Modeling of molecules, chemical processes and reactions. Abstract Modeling of chemical kinetics Computer modeling of mechanisms of chemical reactions

Simulation of the kinetics of homogeneous chemical reactions

Stages in the development of chemical kinetics

Chemical kinetics as a science of the rates of chemical reactions began to take shape in the 50-70s. 19th century

In 1862-1867. Norwegian scientists Guldberg and Waage gave the initial formulation of the law of mass action: during a chemical reaction:

Concentration of the i-th substance, ;

Speed constant;

Stoichiometric coefficients.

Chemical kinetics was fully formulated in the works of van't Hoff and Arrhenius in the 1980s. 19th century; the meaning of reaction orders was explained and the concept of activation energy was introduced. Van't Hoff introduced the concepts of mono-, bi- and polymolecular reactions:

where n is the order of the reaction.

Van't Hoff and Arrhenius, who developed his ideas, argued that temperature is not the cause of the reaction, temperature is the cause of the change in the reaction rate:

(Arrhenius in 1889), (1.3)

where A is a pre-exponential factor;

E - activation energy;

R is the gas constant;

T is temperature.

Since 1890, the value of the activation energy has become a universal measure of the reactivity of the converted substances. Thus, in the period 1860-1910. formal kinetics was created. The clarity and sparseness of the main postulates distinguish the chemical kinetics of the period of van't Hoff and Arrhenius.

Subsequently, the original integrity is lost, many "kinetics" appear: the kinetics of gas-phase and liquid-phase reactions, catalytic, enzymatic, topochemical, etc.

However, two concepts remain the most important for the chemist to this day:

The law of mass action as the law of a simple reaction.

The complexity of the mechanism of a chemical reaction.

Basic concepts of chemical kinetics

Kinetics of homogeneous chemical reactions

The rate of a chemical reaction is the change in the number of moles of reactants as a result of chemical interaction per unit time per unit volume (for homogeneous reactions) or per unit surface (for heterogeneous processes):

where W is the rate of a chemical reaction, ;

V - volume, m3;

N is the number of moles;

t - time, s. According to equation (1.4), introducing the concentration, we obtain

where C - concentration, mol/m3,

For reactions proceeding at a constant volume, the second term in equation (1.6) is equal to zero and, therefore,

One of the basic laws of chemical kinetics, which determines the quantitative laws governing the rates of elementary reactions, is the law of mass action.

According to the kinetic law of mass action, the rate of an elementary reaction at a given temperature is proportional to the concentrations of reacting substances in powers showing the number of interacting particles:

where W is the rate of a chemical reaction;

Speed constant;

Concentrations of initial substances, ;

Corresponding stoichiometric coefficients in the gross equation of a chemical reaction.

Equation (1.8) is valid for elementary reactions. For complex reactions, the exponents in equation (1.8) are called reaction orders and can take on other than integer values.

The rate constant of a chemical reaction is a function of temperature, and the dependence on temperature is expressed by the Arrhenius law:

where is the pre-exponential factor;

E - activation energy, ;

T - temperature, K;

R is the gas constant, .

Consider a homogeneous reaction

where a, b, c, d are stoichiometric coefficients.

According to the law of mass action (1.8), the rate of this reaction will be written as follows:

There is a relationship between the reaction rates for individual components (we denote them WA, WB, WC, WD) and the overall reaction rate W

From this follow the following expressions:

To apply the law of mass action to a complex chemical reaction, it is necessary to represent it in the form of elementary stages and apply this law to each stage separately.

Kinetic equations

Kinetic equations relate the rate of a reaction to the parameters on which it depends. The most important of these parameters are concentration, temperature, pressure, catalyst activity.

For batch reactors, in which the concentrations of reactants at each point of the reaction volume during the reaction continuously change with time, the rate of a chemical reaction is the number of moles of a given substance that reacts per unit time per unit volume:

or per unit surface, for heterogeneous catalytic reactions

where Wi is the rate of a chemical reaction, mol/m3s;

Ni is the current amount of the i-th component of the reaction mixture, mol;

V is the volume of the reaction mixture or catalyst bed (reactor volume), m3;

S - catalyst surface, m2;

0 - specific surface area of the catalyst, m2/m3;

t - time, s.

