Le Chatelier's principle. Shift in chemical equilibrium. Le Chatelier's Principle Le Chatelier's Principle Examples

Biographical milestones

Le Chatelier was born in Paris in the family of a mining engineer. From an early age, his father instilled in his son an interest in science. My mother raised me in strictness and discipline under the motto “Order is one of the most perfect forms of civilization.” Le Chatelier received his primary and secondary education at Rolland College, while simultaneously studying at the Military Academy.

He received his education at the Polytechnic School, and later at the Higher Mining School of Paris. During his studies, Le Chatelier worked for A.E. Saint-Clair Deville in the laboratory, attended lectures at the College de France. He was interested in natural sciences, ancient languages, and religious issues.

He worked as a mining engineer in Besançon and Paris.

In 1875 he got married.

From 1878 to 1919 - professor at the Higher Mining School and almost simultaneously (1898-1907) - professor at the Collège de France.

1886 - Knight of the Legion of Honor.

In the period from 1907 to 1925. worked at the University of Paris as an associate professor and head of the department of chemistry.

In 1898 he succeeded Paul Schützenberg at the Collège de France, where he taught inorganic chemistry.

1907 – chief inspector of mines.

Since 1907 - member of the Paris Academy of Sciences.

In 1916, the Royal Society of London awarded Le Chatelier the Davy Medal.

Since 1931 - President of the French Chemical Society. He was a member of many academies of sciences and scientific societies, including a foreign corresponding member of the St. Petersburg Academy of Sciences and an honorary member of the USSR Academy of Sciences.

Le Chatelier died in 1936 at the age of 85.

Scientific activity

The main scientific achievements include:

1. He studied the processes of combustion, ignition, explosions, and detonation of firedamp (together with F. Mallard and P. E. M. Berthelot).
2. He proposed a method for determining the heat capacities of gases at high temperatures.
3. He studied chemical and technological processes in metallurgy.
4. He formulated the law of displacement of chemical equilibrium, according to which the equilibrium in an equilibrium system under external influence will shift in the direction opposite to the given action (Le Chatelier's principle).
5. He designed a thermoelectric pyrometer that allows one to determine the temperature of bodies by their color; created a metallographic microscope that helps to study opaque bodies, improved methods for studying the structure of metals and alloys.
6. He confirmed the analogy between solutions and alloys by studying the temperature regime of crystallization of systems consisting of two metals and two salts.
7. He studied methods of preparation and properties of cements, investigated the problems of burning cement and its hardening. He created the theory of “crystallization” - the theory of cement hardening.
8. He derived a thermodynamic equation that establishes the relationship between the temperature of the dissolution process, solubility and heat of fusion of a substance.
9. Invented the platinum-rhodium thermocouple.
10. Discovered the conditions for the synthesis of ammonia.

The equilibrium state for a reversible reaction can last indefinitely (without outside intervention). But if an external influence is exerted on such a system (change the temperature, pressure or concentration of final or initial substances), then the state of equilibrium will be disrupted. The speed of one of the reactions will become greater than the speed of the other. Over time, the system will again occupy an equilibrium state, but the new equilibrium concentrations of the initial and final substances will differ from the original ones. In this case, they talk about a shift in chemical equilibrium in one direction or another.

If, as a result of an external influence, the rate of the forward reaction becomes greater than the rate of the reverse reaction, this means that the chemical equilibrium has shifted to the right. If, on the contrary, the rate of the reverse reaction becomes greater, this means that the chemical equilibrium has shifted to the left.

When the equilibrium shifts to the right, the equilibrium concentrations of the starting substances decrease and the equilibrium concentrations of the final substances increase compared to the initial equilibrium concentrations. Accordingly, the yield of reaction products also increases.

A shift of chemical equilibrium to the left causes an increase in the equilibrium concentrations of the starting substances and a decrease in the equilibrium concentrations of the final products, the yield of which will decrease.

The direction of the shift in chemical equilibrium is determined using Le Chatelier’s principle: “If an external influence is exerted on a system in a state of chemical equilibrium (change temperature, pressure, concentration of one or more substances participating in the reaction), this will lead to an increase in the rate of that reaction, the occurrence of which will compensate (reduce) the impact."

