Distance between liquid molecules. Distance between molecules in gases, liquids and solids

1. The structure of gaseous, liquid and solids

Molecular kinetic theory makes it possible to understand why the substance may be in a gaseous, liquid and solid states.
Gases. In the gases, the distance between atoms or molecules on average many times more than the sizes of the molecules themselves ( fig.8.5.). For example, at atmospheric pressure, the volume of the vessel is ten thousand times higher than the volume of molecules in it.

Gases are easily compressed, while the average distance between molecules decreases, but the molecule shape does not change ( fig.8.6.).

Molecules with huge speeds - hundreds of meters per second - moving in space. Following, they bounce apart from each other in different directions like billiard balls. The weak forces of attraction of gas molecules are not able to keep them among each other. therefore gases can be largerly expanded. They do not retain either forms or volume.
Numerous blows of molecules about the wall of the vessel create gas pressure.

Liquids. Liquid molecules are located almost close to each other ( fig.8.7) Therefore, the fluid molecule behaves differently than the gas molecule. In liquids, there is a so-called neighboring order, i.e. the ordered arrangement of molecules is maintained at distances equal to several molecular diameters. The molecule fluctuates near its equilibrium position, facing neighboring molecules. Only from time to time it makes another "jump", falling into a new equilibrium position. In this position of the equilibrium, the repulsion force is equal to the strength of attraction, that is, the total power of the interaction of the molecule is zero. Time smear Life Water molecules, i.e., the time of its oscillations about one particular equilibrium position at room temperature is equal to an average of 10 -11 s. The time of one oscillation is significantly less (10 -12 -10 -13 C). With increasing temperature, the time of the settling life molecules decreases.

The nature of the molecular movement in liquids for the first time established by the Soviet physicist Ya.I. Freklem, makes it possible to understand the basic properties of liquids.
Liquid molecules are located directly to each other. With a decrease in the volume of repulsion strength, it becomes very high. This is explained small compressibility of liquids.
As known, fluids fluid, i.e. do not save your form. You can explain this. External force noticeably does not change the number of robes of molecules per second. But the jumps of molecules from one settled position to another occur mainly in the direction of the external force ( fig.8.8.). That is why the liquid flows and takes the shape of the vessel.

Solid bodies. Atoms or molecules of solid bodies, in contrast to atoms and molecules of liquids, fluctuate about certain equilibrium positions. For this reason, solid bodies retain not only volume, but also. The potential energy of the interaction of solid molecules is significantly more of their kinetic energy.
There is another important distinction between liquids and solid bodies. The liquid can be compared with the crowd of people where individual individuals are restless restless in place, and a solid body is similar to a slender cohort of the same individuals that are not at night, but withstand a few distances among themselves. If you connect the centers of the equilibrium positions of atoms or solid ions, then the correct spatial grill is called crystal.
Figures 8.9 and 8.10 depict crystal lattices of cook salt and diamond. Internal order in the location of crystal atoms leads to proper external geometric forms.

Figure 8.11 shows Yakut diamonds.

In the gas distance L between molecules many more sizes of molecular 0: " l \u003e\u003e R 0.
In liquids and solid tell≈r 0. Liquid molecules are located in disarray and jump from time to time from one settled position to another.
The crystalline solid bodies of molecules (or atoms) are located strictly ordered.

2. Perfect gas in molecular kinetic theory

The study of any field of physics always begins with the introduction of a certain model, within which study is underway. For example, when we studied the kinematics, the body model was a material point, etc. As you already guessed, the model will never correspond to the actual processes, but often it is very much approaching this correspondence.

