The mechanisms of chemical transformations and their rates are studied by chemical kinetics. Chemical processes take place over time various speeds. Some happen quickly, almost instantly, while others take a very long time to occur.

In contact with

Speed ​​reaction- the rate at which reagents are consumed (their concentration decreases) or reaction products are formed per unit volume.

Factors that can affect the rate of a chemical reaction

The following factors can affect how quickly a chemical interaction occurs:

• concentration of substances;
• the nature of the reagents;
• temperature;
• the presence of a catalyst;
• pressure (for reactions in a gaseous medium).

Thus, by changing certain flow conditions chemical process, you can influence how fast the process will proceed.

In the process of chemical interaction, the particles of the reacting substances collide with each other. The number of such coincidences is proportional to the number of particles of substances in the volume of the reacting mixture, and hence proportional to the molar concentrations of the reagents.

Law of acting masses describes dependency reaction rate on the molar concentrations of substances that interact.

For an elementary reaction (A + B → ...), this law is expressed by the formula:

υ \u003d k ∙С A ∙С B,

where k is the rate constant; C A and C B are the molar concentrations of the reactants, A and B.

If one of the reacting substances is in a solid state, then the interaction occurs at the interface, in connection with this, the concentration solid matter is not included in the equation of the kinetic law of acting masses. To understand the physical meaning of the rate constant, it is necessary to take C, A and C B equal to 1. Then it becomes clear that the rate constant is equal to the reaction rate at reagent concentrations equal to unity.

The nature of the reagents

Since in the process of interaction they are destroyed chemical bonds reacting substances and new bonds of reaction products are formed, then the nature of the bonds participating in the reaction of the compounds and the structure of the molecules of the reacting substances will play an important role.

Surface area of ​​contact of reagents

Such a characteristic as the surface area of ​​contact of solid reagents, sometimes quite significantly, affects the course of the reaction. Grinding a solid allows you to increase the surface area of ​​contact of the reagents, and hence speed up the process. The area of ​​contact of solutes is easily increased by the dissolution of the substance.

Reaction temperature

As the temperature increases, the energy of the colliding particles will increase, it is obvious that with an increase in temperature, the chemical process itself will accelerate. A clear example of how an increase in temperature affects the process of interaction of substances can be considered the data given in the table.

Table 1. Effect of temperature change on the rate of water formation (О 2 +2Н 2 →2Н 2 О)

For a quantitative description of how temperature can affect the rate of interaction of substances, the van't Hoff rule is used. Van't Hoff's rule is that when the temperature rises by 10 degrees, there is an acceleration of 2-4 times.

The mathematical formula describing the van't Hoff rule is as follows:

Where γ is temperature coefficient speed chemical reaction(γ = 2−4).

But the Arrhenius equation describes the temperature dependence of the rate constant much more accurately:

Where R is the universal gas constant, A is a factor determined by the type of reaction, E, A is the activation energy.

The activation energy is the energy that a molecule must acquire in order for a chemical transformation to occur. That is, it is a kind of energy barrier that will need to be overcome by molecules colliding in the reaction volume in order to redistribute bonds.

The activation energy does not depend on external factors, but depends on the nature of the substance. The value of the activation energy up to 40 - 50 kJ / mol allows substances to react with each other quite actively. If the activation energy exceeds 120 kJ/mol, then the substances (at ordinary temperatures) will react very slowly. A change in temperature leads to a change in the number of active molecules, that is, molecules that have reached an energy greater than the activation energy, and therefore capable of chemical transformations.

Catalyst action

A catalyst is a substance that can speed up a process, but is not part of its products. Catalysis (acceleration of the course of a chemical transformation) is divided into · homogeneous, · heterogeneous. If the reactants and the catalyst are in the same states of aggregation, then catalysis is called homogeneous, if different, then heterogeneous. The mechanisms of action of catalysts are diverse and quite complex. In addition, it should be noted that catalysts are characterized by selectivity of action. That is, the same catalyst, accelerating one reaction, may not change the rate of another in any way.

Pressure

If the transformation involved gaseous substances, then the change in pressure in the system will affect the rate of the process . This happens because that for gaseous reactants, a change in pressure leads to a change in concentration.