For continuous full displacement reactors, in which, under steady state, the concentration of a substance continuously changes along the length of the apparatus, the rate of a chemical reaction is the number of moles of a substance passing through the reactor per unit time, reacting per unit volume:

where ni is the molar flow rate of the i-th component of the reaction mixture, mol/s;

Reaction mixture feed rate, m3/s;

Contact time, s.

For a fully mixed continuous reactor, at steady state,

where ni0 is the initial amount of the i-th component of the reaction mixture, mol/s.

In practice, the rate of change in the molar concentration of Ci (mol/m3; mol/l) is usually measured.

For batch reactor

For continuous reactor

where is the volumetric feed rate of the reaction mixture, m3/s.

If the reaction is not accompanied by a change in volume, then for a plug-flow reactor

For continuous stirring reactor

where xi is the degree of transformation, ;

Average residence time, = V/, s.

Methods for solving kinetic equations

Kinetic models are systems of ordinary differential equations whose solution is a function of the concentrations of reactants from an independent time argument.

To solve differential equations - integration - apply:

tabular method (using tables of integrals) - used for the simplest differential equations;

· Analytical methods are used to solve differential equations of the first order;

· Numerical methods, the most universal, allowing to solve systems of differential equations of any complexity, are the basis of computer methods for the analysis of chemical and technological processes.

Numerical Methods

The simplest numerical method for solving ordinary differential equations is the Euler method. This method is based on the approximation of the derivative with small changes in the argument.

For example, the equation for the rate of a chemical reaction is described by the equation

where CA is the concentration of a substance, mol / l;

Time, s.

For small t, we can approximately assume that

the quantity is called the integration step. Solving equation (1.23), we obtain the general Euler formula

where is the right side of the differential equation (for example,

By setting the initial conditions: at t = 0 C = C0, the value of the integration step h, as well as the parameters of the equation, using formula (1.24) you can carry out a step-by-step calculation and obtain a solution to this equation (Fig. 1.1).

Rice. 1.1. Graphical illustration of Euler's method

organizing cyclic calculations according to equation (1.24), we obtain for the kinetic model the change in the concentrations of reacting substances with time.

The value of the integration step is chosen based on the achievement of the minimum counting time and the smallest calculation error.

General representations of one-step methods for solving ordinary differential equations

Let there be a differential equation

satisfying the initial condition

It is required to find a solution to problem (1.25), (1.26) on the segment . Let's split the segment with points

This set of points is called a grid, and the points xi (i = i, n) are grid nodes.

One-step numerical methods give approximations yn to the values of the exact solution y(xn) at each grid node xn based on the known approximation yn-1 to the solution at the previous node xn-1. In general, they can be represented as follows:

For explicit one-step methods, the function F does not depend on yn+1.

denoting

explicit one-step methods will also be written in the form

Explicit Runge-Kutta Type Methods

The idea of this method is based on the calculation of the approximate solution y1 at the node x0 + h as a linear combination with constant coefficients :

The numbers are chosen so that the expansion of the expression (1.29) in powers of h coincides with the expansion in the Taylor series:

This is equivalent to the following. If we introduce an auxiliary function

then its expansion in powers of h should start from the maximum possible degree:

If it is possible to define these constants in such a way that the expansion has the form (1.32), then formula (1.29) with the chosen coefficients is said to have order of accuracy s.

Value

is called the error of the method at a step, or the local error of the method, and the first term in the expression (1.32)

is called the leading term of the local error of the method.

It is proved that if q = 1, 2, 3, 4, then it is always possible to choose the coefficients in such a way as to obtain a Runge-Kutta type method of order of accuracy q. For q = 5, it is impossible to construct a Runge-Kutta type method (1.29) of the fifth order of accuracy; it is necessary to take more than five terms in the combination (1.29).

Study of the kinetics of homogeneous chemical reactions

The study of the kinetic regularities of the course of a chemical reaction by the method of mathematical modeling consists in determining the change in the concentrations of reacting substances over time at a given temperature.