Molecular physics, and in particular MTT, is no exception. Many scientists worked on the problem of describing the model, starting from the eighteenth century: M. Lomonosov, D. Joule, R. Clausius (Fig. 1). The latter, in fact, introduced in 1857 the model of the ideal gas. A qualitative explanation of the basic properties of a substance based on molecular-kinetic theory is not particularly difficult. However, the theory establishes quantitative relations between the values \u200b\u200bmeasured on the experiment (pressure, temperature, etc.) and the properties of the molecules themselves, their number and speed of movement, is very complex. In the gas under normal pressures, the distance between molecules is many times higher than their dimensions. In this case, the interaction force of molecules is negligible to small and the kinetic energy of molecules a lot more potential interaction energy. Gas molecules can be considered as material Points Or very small solid balls. Instead real Gaza, between whose molecules there are complex interaction forces, we will consider it the model is the perfect gas.

Perfect Gas.- Gas model, in which molecules and gas atoms are represented as very small (endangered sizes) elastic balls that do not interact with each other (without direct contact), but only face (see Fig. 2).

It should be noted that the rarefied hydrogen (under very small pressure) almost fully satisfies the models of the ideal gas.

Fig. 2.

Perfect Gas. - It is gas, the interaction between the molecules of which is negligible. Naturally, in the collision of the molecules of the perfect gas on them there is an repulsion force. Since gas molecules we can according to the model to be considered material dots, then we neglect the dimensions of molecules, considering that the volume they occupy is much less than the volume of the vessel.
Recall that only those properties of the real system are taken into account in the physical model, which is absolutely necessary to explain the studied patterns of the behavior of this system. No model can pass all the properties of the system. Now we have to solve a rather narrow task: to calculate with the help of a molecular-kinetic theory, the pressure of the perfect gas on the walls of the vessel. For this problem, the model of the ideal gas is quite satisfactory. It leads to the results that are confirmed by experience.

3. Gas pressure in molecular kinetic theory Let the gas be in a closed vessel. Pressure gauge shows gas pressure p 0. How does this pressure occur?
Each gas molecule, hitting the wall, for a small period of time acts on it with some force. As a result of erratic blows of the wall, the pressure is rapidly changing over time as follows as shown in Figure 8.12. However, the actions caused by the blows of individual molecules are so weak that they are not registered manometer. The pressure gauge records the average force acting on each unit of the surface area of \u200b\u200bits sensing element - the membrane. Despite small pressure changes, the average pressure value p 0practically turns out to be quite a certain amount, since there are a lot of blows about the wall, and the masses of molecules are very small.

The perfect gas is a real gas model. According to this model, the gas molecule can be viewed as material points, the interaction of which occurs only in their collision. Facing the wall, gas molecules put pressure on it.

4. Micro and gas macroparameters

Now you can proceed to describing the parameters of the ideal gas. They are divided into two groups:

Parameters of perfect gas

That is, microparameters describe the condition of a separate particle (microtela), and macroparameters are the condition of the entire portion of the gas (macotel). We now write a relation that connects some parameters with others, or the main MKT equation:

Here: - average particle speed;

Definition. - concentration Gas particles - the number of particles per unit volume; ; unit - .

5. Average Speed \u200b\u200bSpeed \u200b\u200bMolecules

To calculate the average pressure, you need to know the average velocity of molecules (more precisely, the average speed of the speed). This is not a simple question. You are accustomed to the fact that the speed has every particle. The average speed of molecules depends on the movement of all particles.
Middle values. From the very beginning it is necessary to abandon the attempts to trace the movement of all molecules from which gas consists. They are too much, and they are moving very difficult. We do not need to know how each molecule is moving. We must find out how the result is the movement of all gas molecules.
The nature of the movement of the entire totality of gas molecules is known from experience. Molecules are involved in a messy (thermal) movement. This means that the speed of any molecule can be both very large and very small. The direction of movement of molecules is inconspicuously changing with their collisions with each other.
Speed \u200b\u200bof individual molecules can be any, however average The value of the module of these speeds is quite defined. In the same way, the growth of students in the class of unequal, but its average value is a certain number. To find this number, it is necessary to fold the growth of individual students and divide this amount by the number of students.
The average speed of the speed. In the future, we will need the average value of not the speed, and the square of the speed. The average kinetic energy of molecules depends on this value. And the average kinetic energy of molecules, as we will soon be convinced, has very great importance In the whole molecular kinetic theory.
Denote the velocity modules of individual gas molecules through. The average speed of the speed is determined by the following formula:

where N. - The number of molecules in the gas.
But the square of the module of any vector is equal to the sum of the squares of its projections on the axis of coordinates Oh, oy, oz. therefore