For example, as the concentration of starting substances increases, the rate of the forward reaction increases and the equilibrium shifts to the right. When the concentration of the starting substances decreases, on the contrary, the rate of the reverse reaction increases, and the chemical equilibrium shifts to the left.

When the temperature increases (i.e. when the system is heated), the equilibrium shifts towards the endothermic reaction, and when it decreases (i.e. when the system cools) - towards the exothermic reaction. (If the forward reaction is exothermic, then the reverse reaction will necessarily be endothermic, and vice versa).

It should be emphasized that an increase in temperature, as a rule, increases the rate of both forward and reverse reactions, but the rate of an endothermic reaction increases to a greater extent than the rate of an exothermic reaction. Accordingly, when the system is cooled, the rates of forward and reverse reactions decrease, but also not to the same extent: for an exothermic reaction it is significantly less than for an endothermic one.

A change in pressure affects the shift in chemical equilibrium only if two conditions are met:

it is necessary that at least one of the substances participating in the reaction be in a gaseous state, for example:

CaCO 3 (s) CaO (s) + CO 2 (g) - a change in pressure affects the displacement of the equilibrium.

CH 3 COOH (liquid) + C 2 H 5 OH (liquid) CH 3 COOC 2 H 5 (liquid) + H 2 O (liquid) – a change in pressure does not affect the shift in chemical equilibrium, because none of the starting or final substances is in a gaseous state;

if several substances are in the gaseous state, it is necessary that the number of gas molecules on the left side of the equation for such a reaction is not equal to the number of gas molecules on the right side of the equation, for example:

2SO 2 (g) + O 2 (g) 2SO 3 (g) – pressure changes affect the equilibrium shift

I 2(g) + H 2(g) 2НI (g) – pressure change does not affect the equilibrium shift

When these two conditions are met, an increase in pressure leads to a shift in equilibrium towards a reaction, the occurrence of which reduces the number of gas molecules in the system. In our example (catalytic combustion of SO 2) this will be a direct reaction.

A decrease in pressure, on the contrary, shifts the equilibrium towards the reaction that occurs with the formation of a larger number of gas molecules. In our example, this will be the opposite reaction.

An increase in pressure causes a decrease in the volume of the system, and therefore an increase in the molar concentrations of gaseous substances. As a result, the rate of forward and reverse reactions increases, but not to the same extent. A decrease in pressure according to a similar scheme leads to a decrease in the rates of forward and reverse reactions. But at the same time, the reaction rate, towards which the equilibrium shifts, decreases to a lesser extent.

The catalyst does not affect the equilibrium shift, because it speeds up (or slows down) both the forward and reverse reactions to the same extent. In its presence, chemical equilibrium is only established faster (or slower).

If a system is affected by several factors simultaneously, then each of them acts independently of the others. For example, in the synthesis of ammonia

N 2(gas) + 3H 2(gas) 2NH 3(gas)

the reaction is carried out by heating and in the presence of a catalyst to increase its speed. But the effect of temperature leads to the fact that the equilibrium of the reaction shifts to the left, towards the reverse endothermic reaction. This causes a decrease in the output of NH 3. To compensate for this undesirable effect of temperature and increase the yield of ammonia, the pressure in the system is simultaneously increased, which shifts the equilibrium of the reaction to the right, i.e. towards the formation of fewer gas molecules.

In this case, the most optimal conditions for the reaction (temperature, pressure) are selected experimentally, under which it would proceed at a sufficiently high speed and give an economically viable yield of the final product.

Le Chatelier's principle is similarly used in the chemical industry in the production of a large number of different substances that are of great importance for the national economy.

Le Chatelier's principle is applicable not only to reversible chemical reactions, but also to various other equilibrium processes: physical, physicochemical, biological.

The adult human body is characterized by the relative constancy of many parameters, including various biochemical indicators, including the concentrations of biologically active substances. However, such a state cannot be called equilibrium, because it is not applicable to open systems.

The human body, like any living system, constantly exchanges various substances with the environment: it consumes food and releases products of their oxidation and decay. Therefore, it is typical for an organism steady state, defined as the constancy of its parameters at a constant rate of exchange of matter and energy with the environment. To a first approximation, a stationary state can be considered as a series of equilibrium states interconnected by relaxation processes. In a state of equilibrium, the concentrations of substances participating in the reaction are maintained due to the replenishment of the initial products from the outside and the removal of the final products to the outside. A change in their content in the body does not lead, unlike closed systems, to a new thermodynamic equilibrium. The system returns to its original state. Thus, the relative dynamic constancy of the composition and properties of the internal environment of the body is maintained, which determines the stability of its physiological functions. This property of a living system is called differently homeostasis.

