Features of the molecular structure of liquids

The liquid occupies an intermediate position in properties and structure between gases and solid crystalline substances. Therefore, it has the properties of both gaseous and solids. In the molecular kinetic theory, various aggregate states of a substance are associated with a different degree of ordering of molecules. For solids, the so-called long range order in the arrangement of particles, i.e. their orderly arrangement, repeating over long distances. In liquids, the so-called short range order in the arrangement of particles, i.e. their ordered arrangement, repeating at distances, is comparable with interatomic ones. At temperatures close to the crystallization temperature, the liquid structure is close to that of a solid. At high temperatures, close to the boiling point, the structure of the liquid corresponds to the gaseous state - almost all molecules participate in chaotic thermal motion.

Liquids, like solids, have a certain volume, and like gases, they take the shape of the vessel in which they are located. Gas molecules are practically not interconnected by the forces of intermolecular interaction, and in this case the average energy thermal motion gas molecules are much greater than the average potential energy due to the forces of attraction between them, so the gas molecules scatter in different directions and the gas occupies the volume provided to it. In solid and liquid bodies, the forces of attraction between molecules are already significant and keep the molecules at a certain distance from each other. In this case, the average energy of the thermal motion of molecules is less than the average potential energy due to the forces of intermolecular interaction, and it is not enough to overcome the forces of attraction between molecules, so solids and liquids have a certain volume.

The pressure in liquids increases very sharply with increasing temperature and decreasing volume. The volumetric expansion of liquids is much less than that of vapors and gases, since the forces that bind molecules in a liquid are more significant; the same remark applies to thermal expansion.

The heat capacities of liquids usually increase with temperature (albeit slightly). The C p /C V ratio is practically equal to one.

The theory of fluid has not been fully developed to date. The development of a number of problems in the study of the complex properties of a liquid belongs to Ya.I. Frenkel (1894–1952). He explained the thermal motion in a liquid by the fact that each molecule oscillates for some time around a certain equilibrium position, after which it jumps to a new position, which is at a distance of the order of the interatomic distance from the initial one. Thus, the molecules of the liquid move quite slowly throughout the mass of the liquid. With an increase in the temperature of the liquid, the frequency of oscillatory motion increases sharply, and the mobility of molecules increases.

Based on the Frenkel model, it is possible to explain some distinctive features properties of the liquid. Thus, liquids, even near the critical temperature, have a much greater viscosity than gases, and the viscosity decreases with increasing temperature (rather than increases, as in gases). This is explained by a different nature of the momentum transfer process: it is transferred by molecules that jump from one equilibrium state to another, and these jumps become much more frequent with increasing temperature. Diffusion in liquids occurs only due to molecular jumps, and it occurs much more slowly than in gases. Thermal conductivity liquids is due to the exchange of kinetic energy between particles oscillating around their equilibrium positions with different amplitudes; sharp jumps of molecules do not play a noticeable role. The mechanism of heat conduction is similar to its mechanism in gases. characteristic feature liquid is its ability to have free surface(not limited by solid walls).

Several theories have been proposed for the molecular structure of liquids.

1. Zone model. AT this moment time, a liquid can be considered as consisting of regions where the molecules are arranged in the correct order, forming a kind of microcrystal (zone). These areas are, as it were, separated by a substance in a gaseous state. Over time, these areas form in other places, and so on.

2. The theory of quasi-crystalline structure. Consider a crystal at absolute zero temperature (see Fig. 9.9.)

We select an arbitrary direction in it and plot the dependence of the probability P of finding a gas molecule at a certain distance from another molecule placed at the origin (Fig. 9.9. a), while the molecules are located at the nodes of the crystal lattice. At a higher temperature (Fig. 9.9, b) molecules oscillate around fixed equilibrium positions, near which they spend most of their time. The strict periodicity of the repetition of probability maxima in an ideal crystal extends arbitrarily far from the chosen particle; therefore, it is customary to say that a "long-range order" exists in a solid.

In the case of a liquid (Fig. 9.9, in) near each molecule, its neighbors are located more or less regularly, but far away this order is violated (short-range order). On the graph, the distances are measured in fractions of the radius of the molecule (r/r 0).

DISTRIBUTION OF MOLECULES IN A POTENTIAL FIELD

GRAVITY FORCES (BOLTZMANN DISTRIBUTION)

When deriving the basic equation of the MKT of gases and the Maxwell distribution, it was assumed that external forces do not act on gas molecules, which means that the molecules are distributed uniformly over the volume. However, the molecules of any gas are always in the potential field of the Earth's gravity. Gravity, on the one hand, and thermal motion of molecules, on the other hand, lead to a certain stationary state, in which the gas pressure decreases with increasing height.

Let's get the law of pressure change with height, assuming that over the entire height: the gravitational field is uniform (g = const); the temperature is the same (T = const); the masses of all molecules are the same.

Let the pressure p be at height h. Then at height h + dh the pressure is p + dp. Moreover, if dh >0, then dp< 0. (р + dp) – р = – r·g·dh. Из уравнения состояния Менделеева-Клапейрона, имеем:

Now or .

Let's integrate the right and left sides:

; .

Where, . (26)

This is the so-called barometric formula. It allows you to determine the pressure of the atmosphere as a function of altitude above sea level:

. (27)

Because pressure is directly proportional to the concentration of molecules, then you can get the law of change in the concentration of molecules with height, provided that the temperature does not change with height (T = const):

. (28)

Considering that M = m∙N A , and R = k∙N A from (27) we get:

Because mgh = U(h) is the potential energy of one molecule at height h, then

(30)

is the Boltzmann distribution.

NUMBER OF COLLISIONS AND AVERAGE FREE PATH OF IDEAL GAS MOLECULES.

As a result of chaotic motion, gas molecules continuously collide with each other. Between two successive collisions, the molecule travels a certain path λ, which is called the mean free path . In the general case, the length of this path is different, but since the number of collisions is very large, and the movement is random, then under constant external conditions we can talk about medium length free run - . If the molecules of a given gas experience 1 second on average collisions, then

where is the arithmetic mean velocity of molecules.