The average values \u200b\u200bof values \u200b\u200bcan be determined by formulas like formula (8.9). There is an aspect ratio between the average value and average values \u200b\u200bof the squares of projections as the ratio (8.10):

Indeed, equality (8.10) is fair for each molecule. Conducting such equalities for individual molecules and dividing both parts of the obtained equation to the number of molecules N.We will come to formula (8.11).
Attention! As directions of three axes Oh, oy. and Oz.due to the random movement of molecules is equal, the average values \u200b\u200bof the squares of speed projections are equal to each other:

See, from chaos floats a certain pattern. Would you be able to figure it out?
Given the ratio (8.12), we substitute in formula (8.11) instead of and. Then for the middle square of the speed projection, we get:

i.e. the average velocity projection square is 1/3 of the middle square of the speed itself. Multiplier 1/3 appears due to the three-dimensionality of the space and, accordingly, the existence of three projections from any vector.
The speed of molecules change randomly, but the average square of the speed is quite a certain amount.

6. The main equation of molecular-kinetic theory
We proceed with the conclusion of the main equation of the molecular-kinetic theory of gases. In this equation, the dependence of the gas pressure from the average kinetic energy of its molecules is established. After the output of this equation in the XIX century. And experimental proof of his justice began the rapid development of a quantitative theory, which continues to today.
Proof of almost any statement in physics, the withdrawal of any equation can be done with varying degrees of strictness and persuasiveness: very simplistic, more or less strictly or with full rigor, affordable modern science.
The strict output of the equation of the molecular-kinetic theory of gases is quite complicated. Therefore, we are limited to a strongly simplified, schematic conclusion of the equation. Despite all simplifications, the result will turn out true.
The output of the main equation. Calculate gas pressure on the wall CD vessel Abcd. Square S.perpendicular to the coordinate axis OX. (fig.8.13).

When you hit the molecule about the wall, its impulse changes :. Since the molecule speed module does not change when hitting, . According to the second law of Newton, the change in the molecule pulse is equal to the impulse by the strength of the vessel wall on it, and according to the third law of Newton, the impulse in the module of the force with which the molecule has affected the wall. Therefore, as a result of the impact of the molecule on the wall, the force, the impulse of which is equal to.

What is the average distance between the saturated water vapor molecules at 100 ° C?

Task number 4.1.65 from "Collection of tasks to prepare for entrance exams in physics UGNTU "

Given:

\\ (t \u003d 100 ^ \\ CIRC \\) C, \\ (L -? \\)

The solution of the problem:

Consider water vapor in some arbitrary quantities equal to \\ (\\ nu \\) mole. To determine the volume \\ (V \\), which occupied by this amount of water vapor, you need to use the Klapaireron-Mendeleev equation:

In this formula \\ (R \\) is a universal gas constant, equal to 8.31 J / (mol · K). The pressure of saturated water vapor \\ (P \\) at a temperature of 100 ° C is 100 kPa, it is famous factAnd every student should know him.

To determine the amount of water vapor molecules \\ (n \\), we use the following formula:

Here \\ (n_a \\) is the number of Avogadro, equal to 6.023 · 10 23 1 / mol.