During the life of an organism in a stationary state, in contrast to a closed equilibrium system, an increase in entropy occurs. However, along with this, the reverse process also occurs simultaneously - a decrease in entropy due to the consumption of nutrients with a low entropy value from the environment (for example, high-molecular compounds - proteins, polysaccharides, carbohydrates, etc.) and the release of decomposition products into the environment. According to the position of I.R. Prigogine, the total production of entropy for an organism in a stationary state tends to a minimum.

A major contribution to the development of nonequilibrium thermodynamics was made by I. R. Prigozhy, Nobel Prize winner in 1977, who argued that “in any nonequilibrium system there are local areas that are in an equilibrium state. In classical thermodynamics, equilibrium refers to the entire system, but in nonequilibrium, only to its individual parts.”

It has been established that entropy in such systems increases during embryogenesis, during regeneration processes and the growth of malignant neoplasms.

Reactions that proceed in one direction and go to completion are called irreversible. There aren't many of them. Most reactions are reversible, i.e. they flow in opposite directions and do not go all the way. For example, the reaction J 2 + H 2 D 2HJ at 350°C is a typical reversible reaction. In this case, a mobile chemical equilibrium is established and the rates of the direct and reverse processes are made equal.

Chemical equilibrium– a state of a system of reacting substances in which the rates of forward and reverse reactions are equal.

Chemical equilibrium is called dynamic equilibrium. At equilibrium, both forward and reverse reactions occur; their rates are the same, as a result of which changes in the system are not noticeable.

The concentrations of reactants that are established at chemical equilibrium are called equilibrium concentrations. They are usually denoted using square brackets, for example, , , .

A quantitative characteristic of chemical equilibrium is a value called the chemical equilibrium constant. For the reaction in general form: mA + nB = pC + qD

The chemical equilibrium constant has the form:

It depends on the temperature and nature of the reactants, but does not depend on their concentration. The equilibrium constant shows how many times the rate of the forward reaction is greater than the rate of the reverse reaction if the concentration of each of the reactants is 1 mol/l. This is the physical meaning of K.

The direction of displacement of the chemical equilibrium with changes in the concentration of reactants, temperature and pressure (in the case of gas reactions) is determined by the general situation known as principle of mobile equilibrium or Le Chatelier's principle: if any external influence is made on a system that is in equilibrium (concentration, temperature, pressure changes), then it favors the occurrence of one of two opposite reactions, which weakens the influence.

It should be noted that all catalysts equally accelerate both forward and reverse reactions and therefore do not affect the shift in equilibrium, but only contribute to its faster achievement.

Examples of problem solving

Example 1.

Calculate the temperature coefficient of the reaction rate, knowing that with an increase in temperature by 70 °C, the rate increases 128 times.

Solution:

For the calculation we use the Van't Hoff rule:

Answer: 2

Example 2.

At what temperature will a certain reaction complete in 0.5 minutes, if at 70°C it completes in 40 minutes? The reaction temperature coefficient is 2.3.

Solution:

For the calculation we use the Van't Hoff rule . Find t 2:

Answer: 122.6 0 C

Example 3.

How many times will the rate of the direct reaction N 2 (g) + 3H 2 (g) = NH 3 (g) change if the pressure in the system is doubled?

Solution:

An increase in pressure in the system by 2 times is equivalent to a decrease in the volume of the system by 2 times. In this case, the concentrations of reactants will increase by 2 times. According to the law of mass action, the initial reaction rate is V n = k·· 3.

After increasing the pressure by 2 times, the concentrations of nitrogen and hydrogen will increase by 2 times, and the reaction rate will become equal to V k = k·2·2 3 3 = k·32·3. The ratio V to /V n shows how the reaction rate will change after a change in pressure. Therefore, V k /V n = k 32 3 /(k 3) = 32.

Answer: the reaction rate will increase by 32 times.

Example 4.