We consider ideal gas molecules as spheres. Obviously, a collision will occur if two molecules approach up to a distance equal to two radii, i.e., the diameter of the molecules d. Minimum distance, by which the centers of two molecules approach during a collision, is called the effective diameter of the molecules. This parameter depends on , and hence on the gas temperature.

To define, imagine a molecule with an effective diameter d, which moves with a speed among other molecules, which at the same time remain motionless. This molecule will collide with all molecules whose centers lie inside a "broken" cylinder of radius d. This means that is equal to the number of molecules in the volume of this cylinder

where n is the concentration of molecules, and V is the volume of the cylinder: . With this in mind -

. (32)

Taking into account the motion of other molecules increases the number of collisions by a factor. Finally, for z we get:

. (33)

Then (34)

Because p ~ n, then for different external conditions we have:

For air at n.o. (p \u003d 760 mm Hg; t 0 \u003d 0 0 С): z \u003d 10 9 s -1, a \u003d 5 ∙ 10 -8 m.

TRANSFER PHENOMENA

In thermodynamically nonequilibrium systems, i.e. in systems for which the values ​​of macroparameters (T, p, ) are different at its different points, irreversible processes occur, which are called transport phenomena . As a result of such processes, energy is transferred from one local area of ​​the system to another (the phenomenon of thermal conductivity), mass (the phenomenon of diffusion), momentum (internal friction), charge, etc. This leads to the alignment of the values ​​of macroparameters by the volume of the system. It is clear that the transfer of any value is explained by the transition from place to place of a certain number of particles (molecules and atoms) as a result of their chaotic movement.

We obtain the general transport equation along an arbitrary direction. Let's direct the axis O along it X(Figure 3). Let us mentally single out an element of the plane with area ∆S, perpendicular to O X. Due to the randomness of the movement during the time ∆t through ∆S in the direction of O X move N particles:

(1)

Here n is the concentration of molecules (atoms), and is their arithmetic mean velocity. Passing through ∆S, each molecule transfers its inherent mass, charge, momentum, energy, or some other of its characteristics. Let us denote the value of the quantity carried by one molecule by the letter φ. Then during the time ∆t through the area ∆S in the direction of the O axis X quantity will be transferred physical quantity

(2).

Obviously, if the concentration on the right is also n, then the same number of particles will move from right to left. Those. the resulting carry in this case zero: ∆N = 0 and ∆Nφ = 0.

If the medium is inhomogeneous, i.e. either the concentration of particles or the values ​​of φ for particles on the left and right are not the same, then transitions from regions where the value of (nφ) is larger to the region where it is smaller will be more likely. If we assume that (nφ) 1 > (nφ) 2, then the resulting transfer of the value of φ will be determined by the relation: . (3)

The minus sign in (3) reflects the fact that the value (nφ) decreases in the transfer direction.

Let us find out at what distance from ∆S on the left and right the values ​​(nφ) should be taken. Because change physical characteristics molecules occurs only during collisions, and before the collision each of the molecules has traveled a distance equal to the free path, then we can assume that (nφ) molecules remain unchanged at a distance equal to the free path to the left and right of ∆S. Divide and multiply the right side of (3) by 2:

The distribution of quantities along any direction is determined by a characteristic called the gradient. A gradient is a change in magnitude over a distance equal to a unit length.

In this case, at the point with coordinate X 2 the value of the transferable value is (nφ) 2, and at the point X 1 – (nφ) 1 , then under the gradient of the value nφ, transferred along the O axis X, one should understand the relationship:

.

Then the gradient of nφ in the region ∆S.

. (5)

(5) is the general transfer equation.

Diffusion is the transfer of mass of matter . Provided that the masses of the molecules are the same (m 0 = const), the gas temperature is the same in volume (T = const) and the distribution of velocities is uniform over the volume ( = const), substituting the mass of the molecule in (5) instead of φ, we obtain:

Or . (6)

This is Fick's law. D = is the diffusion coefficient. [D] \u003d m 2 / s.

Thermal conductivity is the transfer of energy . Provided that the concentration of molecules over the entire volume of gas (n \u003d const), the masses of the molecules are the same (m 0 \u003d const), the distribution of velocities over the volume is uniform ( \u003d const), and the average kinetic energy of the translational motion of one molecule, we get the Fourier law:

, or . (7)

- coefficient of thermal conductivity. [χ] \u003d W / (m K) \u003d kg m / (s 3 K).

Viscosity is the transfer of momentum between parallel layers that move in an orderly manner at velocities u 1 and u 2. Provided that over the entire volume of the gas the concentration of molecules is n = const, the masses of the molecules are the same (m 0 = const), the distribution of velocities over the volume is uniform ( = const), and the momentum modulus of one molecule, associated with the speed of the ordered movement of the layers φ = p = m 0 u, for the momentum of the interaction force of the layers we have:

Or . ()

This is Newton's equation, which determines the magnitude of the force of internal friction (viscosity). is the transverse velocity gradient characterizing the rate of change of velocity in the direction X perpendicular to the movement of the rubbing layers. η – dynamic coefficient of viscosity . [η] = Pa s.

MOLECULAR FORCES

The forces of interaction between molecules, or, as they are also called, Van der Waals forces, are electrical in nature. These are the Coulomb forces of interaction of charged particles that make up atoms and molecules. They appear at distances commensurate with the size of the molecules themselves and decrease very quickly with increasing distance. At the same time, attractive forces (interaction of opposite charges) and repulsive forces (interaction of like charges) act simultaneously. Because real particles are not point, then the magnitude of these forces depends on the distance between them in different ways.

There are three types of van der Waals forces:

a) orientation - act between polar molecules:

,

where р is the electric dipole moment of the particles, r is the distance between them, k is the Boltzmann constant, Т is the thermodynamic temperature.

b) induction – describe the interaction of molecules, polarization

charges in which arises under the influence of electric fields of neighboring particles:

.