Let the chemical reactions take place

Based on the law of mass action, we write the equations for the rates of chemical reactions and compose a kinetic model:

where CA, CB, CC, CD are the concentrations of substances, mol/l;

ki is the rate constant of the i-th chemical reaction of the first order, s-1; (for second-order reactions, the dimension of the constant; for third-order reactions, the dimension of the constant);

Wi is the rate of the i-th chemical reaction, mol/ls; t - reaction time, s.

Rice. 1.2. Block diagram for calculating the kinetics of a homogeneous chemical reaction by the Euler method

The system of ordinary differential equations of the first order (1.35) can be solved using the numerical Euler method, the algorithm of which is written according to equation (1.24).

The block diagram for calculating the kinetics of a homogeneous chemical reaction by the Euler method is shown in fig. 1.2.

Examples of programs for calculating the kinetics of homogeneous chemical reactions are given in Appendix A. The results of the study on the mathematical model (1.35) of the effect of temperature on the degree of conversion of the initial reagent and on the concentration of substances are shown in Fig. 1.3, 1.4.

The obtained results allow us to draw a conclusion about the optimal time of the process in order to obtain the target product. The mathematical model (1.35) also makes it possible to investigate the effect of the feedstock composition on the yield of reaction products.

It must be taken into account that the rate of a chemical reaction depends on temperature, therefore, in order to use the kinetic model (1.35) to study the process at different temperatures, it is necessary to introduce the dependence of the rate constant of a chemical reaction on temperature according to the Arrhenius equation (1.9).

The fourth-order Runge-Kutta algorithm can be written as follows:

where ai are the Runge-Kutta coefficients, which are calculated using the following formulas:

Literature

kinetics chemical homogeneous

1. Panchenkov G. M., Lebedev V. P. Chemical kinetics and catalysis. - M.: Chemistry, 1985. - 589 p.

2. Yablonsky G. S., Bykov V. I., Gorban A. I. Kinetic models of catalytic reactions. - Novosibirsk: Nauka, 1983. - 254 p.

3. Kafarov VV Methods of cybernetics in chemistry and chemical technology. - M.: Chemistry, 1988. - 489 p.

4. Kravtsov A. V., Novikov A. A., Koval P. I. Methods of analysis of chemical and technological processes. - Tomsk: TPU publishing house, 1994. - 76 p.

5. Kafarov VV, Glebov MV Mathematical modeling of the main processes of chemical production. - M.: Higher. school, 1991. - 400 p.

6. Moizes O. E., Koval P. I., Bazhenov D. A., Kuzmenko E. A. Informatics: textbook. allowance. In 2 hours - Tomsk, 1999. - 150 p.

7. L. I. Turchak, Fundamentals of Numerical Methods. - M.: Nauka, 1987. - 320 p.

8. Ofitserov D. V., Starykh V. A. Programming in the integrated environment Turbo-Pascal. - Minsk: Belarus, 1992. - 240 p.

9. Beskov V. S., Flor K. V. Modeling of catalytic processes and reactors. - M.: Chemistry, 1991. - 252 p.

10. Rud R., Praustnitz J., Sherwood T. Properties of gases and liquids

/ ed. B. I. Sokolova. - L.: Chemistry, 1982. - 591 p.

11. Tanatarov M. A. et al. Technological calculations of oil processing plants. - M.: Chemistry, 1987. - 350 p.

12. Zhorov Yu. M. Thermodynamics of chemical processes. - M.: Chemistry, 1985

13. Calculations of the main processes and apparatuses of oil refining: a reference book / ed. E. N. Sudakova. - M.: Chemistry, 1979. - 568 p.

14. Kafarov VV Separation of multicomponent systems in chemical technology. Methods of calculation. - M.: Moscow Institute of Chemical Technology, 1987. - 84 p.

KINET
Program for numerical simulation of kinetics
complex chemical reactions

The KINET program is designed to solve direct and inverse kinetic problems. As the initial data, the kinetic scheme (mechanism) of the process is set in the form of a set of simple reactions indicating the rate constants, and the reaction equations can be written in a form close to the usual chemical notation. In addition, the process conditions are indicated - the initial concentrations of the reagents and the temperature, as well as the time interval at which the solution is required. In the case of an inverse kinetic problem, it is also necessary to specify the experimental kinetic curves.