The endothermic reaction of phosphorus pentachloride decomposition proceeds according to the equation PC1 5 (g) ↔ PC1 3 (g) + C1 2 (g); ∆H = +92.59 kJ. How to change: a) temperature; b) pressure; c) concentration to shift the equilibrium towards the direct reaction - decomposition of PC1 5?

Solution:

A displacement or shift in chemical equilibrium is a change in the equilibrium concentrations of reacting substances as a result of a change in one of the reaction conditions. The direction in which the equilibrium has shifted is determined by Le Chatelier's principle: a) since the decomposition reaction of PC1 5 is endothermic (H > 0), then to shift the equilibrium towards the direct reaction, the temperature must be increased: b) since in this system the decomposition of PC1 5 leads to an increase in volume (two gaseous molecules are formed from one gas molecule), then to shift the equilibrium towards a direct reaction it is necessary to reduce the pressure; c) a shift in equilibrium in the indicated direction can be achieved either by increasing the concentration of PC1 5 or by decreasing the concentration of PC1 3 or Cl 2.

Henri Le Chatelier formulated the principle that now bears his name.

The essence of the principle: a system that is in a state of stable chemical equilibrium, under external influence (changes in temperature, pressure, concentration of reactants, etc.) tends to return to a state of equilibrium, compensating for the effect.

The equilibrium will shift until a new equilibrium position occurs that corresponds to the new conditions.

It has been repeatedly hypothesized that the principle La Chatelier:

- can be considered as a type of feedback (there is an impact on the system, and there is its response);

- can be used not only in the field of chemical reactions, but also in psychology, sociology, ecology, etc.

The existence of negative feedbacks in inanimate Nature was probably first pointed out by Henri Louis Le Chatelier(1850-1936) - French scientist in the field of physical chemistry and metals. In 1884, he formulated the general law of displacement of chemical equilibrium depending on external factors, called Le Chatelier's principle. In the physical and chemical sciences there is a law of equilibrium formulated by A. L. Le Chatelier. He says that systems that are in a certain equilibrium show a tendency to maintain it and exert internal resistance to the forces that change it. For example, let water and ice be in equilibrium in a vessel at O ​​C and normal atmospheric pressure. If the vessel is heated, then part of the ice melts, absorbing heat and thus continuing to maintain the previous temperature of the mixture. If you increase the external pressure, then part of the ice again turns into water, occupying less volume, which weakens the increasing pressure.

Other liquids, unlike water, when frozen do not increase in volume, but decrease; Under the same mixture conditions, under increasing pressure they exhibit the opposite change: part of the liquid freezes; the pressure is obviously weakened by this as in the previous case. Le Chatelier’s principle is applied to solutions, chemical reactions, and body movements at every step, allowing one to anticipate systemic changes in a wide variety of cases.

But the same law, as many observations show, is applicable to biological, mental, and social systems that are in equilibrium. For example, the human body responds to external cooling by enhancing internal oxidative and other processes that produce its heat; to overheating - by increasing evaporation processes that take away heat. A normal psyche, when due to external conditions the number of sensations for it decreases, for example when a person goes to prison, seems to compensate for this deficiency by strengthening the work of fantasy, as well as developing attention to detail; on the contrary, when overloaded with impressions, attention directed to particulars decreases, the activity of fantasy weakens, etc.

It is clear that the question of the universality of Le Chatelier’s law cannot be posed and systematically studied by any of the special sciences: physical chemistry does not care about mental systems, biology - about inorganic ones, psychology - about material ones. But from a general organizational point of view, the question is obviously not only quite possible, but completely inevitable.

Bogdanov A.A. , Tectology: General organizational science in 2 books, Book 1, M., Economics, 1989, p. 139.

2.6. Shift in chemical equilibrium. Le Chatelier's principle

If the system is in a state of equilibrium, then it will remain in it as long as external conditions remain constant.

The most important are cases of imbalance due to changes in the concentration of any of the substances involved in the equilibrium, pressure or temperature.

Let's consider each of these cases.

When the concentration of any substance participating in equilibrium increases, the equilibrium shifts towards the consumption of this substance; When the concentration of a substance decreases, the equilibrium shifts towards the formation of this substance.