Experimental determination of the rate of a chemical reaction

It is possible to determine the rate of a chemical transformation experimentally by obtaining data on how the concentration of reacting substances or products changes per unit time. Methods for obtaining such data are divided into

• chemical,
• physical and chemical.

Chemical Methods quite simple, accessible and accurate. With their help, the speed is determined by directly measuring the concentration or amount of a substance of reactants or products. In the case of a slow reaction, samples are taken to monitor how the reagent is consumed. After that, the content of the reagent in the sample is determined. By sampling at regular intervals, it is possible to obtain data on the change in the amount of a substance during the interaction. The most commonly used types of analysis are titrimetry and gravimetry.

If the reaction proceeds quickly, then in order to take a sample, it has to be stopped. This can be done by cooling abrupt removal of the catalyst, it is also possible to dilute or transfer one of the reagents to a non-reactive state.

Methods of physicochemical analysis in modern experimental kinetics are used more often than chemical ones. With their help, you can observe the change in the concentrations of substances in real time. There is no need to stop the reaction and take samples.

Physico-chemical methods are based on the measurement physical property, depending on the quantitative content of a certain compound in the system and changing with time. For example, if gases are involved in the reaction, then pressure can be such a property. Electrical conductivity, refractive index, and absorption spectra of substances are also measured.

The subject of chemical kinetics.

Thermodynamics takes into account only the initial and final state of the system, allows to predict with great accuracy the fundamental possibility of the process, but it does not provide any information about the mechanism of the process, about its changes over time.

All these questions physical chemistry are discussed in the section of chemical kinetics.

The branch of physical chemistry devoted to the regularities of the course of chemical processes in time is called chemical kinetics.

Problems of chemical kinetics:

1. experimental study of reaction rates and their dependence on the flow conditions (concentration of reacting substances, temperature, presence of other substances, etc.);

2. Establishment of the reaction mechanism, that is, the number of elementary stages and the composition of the resulting intermediate products.

A quantitative description of the dependence of the reaction rate on the concentration of reactants is based on the basic postulate of chemical kinetics and is the subject of formal kinetics.

AT general view A chemical reaction can be written as follows:

ν 1 А 1 + ν 2 А 2 +…+ ν i А i ν 1 ´А 1 ´ + ν 2 ´А 2 ´ +…+ν n ´А n ´,

where ν i and ν n ´ are the stoichiometric coefficients of the initial substances and reaction products, respectively; А i and А n ´ are initial substances and reaction products.

The rate of a chemical reaction υ is the change in the amount of reacting substances per unit time per unit volume (measured in mol / (l∙s)).

Since the amount of reactants varies with time, the reaction rate is a function of time. One can introduce the concept average reaction rate considered in a certain period of time:

where n 1 and n 2- concentration of one of the initial substances in the initial t1 and final t2 moment of time.

The reaction rate is determined by the decrease in the amount of one of the reacting substances (with the “-” sign) or by the increase in the amount of one of the formed substances (with the “+” sign) per unit time per unit volume.

With a decrease in the hourly interval, when, we obtain an expression for true speed at this point in time:

If the volume of the system is constant ( V=const), then we can use the concept of concentration:

This equation is considered for reactions in solutions, when the change in volume can be neglected.

Chemical reactions proceed, as a rule, through several stages. The rate of the overall reaction is determined by the rate of the slowest step, called limiting.

The reaction rate depends on many factors: the nature and concentration of reactants, temperature, the presence of other substances (catalysts, inhibitors), etc.

In general, according to law of mass action, can be written that the rate of a chemical reaction is directly proportional to the product of the concentrations of the reacting substances in some powers equal to the order of the reaction for a given substance:

,

(1)

where is the rate of a chemical reaction;

k- rate constant of a chemical reaction;

- concentration of reacting substances;

n i is the order of the reaction for a given substance.

Expression (1) is called basic postulate of chemical kinetics. Wherein v i = n i in those cases where the reaction proceeds in one stage, as well as for all reactions that proceed under equilibrium conditions (regardless of the fact that under conditions far from equilibrium, they can proceed through a number of intermediate stages). In most cases, the reaction order is not equal to the stoichiometric coefficient (for multistage reactions) and is determined experimentally.