Here: р ind = ε 0 αЕ – acquired electric dipole moment of particles; α is the polarizability of molecules.

in) dispersion - determine the interaction of molecules, in which an asymmetric charge distribution occurs randomly, in the process of electrons moving along orbits, which leads to the formation of instantaneous dipoles:

.

In general, all three types of forces can act simultaneously:

F m \u003d F o + F and + F d.

Let us consider the dependence of intermolecular interaction forces on distance. The forces of attraction F pr are considered negative, and the forces of repulsion F from are considered positive. The sum of these forces gives the resultant - Fres = f(r). At some distance r 0 between the molecules |F pr | = |F from | and the resulting force F \u003d F pr + F from \u003d 0. If r< r 0 , то преобладают силы отталкивания. Если r >r 0 , then the forces of attraction prevail. However, at a distance of r > 10 -9 m, the van der Waals forces quickly tend to zero.

The system of interacting molecules is characterized by a certain reserve of potential energy, which depends on r in a complex way, E p = f(r):

r → ∞ – E p → 0 ;

r > r 0 and r → r 0 - E p → E p min, E p< 0 ;

r \u003d r 0 - E p \u003d E p min, E p< 0;

r< r 0 и уменьшается – Е п → ∞, Е п > 0.

The smallest potential energy of interaction is called the binding energy of molecules. It is equal to the work that must be done against the forces of attraction in order to separate molecules that are in equilibrium.

The ratio of the minimum potential energy (E p min) and the value of the doubled average energy of thermal motion per one degree of freedom is a criterion for the state of aggregation of a substance. If a:

a) E p min<< kT – газ;

b) E p min » kT – liquid;

c) E p min >> kT is a solid body.

Thus, any substance, depending on the temperature, can be in a gaseous, liquid or solid state of aggregation.

STRUCTURAL FEATURES OF GASES, LIQUIDS AND SOLID BODIES

R.N. Grabovsky. Physics course. 1980, pp. 168-174.

REAL GASES

The equations of the molecular kinetic theory quite well describe the behavior of real gases at a sufficiently high temperature and low pressure. This is understandable, because such a state real gas closest to the ideal gas model, on the basis of which all the conclusions of the MKT are obtained. However, with increasing pressure and decreasing temperature, the average distance between molecules decreases and the forces of molecular interaction increase. For example, at n.o. the volume of molecules is 1/10000 of the volume occupied by the gas, and at a pressure of 500 atm (500 MPa) it will already be half of the total volume of gas. It is quite obvious that under these conditions the laws of the MKT cease to work, for example, PV ¹ const at T = const.

Thus, the task is to obtain such an equation of state for a real gas that would take into account the volume of molecules and their interaction.

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In the problems in this section, they mainly emphasize the idea that the molecules in gases are located at greater distances than in liquids and solids, the forces of attraction between them are insignificant, and therefore gases occupy a large volume. (A similar statement with respect to liquids and solids is, generally speaking, false. For solids, the order of the molecules is also of great importance.)

The second concept that is formed in grade VI when solving problems in this section is the difference in the nature of the movement of molecules in gases, liquids and solids.

58(e). By moving the stopper in the potato gun with a stick (Fig. 14), observe the decrease in air volume. Do the same experiment, filling the tube with water. Explain the difference in compressibility between water and air based on the molecular structure of the substances.

59. How to explain that the steam produced by boiling water occupies about 1700 times more volume than water at the boiling point?

Answer. Vapor molecules are located at such great distances from each other that the attractive forces between them are insignificant and therefore cannot cause vapor condensation at a given temperature (at a given molecular speed).

60(e). Pour half the water into a meter glass tube, and alcohol on top and then mix them. How did the volume of liquid change after that? Explain why.

Answer. The total volume decreased as a result of the denser packing of the molecules.

61. Scientist Bridgman squeezed oil in a steel cylinder with great force. How to explain that oil particles protruded on the outer walls of the cylinder, although there were no cracks in them?

62. If you press the plates of lead and gold together, then after a while you can find lead molecules in gold, and gold molecules in lead. Explain why.

Solution of problems 61 and 62. In solids and liquids, there are small gaps between molecules, despite their dense packing. Molecules move primarily by vibration. The picture is reminiscent of people in a crowded bus, who, despite the tightness, move around, changing places with each other or passing through randomly formed passages.

63(e). Examine the mica plate and split it into thinner leaves. Break and examine the pieces of a large table salt. How can the unequal properties of mica and salt in different directions be explained on the basis of the molecular structure of a substance?

64(e). Break a piece of pitch and explain why a break always produces a smooth surface.

Answer. Var is a thickened liquid, therefore its molecules do not form correctly alternating layers, as in a crystalline body.

The structure of gases, liquids and solids. Features of the structure of solutions. The concept of "reactive field"
Theory of the structure of liquids: comparison with the structure of gases and solids Structure (structure) of liquids. The structure of liquids is currently the subject of close study by physical chemists. For research in this direction, the most modern methods are used, including spectral (IR, NMR, scattering of light of various wavelengths), X-ray scattering, quantum mechanical and statistical calculation methods, etc. The theory of liquids is much less developed than that of gases, since the properties of liquids depend on the geometry and polarity of closely spaced molecules. In addition, the lack of a specific structure of liquids makes it difficult to formalize their description - in most textbooks, liquids are given much less space than gases and crystalline solids. What are the features of each of the three aggregate states of matter: solid, liquid and gas. (table)
1) Solid: the body retains volume and shape
2) Liquids retain volume but easily change shape.
3) Gas has neither shape nor volume.

