“Kinematics of chemical reactions”, “Solutions” for remote learning. Kinematics of chemical reactions

Program topics, questions

for studying

What a student should know and be able to do

Textbooks

Basics chemical thermodynamics

1) Concepts: systems; phase; homogeneous and heterogeneous systems; processes and their classification; system state parameters and functions.

2) Thermal effects processes. Internal energy and enthalpy, their definitions and units of measurement. Hess's law and consequences from it. Enthalpy of formation of substances, phase transitions and chem. reactions.

3) Entropy. Concepts and units of measurement orientation of chemistry. reactions in isolated systems.

4) Gibbs energy. Direction of chemistry. processes in non-isolated systems.

Definitions of thermodynamic concepts.

Factors influencing the value internal energy(), enthalpy (
), entropy (S), Gibbs energy (G)

Be able to count heat balances reactions, entropy change

Make calculations and draw a conclusion about the possibility (impossibility)

1) Korovin N.V. general chemistry. 2005 (from 115 – 142)

2) Glinka N.L. General Chemistry 2006 (from 170 – 185)

3) Glinka N. L – problems and exercises in general chemistry 2006 “No. 283, 293, 295, 299 – table 5. pp. 223 – 225; No. 303, 304, 310, 311."

Kinematics chem. reactions

1) The concept of reaction speed.

2) Influence (How? Why?) on the rate of chemistry. reactions of the nature of substances, concentration, t°, pressure, surface of reacting substances, catalyst.

Explain how and why the rate of chemical reactions changes with changes in concentration, pressure, t°, catalyst.

Be able to write a mathematical expression

3) Equilibrium of the system. Chemical balance. Equilibrium constant. Le Chatelier's principle.

Law of mass action (LAM) for any chemical. systems.

Be able to determine in the direction of which reaction a chemical shift will occur. equilibrium when changing the concentration, pressure, t°, substances of the system.

1) 166- 201, 148 – 152

2) 186 – 200

3) "No. 325, 326, 330, 332, 336, 358, 363, 365, 383."

Solutions

1) Methods of expressing the concentration of solutions.

2) Energy phenomena during dissolution.

3) Pressure changes saturated steam solution, its crystallization and boiling temperatures. Raoult's laws. Osmotic pressure solutions. Van't-Hoff's law.

4) Electrolytic dissociation. Strong and weak electrolytes.

5) Features of the application of Raoult’s and van’t-Hoff’s laws to electrolyte solutions. Isotonic coefficient.

6) Hydrolysis of salts

7) Electrolytic dissociation of water. Ionic product of water. Hydrogen index.

Know the formulas that express mass fractions dissolved substance, molar, molal and equivalent (normal) concentrations of solutions, be able to make the corresponding calculations.

Be able to write equations for hydrolysis reactions various types salts and indicate the medium of their solution.

1) 204 – 243

2) 216 – 259

3) "No. 392, 414, 415, 428, 437."

3) 464, 466, 474, 478, 480, 483

3) 603, 607.

Dispersed systems

1) The concept of dispersed systems, their classification according to the particle size of the dispersed phase, state of aggregation dispersed phase and dispersed medium, interaction of parts of the dispersed system, structurally mechanical properties. Preparation of disperse systems.

2) Properties of lyophobic sols: molecular - kinetic, optical, electrokinetic. Stability of dispersed systems. Sedimentation and coagulation.

3) Lyophilic colloidal solutions. Surface active substances.

4) Characteristics of suspensions, emulsions, foams, aerosols, powders

Be able to classify disperse systems according to the degree of dispersion.

Be able to write the formula of a micelle colloidal solution.

Determine the coagulating ion in a mixture of electrolytes.

Know the definition and structure of suspensions, emulsions, aerosols, foams, and their areas of application.

Explain the properties of dispersed systems.

In chemical reactions, something similar to “ionization” occurs. For example, two substances and combine in the main substance; then, after thinking a little, we can call an atom ( - what we call an electron, and - what we call an ion). After such a replacement, as before, we can write the equilibrium equation

. (42.9)

This formula, of course, is inaccurate, because the “constant” depends on the volume to which it is allowed to combine, etc., but by turning to thermodynamic arguments, one can give meaning to the value in terms of an exponential factor, and then it turns out that it is closely related to the energy required for a reaction.