The coefficient of proportionality in the basic postulate of chemical kinetics is called reaction rate constant k . The physical meaning of the coefficient k can be established if we take the concentration of the reacting substances equal to 1, then the rate constant of a chemical reaction will be equal to the value of the reaction rate. Rate constant k depends on the nature of the reacting substances, temperature, but does not depend on the concentration of the starting substances.

Question number 3

What factors affect the rate constant of a chemical reaction?

Reaction rate constant (specific reaction rate) is the coefficient of proportionality in the kinetic equation.

The physical meaning of the reaction rate constant k follows from the equation of the law of mass action: k numerically equal to the reaction rate at a concentration of each of the reactants equal to 1 mol / l.

The reaction rate constant depends on the temperature, on the nature of the reactants, on the presence of a catalyst in the system, but does not depend on their concentration.

1. Temperature. With an increase in temperature for every 10 ° C, the reaction rate increases by 2-4 times (Van't Hoff's Rule). With an increase in temperature from t1 to t2, the change in the reaction rate can be calculated by the formula: (t2 - t1) / 10 Vt2 / Vt1 = g (where Vt2 and Vt1 are the reaction rates at temperatures t2 and t1, respectively; g is the temperature coefficient of this reaction). Van't Hoff's rule is applicable only in a narrow temperature range. More accurate is the Arrhenius equation: k = A e –Ea/RT where A is a constant depending on the nature of the reactants; R is the universal gas constant; Ea is the activation energy, i.e., the energy that colliding molecules must have in order for the collision to lead to a chemical transformation. Energy diagram of a chemical reaction. Exothermic reaction Endothermic reaction A - reagents, B - activated complex (transition state), C - products. The higher the activation energy Ea, the more the reaction rate increases with increasing temperature. 2. The contact surface of the reactants. For heterogeneous systems (when substances are in different states of aggregation), the larger the contact surface, the faster the reaction proceeds. The surface of solids can be increased by grinding them, and for soluble substances by dissolving them. 3. Catalysis. Substances that participate in reactions and increase its rate, remaining unchanged by the end of the reaction, are called catalysts. The mechanism of action of catalysts is associated with a decrease in the activation energy of the reaction due to the formation of intermediate compounds. In homogeneous catalysis, the reactants and the catalyst make up one phase (they are in the same state of aggregation), while in heterogeneous catalysis they are different phases (they are in different states of aggregation). In some cases, the course of undesirable chemical processes can be drastically slowed down by adding inhibitors to the reaction medium (the phenomenon of "negative catalysis").

Question number 4

Formulate and write down the law of mass action for the reaction:

2 NO+O2=2NO2

LAW OF MASS ACTION: The rate of a chemical reaction is proportional to the product of the concentrations of the reactants. for the reaction 2NO + O2 2NO2, the law of mass action will be written as follows: v=kС2(NO)·С(O2), where k is the rate constant, depending on the nature of the reactants and temperature. The rate in reactions involving solids is determined only by the concentration of gases or dissolved substances: C + O2 \u003d CO2, v \u003d kCO2

Factor k in the kinetic equations (1.3) - (1.8), showing the speed at which the process proceeds at concentrations of reacting substances equal to unity, is called the rate constant of the chemical process.

Along with the rate, the rate constant of a chemical process is the main parameter in chemical kinetics.

The rate constants of reactions of different orders have different dimensions. From equation (1.5) it follows that the dimension of the rate constant for the first-order reaction t -1 ; from equation (1.7) is the dimension of the second-order rate constant c -1 t -1 ; the third-order rate constant, as follows from Eq. (1.8), has the dimension c -2 t -1 , where c -concentration, t - time.

The concentration is usually measured in mol/l, and the time is in seconds ( With). Then the dimension of the first-order rate constant from -1 , the second - l.mol -1 s -1, third - l 2 .mol ​​-2 .s -1.

The reaction rate constant depends on which compound it is measured for. For example, in the dimerization reaction of nitrogen dioxide

the rate of disappearance of NO 2 is twice that of the appearance of N 2 O 4 .