Then each molecule accounts for the volume cube \\ (v_0 \\), obviously determined by the formula:

\\ [(V_0) \u003d \\ FRAC (V) (N) \\]

\\ [(V_0) \u003d \\ FRAC ((\\ Nu RT)) ((P \\ Nu (n_a))) \u003d \\ FRAC ((RT)) ((p (n_a))) \\]

Now look at the chart to the task. Each molecule is conditionally in its cube, the distance between two molecules may vary from 0 to \\ (2D \\), where \\ (D \\) is the length of the edge of the cube. The average distance \\ (L \\) will be equal to the length of the edge of the Cuba \\ (D \\):

The length of the edge \\ (D \\) can be found like this:

As a result, we will get such a formula:

We translate the temperature in the Kelvin scale and consider the answer:

Answer: 3.72 nm.

If you do not understand the solution and you have some kind of question or you have found an error, then boldly leave the comment below.

Molecular kinetic theory gives an explanation that all substances can be in three aggregate states: in solid, liquid and gaseous. For example, ice, water and water vapor. Often the plasma is considered the fourth condition of the substance.

Aggregate states of matter (from Latin aggrego. - I attach, linking) - the state of the same substance, transitions between which are accompanied by a change in its physical properties. This is the change in the aggregate states of the substance.

In all three states of the molecule of the same substance, they do not differ from each other, only their location, the nature of the thermal motion and the forces of intermolecular interaction changes.

Movement of molecules in gases

In gases, the distance between molecules and atoms is significantly larger than the dimensions of molecules, and attraction forces are very small. Therefore, gases do not have their own form and permanent amount. Gases are easily compressed because repulsion forces on large distances Also small. Gases have a property to expand indefinitely, filling out all the volume provided to them. Gas molecules are moving with very big speeds, encounter each other, bounce apart from each other in different directions. Numerous blows of molecules about the wall of the vessel create gas pressure.

Movement of molecules in liquids

In liquids, the molecule not only fluctuate near the position of the equilibrium, but also make a jump from one equilibrium position in the neighboring. These jumps occur periodically. The time cut between such jumps was called average settling time (or average relaxation time) And is indicated by the letter?. In other words, relaxation time is the time of oscillations of about one definite position of equilibrium. At room temperature, this time is an average of 10 -11 s. The time of one oscillation is 10 -12 ... 10 -13 s.

The time of classroom life decreases with an increase in temperature. The distance between liquid molecules is less than the dimensions of molecules, the particles are located close to each other, and the intermolecular attraction is large. Nevertheless, the location of fluid molecules is not strictly ordered throughout the volume.

Liquids, like solid bodies, retain their volume, but do not have their own form. Therefore, they take the shape of the vessel in which there are. The liquid has such a property as fluidity. Due to this property, the liquid does not resist the change in the shape, it is slightly compressed, and its physical properties The same in all directions inside the liquid (isotropy of liquids). For the first time, the nature of the molecular movement in liquids was established by the Soviet physicist Yakov Ilyich Frenkel (1894 - 1952).

Movement of molecules in solid bodies

Molecules and solid body atoms are located in a certain order and form crystal lattice . Such solids are called crystalline. Atoms make oscillatory movements near the position of the equilibrium, and the attraction between them is very large. Therefore, solid bodies in normal conditions retain volume and have their own form.

Physics

The interaction between atoms and molecules of the substance. The structure of solid, liquid and gaseous bodies

Between the substance molecules operate at the same time the strength of the attraction and force of the repulsion. These forces are largely dependent on the distances between molecules.

According to the experimental I. theoretical studies Intermolecular interaction forces are inversely proportional nth degree Distances between molecules:

where for the forces of attraction n \u003d 7, and for the forces of the repulsion.

The interaction of two molecules can be described using the graph of the dependence of the projection of the resultant forces of attraction and repulsion of molecules from the distance R between their centers. We will send the axis R from the molecule 1, the center of which coincides with the origin of the coordinates, to the center of the molecule 2 from it (Fig. 1).

Then the projection of the repulsion force of the molecule 2 from the molecule 1 on the R axis will be positive. The projection of the strength of attraction of a molecule 2 to the molecule 1 will be negative.