Let's try to understand this formula as the result of collisions, in approximately the same way as we comprehended the evaporation formula, counting the electrons escaping into space and those returning back per unit time. Suppose that in collisions and sometimes form a connection. And let us also assume that this is a complex molecule that participates in a general dance and is hit by other molecules, and from time to time it receives energy sufficient to explode and fall apart again and.

Note that in chemical reactions the situation is that if the approaching atoms have too little energy, then, although this energy is sufficient for the reaction, the fact of the collision of atoms does not necessarily mean the start of the reaction. Usually the collision is required to be more "hard", a "soft" collision between and may not be enough to start a reaction, even if the process releases enough energy for the reaction. Let's pretend that common feature chemical reactions is a requirement according to which a simple collision is not enough to combine and form, but it is necessary that they collide with a certain amount of energy. This energy is called activation energy, that is, the energy needed to “activate” a reaction. Let be the excess energy that is necessary for collisions to cause a reaction. Then the speed with which and generate must contain the product of the number of atoms and , multiplied by the speed with which an individual atom hits a certain area of ​​magnitude , and by the value (the probability that the atoms have sufficient energy):

. (42.10)

Now we need to find the speed of the reverse process. There is some possibility that they will break up again. To separate, they do not have enough energy to ensure their separate existence. But since it is not easy for molecules to connect, there must be some kind of barrier through which they must cross in order to fly apart. They must stock up not only with the energy necessary for their existence, but also take something in reserve. It turns out something like climbing a hill before descending into a valley; first you have to climb to a height, then go down, and only after that disperse (Fig. 42.1). Thus, the rate of transition in and is proportional to the product - the initial number of molecules per :

. (42.11)

The constant is the sum of the volume of atoms and the frequency of collisions; it can be obtained, as in the case of evaporation, by multiplying the area and thickness of the layer, but we will not do this now. What interests us now is the fact that when these speeds are equal, their ratio is equal to one. This suggests that, as before, , where contains cross sections, velocities and other factors that do not depend on the numbers .

Fig. 42.1. Energy ratio in a reaction.

Interestingly, the reaction rate still varies as , although this constant no longer has any relation to the one we encountered in the problem of concentrations; activation energy is very different from energy. Energy regulates the proportions and at which equilibrium is established, but if we want to know whether it quickly turns into , then this has nothing to do with equilibrium, and another energy appears, the activation energy, which, using the exponential, controls the rate of reaction.

Moreover, it is not a fundamental constant like . Suppose that the reaction occurs on the surface of the wall, or on some other surface, then they can spread over it in such a way that combining into will be an easier matter for them. In other words, you can dig a “tunnel” through a mountain or rip off the top of a mountain. Due to the conservation of energy, no matter which path we take, the result will be the same: from and we get , so the energy difference does not depend on the path along which there is a reaction, however, the activation energy is very dependent on this path. This is why the rates of chemical reactions are so sensitive to external conditions. You can change the reaction rate by changing the surface with which the reagents come into contact; you can make a “set of barrels” and use it to select any speeds if they depend on the properties of the surface. You can introduce a third object into the environment in which the reaction occurs; it can also greatly change the rate of a reaction, such substances with a slight change sometimes greatly influence the rate of a reaction; they are called catalysts. There may be practically no reaction at all, because it is too high for a given temperature, but if you add this special substance - a catalyst, then the reaction proceeds very quickly because it decreases. Therefore, the rate of the reverse reaction is proportional and drops out of the formula for equilibrium concentrations. The correctness of the equilibrium law (42.9), which we wrote in the first place, is absolutely guaranteed regardless of any possible reaction mechanism!

Chemical kinetics is the study of the rate of chemical reactions and its dependence on various factors (concentration of reagents, t, P, catalyst, etc.).

Chemical reactions occur with at different speeds. Some reactions are completed within a fraction of a second (decomposition explosives), others last for minutes, hours, days, others last for tens, hundreds, thousands of years (processes occurring in the earth’s crust).

The rate of a particular reaction can also vary widely depending on the conditions of its occurrence (a mixture of hydrogen and oxygen at ordinary temperature can remain unchanged for an unlimited time; when an appropriate catalyst is introduced into it, it reacts very violently; at 630 ° C it reacts without a catalyst ).

A phase is a part of a system that differs in its physical and chemical properties from other parts of the system and is separated from them by an interface, upon passage through which the properties of the system change sharply.