Arrhenius equation

The rate constant of a chemical reaction, as a rule, increases sharply with increasing temperature. Typically, an increase in the temperature of the reaction mixture by 10°C leads to an increase in the reaction rate by 2-4 times. The dependence of the reaction rate constant on temperature in most cases can be described by the Arrhenius equation

, (1.9)

where E a- activation energy;

R- universal gas constant, equal to 8.3 J / (mol.K),

BUT - pre-exponential factor - a frequency factor having the dimension of a rate constant.

The larger the value E a , the faster the reaction rate increases with temperature. If the reactions are simple, the value E a shows what is the minimum excess energy per 1 mole that the reacting particles must have in order for them to react. Particles whose energy is greater than or equal to E a, called active.

For complex reactions consisting of several stages, the parameter E a in equation (1.9) does not always have a simple physical meaning and is often a function of the activation energy of individual stages. However, in this case the parameter E a considered to be the activation energy, although it is more correct to call it the effective or empirical activation energy.

Options E a and BUT can be determined from the dependence of the reaction rate constant on temperature using equation (1.9), written as:

(1.10)

From the dependency graph ln k from 1/T(Fig. 1.2) are easy to find ln BUT and E a /R , and of them BUT and E a. Basically, to determine E a and BUT it is enough to know the rate constants k 1 and k 2 at two temperatures T 1 and T 2

Figure 1.2 - Arrhenius dependence of the reaction rate on temperature

Then, according to equation (1.10)

Such a definition E a , as a rule, does not provide sufficient accuracy, and it is recommended to determine the activation energy using at least four values ​​of the rate constant at four different temperatures in the range of at least 30-40 °C.

Zero order reaction

When carrying out homogeneous nitration of benzene, toluene, ethylbenzene with a large excess of nitric acid (5 mol HNO 3 per 0.1 mol of nitrated compound), it was found that the nitration rate remains unchanged until all the nitrated compound has reacted.

Therefore, the reaction has zero order:

The rate constant for the nitration of benzene, toluene, and ethylbenzene under these conditions is the same and does not depend on the concentration of the nitrated compound. This is explained by the fact that the rate of formation of the nitronium cation during autoprotolysis of nitric acid is lower than the rate of nitration of the aromatic compound:

and since Nitric acid present in large excess, its concentration remains practically unchanged during the reaction.

The probability of the formation of new molecules when the particles of the initial substances meet will depend on the process of rearrangement of their electron shells. A necessary condition for this is the possibility of overlapping of the electronic orbitals of atoms with the breaking of old and the formation of new bonds, which cannot always be realized due to the geometric structure of the interacting particles. For example, in order for an elementary act of the bimolecular chemical reaction A + B®AB to take place, the distance between the particles A and B and their mutual orientation must become such that the rearrangement of their electron shells is possible.

The overlapping of electron orbitals is carried out in the process of particles approaching. This increases both the energy of attraction and the energy of repulsion. Changing the ratio of these energies depending on the distance between the particles can lead to the emergence of an energy barrier, the overcoming of which is a necessary condition for the implementation of an elementary act. Therefore, for many reactions there is a minimum threshold energy, called activation energy(E ak), which the encountered particles must have in order for a chemical reaction to occur. The main source of energy to overcome this energy barrier is kinetic energy thermal motion particles, which depends on temperature. Therefore, the probability of an elementary act (reaction rate constant) will depend on the temperature.

Svante Arrhenius ( Arrhenius) proposed to describe the temperature dependence of the reaction rate constant by the equation

where k 0 is the pre-exponential factor; E ak is the activation energy; R is the universal gas constant; T– temperature (K).

In practice, for most reactions in a small temperature range, the pre-exponential factor and activation energy are considered constants, independent of temperature.

The theory of elementary chemical reactions determines the physical meaning of these constants and makes it possible to calculate their values. There are two main models for describing the elementary act of a reaction: the theory of active collisions and the theory of the transition state.

Theory of active collisions.