The program independently compiles a system of differential equations and integrates it. The results are presented in numerical and graphical form and can be exported for use in other programs.

Some examples of the application of the KINET program are given in the book: “Workshop on physical chemistry: Kinetics and catalysis. Electrochemistry” (Abramenkov A.V., Ageev E.P., Atyaksheva L.F. et al. Edited by V.V. Lunin and E.P. Ageev). M.: Ed. Center "Academy", 2012. Section I.8, "Mathematical modeling of the kinetics of complex reactions", pp. 70-102. See the UserGuide.pdf file for a detailed user guide.

System requirements:

OS Windows XP/Vista/7 (32 or 64 bit),
3.7 MB on disk or flash drive for program files,
screen resolution of at least 1024 x 768 (preferably higher).

Program installation instructions

To install the KINET program, just unpack the downloaded archive (preserving the internal structure of subfolders) into the "Program Files" folder or any other folder and create a shortcut on the desktop to launch the wkinet.exe executable file.

Inside the Kinet folder, the locale subfolder contains a translation of the program interface into Russian. In the absence of this subfolder, the program will remain operational, but will have an English interface.

Individual settings are stored in the kinet.ini file in the standard data storage folder in the user profile. On modern versions of Windows, this is usually C:\Users\<Имя пользователя>\Application Data\Kinet\

The program does not write anything to the Windows registry, so to completely remove it from the computer, it is enough to delete the main Kinet folder with program files and the Kinet folder in the user profile (see above).

The KINET program is distributed freely (see the license agreement in the file Kinet\doc\license_en.txt).

For the first calculation of scheme A, I use either practical experience or known dependencies, the flow parameter is set to 2'', and for scheme B with flow parameters 4'', the first calculation is carried out, since all the initial data of the system will be known, the values obtained as a result of calculations flow 2, 4' will not coincide with the preset values 2'',4'', calculate the error, set a new value of the parameter 2'',4'' close to the calculated ones, and carry out the 2nd calculation, the approximation operation is repeated until until the value of the total error becomes lower than the required accuracy of the calculation.

The rate of internal diffusion can be increased by increasing the pore size and reducing the length, however, this reduces the total surface of the catalyst, and hence the number of active centers, and hence its activity, in connection with this, for each process there is a catalyst with an optimal pore size, on the other hand, internal diffusion control can be overcome by reducing the particle size of the catalyst, in this case the process becomes more complicated, since the finely dispersed catalyst easily carries the raw material into the adjacent equipment with the flow, the stage of absorption of the substrate on the active centers of the catalyst, the absorption is activated, the active center must be tuned to the substrate: weak absorption does not cause activation substrate molecules, while an excessively strong one hinders the desorption of active site products. Rearrangement of the electron density in the absorbed substrate molecules with the formation of a product associated with the active center. Desorption of the product with the active site speed 3-4-5 stage increase by raising the temperature. Diffusion of the product through the boundary layer into the volume of the flow, mixing is used to speed up.

Any catalyst is characterized by the following parameters:

1) Activity, that is, the ability to accelerate the reaction compared to the absence of a catalyst - the higher, the better, the activity depends on 2 factors: A) on the ability of active centers to reduce the activation energy of processes. B) on the number of active centers.

2) The volumetric rate of return of raw materials shows how much raw material can be passed through a unit volume of the catalyst for a given unit of conversion

4) The ability of a catalyst to work for a long time without loss of activity A) catalytic reaction B) catalyst reactions leading to loss of catalytic activity centers, as well as electron donor substances such as CO2, H2O, NH3, these polar substances are absorbed on the active centers, blocking the access of the substrate, after the removal of these substances from the feedstock, the substances are desorbed from the active centers and the properties of the catalysts are restored. Coke is burned from the surface of the catalyst, for the normal operation of the catalysts it is necessary to remove poisons from the raw material. Irreversible deactivation occurs if the substance interacts with the destruction of the active center of the catalyst, it is impossible to regenerate, it is extremely important to replace the widespread platinum catalysts that are afraid of oxygen-nitrogen and sulfur-containing compounds. In order for the catalyst to work for a long time, it is necessary to carry out hydrotreating, after cleaning the content of S, N

5) Ignition temperature - the minimum temperature at which the catalytic process proceeds at a rate acceptable for industrial use. In practice, the process is usually started at a temperature slightly above the ignition temperature, and as activity is lost, the temperature is gradually raised to the maximum possible, after reaching this temperature, the catalyst is put on regeneration.