Systems consisting of one phase are called homogeneous, systems consisting of several phases are called heterogeneous. Accordingly, reactions in which the interacting substances are in the same phase are called homogeneous, and reactions in which substances combine in different phases are called heterogeneous.

The rate of a homogeneous chemical reaction is usually expressed by the change in the concentration of reactants or the resulting reaction products per unit time. Concentrations starting materials decrease during the reaction, and the concentrations of reaction products increase over time. The rate of a homogeneous chemical reaction decreases as the starting materials are consumed.

The average reaction speed vav in the time interval from t1 to t2 is determined by the relation:

; .

Rice. 5.1. Changes in the concentration of starting substances over time.

Instantaneous speed is the rate of reaction in this moment time t. It is determined by the derivative of concentration with respect to time:

Rice. 5.2. Change in the concentration of reactants over time.

The reaction rate is always considered positive. If in the calculations we take the change in the concentration of the starting substances, then in the specified expression a “-” sign is placed; if this concerns reaction products, then the “+” sign should be taken.

Factors affecting the rate of a chemical reaction:

the nature of the reacting substances;

concentration of reagents;

temperature;

catalysts;

dispersion (for solids);

acidity of the medium (for reactions in solutions);

reactor shape (for chain reactions);

intensity of illumination with visible or UV rays (for photochemical reactions);

intensity of irradiation with rays (for radiation-chemical reactions), etc.

Nature of reactants

2NO + O2 = 2NO2 – goes under standard conditions.

2CO + O2 = 2CO2 – does not react under standard conditions, although the equations of these reactions are superficially similar, but the nature of the substances is different.

Reagent concentration

A necessary prerequisite for the interaction of substances is the collision of molecules. The number of collisions, and hence the rate of a chemical reaction, depends on the concentration of reactants: than more molecules, the more collisions there are.

Law of mass action

For the reaction aA + bB ® cC, the rate of the direct reaction is

,

where [A], [B] are the molar concentrations of reactants A and B; k is the rate constant of the chemical reaction (given).

The physical meaning of the rate constant: it is equal to the reaction rate when [A] = 1 mol/l and [B] = 1 mol/l.

Homogeneous reaction: 2NO(g) + O2(g) = 2NO2(g)

v=k×2·.

Heterogeneous reaction: C(solid) + O2(g) = CO2(g)

It is believed that the surface area of ​​the coal on which the reaction occurs remains constant for a long time and is taken into account by the coefficient k.

Effect of temperature on the rate of homogeneous reactions

An increase in temperature increases the speed of movement of molecules and, accordingly, causes an increase in the number of collisions between them. The latter also entails an increase in the rate of chemical reaction.

Quantitatively, the effect of temperature on the rate of homogeneous chemical reactions can be expressed in approximate form by the van’t Hoff rule:

An increase in temperature by 10° increases the rate of homogeneous chemical reactions by approximately 2–4 times.

Rice. 5.3. Change in reaction speed depending on increase

reaction temperature.

Mathematically it would look like this:

,

where is the temperature coefficient of the reaction rate, equal to approximately 2÷4.

If every collision resulted in an act of interaction, all reactions would have to occur at the speed of an explosion. In fact, only a small number of collisions lead to acts of interaction. A reaction is caused by collisions only of active molecules whose energy reserve is sufficient to perform an elementary act of reaction. The number of active collisions at a given temperature is proportional to the total content of reacting molecules. With increasing temperature, the number of active collisions increases much more than total number collisions.

In order for the molecules to react during a collision, the chemical bonds must be “loose.” To do this, the molecule must have an increased energy reserve. Molecules that have this necessary supply energies are called activated. When substances are heated, activation of molecules occurs due to their acceleration forward movement, and also due to increased vibrational motion of atoms and atomic groups in the molecules themselves. All this leads to weakening of the bonds inside the molecules. Thus, in order for molecules to react, they need to overcome some energy barrier.

In accordance with the above, the change in the energy of the A + B system during its transformation into S can be graphically represented as follows (Fig. 5.4.)

The S molecule is formed from A and B as a result of the redistribution of atoms and chemical bonds. To form the S molecule, activated molecules A and B, upon collision, first form an activated complex AB, within which a redistribution of atoms occurs. The energy required to excite a molecule to the activation energy of the complex is called the activation energy Ea.