The repulsion force (Fig. 2) is much more attraction forces at low distances, but much faster declining with increasing R. Attraction forces are also rapidly decreasing with increasing R, so, starting from a certain distance, the interaction of molecules can be neglected. The greatest distance Rm, on which molecules still interact, is called a radius of molecular action .

The repulsion force in the module is equal to the forces of attraction.

The distance corresponds to a stable equilibrium mutual position molecules.

In various aggregate states of substance, the distance between its molecules is different. Hence the difference in the power interaction of molecules and a significant difference in the nature of the movement of molecules of gases, liquids and solids.

In the gases of the distance between molecules several times higher than the dimensions of the molecules themselves. As a result, the interaction force between the gas molecules is small and the kinetic energy of the thermal motion of molecules far exceeds the potential energy of their interaction. Each molecule moves freely from other molecules with huge speeds (hundreds of meters per second), changing the direction and velocity module in collisions with other molecules. The length of the free range of gas molecules depends on the pressure and temperature of the gas. Under normal conditions.

In liquids, the distance between molecules is significantly less than in gases. The interaction forces between molecules are large, and the kinetic energy of the movement of molecules is commensurate with the potential energy of their interaction, as a result of which fluid molecules make oscillations about a certain equilibrium position, then jump into new equilibrium positions through very small periods of time, which leads to fluid flow. Thus, the fluid molecules make mainly oscillatory and translational movements. IN solid bodies The interaction forces between molecules is so great that the kinetic energy of the movement of molecules is much less than the potential energy of their interaction. Molecules make only oscillations with a small amplitude of about some permanent position of equilibrium - the node of the crystal lattice.

This distance can be estimated, knowing the density of the substance and molar mass. Concentration -the number of particles per unit volume is associated with density, molar mass and the number of Avogadro by the ratio.

Physics. Molecules. Location of molecules in a gaseous, liquid and solid distance.

1. 
   
   
2. In the gaseous state of the molecule is not connected with each other, are at a high distance from each other. Movement Brownian. Gas can be relatively easy to compress.
   In liquid - molecules close to each other, fluctuate together. Almost do not give in compression.
   In Firdom - molecules are strict (in crystalline lattices), there is no molecules. Compression does not succumb.
3. The structure of the substance and the start of chemistry:
   http://samlib.ru/a/anemow_e_m/aa0.shtml
   (without registration and SMS messages, in a handy text format: You can use Ctrl + C)
4. It is impossible to agree with the fact that the molecule is not moving in the solid state.

   Movement of molecules in gases

   In gases, the distance between molecules and atoms is significantly larger than the dimensions of molecules, and attraction forces are very small. Therefore, gases do not have their own form and constant volume. Gases are easily compressed, because repulsion strength at long distances are also small. Gaza possess the property to unlimited expanding, filling the entire volume provided to them. Gas molecules move with very large speeds, encounter each other, bounce apart from each other in different directions. Numerous blows of molecules about the wall of the vessel create gas pressure.

   Movement of molecules in liquids

   In liquids, the molecule not only fluctuate near the position of the equilibrium, but also make a jump from one equilibrium position in the neighboring. These jumps occur periodically. The time segment between such jumps was the name of the average time of the settling life (or average relaxation time) and is indicated by the letter?. In other words, relaxation time is the time of oscillations about one particular equilibrium position. At room temperature, this time is an average of 10-11 seconds. The time of one oscillation is 10-1210-13 s.

   The time of classroom life decreases with an increase in temperature. The distance between liquid molecules is less than the dimensions of molecules, the particles are located close to each other, and the intermolecular attraction is large. Nevertheless, the location of fluid molecules is not strictly ordered throughout the volume.