These states of the same substance differ not in the sort of molecules (it is the same), but in the way the molecules are located and move.
1) In gases, the distance between molecules is much more sizes the molecules themselves
2) Molecules of a liquid do not diverge over long distances and the liquid under normal conditions retains its volume.
3) Particles of solid bodies are arranged in a certain order. Each of the particles moves around a certain point in the crystal lattice, like a clock's pendulum, that is, it oscillates.
When the temperature drops, liquids solidify, and when they rise above the boiling point, they pass into a gaseous state. This fact alone indicates that liquids occupy an intermediate position between gases and solids, differing from both. However, the liquid has similarities with each of these states.
There is a temperature at which the boundary between gas and liquid completely disappears. This is the so-called critical point. For each gas, the temperature is known, above which it cannot be liquid at any pressure; at this critical temperature, the boundary (meniscus) between the liquid and its saturated vapor disappears. The existence of a critical temperature ("absolute boiling point") was established by DIMendeleev in 1860. The second property that unites liquids and gases is isotropy. That is, at first glance it can be assumed that liquids are closer to gases than to crystals. Just like gases, liquids are isotropic, i.e. their properties are the same in all directions. Crystals, on the contrary, are anisotropic: the refractive index, compressibility, strength, and many other properties of crystals turn out to be different in different directions. Solid crystalline substances have an ordered structure with repeating elements, which makes it possible to study them by X-ray diffraction (the method of X-ray diffraction analysis has been used since 1912).

What do liquids and gases have in common?
A) isotropic. The properties of a liquid, like those of gases, are the same in all directions, i.e. are isotropic, unlike crystals, which are anisotropic.
B) Liquids, like gases, do not have a definite shape and take the form of a vessel (low viscosity and high fluidity).
Molecules and liquids and gases make fairly free movement, colliding with each other. Previously, it was believed that within the volume occupied by the liquid, any distance exceeding the sum of their radii was assumed to be equally probable, i.e. the tendency towards an ordered arrangement of molecules was denied. Thus, to a certain extent, liquids and gases were opposed to crystals.
As research progresses, more facts indicated the presence of similarities between the structure of liquids and solids. For example, the values ​​of heat capacities and compressibility coefficients, especially near the melting point, practically coincide with each other, while these values ​​for liquid and gas differ sharply.
Already from this example it can be concluded that the picture of thermal motion in liquids at a temperature close to the solidification temperature resembles thermal motion in solids, and not in gases. Along with this, one can also note such significant differences between the gaseous and liquid states of matter. In gases, molecules are distributed over space in a completely random way, i.e. the latter is considered an example of structureless education. The liquid still has a certain structure. This is experimentally confirmed by X-ray diffraction, which shows at least one clear maximum. The structure of a liquid is the way its molecules are distributed in space. The table illustrates the similarities and differences between the gas and liquid states.
Gas phase Liquid phase
1. The distance between molecules l is usually (for low pressures) much larger than the radius of the molecule r: l  r ; practically the entire volume V occupied by the gas is free volume. In the liquid phase, on the contrary, l 2. The average kinetic energy of particles, equal to 3/2kT, is greater than the potential energy U of their intermolecular interaction. The potential energy of the interaction of molecules is greater than the average kinetic energy of their movement: U3/2 kT
3. Particles collide during their translational motion, the collision frequency factor depends on the mass of the particles, their size and temperature. Each particle oscillates in the cage created by the molecules surrounding it. The oscillation amplitude a depends on the free volume, a  (Vf/ L)1/3
4. Diffusion of particles occurs as a result of their translational motion, the diffusion coefficient D  0.1 - 1 cm2 / s (p  105 Pa) and depends on the gas pressure
(D  p-1) Diffusion occurs as a result of a particle jumping from one cell to another with an activation energy ED,
D  e-ED/RT in non-viscous liquids
D  0.3 - 3 cm2 / day.
5. The particle rotates freely, the rotation frequency r is determined only by the moments of inertia of the particle and temperature, the rotation frequency r T1/2 Er/RT
However, the liquid state is close to the solid state in a number of important indicators (quasi-crystallinity). The accumulation of experimental facts indicated that liquids and crystals have much in common. Physical and chemical studies of individual liquids have shown that almost all of them have some elements of the crystal structure.
First, the intermolecular distances in a liquid are close to those in a solid. This is proved by the fact that during the melting of the latter, the volume of the substance changes insignificantly (usually it increases by no more than 10%). Secondly, the energy of intermolecular interaction in a liquid and in a solid differs insignificantly. This follows from the fact that the heat of fusion is much less than the heat of evaporation. For example, for water Hpl= 6 kJ/mol, and Hsp= 45 kJ/mol; for benzene Hpl = 11 kJ/mol, and Htest = 48 kJ/mol.
Thirdly, the heat capacity of a substance during melting changes very little, i.e. it is close for both of these states. Hence it follows that the nature of the motion of particles in a liquid is close to that in a solid. Fourthly, a liquid, like a solid body, can withstand large tensile forces without breaking.
The difference between a liquid and a solid lies in fluidity: a solid retains its shape, a liquid changes it easily even under the influence of a small effort. These properties stem from such features of the structure of a liquid as strong intermolecular interaction, short-range order in the arrangement of molecules, and the ability of molecules to change their position relatively quickly. When a liquid is heated from the freezing point to the boiling point, its properties change smoothly, with heating, its similarities with a gas gradually increase.
Each of us can easily recall many substances that he considers liquids. However, it is not so easy to give an exact definition of this state of matter, since liquids have such physical properties that in some respects they resemble solids, and in others they resemble gases. The similarity between liquids and solids is most pronounced in glassy materials. Their transition from solid to liquid with increasing temperature occurs gradually, and not as a pronounced melting point, they simply become softer and softer, so that it is impossible to indicate in which temperature range they should be called solids, and in which they should be called liquids. We can only say that the viscosity of a glassy substance in the liquid state is less than in the solid state. Solid glasses are therefore often referred to as supercooled liquids. Apparently the most characteristic property liquids, which distinguishes them from solids, is their low viscosity, i.e. high fluidity. Thanks to her, they take the shape of the vessel in which they are poured. At the molecular level, high fluidity means a relatively large freedom of fluid particles. In this, liquids resemble gases, although the forces of intermolecular interaction of liquids are greater, the molecules are closer and more limited in their movement.
What has been said can be approached in another way - from the point of view of the idea of ​​long-range and short-range order. Long-range order exists in crystalline solids, the atoms of which are arranged in a strictly ordered manner, forming three-dimensional structures that can be obtained by repeated repetition of the unit cell. There is no long-range order in liquid and glass. This, however, does not mean that they are not ordered at all. The number of nearest neighbors for all atoms is almost the same, but the arrangement of atoms as they move away from any selected position becomes more and more chaotic. Thus, order exists only at small distances, hence the name: short-range order. An adequate mathematical description of the structure of a liquid can only be given with the help of statistical physics. For example, if a liquid consists of identical spherical molecules, then its structure can be described by the radial distribution function g(r), which gives the probability of finding any molecule at a distance r from the given one, chosen as a reference point. Experimentally, this function can be found by studying the diffraction of X-rays or neutrons, and with the advent of high-speed computers, it began to be calculated by the method computer simulation, based on available data on the nature of forces acting between molecules, or on assumptions about these forces, as well as on the laws of Newtonian mechanics. Comparing the radial distribution functions obtained theoretically and experimentally, one can verify the correctness of the assumptions about the nature of intermolecular forces.
In organic substances, the molecules of which have an elongated shape, in one or another temperature range, regions of the liquid phase with a long-range orientational order are sometimes found, which manifests itself in a tendency to parallel alignment of the long axes of the molecules. In this case, orientational ordering can be accompanied by coordination ordering of molecular centers. Liquid phases of this type are commonly referred to as liquid crystals. The liquid-crystalline state is intermediate between crystalline and liquid. Liquid crystals have both fluidity and anisotropy (optical, electrical, magnetic). Sometimes this state is called mesomorphic (mesophase) due to the absence of long-range order. The upper limit of existence is the temperature of enlightenment (an isotropic liquid). Thermotropic (mesogenic) FAs exist above a certain temperature. Typical are cyanobiphenyls. Lyotropic - when dissolved, for example, aqueous solutions of soaps, polypeptides, lipids, DNA. The study of liquid crystals (mesophase - melting in two stages - cloudy melt, then transparent, transition from a crystalline phase to a liquid through an intermediate form with anisotropic optical properties) is important for the purposes of technology - liquid crystal indication.
Molecules in a gas move randomly (randomly). In gases, the distance between atoms or molecules is, on average, many times greater than the size of the molecules themselves. Molecules in a gas move at high speeds (hundreds of m/s). Colliding, they bounce off each other like perfectly elastic balls, changing the magnitude and direction of the velocities. At large distances between the molecules, the attractive forces are small and are not able to keep the gas molecules next to each other. Therefore, gases can expand indefinitely. Gases are easily compressed, the average distance between molecules decreases, but still remains large in size. Gases do not retain either shape or volume, their volume and shape coincide with the volume and shape of the vessel they fill. Numerous impacts of molecules on the walls of the vessel create gas pressure.
Atoms and molecules of solids vibrate around certain equilibrium positions. Therefore, solids retain both volume and shape. If you mentally connect the centers of equilibrium positions of atoms or ions of a solid body, then you get a crystal lattice.
The molecules of a liquid are located almost close to each other. Therefore, liquids are very poorly compressible and retain their volume. Molecules of a liquid vibrate around the equilibrium position. From time to time, the molecule makes transitions from one settled state to another, as a rule, in the direction of the action of an external force. The time of the settled state of the molecule is small and decreases with increasing temperature, and the time of the transition of the molecule to a new settled state is even shorter. Therefore, liquids are fluid, do not retain their shape and take the shape of the vessel into which they are poured.