Rice. 5.4. Enthalpy change diagram for endothermic (a)

and exothermic (b) processes.

Figure a) shows that the reaction products have a greater energy reserve than the starting substances, that is, the reaction A + B ® S is endothermic. The difference between the energy of the reaction products and the starting materials is the thermal effect of the reaction.

The corresponding graph for the exothermic reaction C + D → P is shown in Figure b).

The relationship between the reaction rate constant k and the activation energy Ea is determined by the Arrhenius equation:

,

where A is a pre-exponential coefficient associated with the probability and number of collisions.

Logarithm of the Arrhenius equation:

or

gives the equation of a straight line. Knowing the rate constants at several temperatures allows us to determine the activation energy of a given reaction:

The tangent of the angle of inclination of this straight line to the abscissa axis is equal to:

.

Activation energy is the factor by which the nature of the reactants affects the rate of a chemical reaction.

- “quick” reactions ( ion reactions in solutions);

- reactions with measurable speed

(Н2SO4 + Na2S2O3 = Na2SO4 + SO2 + S + H2O);

- “slow” reactions

(synthesis of NH3 at normal temperatures).

The reaction path can be changed by introducing catalysts into the system.

Catalysts are substances that affect the rate of a chemical reaction, but their chemical composition remains the same after intermediate steps. The effect of catalysts on the rate of chemical reactions is called catalysis.

Catalysts can lower the activation energy by directing a reaction along a new path. A decrease in activation energy leads to an increase in the proportion of reactive particles and, consequently, to an acceleration of the interaction process. Catalysts that speed up a reaction are called positive. Negative catalysts (inhibitors) are also known. They slow down the reaction by binding active intermediate molecules or radicals, and thereby prevent the reaction from proceeding.

Catalysts are divided into homogeneous and heterogeneous. Homogeneous are in the same state of aggregation with at least one of the reagents.

Homogeneous catalysis most often occurs through the formation of unstable intermediates. For example, the reaction A + B → C requires high energy activation Ea. In the presence of a catalyst, the reactions A + K → AK and AK + B → C + K occur, where K is the catalyst.

Rice. 5.6. Energy diagram of the reaction A + B = C

without catalyst and with catalyst.

If the largest of the activation energies Ea" and Ea"" for these sequential reactions is less than the activation energy for the reaction without a catalyst, Ea, then the catalyst is positive.

Example of a homogeneous catalyst:

SO2 + O2 = SO3 - almost no use;

2NO + O2 = NO2 - intermediate state;

SO2 + NO2 = SO3 + NO – actively occurring reaction ( nitrous method sulfuric anhydride, and from it - sulfuric acid).

Chain reactions.

Reactions involving free radicals, are called chain. A radical is a short-lived valence-unsaturated particle.

There are two types of chain reactions:

with unbranched chains;

with branched chains.

The first type is the photochemical synthesis of HCl. The chain arises as a result of the formation of atoms - radicals. ECl-Cl =58.0 kcal/mol; EH-H = 104.2 kcal/mol.

Cl2 + hn = 2Cl× chain nucleation

chain development

………………………….

open circuit

Due to external source energy (light, electrical discharge, heating, exposure to ά-, β- or γ- radiation) free radicals or atoms with free valencies are formed. They interact with molecules. A new active particle is again formed in each link of the chain. By repeating the same elementary processes, a chain reaction occurs. Its duration can be very long. In the above reaction, up to 100 thousand HCl molecules are formed for each absorbed quantum. The collision of two identical radicals, provided that the energy released can be transferred to a third body, leads to chain termination. The cause of termination can be not only the recombination of free radicals, but also their capture by the wall of the reaction vessel, the interaction of the radical with impurities, as well as the formation of a low-active radical (volume termination). Therefore, the rate of the chain reaction is very sensitive to the presence of foreign particles and the shape of the vessel.

In branched chain reactions a single reaction of one free radical produces more than one new free radical.

The radicals formed in reaction I ensure the development of an unbranched chain, and the oxygen atom, which has two free valences (reaction II), forms two radicals that begin branching. Arises great amount free radicals. The “reproduction” of radicals leads to an avalanche-like course of the process, which can cause an explosion:

However, even in these processes, circuit breaks occur. Moreover, a rapid increase in the speed of the process is observed only in the case when the rate of branching outstrips the rate of termination.