6) Catalyst cost

7) Mechanical strength of granules

8) For catalysts operating in a moving bed, wear resistance is an important characteristic.

9) Inter-regeneration run time during which the catalyst does not require regeneration

10) Catalyst selectivity - the ability to selectively accelerate one of several possible reactions under given reaction conditions

11) Overall service life

It is customary to call a chemical reactor an apparatus in which chemical transformations proceed accompanied by heat and mass transfer.

Reactor classifications: reactors are classified according to hydrodynamic conditions: A) fully mixed reactors (RIS) B) plug-flow reactors (RIV)

According to the organization of the process in time: A) continuous reactors with a constant supply of raw materials B) periodic effects operating cyclically C) semi-continuous (semi-periodic) the reactor operates continuously, and the loading of raw materials or the output of the product are carried out periodically

According to the thermal regime: A) an adiobatic reactor is without heat exchange with the environment B) an isothermal regime C) a polythermal regime D) an autothermal polytropic regime.

By the nature of the change in parameters in time A) stationary mode - parameters of constant time at each point of the apparatus B) to stationary mode

By design features: A) capacitive reactors - reactors with and without stirrers B) column reactors - columns with plates, packing with a moving or fixed layer of solid matter C) reactors of the ʼʼHeat exchangerʼʼ type D) reactors of the reaction furnace type - shaft, drum, shelf furnaces, furnaces fluidized bed, and so on. To describe the processes occurring in reactors, mathematical models are used; the model is built according to a hierarchical principle; therefore, the model has a multilevel structure. First, a lower level model is built, then a higher level model is built. Model levels:

1) The molecular level takes into account the interaction at distances of the order of molecules, expressed by the laws of chemical kinetics and chemical equilibrium

2) The low volume level considers the element of the reaction volume, for example, a catalyst grain, a gas bubble, a packing element, an elementary volume of the reactor, the regularities of the first level are supplemented by heat and gas transfer

3) The level of the working area of the devices - the statistical sevacuity of the elements of a small volume of the device: the total volume of the device - catalyst layer, packing layer, foam volume, the level takes into account defects associated with flow movement, momentum transfer.

4) The level of the apparatus takes into account the relative position of the working zones (several layers of catalyst, several plates, and so on), the model must take into account the ongoing chemical process, the phenomenon of heat and mass transfer, in connection with this, the model of the 2nd level includes the equation of material balance and the equation of heat balance.

Modeling of chemical reactions - concept and types. Classification and features of the category "Modeling of chemical reactions" 2017, 2018.

purpose of work

1. Get acquainted with the methods of constructing kinetic models of heterogeneous chemical reactions.
2. Compile a kinetic model of a heterogeneous chemical reaction in accordance with a given mechanism.
3. Choose a numerical method and develop a calculation program.
4. Investigate the dynamics of changes in the concentrations of the reactants of the reaction and intermediate compounds.

Kinetics of heterogeneous chemical reactions

The foundations of heterogeneous chemical kinetics were laid down in the works of Langmuir, Temkin, and others. In these works, the concept of an ideal adsorbed layer was formulated, based on an analogy with the concepts of homogeneous kinetics. This model uses the following assumptions:

1) the equivalence of all sections of the catalyst surface and the independence of the chemisorption energy from the degree of surface coverage with various adsorbents;
2) the invariability of the catalyst and the independence of its properties from the composition of the reaction mixture and its effect on the catalyst;
3) equilibrium distribution of energy.

The formal analogue of the kinetic law of acting masses for elementary processes on solid surfaces is the law of acting surfaces (LSA) .

According to his original formulation, the rate of a chemical reaction is proportional to the product of the surface concentrations of the reactants in powers equal to the stoichiometric ratios in which they interact (1.38).