For example, for the reaction

Let us introduce an additional amount of hydrogen into the system. According to the law of mass action, an increase in the concentration of hydrogen will entail an increase in the rate of the forward reaction - the HI synthesis reaction, while the rate of the reverse reaction will not change. In the forward direction, the reaction will now proceed faster than in the reverse direction, i.e. balance shifts to the right, i.e. in the direction of the forward reaction. When the concentrations change in the opposite direction, they speak of balance shift to the left– in the direction of the reverse reaction.

2. When the pressure increases by compressing the system, the equilibrium shifts towards a decrease in the number of gas molecules, i.e. in the direction of decreasing pressure; when the pressure decreases, the equilibrium shifts towards an increase in the number of gas molecules, i.e. towards increasing pressure.

For reaction

an increase in pressure should shift the equilibrium to the right (on the left the number of moles of gases is 3, on the right - 2).

In the case when the reaction proceeds without changing the number of gas molecules, the equilibrium is not disturbed during compression or expansion of the system. For example, in the system

equilibrium is not disturbed when volume changes; the HI output is independent of pressure.

3. As the temperature increases, the equilibrium shifts in the direction of the endothermic reaction, and as the temperature decreases, in the direction of the exothermic reaction.

Thus, ammonia synthesis is an exothermic reaction ( ΔH)

shifts to the left - towards the decomposition of ammonia, since this process occurs with the absorption of heat.

Conversely, the synthesis of nitric oxide (II) is an endothermic reaction ( ΔН>0)

Therefore, as the temperature increases, the equilibrium in the system
shifts to the right towards the formation of NO.

The patterns that appear in the considered examples of chemical imbalance are special cases of the general Le Chatelier's principle:

If any impact is exerted on a system that is in equilibrium, then as a result of the processes occurring in it, the equilibrium will shift in such a direction that the impact will decrease.

Heterogeneous chemical equilibrium also obeys Le Chatelier's principle, but solid starting materials and reaction products do not affect the shift of heterogeneous chemical equilibrium.

2.7. Solving typical problems

Example 1. Calculate the equilibrium concentrations of hydrogen and iodine if it is known that their initial concentrations were 0.02 mol/l, and the equilibrium concentration of НI was 0.03 mol/l. Calculate the equilibrium constant.

Solution. From the reaction equation

H 2 +I 2 ↔ 2HI

it can be seen that the formation of 0.03 mol of HI requires 0.015 mol of hydrogen and the same amount of iodine, therefore, their equilibrium concentrations are equal and amount to 0.02 - 0.015 = 0.005 mol/l, and the equilibrium constant

.

Example 2. In system
equilibrium concentrations of substances
=0.3 mol/l,
=0.2 mol/l and
=1.2 mol/l. Calculate the equilibrium constant of the system and the initial concentrations of chlorine and carbon monoxide.

Solution. From the reaction equation it is clear that for the formation of 1.2 mol
1.2 moles are consumed
And
. Therefore, the initial concentration of chlorine is 0.3 + 1.2 = 1.5 mol/l, carbon monoxide 0.2 + 1.2 = 1.4 mol/l. Equilibrium constant

Example 3. How many times will the reaction rate of interaction of carbon (II) monoxide with oxygen increase if the concentrations of the starting substances are increased threefold?

Solution. 1) Write down the reaction equation:

According to the law of mass action

2) Let us denote
, Then:

3) When the concentration of the starting substances increases by 3 times, we obtain:

, A

4) Calculate the reaction rate :

, i.e. the reaction rate will increase 27 times.

Example 4. How many times will the rate of a chemical reaction increase when the temperature increases by 40˚C if the temperature coefficient of the reaction rate is 3?

Solution. According to the van't Hoff rule:

, i.e. the reaction rate will increase 81 times.

Example 5. The reaction at a temperature of 30˚C takes 2 minutes. How long will it take for this reaction to complete at a temperature of 60˚C if the temperature coefficient of rate is 2?

Solution. 1) In accordance with the van’t Hoff rule:

2) The reaction rate is inversely proportional to the reaction time, therefore:

Example 6. The reaction for the formation of nitric oxide (IV) is expressed by the equation

How will the rate of forward and reverse reactions change if the pressure is increased by 3 times and the temperature remains constant? Will this change in speed cause a shift in equilibrium?