For such reactions, the change in concentration active centers in time can be expressed by the following relation:

,

where C is the number of active centers in the reaction zone;

Rate of nucleation of active centers;

f – chain branching rate constant;

g – circuit breakage rate constant.

Chemical reactions are divided into reversible and irreversible

Chemically irreversible reactions under these conditions proceed almost to completion, until the complete consumption of one of the reacting substances (NH4NO3 → 2H2O + N2O - no attempt to obtain nitrate from H2O and N2O leads to a positive result).

Chemically reversible reactions occur simultaneously under given conditions in both forward and reverse directions. Not reversible reactions less than reversible. An example of a reversible reaction is the interaction of hydrogen with iodine:

; .

After some time, the rate of HI formation will become equal speed its decomposition:

; .

In other words, chemical equilibrium will occur:

Rice. 5.7. Changing the speed of forward (1) and reverse (2) reactions

over time.

Chemical equilibrium is the state of a system in which the rate of formation of reaction products is equal to the rate of their conversion into the original reagents.

Chemical equilibrium is dynamic, that is, its establishment does not mean the cessation of the reaction.

Signs of a true chemical equilibrium:

the state of the system remains unchanged over time in the absence of external influences;

the state of the system changes under the influence of external influences, no matter how small they may be;

the state of the system does not depend on which side it approaches equilibrium.

Based on the equality of the rates of forward and reverse reactions at equilibrium, we can write:

.

Thus, we see that at steady equilibrium, the product of the concentrations of the reaction products divided by the product of the concentrations of the starting substances, in powers equal to the corresponding stoichiometric coefficients, for a given reaction at a given temperature is constant value, called the equilibrium constant.

In general terms for the reaction

the expression for the equilibrium constant should be written:

.

The concentrations of reactants at steady state are called equilibrium concentrations.

In the case of heterogeneous reversible reactions, the expression Kc includes only the equilibrium concentrations of gaseous and dissolved substances. So, for the reaction CaCO3 ↔ CaO + CO2

Under constant external conditions, the equilibrium position is maintained indefinitely. When changing external conditions the equilibrium position may change. Changes in temperature and concentration of reagents (pressure for gaseous substances) lead to a violation of the equality of the rates of forward and reverse reactions and, accordingly, to a violation of equilibrium. After some time, the equality of speeds will be restored. But the equilibrium concentrations of reagents under new conditions will be different. System transition from one equilibrium state to another is called a displacement or shift of equilibrium. Chemical equilibrium can be compared to the position of a balance beam. Just as it changes from the pressure of a load on one of the cups, the chemical equilibrium can shift towards a forward or reverse reaction depending on the process conditions. Each time a new equilibrium is established, corresponding to new conditions.

The numerical value of the constant usually changes with temperature. At constant temperature, Kc values ​​​​do not depend on pressure, volume, or concentrations of substances.

Knowing the numerical value of Kc, it is possible to calculate the values ​​of the equilibrium concentrations or pressures of each of the reaction participants.

For example, suppose that you need to calculate the equilibrium concentration of HI resulting from the reaction H2 + I2 ↔ 2HI. Let's denote initial concentrations H2 and I2 through C, and their change at the moment of equilibrium through x (mol/l). Then the equilibrium concentrations of the reactants are:

= (C – x);

= (C – x) = ; = 2x.

We have

. Based on this expression, it is possible to calculate x and, therefore, the equilibrium concentrations of the reagents.

For reactions involving gases, it is more convenient to use partial pressures of substances. The equilibrium constant in this case is denoted by Kp.

.

There is a connection between Kc and Kr. Using the example of the ammonia synthesis reaction, we will find it. N3+ 3H2 ↔ 2NH3; Concentrations of substances in

gas environment

can be expressed as the ratio of the number of moles n of a substance to the volume of the system V:

The value of n can be found from the Mendeleev–Clapeyron equation: .

РV = nRT => n =.

.

We get

We express the value of Ks through the obtained value:

,

Or you can write it another way:

After minor transformations we get:

.

where is the difference in coefficients in the reaction equation

For reactions occurring without a change in volume we obtain:

.

There is a connection between the change in the isobaric-isothermal potential of a chemical reaction and the equilibrium constant, expressed through the partial pressure of components A, B, C, D, E at equilibrium.