Let an elementary chemical reaction take place

In this case, all substances interact from the adsorbed state. Let zi be the fraction of the surface occupied by the i-th adsorbed substance. Then, in accordance with the law of acting surfaces, the rate of irreversible reaction (1.38) can be written as

where W is the rate of a chemical reaction;

k is the rate constant; is the fraction of the surface occupied by the i-th adsorbed particle; - free surface fraction; i - stoichiometric coefficients of stages;

Change in the number of moles during a chemical reaction.

If not all substances interact from the adsorbed state, but react directly from the gas phase, then in a more general form the expression of the law of acting surfaces is written as follows:

where - partial pressures (concentrations) of substances reacting from the gas phase; - stoichiometric coefficients;

n, m - the amount of substances adsorbed on the catalyst surface and reacting from the gas phase.

Example: let hydrogen be adsorbed on the active site of the catalyst Z with the formation of an adsorbed surface compound ZH2:

then, on the basis of the ZDP, the rate of this elementary chemical reaction can be written as

As the main factor determining the kinetic dependences, the displacement factor, the “struggle” of the components of the reaction mixture for places on the catalyst surface, was initially considered. In this case, an additional assumption was made about the high rate of adsorption and desorption stages in comparison with the actual chemical transformations. Subsequent studies have shown the significant limitations of these assumptions. Nevertheless, Hinshelwood, Schwab, Hougen, Watson, and others derived equations on their basis that satisfactorily describe the kinetic experiment in a certain range of parameters. Typical formula of the kinetic equation

where k is the rate constant;

Сi is the concentration of the i-th reagent of the gaseous medium;

Equilibrium constant of the adsorption stage of the i-th component;

i - stoichiometric coefficient.

The most general description of the kinetics of complex reactions is given in the Horiuchi-Temkin theory of stationary reactions.

Juro Horiuchi introduced the following concepts: independent intermediates, stoichiometric number, reaction route, independent reaction routes.

Stoichiometric numbers are numbers chosen so that after multiplying the chemical equations of each step by the corresponding stoichiometric number and then adding the equations, all intermediates cancel out. The resulting equation is called the gross equation. Each set of stoichiometric numbers leading to the exclusion of intermediates is called a reaction route.

In the theory of stationary reactions, the concepts of "stage run", "run along the route" and "reaction rate along the basic route" are introduced. The number of runs of a stage is understood as the difference between the number of acts of an elementary reaction in the forward and reverse directions. Then the rate of a simple reaction is equal to the number of its runs per unit of time in a unit reaction space. One run along the route means that there have been as many runs of each of the stages as its stoichiometric number for this route. In the case when the formation of an intermediate molecule in one of the stages is compensated by the consumption of this molecule in another stage, a stationary reaction mode is realized. If during this stage not the final product is formed, but a new intermediate substance, then it must also be consumed in another stage. Full compensation for the formation and consumption of intermediate substances means the completion of a run along any of the routes.

Thus, the rate of a stationary reaction is determined by individual runs along all possible routes. As a result, all stage runs for a given time will be uniquely determined in terms of basic routes. The reaction rate along the basic route is the number of runs along the basic route per unit time in a unit reaction space, provided that all runs of the stages are distributed along the routes of this basis. The reaction rate as a whole is set by the rates along the basic routes.

The stationarity condition for the elementary stages of chemical reactions can be written as follows:

where are the rates of elementary stages (s-th, direct and reverse); - speed along the route P;

Stoichiometric coefficient of the s-th stage, route R.

Based on equation (1.44), we obtain an equation called the equation of stationary reactions:

where, ... - speeds along the routes;

Speeds of elementary stages in the forward and reverse directions;

Stoichiometric coefficient of the i-th stage along the j-th route.

With the help of this equation, the derivation of kinetic equations for heterogeneous chemical reactions in explicit form is facilitated - for linear mechanisms and, in some cases, for nonlinear ones.

In physical chemistry, the rate of a chemical reaction is determined according to the equation:

where dq is the change in the mass of the reactant, mol.

dt– increment of time, s.

V is a measure of the reaction space.

There are homogeneous chemical reactions in which all the participating substances are within the same phase (gas or liquid). For such reactions, the measure of the reaction space is the volume, and the dimension of the speed will be: .