Solution. Let before the pressure increase the equilibrium concentrations of nitric oxide (II), oxygen and nitric oxide (IV) were: = a, = b,

C, then the rate of the forward reaction

,

reverse reaction speed

.

When the pressure increases by 3 times, the concentrations of all reagents will increase by the same amount: = 3a, = 3b, = 3c.

The rate of the forward reaction will become:

The speed of the reverse reaction will become:

.

The rate of the forward reaction increased by 27 times, and the reverse reaction by 9 times. The equilibrium will shift towards the forward reaction, which is consistent with Le Chatelier's principle.

Example 7. How do they affect the balance in the system?

, (ΔН

a) decrease in pressure;

b) increase in temperature;

c) increasing the concentration of starting substances?

Solution. According to Le Chatelier's principle, a decrease in pressure will lead to a shift in equilibrium towards the reaction leading to an increase in its volume, i.e. towards the opposite reaction. An increase in temperature will lead to a shift in equilibrium towards the endothermic reaction, i.e. towards the opposite reaction. And finally, an increase in the concentration of the starting substances will lead to a shift in equilibrium towards the formation of reaction products, i.e. towards direct reaction.

Example 8. Consider the chemical equilibrium

Let us determine the equilibrium concentrations of NH 3 for two equilibrium mixtures:

1. = 0.1 M and = 0.1 M.

2. =1.0 M and = 0.1 M.

Equilibrium constant K = 6.0 ∙ 10 -2 at 525 ˚С

Solution. Let's create an expression for the chemical equilibrium constant, substitute known quantities into it and carry out calculations.

First version of chemical equilibrium:

where

Second version of chemical equilibrium

where

Conclusion. As the concentration of N2 (reagent) in the equilibrium mixture increases, the concentration of NH3 (reaction product) increases.

2.8. Problems to solve independently

1. How many times should the hydrogen concentration in the system be increased?

so that the reaction rate increases 125 times?

2. How will the reaction rate change?

what if the pressure in the system is doubled?

3. The reaction between nitric oxide (II) and chlorine proceeds according to the equation

How does the reaction rate change with increasing:

a) the concentration of nitric oxide doubled;

b) chlorine concentration doubled;

c) the concentrations of both substances are doubled?

4. At 150˚C, some reaction is completed in 16 minutes. Taking the temperature coefficient equal to 2.5, calculate the time period after which this reaction will end at 80˚C.

5. At a temperature of 40˚С the reaction takes 36 minutes, and at 60˚С – in 4 minutes. Calculate the temperature coefficient of the reaction rate.

6. The rate of some reaction at 100 0 C is equal to 1. How many times slower will the same reaction proceed at 10 0 C (the temperature coefficient of the rate is taken equal to 2)?

7. When the reaction mixture was cooled from 50 0 to 20 0 C, the rate of the chemical reaction decreased by 27 times. Calculate the temperature coefficient of this reaction.

8. Write a mathematical expression for the chemical equilibrium constant for each of the following reactions:

When completing this task, pay special attention to the fact that some substances - participants in the reactions - are in a solid state.

9. Calculate the equilibrium constant of the reaction

if the equilibrium concentrations are equal

10. Apply Le Chatelier's principle to predict conditions that increase the yield of the following reactions by shifting the equilibrium:

, (ΔН

11. Among the reactions given, indicate those for which an increase in pressure shifts the chemical equilibrium to the right:

A)
;

b)
;

V)
;

G)
;

d)
;

12. At a certain temperature the equilibrium constant of the process is

The initial concentrations of Н2 and НСО were 4 mol/l and 3 mol/l, respectively. What is the equilibrium concentration of CH 3 OH?

13. The reaction proceeds according to the equation 2A ↔ B. The initial concentration of substance A is 0.2 mol/l. The equilibrium constant of the reaction is 0.5. Calculate the equilibrium concentrations of the reactants.

14. At a certain temperature, the equilibrium concentration of sulfuric anhydride formed as a result of the reaction is

,

was 0.02 mol/l. The initial concentrations of sulfur dioxide and oxygen were 0.06 and 0.07 mol/l, respectively. Calculate the equilibrium constant of the reaction.