For a temperature of 298 it looks like this:

If any impact is exerted on a system that is in equilibrium, then those processes in the system that tend to reduce this impact to a minimum are strengthened.

Influence of concentrations of reacting substances on the state

.

equilibrium

.

As the concentration of O2 (the denominator in this expression) increases, the concentration of SO3 (the numerator) must increase. This follows from the fact that Kc=const. Thus, an increase in O2 concentration will shift the equilibrium to more full use SO2 and greater yield SO3.

The influence of pressure on the state of equilibrium

Pressure is essential in reactions between gases.

As a result of increasing pressure, the concentration of reactants increases and, accordingly, the reaction rate.

Let's consider possible cases.

A). In a reaction, the sum of moles of starting materials is equal to the sum of moles of reaction products. The total corresponding volumes of gases will also be equal.

.

If you increase the pressure in a closed reaction vessel, for example, by 2 times, then the volume will also change by half. Accordingly, the concentration of gases will double. The rate of forward and reverse reactions increases, but by an equal amount. Therefore, no shift in chemical equilibrium occurs.

.

Thus, if the volumes of the initial and final gaseous products of an equilibrium system are equal, then a change in pressure does not upset the equilibrium.

B). The sum of the moles of the starting substances is greater than the sum of the moles of the resulting products:

N2 + 3H2 Û 2NH3.

From four moles of starting substances, two moles of products are formed - the reaction proceeds with a decrease in volume. [As the pressure increases, the concentration of the starting substances will increase in to a greater extent, than the concentration of products, which leads to a shift in equilibrium towards the formation of ammonia.]

.

IN). The sum of moles of starting substances is less than the sum of moles of products:

N2O4<=>2NO2;

.

The direct reaction leads to an increase in the number of moles of the substance in the system, that is, to an increase in pressure.

When the reverse reaction occurs, on the contrary, the pressure in the system drops. If, when equilibrium is established, the pressure is increased, the system will react, tending to the initial state. The equilibrium will shift towards the reverse reaction, accompanied by a decrease in pressure, that is, towards the formation of N2O4. If the pressure is reduced, then the equilibrium will shift towards the direct reaction, accompanied by an increase in pressure, that is, towards the formation of NO2.

when pressure changes, the equilibrium shifts only in those reversible reactions that are accompanied by a change in the volume of gaseous substances;

an increase in pressure shifts the equilibrium to the side smaller volumes, decrease – towards higher volumes.

The influence of temperature on the state of equilibrium

2H2 + O2<=>2H2O(g) + 484.9 kJ.

The process of water formation is exothermic, decomposition is endothermic.

In accordance with Le Chatelier's principle, when heat is supplied to this equilibrium system, the equilibrium should shift towards the endothermic reaction, that is, it should lead to the decomposition of water. As a result, there will be a decrease in the equilibrium concentration of water vapor and an increase in the equilibrium concentrations of hydrogen and oxygen.

Cooling this system will intensify the exothermic process.

Consider the system:

N2 + 3H2<=>2NH3 + 92kJ.

A decrease in temperature shifts the equilibrium to the right, that is, it increases the yield of NH3. However, in industry this process is carried out at quite high temperatures. This is due to the fact that when low temperatures the rate of equilibrium is low, although the yield of the target product is higher.

Thus, when an equilibrium system is heated, the equilibrium shifts towards an endothermic reaction, and when cooled, towards an exothermic reaction.

The influence of catalysts on the state of equilibrium

The introduction of catalysts into an equilibrium system does not cause a shift in equilibrium, since the catalyst, while accelerating the forward reaction, also accelerates the reverse reaction to the same extent. But the introduction of catalysts makes it possible to achieve equilibrium in a shorter time.

Bibliography

Glinka N.L. General chemistry. – M.: Chemistry, 1978. – P. 166-191.

Shimanovich I.E., Pavlovich M.L., Tikavyi V.F., Malashko P.M. General chemistry in formulas, definitions, diagrams. – Mn.: Universitetskaya, 1996. – P. 102-115.

Karapetyants M.Kh. Introduction to the theory of chemical processes. – M.: graduate School, 1981. – P. 75-90.

Vorobyov V.K., Eliseev S.Yu., Vrublevsky A.V. Practical and independent work in chemistry. – Mn.: UE “Donarit”, 2005. – P. 39-46.

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