Heterogeneous chemical reactions occur between substances in different phases (gas-solid, gas-liquid, liquid-liquid, solid-liquid). In this case, the actual chemical reaction is realized at the interface, which is the measure of the reaction space.

For heterogeneous reactions, the dimension of the rate is different: .

The change in the mass of the reacting substances has its own sign. For the initial substances, the mass decreases during the reaction, the change in mass has a negative sign, and the velocity takes on a negative value. For the products of a chemical reaction, the mass increases, the change in mass is positive, and the sign of the velocity is also assumed to be positive.

Consider a simple chemical reaction

Simple reactions include those that are carried out in one stage and go to the end, i.e. are irreversible.

Let us determine the rate of such a chemical reaction. To do this, first of all, it is necessary to decide which of the substances will be used to determine the reaction rate: after all, A and B are the initial substances, and the change in their masses is negative, and C is the final product, and its mass increases with time. In addition, not all stoichiometric coefficients in the reaction are equal to one, which means that if the flow rate A for some time is 1 mole, the flow rate B for the same time will be 2 moles, and, accordingly, the speed values calculated from the change in the masses of A and B will be twice as different.

For a simple chemical reaction, a single measure of rate can be proposed, which is defined as follows:

where r i– speed for the i-th participant of the reaction

Si is the stoichiometric coefficient of the i-th participant in the reaction.

The stoichiometric coefficients for the starting materials are assumed to be positive, for the reaction products they are negative.

If the reactions take place in an isolated system that does not exchange matter with the external environment, then only a chemical reaction leads to a change in the masses of matter in the system, and, consequently, their concentrations. In such a system, the only reason for the change in concentrations FROM is a chemical reaction. For this particular case

The rate of a chemical reaction depends on the concentrations of the substances involved and on the temperature.

where k is the rate constant of a chemical reaction, S A, S B- the concentration of substances, n 1 , n 2– orders for the respective substances. This expression is known in physical chemistry as the law of mass action.

The higher the concentration values, the higher the rate of the chemical reaction.

Order ( n) is determined experimentally and is related to the mechanism of a chemical reaction. The order can be an integer or a fractional number, there are also zero-order reactions for some substances. If the order is i th substance is zero, then the rate of a chemical reaction does not depend on the concentration of this substance.

The value of the rate of a chemical reaction depends on the temperature. In accordance with the Arrhenius law, the rate constant changes with temperature:

where BUT is the pre-exponential factor;

E is the activation energy;

R is the universal gas constant, constant;

T- temperature.

As well as the value of the order of the reaction, the values of the activation energy and the pre-exponential factor are determined experimentally for a particular reaction.

If a chemical reaction is carried out in a heterogeneous process, then its rate is also affected by the process of supplying the initial substances and removing products from the chemical reaction zone. Thus, a complex process takes place, in which there are diffusion stages (supply, withdrawal) and a kinetic stage - the actual chemical reaction. The rate of the entire process as a whole, observed in the experiment, is determined by the rate of the slowest stage.

Thus, by influencing the rate of the diffusion stage of the process (mixing), we affect the rate of the entire process as a whole. This influence affects the value of the pre-exponential factor A.

Most chemical reactions are not simple (that is, they do not go in one stage and not to the end) - complex chemical reactions:

a) AB - reversible;

b) A→B; В→С - consecutive;

c) A→B; A→C - parallel.

For a complex chemical reaction no single measure of speed. Unlike simple, here we can talk about the rate of formation and destruction of each chemical. Thus, if chemical reactions occur in the system and involve n substances, for each n substances have their own value of speed.

For any of the substances, the rate of formation and destruction is the algebraic sum of the rates of all stages involving this substance.

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KINET
Program for numerical simulation of kinetics
complex chemical reactions

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Kinetics of heterogeneous chemical reactions

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Categories

Editor's Choice

Modeling of molecules, chemical processes and reactions. Abstract Modeling of chemical kinetics Computer modeling of mechanisms of chemical reactions

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KINETProgram for numerical simulation of kinetics complex chemical reactions

System requirements:

Program installation instructions

Kinetics of heterogeneous chemical reactions

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Popular entries

The last notes

KINET
Program for numerical simulation of kinetics
complex chemical reactions