TOPIC 3. ATOMIC STRUCTURE AND PERIODIC SYSTEM OF ELEMENTS D.I. MENDELEEV

3.1. The first models of atomic structure

In 1897, J. Thomson (England) discovered the electron, and in 1909, R. Mulliken determined its charge, which is equal to 1.6 · 10 -19 C. The mass of an electron is 9.11 ∙ 10 -28 g. In 1904, J. Thomson proposed a model of the structure of the atom, according to which the atom can be represented as a positive sphere with interspersed electrons.

In 1910, in the laboratory of E. Rutherford (England), in experiments on bombarding metal foil with α-particles, it was established that some α-particles were scattered by the foil. From this Rutherford concluded that at the center of the atom there is a positively charged small nucleus surrounded by electrons. The radii of the nuclei lie within the range of 10 -14 – 10 -15 m, i.e. 10 4 – 10 5 times smaller than the size of an atom. Rutherford predicted the existence of the proton and its mass, which is 1800 times the mass of the electron.

In 1910, Rutherford proposed a nuclear planetary model of the atom, consisting of a heavy nucleus around which electrons move in orbit, like the planets of the solar system. However, as the theory of the electromagnetic field shows, electrons in this case should move in a spiral, continuously emitting energy, and fall onto the nucleus.

Atomic spectra. When heated, a substance emits rays (radiation). If radiation has one wavelength, then it is called monochromatic. In most cases, radiation is characterized by several wavelengths. When the radiation is decomposed into monochromatic components, a radiation spectrum is obtained, where its individual components are expressed as spectral lines. In Fig. 3.1. The atomic spectrum of hydrogen is shown. The wavelengths corresponding to the atomic spectrum of hydrogen are determined by the Balmer equation

. (3.1)

where λ – wavelength; R – Rydberg constant (109678 cm -1); n and m are integers (n = 1 for the Lyman series, n = 2 for the Balmer series, n = 3 for the Paschen series; m = 2, 3, 4 for the Lyman series, m = 3, 4, 5 for the Balmer, m = 4, 5, 6 – for the Paschen series).

Quanta and the Bohr model. In 1900, M. Planck (Germany) suggested that substances absorb and emit energy in discrete portions, which he called quanta. Quantum energy E proportional to the frequency of radiation (oscillation) ν:

,

where – h – Planck’s constant (6.626∙10 -34 J s); ν = с/λ, с – speed of light; λ – wavelength.

In 1913, the Danish scientist N. Bohr, using the Rutherford model and Planck’s theory, proposed a model of the structure of the hydrogen atom, according to which electrons move around the nucleus not in any, but only in allowed orbits, in which the electron has certain energies. When an electron moves from From one orbit to another, an atom absorbs or emits energy in the form of quanta. Each orbit has a number n (1, 2, 3, 4,...), which is called the principal quantum number. Bohr calculated the radii of the orbits. The radius of the first orbit was 5.29∙10 -13 m, the radius of other orbits was equal to:

The electron energy (eV) depended on the value of the main quantum

The negative sign of energy means the stability of a system, which is more stable the lower (the more negative) its energy. The hydrogen atom has minimum energy when the electron is in the first orbit (n=1). This condition is called main. When an electron moves to higher orbits, the atom becomes excited. This state of the atom is unstable.

Rice. 3.1. Diagram of energy levels and quantum transitions of the hydrogen atom

When moving from the upper orbit to the lower one, the atom emits a quantum of light, which is experimentally detected in the form of a series of atomic spectrum (Fig. 3.1.). The values ​​of n and m in equation (3.1) correspond to the values ​​of the principal quantum numbers from which the electron moves (m) and to which the electron moves (n). Bohr's theory made it possible to calculate the energy of electrons, the values ​​of energy quanta emitted during the transition of an electron from one level to another. Bohr's theory received experimental confirmation. However, She could not explain the behavior of an electron in a magnetic field and all atomic spectral lines. Bohr's theory turned out to be unsuitable for multi-electron atoms. There was a need for a new model of the atom, based on discoveries in the microcosm.

3.2. Quantum mechanical model of the hydrogen atom

The dual nature of the electron. In 1905, A. Einstein predicted that any radiation is a stream of energy quanta, called photons. From Einstein's theory it follows that light has a dual (particle-wave) nature.

