecular kinetic theory.
- What observations and experiments confirm the main provisions of the molecular kinetic theory?
- What is a molecule? atom?
- What is relative molecular weight called? What formula expresses this concept?
- What is the quantity of a substance called? What formula expresses this concept? What is the unit of quantity of a substance?
- What is Avogadro's constant called?
- What is the molar mass of a substance? What formula expresses the meaning of this concept? What is the unit molar mass?
- What is the nature of intermolecular forces?
- What properties do molecular interaction forces have?
- How do interaction forces depend on the distance between them?
- Describe the nature of molecular motion in gases, liquids and solids.
- What is the nature of particle packing in gases, liquids and solids?
- What is the average distance between molecules for gases, liquids and solids?
- List the basic properties of gases, liquids, and solids.
- What is called Brownian motion?
- What does Brownian motion indicate?
- What is diffusion called? Give examples of diffusion in gases, liquids and solids.
- 18. How does the rate of diffusion depend on the temperature of bodies?
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 of which the bodies are composed. The MCT structure of matter is based on three principles:
- Matter consists of particles - molecules, atoms and ions. These particles contain smaller elementary particles. A molecule is the smallest stable particle of a given substance. The molecule has the basic chemical properties of a substance. 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.
- The particles that make up matter are in continuous chaotic (disorderly) motion.
- 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). The sizes of molecules are larger than the sizes of atoms. Since molecules are made up of several atoms, the greater the number of 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. By 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 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), repulsion forces Fr 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 in 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.
Definition 1
Molecular kinetic theory is the doctrine of the structure and properties of matter, based on the idea of the existence of atoms and molecules, as the smallest particles of chemical substances.
Basic principles of the molecular kinetic theory of a molecule:
- All substances can be in liquid, solid and gaseous states. They are formed from particles that are made up of atoms. Elementary molecules can have complex structure, that is, to have several atoms in its composition. Molecules and atoms are electrically neutral particles that, under certain conditions, acquire additional electric charge and become positive or negative ions.
- Atoms and molecules move continuously.
- Particles with electrical nature forces interact with each other.
The main provisions of the ICT and their examples were listed above. There is little gravitational influence between the particles.
Figure 3. 1. 1. Trajectory of a Brownian particle.
Definition 2
The Brownian motion of molecules and atoms confirms the existence of the basic principles of molecular kinetic theory and experimentally substantiates it. This thermal movement of particles occurs with molecules suspended in a liquid or gas.
Experimental substantiation of the main provisions of the molecular kinetic theory
In 1827, R. Brown discovered this movement, which was caused by random impacts and movements of molecules. Since the process occurred chaotically, the blows could not balance each other. Hence the conclusion is that the speed of a Brownian particle cannot be constant, it is constantly changing, and the directional movement is depicted in the form of a zigzag, shown in Figure 3. 1. 1.
A. Einstein spoke about Brownian motion in 1905. His theory was confirmed in the experiments of J. Perrin in 1908 - 1911.
Definition 3
Corollary of Einstein's theory: offset square< r 2 >Brownian particle relative to the initial position, averaged over many Brownian particles, is proportional to the observation time t.
Expression< r 2 >= D t explains the diffusion law. According to theory, we have that D increases monotonically with increasing temperature. Random movement is visible in the presence of diffusion.
Definition 4
Diffusion- this is the definition of the phenomenon of penetration of two or more contacting substances into each other.
This process occurs quickly in a heterogeneous gas. Thanks to examples of diffusion with different densities, a homogeneous mixture can be obtained. When oxygen O2 and hydrogen H2 are in the same vessel with a partition, when it is removed, the gases begin to mix, forming a dangerous mixture. The process is possible when hydrogen is at the top and oxygen is at the bottom.
Interpenetration processes also occur in liquids, but much slower. If we dissolve a solid, sugar, in water, we obtain a homogeneous solution, which is a clear example of diffusion processes in liquids. Under real conditions, mixing in liquids and gases is masked by rapid mixing processes, for example, when convection currents occur.
The diffusion of solids is characterized by its slow speed. If the surface of interaction between metals is cleaned, you can see that over a long period of time atoms of another metal will appear in each of them.
Definition 5
Diffusion and Brownian motion are considered related phenomena.
When particles of both substances interpenetrate, the movement is random, that is, chaotic thermal movement of molecules is observed.
The forces acting between two molecules depend on the distance between them. Molecules contain positive and negative charges. At large distances, the forces of intermolecular attraction predominate; at small distances, the forces of repulsion predominate.
Drawing 3 . 1 . 2 shows the dependence of the resulting force F and potential energy E p of interaction between molecules on the distance between their centers. At a distance r = r 0, the interaction force becomes zero. This distance is conventionally taken as the diameter of the molecule. When r = r 0 potential energy interaction is minimal.
Definition 6
To move two molecules apart with a distance r 0, you should communicate E 0, called binding energy or potential well depth.
Figure 3. 1. 2.The power of interaction F and potential energy of interaction E r two molecules. F > 0– repulsive force, F< 0 – force of attraction.
Since molecules are small in size, simple monatomic ones can be no more than 10 - 10 m. Complex ones can reach sizes hundreds of times larger.
Definition 7
The random chaotic movement of molecules is called thermal movement.
As temperature increases, the kinetic energy of thermal motion increases. At low temperatures, the average kinetic energy, in most cases, turns out to be less than value depth of the potential well E 0 . This case shows that molecules flow into liquid or solid with an average distance between them r 0 . If the temperature rises, then the average kinetic energy of the molecule exceeds E 0, then they fly apart and form a gaseous substance.
In solids, molecules move randomly around fixed centers, that is, equilibrium positions. They can be distributed in space in an irregular manner (in amorphous bodies) or with the formation of ordered volumetric structures (crystalline bodies).
Aggregate states of substances
The freedom of thermal movement of molecules is visible in liquids, since they are not tied to centers, which allows movement throughout the entire volume. This explains its fluidity.
Definition 8
If the molecules are located closely, they can form ordered structures with several molecules. This phenomenon is called short-range order. Long range order characteristic of crystalline bodies.
The distance between molecules in gases is much greater, so active forces are small, and their movements go along a straight line, awaiting the next collision. The value of 10 – 8 m is the average distance between air molecules under normal conditions. Since the interaction of forces is weak, the gases expand and can fill any volume of the vessel. When their interaction tends to zero, they speak of an ideal gas.
Kinetic model of an ideal gas
In µt, the amount of substance is considered proportional to the number of particles.
Definition 9
Mole is the amount of substance containing as many particles (molecules) as there are atoms in 0.012 kg of carbon C12. A carbon molecule consists of one atom. It follows that 1 mole of a substance has the same number of molecules. This number called constant Avogadro N A: N A = 6.02 ċ 1023 mol – 1.
Formula for determining the amount of a substance ν is written as the ratio N of the number of particles to Avogadro’s constant N A: ν = N N A .
Definition 10
Mass of one mole of substance is called the molar mass M. It is fixed in the form of the formula M = N A ċ m 0.
The expression of molar mass is made in kilograms per mole (kg/mol).
Definition 11
If a substance contains one atom, then we can talk about the atomic mass of the particle. A unit of an atom is 1 12 masses of the carbon isotope C 12, called atomic mass unit and is written as ( A. e.m.): 1 a. e.m. = 1.66 ċ 10 – 27 kg.
This value coincides with the mass of the proton and neutron.
Definition 12
The ratio of the mass of an atom or molecule of a given substance to 1 12 mass of a carbon atom is called relative mass.
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