Kinetic theory of liquids The kinetic theory of liquids developed by Ya. I. Frenkel considers a liquid as dynamic system particles, resembling partly the crystalline state. At temperatures close to the melting point, thermal motion in a liquid is reduced mainly to harmonic oscillations of particles around certain average equilibrium positions. In contrast to the crystalline state, these equilibrium positions of molecules in a liquid are temporary for each molecule. After oscillating around one equilibrium position for some time t, the molecule jumps to a new position located in the neighborhood. Such a jump occurs with the expenditure of energy U, so the “settled life” time t depends on temperature as follows: t = t0 eU/RT, where t0 is the period of one oscillation around the equilibrium position. For water at room temperature t » 10-10s, t0 = 1.4 x 10-12s, i.e. one molecule, having made about 100 vibrations, jumps to a new position, where it continues to oscillate. From the X-ray and neutron scattering data, one can calculate the particle distribution density function  as a function of the distance r from one particle chosen as the center. In the presence of long-range order in a crystalline solid, the function (r) has a number of distinct maxima and minima. Due to the high mobility of particles, only short-range order is preserved in a liquid. This clearly follows from the X-ray patterns of liquids: the function (r) for a liquid has a clear first maximum, a diffuse second, and then (r) = const. The kinetic theory describes melting as follows. In the crystal lattice of a solid, there are always a small number of vacancies (holes) that slowly wander around the crystal. The closer the temperature is to the melting temperature, the higher the concentration of "holes" and the faster they move through the sample. At the melting point, the formation of “holes” acquires an avalanche-like cooperative character, the system of particles becomes dynamic, long-range order disappears, and fluidity appears. The decisive role in melting is played by the formation of free volume in the liquid, which makes the system fluid. The most important difference between a liquid and a solid crystalline body is that there is a free volume in the liquid, a significant part of which has the form of fluctuations (“holes”), the wandering of which through the liquid gives it such a characteristic quality as fluidity. The number of such “holes”, their volume and mobility depend on temperature. At low temperature, the liquid, if it has not turned into a crystalline body, becomes an amorphous solid with very low fluidity due to a decrease in the volume and mobility of the "holes". Along with kinetic theory In recent decades, the statistical theory of liquids has been successfully developed.