   Fluids, like firm bodies, retain their volume, but do not have their own form. Therefore, they take the shape of the vessel in which there are. The liquid has such a property as fluidity. Due to this property, the liquid does not resist the change in the shape, it is slightly compressed, and the physical properties are the same in all directions inside the liquid (isotropy of liquids). For the first time, the nature of the molecular movement in fluids was established by Soviet physicist Yakov Ilyich Frenkel (1894 1952).

   Movement of molecules in firm bodies

   Molecules and firm body atoms are located in a certain order and form a crystal lattice. Such solids are called crystalline. Atoms make oscillatory movements near the position of the equilibrium, and the attraction between them is very large. Therefore, firm bodies in normal conditions retain the volume and have their own forms

5. In gaseous-moving randomno, drove
   In liquid moving in accordance with each other
   In solid - do not move.

Consider how it changes depending on the distance between molecules the projection of the resulting interaction force between them to the direct connecting the centers of molecules. If the molecules are at distances exceeding their dimensions several times, then the strength of the interaction between them does not affect. The strength of the interaction between molecules is short-range.

At distances exceeding 2-3 diameters of molecules, the repulsion force is almost equal to zero. Only the force of attraction is noticeable. As the distance decreases, the attraction force increases and the repulsion force begins at the same time. This force increases very quickly when the electronic shells of molecules begin to overlap.

Figure 2.10 graphically depicts the dependence of the projection F. r. the strength of the interaction of molecules from the distance between their centers. On distance r. 0, approximately equal amount Radius molecules F. r. = 0 Since the attraction force is equal to module the power of repulsion. For r. > r. 0 between molecules is the force of attraction. The projection of the force acting on the right molecule is negative. For r. < r. 0 there is an repulsion force with a positive value of projection F. r. .

The origin of the strength of elasticity

The dependence of the interaction forces of molecules from the distance between them explains the emergence of the force of elasticity during compression and tension tel. If you try to bring the molecules to the distance, fewer g0, then the force preventing approaching. On the contrary, when the molecules is removed from each other, the force of attraction that returns the molecules into the initial positions after the external exposure is stopped.

With a small displacement of molecules from equilibrium positions, the strength of attraction or repulsion is growing linearly with increasing displacement. On a small section, the curve can be considered a straight line (the thickened portion of the curve in Fig. 2.10). That is why, with small deformations, it turns out to be a fair law of a thief, according to which the force of elasticity is proportional to the deformation. With big displacements of molecules, the law of the thief is already unfair.

Since during deformation of the body, distances between all molecules change, then the share of neighboring layers of molecules has a slight piece of general deformation. Therefore, the bike law is performed in deformations, in millions of times greater than the dimensions of molecules.

Atomic-power microscope

On the action of the repulsion forces between atoms and molecules at low distances, the device of an atomic-power microscope (AFM) was founded. This microscope, in contrast to the tunnel, allows you to obtain images of non-conductive electricity surfaces. Instead of a tungsten is an AFM, a small diamond fragment is used, pointed to atomic sizes. This fragment is fixed on a thin metal holder. With the rapprochement of the island with the surface under study, the electronic clouds of diamond atoms and surfaces begin to overlap and repulsion force arise. These forces deflect the tip of the diamond island. The deviation is recorded using a laser beam, reflected from the mirror attached on the holder. The reflected beam drives a piezoelectric manipulator, similar to the manipulator of the tunnel microscope. The feedback mechanism provides such a height of the diamond needle over the surface so that the bending of the holder plate remains unchanged.

In Figure 2.11, you see the image of the polymeric chains of Alanine amino acids, obtained using AFM. Each tubercle is one amino acid molecule.

At present, nuclear microscopes are currently designed, the device of which is based on the action of the molecular forces of attraction at distances, several times higher than the size of the atom. These forces are approximately 1000 times less repulsion forces in AFM. Therefore, a more complex sensitive system for registering forces is applied.

Atoms and molecules consist of electrically charged particles. Due to the action of electrical forces at low distances, the molecules are attracted, but begin to repel when the electronic shells of atoms overlap.