In 1924, Louis de Broglie (France) suggested that the electron is also characterized by wave-particle duality. This was later confirmed by diffraction experiments on crystals. De Broglie proposed an equation relating the wavelength λ of an electron or any other particle with mass m and speed ν,

. (3.2)

De Broglie called waves of matter particles material waves. They are characteristic of all particles or bodies. However, as equation (3.2) implies, for macrobodies the wavelength is so small that it cannot currently be detected. So, for a body with a mass of 1000 kg moving at a speed of 108 km/h (30 m/s) λ = 2.21·10 -38 m.

In 1927, W. Heisenberg (Germany) postulated the uncertainty principle, according to which the position and momentum of a subatomic particle (microparticle) is fundamentally impossible to determine at any time with absolute accuracy. At any given time, only one of these properties can be determined. E. Schrödinger (Austria) in 1926 derived a mathematical description of the behavior of an electron in an atom.

The works of Planck, Einstein, Bohr, de Broglie, Heisenberg, as well as Schrödinger, who proposed the wave equation, laid the foundation for quantum mechanics, which studies the movement and interaction of microparticles.

Orbital. In accordance with quantum mechanical concepts, it is impossible to accurately determine the energy and position of the electron, therefore, in the quantum mechanical model of the atom, a probabilistic approach is used to characterize the position of the electron. The probability of finding an electron in a certain region of space is described by the wave function ψ, which characterizes the amplitude of the wave as a function of the electron’s coordinates. In the simplest case, this function depends on three spatial coordinates and is called orbital. According to the definition of ψ, An orbital is a region of space in which an electron is most likely to be found. It should be noted that the concept of an orbital differs significantly from the concept of an orbit, which in Bohr's theory meant the path of an electron around the nucleus of an atom. The size of the region of space that an orbital occupies is usually such that the probability of finding an electron inside it is at least 95%.

Since the electron carries a negative charge, its orbital represents a certain charge distribution, which is called electronic cloud.

Quantum numbers. To characterize the behavior of an electron in an atom, quantum numbers were introduced: principal, orbital, magnetic and spin.

Principal quantum numbern determines the energy and size of electron orbitals. The main quantum number takes values ​​1,2,3,4,5,... and characterizes the shell or energy level. The larger n, the higher the energy. Shells (levels) have letter designations: K (n = 1), L (n = 2), M (n = 3), N (n = 4), Q (n = 5), electron transitions from one shell (level ) to the other are accompanied by the release of energy quanta, which can appear in the form of spectra (see Fig. 3.1).

Orbital quantum numberl determines the shape of the atomic orbital. Electronic shells are split into subshells, so the orbital quantum number also characterizes the energy sublevels in the electron shell of an atom.

Orbital quantum numbers take an integer value from 0 to (n-1). Subshells are also designated by letters:

Subshell (sublevel)…………………s p d f

Orbital quantum number, l……………0 1 2 3

Electrons with an orbital quantum number of 0 are called s- electrons. Orbitals and, accordingly, electron clouds have a spherical shape (Fig. 3.2, a).

Electrons with orbital quantum number 1 are called p- electrons. Orbitals and, accordingly, electron clouds have a shape reminiscent of a dumbbell (Fig. 3.2, b).

Electrons with an orbital quantum number of 2 are called d– electrons. The orbitals have the shape of a four-lobed rosette (Fig. 3.2, c).

Electrons with an orbital quantum number of 3 are called f– electrons. The shape of their orbitals is even more complex than the shape of d orbitals.

The first shell (n=1) can have one (s–), the second (n=2) two (s- and p-), the third (n=3) three (s-, p-, d- ), in the fourth (n=4) there are four (s-, p-, d-, f-)-subshells.

Magnetic quantum number m l characterizes the position of the orbital in space (see Fig. 3.2).

Accordingly, in the subshell s ( l= 0) there is one orbital ( m l= 0), in the subshell p ( l= 1) – three orbitals ( m l= -1, 0, +1), in subshell d ( l= 2) five orbitals ( m l = -2, -1, 0, +1, +2).

Atomic orbital. Each electron orbital in an atom (atomic orbital, AO) can be characterized by three quantum numbers n, l And m l .

Conventionally, an atomic orbital is designated in the form of a box.

Accordingly, for the s-subshell there is one AO, for the p-subshell there are three spin AOs. work... Maybe be independent... textbook allowance in Sociology For students universities ...

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