Structure of ice and water. The most important and common liquid under normal conditions is water. This is the most common molecule on Earth! It is an excellent solvent. For example, all biological fluids contain water. Water dissolves many inorganic (salts, acids, bases) and organic substances (alcohols, sugars, carboxylic acids, amines). What is the structure of this liquid? We will again have to return to the issue that we considered in the first lecture, namely, to such a specific intermolecular interaction as the hydrogen bond. Water, both in liquid and crystalline form, exhibits anomalous properties precisely because of the presence of many hydrogen bonds. What are these anomalous properties: high boiling point, high melting point and high enthalpy of vaporization. Let's look first at the graph, then at the table, and then at the diagram of the hydrogen bond between two water molecules. In fact, each water molecule coordinates 4 other water molecules around itself: two due to oxygen, as a donor of two lone electron pairs into two protonized hydrogens, and two due to protonized hydrogens coordinating with the oxygens of other water molecules. In the previous lecture, I showed you a slide with graphs of the melting point, boiling point and enthalpy of vaporization of group VI hydrides depending on the period. These dependences have a clear anomaly for oxygen hydride. All these parameters for water are noticeably higher than those predicted from an almost linear dependence for the following hydrides of sulfur, selenium and tellurium. We explained this by the existence of a hydrogen bond between protonized hydrogen and an electron density acceptor, oxygen. Hydrogen bonding has been studied most successfully using vibrational infrared spectroscopy. The free OH group has a characteristic vibrational energy that causes the OH bond to alternately lengthen and shorten, giving a characteristic band in the infrared absorption spectrum of the molecule. However, if the OH group participates in a hydrogen bond, the hydrogen atom is bound by atoms on both sides and thus its vibration is "damped" and the frequency decreases. The following table shows that an increase in the strength and "concentration" of the hydrogen bond leads to a decrease in the absorption frequency. In the figure, curve 1 corresponds to the maximum of the infrared absorption spectrum of O-H groups in ice (where all H-bonds are tied); curve 2 corresponds to the maximum of the infrared absorption spectrum of the groups O-N individual H2O molecules dissolved in CCl4 (where there are no H-bonds - the solution of H2O in CCl4 is too dilute); and curve 3 corresponds to the absorption spectrum of liquid water. If liquid water had two grades O-N groups - forming hydrogen bonds and not forming them - and some O-N groups in water they would vibrate in the same way (with the same frequency) as in ice (where they form H-bonds), and others - as in the CCl4 environment (where they do not form H-bonds). Then the spectrum of water would have two maxima corresponding to two O-H states groups, their two characteristic oscillation frequencies: with what frequency the group vibrates, with this it absorbs light. But the "two-maximum" picture is not observed! Instead, on curve 3, we see one, very blurred maximum, extending from the maximum of curve 1 to the maximum of curve 2. This means that all O-H groups in liquid water make hydrogen bonds - but all these bonds have a different energy, “loose” (have a different energy), and in different ways. This shows that the picture in which some of the hydrogen bonds in water are broken and some are retained is, strictly speaking, incorrect. However, it is so simple and convenient for describing the thermodynamic properties of water that it is widely used - and we will also refer to it. But keep in mind that it is not entirely accurate.
Thus, IR spectroscopy is a powerful method for studying hydrogen bonding, and many data on the structure of liquids and solids associated due to it have been obtained using this spectral method. As a result, for liquid water the ice-like model (O.Ya. Samoilov's model) is one of the most generally recognized. According to this model liquid water is disturbed by thermal motion (evidence and consequence of thermal motion - Brownian motion, which was first observed by the English botanist Robert Brown in 1827 on pollen under a microscope) an ice-like tetrahedral frame (each water molecule in an ice crystal is connected by hydrogen bonds with reduced energy compared to that in ice - "loose" hydrogen bonds) with four surrounding it water molecules), the voids of this frame are partially filled with water molecules, and the water molecules located in the voids and in the nodes of the ice-like caracas are energetically unequal.

Unlike water, in an ice crystal at the nodes of the crystal lattice there are water molecules of equal energy and they can only perform oscillatory movements. In such a crystal, both short-range and long-range order exist. In liquid water (as for a polar liquid), some elements of the crystal structure are preserved (moreover, even in the gas phase, liquid molecules are ordered into small unstable clusters), but there is no long-range order. Thus, the structure of a liquid differs from the structure of a gas in the presence of short-range order, but it differs from the structure of a crystal in the absence of long-range order. The most convincing evidence of this is the study of X-ray scattering. Three neighbors of each molecule in liquid water are located in one layer and are at a greater distance from it (0.294 nm) than the fourth molecule from the neighboring layer (0.276 nm). Each water molecule in the composition of the ice-like framework forms one mirror-symmetrical (strong) and three centrally symmetrical (less strong) bonds. The first relates to the bonds between the water molecules of a given layer and neighboring layers, the rest - to the bonds between the water molecules of one layer. Therefore, a quarter of all bonds are mirror-symmetrical, and three-quarters are centrally symmetrical. The concept of the tetrahedral environment of water molecules led to the conclusion that its structure is highly openwork and that there are voids in it, the dimensions of which are equal to or greater than the dimensions of water molecules.

Elements of the structure of liquid water. a - elementary water tetrahedron (light circles - oxygen atoms, black halves - possible positions of protons on a hydrogen bond); b - mirror-symmetrical arrangement of tetrahedra; c - centrally symmetrical arrangement; d - location of oxygen centers in the structure of ordinary ice. Water is characterized by significant forces of intermolecular interaction due to hydrogen bonds, which form a spatial network. As we said in the previous lecture, a hydrogen bond is due to the ability of a hydrogen atom connected to an electronegative element to form an additional bond with an electronegative atom of another molecule. The hydrogen bond is relatively strong and amounts to several 20-30 kilojoules per mole. In terms of strength, it occupies an intermediate place between the van der Waals energy and the energy of a typically ionic bond. Energy in a water molecule chemical bond H-O is 456 kJ/mol, and the hydrogen bond energy of H…O is 21 kJ/mol.

Hydrogen compounds
Molecular weight Temperature,  С
freezing boiling
H2Te 130 -51 -4
H2Se 81 -64 -42
H2S 34 -82 -61
H2O 18 0! +100!