The application of the molecular-kinetic theory of gases to the description of an elementary chemical reaction made it possible to create a theory of active collisions, which reveals the physical meaning of the pre-exponential factor in the Arrhenius equation.

According to this theory, the rate of a bimolecular chemical reaction is determined by the number of collisions of molecules per unit time, and not all collisions lead to the formation of a new molecule, but only those in which the kinetic energy of the initial particles is greater than the activation energy of the reaction. Each such active impact leads to the implementation of an elementary act.

When an elementary bimolecular chemical reaction A + B ® AB occurs at a temperature T total number collisions of molecules A and B in a gas can be calculated by the equation

,

where z is the number of collisions per unit volume per unit time; n i is the number of particles per unit volume; is the elastic collision cross section of particles with effective radii r i; is the average relative velocity of particles; – medium molecular mass particles A and B; k is the Boltzmann constant. In this way, .

When passing from the number of particles to the number of moles of the corresponding substances per unit volume (molar concentrations), we obtain

,

where R=k× N A is the universal gas constant; N A is Avogadro's number; C i is the molar concentration.

Example. Let us determine the total number of collisions of H 2 and Cl 2 molecules in 1 cm 3 of the mixture equal volumes gases under normal conditions.

The number of particles of H 2 and Cl 2 in 1 cm 3 1/cm3.

Relative velocity of particles cm/s.

Cross section of elastic collision of molecules s=1.1×10 -14 cm 2 .

The number of collisions of H 2 and Cl 2 particles in 1 cm 3 in 1 second is: .

Since only active collisions lead to the formation of new molecules, the total number of collisions must be multiplied by the function f(E ak), which determines the fraction of collisions of particles with energies greater than the activation energy E ak:

z a=z× f(E ak).

Function f(E ak) can be obtained from the Maxwell-Boltzmann distribution law. Fraction of molecules with energy E greater than the activation energy E ak ( E>E ak) is equal to:

,

where n 0 is the total number of molecules in the system; nE >E ak is the number of molecules that have a kinetic energy greater than the activation energy.

The activation energy of real reactions that do not proceed too fast and not too slowly is of the order of E ak ~ 50÷100 kJ/mol. With this in mind, at temperatures close to standard, the fraction of molecules with energies greater than the activation energy is about ~10 -9 ÷10 -18 , i.e., the fraction of particle collisions leading to their interaction is quite small.

Thus, the number of active collisions depending on the temperature is equal to:

.

Collision geometry is important for many reactions. The colliding active molecules must be properly oriented relative to each other in order to allow the elementary act of interaction to take place. The collision geometry is taken into account by the multiplier R, named steric factor. Then the number of active collisions, taking into account the steric factor ( z a *) will be equal to: z a *=p z a.

Since each active collision leads to the formation of a new molecule, the number of active collisions per unit volume per unit time ( z a *) corresponds, according to the definition of the rate of a chemical reaction, to the number of elementary acts of interaction per unit time per unit volume. In this way, z a *=v,

.

According to the law of mass action, the rate of the chemical reaction A + B ® AB is: . Therefore, the reaction rate constant k will be determined by the expression

or ,

where is the pre-exponential factor.

The product of the elastic collision cross section (s) by average speed molecular motion () represents frequency factor (z 0):

.

Value z 0 is proportional to the number of collisions of molecules per unit volume per unit time (the number of collisions at unit concentrations of particles). The frequency factor weakly depends on temperature and can be considered a constant value, which can be calculated from the molecular kinetic theory of gases.

Steric factor R takes into account the orientation of particles in space at the moment of collision with respect to each other. With a favorable orientation for the formation of new molecules R»1, with unfavorable orientation R<1. Таким образом, k 0 =p×z 0 .

The theory of active collisions does not allow one to calculate the value of the activation energy. Further development of the theory of elementary reactions is associated with the involvement of a quantum mechanical description of the rearrangement of the system of chemical bonds in the molecules of the reacting substances.

Theory of the transition state.