Ice structure. normal ice. Dotted line - H-bonds. Small cavities surrounded by H2O molecules are visible in the openwork structure of ice.
Thus, the structure of ice is an openwork construction of water molecules, connected to each other only by hydrogen bonds. The location of water molecules in the ice structure determines the presence of wide channels in the structure. During the melting of ice, water molecules "fall" into these channels, which explains the increase in the density of water compared to the density of ice. Ice crystals occur in the form of regular hexagonal plates, tabular segregations, and intergrowths of complex shape. Structure normal ice dictated by H-bonds: it is good for the geometry of these bonds (O-H looks directly at O), but not very good for tight van der Waals contact of H2O molecules. Therefore, the structure of ice is openwork, in it H2O molecules envelop microscopic (less than an H2O molecule in size) pores. The openwork structure of ice leads to two well-known effects: (1) ice is less dense than water, it floats in it; and (2) under strong pressure - for example, the blades of a skate melt the ice. Most of the hydrogen bonds that exist in ice are preserved in liquid water. This follows from the smallness of the heat of melting ice (80 cal/g) compared to the heat of boiling water (600 cal/g at 0°C). It could be said that only 80/(600+80) = 12% of the H-bonds existing in ice break in liquid water. However, this picture - that some of the hydrogen bonds in water are broken, and some are preserved - is not entirely accurate: rather, all hydrogen bonds in water become loose. This is well illustrated by the following experimental data.

Structure of solutions. From concrete examples for water, let's move on to other liquids. Different liquids differ from each other in the size of molecules and the nature of intermolecular interactions. Thus, in each specific liquid there is a certain pseudocrystalline structure, characterized by short-range order and, to some extent, resembling the structure obtained when a liquid freezes and turns into a solid. When dissolving another substance, i.e. when a solution is formed, the nature of intermolecular interactions changes and a new structure appears with a different arrangement of particles than in a pure solvent. This structure depends on the composition of the solution and is specific to each particular solution. The formation of liquid solutions is usually accompanied by the process of solvation, i.e. alignment of solvent molecules around solute molecules due to the action of intermolecular forces. Distinguish between near and far solvation, i.e. around the molecules (particles) of the solute, primary and secondary solvate shells are formed. In the primary solvation shell, solvent molecules are in close proximity, which move along with the molecules of the solute. The number of solvent molecules in the primary solvation shell is called the solvation coordination number, which depends on both the nature of the solvent and the nature of the solute. The composition of the secondary solvation shell includes solvent molecules that are located at much greater distances and affect the processes occurring in the solution due to interaction with the primary solvation shell.
When considering the stability of solvates, a distinction is made between kinetic and thermodynamic stability.
In aqueous solutions, the quantitative characteristics of kinetic hydration (O.Ya. Samoilov) are the values ​​i /  and Ei = Ei-E, where i and  are the average residence time of water molecules in the equilibrium position near the i-th ion and in clean water, and Ei and E are the exchange activation energy and the activation energy of the self-diffusion process in water. These quantities are related to each other by an approximate relationship:
i/  exp(Ei/RT)
if EI  0, i/  1 (the exchange of water molecules closest to the ion occurs less frequently (slower) than the exchange between molecules in pure water) - positive hydration
if EI  0, i/  1 (the exchange of water molecules closest to the ion occurs more often (faster) than the exchange between molecules in pure water) - negative hydration

So, for lithium ion EI = 1.7 kJ/mol, and for cesium ion Ei= - 1.4 kJ/mol, i.e. a small "hard" lithium ion holds water molecules more strongly than a large and "diffuse" cesium ion with the same charge. The thermodynamic stability of the formed solvates is determined by the change in the Gibbs energy during solvation (solvG) = (solvH) - T(solvS). The more negative this value, the more stable the solvate. Basically, it is determined negative values solvation enthalpies.
The concept of solutions and theories of solutions. True solutions are obtained spontaneously when two or more substances come into contact, due to the destruction of bonds between particles of one type and the formation of bonds of another type and the distribution of the substance throughout the volume due to diffusion. According to their properties, solutions are divided into ideal and real, solutions of electrolytes and non-electrolytes, dilute and concentrated, unsaturated, saturated and supersaturated. The properties of rastors depend on the nature and magnitude of the MMW. These interactions can be of physical nature (van der Waals forces) and complex physicochemical nature (hydrogen bond, ion-molecular bond, charge transfer complexes, etc.). The process of solution formation is characterized by the simultaneous manifestation of attractive and repulsive forces between the interacting particles. In the absence of repulsive forces, particles would merge (stick together) and liquids could be compressed indefinitely; in the absence of attractive forces, it would be impossible to obtain liquids or solids. In the previous lecture, we considered the physical and chemical theories of solutions.
However, the creation of a unified theory of solutions encounters significant difficulties and at present it has not yet been created, although research is being carried out by the most modern methods quantum mechanics, statistical thermodynamics and physics, crystal chemistry, X-ray diffraction analysis, optical methods, NMR methods. reactive field. In continuation of the consideration of the forces of intermolecular interaction, we will consider the concept of "reactive field", which is important for understanding the structure and structure of condensed matter and real gases, in particular, liquid state, and hence all physical chemistry liquid solutions.
A reactive field occurs in mixtures of polar and non-polar molecules, for example, for mixtures of hydrocarbons and naphthenic acids. Polar molecules act by a field of a certain symmetry (field symmetry is determined by the symmetry of vacant molecular orbitals) and strength H on non-polar molecules. The latter are polarized due to charge separation, which leads to the appearance (induction) of a dipole. A molecule with an induced dipole, in turn, acts on a polar molecule, changing its electromagnetic field, i.e. excites a reactive (response) field. The appearance of a reactive field leads to an increase in the interaction energy of particles, which is expressed in the creation of strong solvation shells for polar molecules in a mixture of polar and nonpolar molecules.
The reactive field energy is calculated according to the following formula: where:
sign "-" - determines the attraction of molecules
S - static electric permeability
 unlimited is the permittivity due to the electronic and atomic polarizability of molecules
NA - Avogadro's number
VM is the volume occupied by 1 mole of a polar substance in an isotropic liquid v = dipole moment
ER is the energy of 1 mole of a polar substance in solution
The concept of "reactive field" will allow us to better understand the structure of pure liquids and solutions. The quantum-chemical approach to the study of the reactive field was developed in the works of M.V. L. Ya. Karpova Thus, the problem of the liquid state is waiting for its young researchers. You and the cards in your hands.