In the elementary act of a chemical reaction, particles of the initial substances participate, which in the course of the reaction turn into particles of products. This transition is carried out, as noted earlier, through the formation of an intermediate unstable particle, which includes all the atoms of the interacting particles, united by a common system of chemical bonds. In the process of this transformation, the distances between the nuclei of the atoms entering the particles change. In the adiabatic approximation model, each mutual arrangement of atomic nuclei corresponds to one specific energy value, i.e., the energy of the system will be determined by the mutual arrangement of atoms. The dependence of the potential energy of a system of interacting particles on their coordinates can be considered as a surface in a multidimensional space - the potential energy surface. This surface can be most clearly illustrated by the example of the bimolecular reaction AB + C ® A + BC, in the elementary act of which three atoms participate.

In the general case, the energy of three interacting atoms depends on the distance between them ( r AB and rBC) and angle a. In an elementary act, the angle a is assumed to be constant (the angle of approach of particle C to particle AB), for example, when particles AB and C collide along the direction of the communication line a=180° (Fig. 6.1). In this case, the potential energy surface will be a function of two variables E(r AB, rBC). The potential energy surface constructed in the Cartesian coordinate system is shown in Fig. 6.2, a.

Rice. 6-1 Spatial arrangement of three atoms during the elementary act of the bimolecular reaction AB + C ® A + BC (collision of particles along the direction of the communication line a=180°).

In the initial state, the energy of the system is minimal with respect to the arrangement of atoms in the AB molecule (determined by r AB) and weakly depends on another coordinate ( rBC). On the diagram (Fig. 6.2, a) corresponds to this state source material valley. In the final state, the energy of the system is minimal with respect to the arrangement of atoms in the HB molecule ( rBC) and weakly depends on another coordinate ( r AB). In the diagram, this state corresponds to product valley. The elementary act of a chemical reaction is the transition of a system from the valley of starting materials to the valley of products. It is energetically favorable that this transition be carried out through the points of minima on the potential energy surface.

Rice. 6-2 Potential energy surface of the reaction AB + C ® A + BC (a) and potential energy isolines (b)

This transition (reaction path) is shown by an arrow on the potential surface diagram, depicted on a plane as a system of lines connecting points with the same potential energy values ​​(Fig. 6.2, b). When moving from one valley to another, the energy of the system first increases and then decreases, the system overcomes the pass (point P). On the left is a “high” plateau, which corresponds to the state of a system of three separate atoms A, B, C (simultaneously r AB and rBC®∞). On the right, the surface "steeply" rises, since the simultaneous decrease in the distances between atoms ( r AB and rBC® 0) leads to a sharp increase in the energy of repulsion of atoms (Fig. 6.2, a).

The state of the system with maximum energy (point P) is called transition state, which corresponds to the formation of a short-lived intermediate by three atoms ( activated complex), which has a high energy content. Thus, an elementary chemical reaction goes through the stage of formation of an activated complex. It is an unstable molecule, which includes all the atoms of the original substances and in which the old chemical bonds have not yet been completely destroyed, and new ones have not yet been completely formed.

In the reaction under consideration, the system passes through an activated complex (ABC) ¹:

All parameters related to the transition state (activated complex) are denoted by the superscript ¹.

If we introduce the concept reaction coordinates (X) - the position of the system on the path of transition from the initial state to the final state (Fig. 6.2, b), then the change in the energy of the system during an elementary act will be a function of one variable E(X). The form of this dependence is shown in the energy diagram in Fig. 6.3.

Maximum on the diagram (point P) corresponds to the transition state. The activation energy of the reaction corresponds to the energy of formation of the activated complex. This is the energy that particles must have in order for an elementary act of a chemical reaction to occur.

Rice. 6‑3 Diagram of the change in the energy of the system during the reaction AB + C ® A + BC

It should be noted that the transition state theory is based on a number of assumptions. The elementary act of the reaction passes through the formation of an activated complex along the path of overcoming the lowest energy barrier. The calculation of the activation energy is carried out using the methods of quantum mechanics. It is believed that the activated complex (ABC) ¹ is an ordinary molecule, in which one vibrational degree of freedom is replaced by translational motion along the reaction coordinate ( X). The system is always in a state of thermodynamic equilibrium. The probability of the transition of the activated complex to the reaction products is determined by transmission coefficient c, which is most often equal to one.