The structure of gases, liquids and solids.

Basic Provisions of Molecular Kinetic Theory:

All substances are made up of molecules, and molecules are made up of atoms.

atoms and molecules are in constant motion,

There are attractive and repulsive forces between molecules.

AT gases the molecules move randomly, the distances between the molecules are large, the molecular forces are small, the gas occupies the entire volume provided to it.

AT liquids molecules are ordered only at small distances, and at large distances, the order (symmetry) of the arrangement is violated - “short range order”. The forces of molecular attraction keep molecules close together. The movement of molecules is “jumps” from one stable position to another (usually within one layer. This movement explains the fluidity of a liquid. A liquid has no shape, but has volume.

Solids - substances that retain their shape, are divided into crystalline and amorphous. crystalline solid bodies have a crystal lattice, in the nodes of which there can be ions, molecules or atoms. They oscillate relative to stable equilibrium positions. Crystal lattices have a regular structure throughout the volume - a “long-range order” of location.

Amorphous bodies retain their shape, but do not have a crystal lattice and, as a result, do not have a pronounced melting point. They are called frozen liquids, since they, like liquids, have a “near” order of molecular arrangement.

Interaction forces of molecules

All molecules of a substance interact with each other by forces of attraction and repulsion. Proof of the interaction of molecules: the phenomenon of wetting, resistance to compression and stretching, low compressibility of solids and gases, etc. The reason for the interaction of molecules is the electromagnetic interaction of charged particles in matter. How to explain it? An atom consists of a positively charged nucleus and a negatively charged electron shell. The charge of the nucleus is equal to the total charge of all electrons, therefore, as a whole, the atom is electrically neutral. A molecule consisting of one or more atoms is also electrically neutral. Consider the interaction between molecules using the example of two immobile molecules. Gravitational and electromagnetic forces can exist between bodies in nature. Since the masses of molecules are extremely small, the negligible forces of gravitational interaction between molecules can be ignored. At very large distances, there is no electromagnetic interaction between molecules either. But, with a decrease in the distance between the molecules, the molecules begin to orient themselves so that their sides facing each other will have charges of different signs (in general, the molecules remain neutral), and attractive forces arise between the molecules. With an even greater decrease in the distance between the molecules, repulsive forces arise as a result of the interaction of negatively charged electron shells of the atoms of the molecules. As a result, the molecule is affected by the sum of the forces of attraction and repulsion. At large distances, the attractive force prevails (at a distance of 2-3 molecular diameters, attraction is maximum), at short distances, the repulsive force. There is such a distance between molecules at which the forces of attraction become equal to the forces of repulsion. This position of the molecules is called the position of stable equilibrium. Molecules located at a distance from each other and connected by electromagnetic forces have potential energy. In the position of stable equilibrium, the potential energy of molecules is minimal. In a substance, each molecule interacts simultaneously with many neighboring molecules, which also affects the value of the minimum potential energy of molecules. In addition, all the molecules of a substance are in continuous motion, i.e. have kinetic energy. Thus, the structure of a substance and its properties (solid, liquid and gaseous bodies) are determined by the ratio between the minimum potential energy of interaction of molecules and the kinetic energy of the thermal motion of molecules.

The structure and properties of solid, liquid and gaseous bodies

The structure of bodies is explained by the interaction of body particles and the nature of their thermal motion.

Solid

Solids have a constant shape and volume, and are practically incompressible. The minimum potential energy of interaction of molecules is greater than the kinetic energy of molecules. Strong interaction of particles. The thermal motion of molecules in a solid is expressed only by oscillations of particles (atoms, molecules) around the position of stable equilibrium.

Due to the large forces of attraction, molecules practically cannot change their position in a substance, which explains the invariance of the volume and shape of solids. Most solids have a spatially ordered arrangement of particles that form a regular crystal lattice. Particles of matter (atoms, molecules, ions) are located at the vertices - the nodes of the crystal lattice. The nodes of the crystal lattice coincide with the position of stable equilibrium of the particles. Such solids are called crystalline.

Liquid

Liquids have a certain volume, but do not have their own shape, they take the shape of the vessel in which they are located. The minimum potential energy of interaction of molecules is comparable to the kinetic energy of molecules. Weak particle interaction. The thermal motion of molecules in a liquid is expressed by oscillations around the position of stable equilibrium within the volume provided to the molecule by its neighbors. Molecules cannot move freely throughout the entire volume of a substance, but transitions of molecules to neighboring places are possible. This explains the fluidity of the liquid, the ability to change its shape.

In liquids, the molecules are quite strongly bound to each other by attractive forces, which explains the invariance of the volume of the liquid. In a liquid, the distance between molecules is approximately equal to the diameter of the molecule. With a decrease in the distance between molecules (compressing a liquid), the repulsive forces sharply increase, so liquids are incompressible. In terms of their structure and nature of thermal motion, liquids occupy an intermediate position between solids and gases. Although the difference between a liquid and a gas is much greater than between a liquid and a solid. For example, during melting or crystallization, the volume of a body changes many times less than during evaporation or condensation.

Gases do not have a constant volume and occupy the entire volume of the vessel in which they are located. The minimum potential energy of interaction of molecules is less than the kinetic energy of molecules. Particles of matter practically do not interact. Gases are characterized by a complete disorder in the arrangement and movement of molecules.

The distance between gas molecules is many times greater than the size of the molecules. Small forces of attraction cannot keep molecules near each other, so gases can expand indefinitely. Gases are easily compressed under the action of external pressure, because. the distances between molecules are large, and the interaction forces are negligible. The pressure of the gas on the walls of the vessel is created by the impacts of moving gas molecules.