Measuring the rate of a chemical reaction. The rate constant is calculated by the formula Rate constant value
Guidelines for laboratory work
On the discipline "Chemistry" for students
Compiled by V.S. Aksenov
Reviewer
Doctor of Chemical Sciences, Professor F.F. Niyazi
The rate of chemical reactions: Guidelines for laboratory work on the discipline "Chemistry" / Kursk. state tech. un-t; Comp. V.S. Aksenov. Kursk, 2003. 20 p.
Methodological materials are presented on the study of the topic "The rate of chemical reactions", the calculation of rates in chemical reactions and the performance of laboratory work.
Designed for students of all specialties studying general chemistry
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Security questions on the topic
1. What is the rate of a chemical reaction? In what units is it measured?
2. What is the true and average reaction rate?
3. What is the kinetic equation of the reaction (the law of mass action)?
4. How is the kinetic equation written for a homogeneous reaction?
5. What are the features of heterogeneous reactions?
6. What is kinetic, diffusion and mixed control in heterogeneous reactions?
7. What are the forms of writing for the kinetic equations of heterogeneous reactions?
8. What is the reaction rate constant? Which reaction conditions affect and which do not affect the rate constant?
10 . When does pressure affect the rate of a chemical reaction?
12 . How does temperature affect the rate of a chemical reaction? Give the van't Hoff equation.
13 . What is the reaction temperature coefficient?
14 . What is catalysis? What process parameters are affected by the catalyst?
The rate of chemical reactions.
Kinetics is the study of the rate of various processes, including chemical reactions. One of the basic concepts in chemical kinetics is the rate of a reaction.
The rate of a chemical reaction V called change in the amount of reactant per unit of time in a unit of reaction space.
In a homogeneous system, the reaction space is the volume of the vessel in which the interaction takes place, and the amount of substance per unit volume is called concentrationFROM and is expressed in mol/l.
Therefore, in the case of a homogeneous process proceeding at a constant volume, the rate of a homogeneous chemical reaction is measured by the change in the concentration of any of the reactants per unit of time.
Usually the time τ is expressed in seconds, so the dimension of the reaction rate is usually mol/l s. During chemical interaction, the concentration of each of the starting substances decreases with time (FROM 2 <С 1 , ΔС<0) , and the concentration of each of the reaction products increases (FROM 2 >C 1 , ΔС>0) . The change in the concentrations of the starting substances and reaction products over time is shown in Fig.1. In chemical kinetics, a distinction is made between the average and true (or instantaneous) rates of a reaction. average speed v is equal to the ratio ΔС/Δτ (ΔС = С 2 -FROM 1 , Δτ = τ 2 -τ 1 ) . In order for the speed to be always positive, the signs ""±"" are placed in front of the fraction.
V = ± -–-
Δτ
The true rate of a chemical reaction V ist determined by the limit to which the ratio tends ∆С/∆τ at τ → 0, i.e. derivative of concentration with respect to time:
V ist = ± -–-
dτ
Dependence of the reaction rate on the concentration of reagents. A necessary condition for the implementation of the act of chemical interaction between molecules must be their collision. Collisions of molecules in a certain reaction space at a given temperature occur more often, the more of these molecules. Therefore, the rate of a chemical reaction depends on the concentration of reactants. As the concentration of the starting substances decreases with time (Fig. 1, curve 1), the reaction rate decreases.
Quantitatively, the dependence of the reaction rate on the concentration of the reactants is expressed law of acting masses, which in the modern formulation looks like this:
at a constant temperature, the rate of a chemical reaction is directly proportional to the product of the concentrations of the reactants, taken in powers equal to the stoichiometric coefficients in the reaction equation.
For reaction a A+b B →m M+n N
the mathematical expression of the law of mass action has the form:
V =k FROM BUT a ·FROM AT b (1)
where V - speed reaction; FROM BUT and FROM AT— concentrations of reagents BUT and AT;a , b are stoichiometric coefficients in the reaction equation; k is the coefficient of proportionality, called the rate constant of a chemical reaction. The dimension of the rate constant is determined by the values of the stoichiometric coefficients a and b and remains such that the speed V had dimension mol/l∙sec. If there is no exact data, the dimension k accept sec ―1 . At FROM BUT = C AT = 1 mol/lk is numerically equal to V . Expression (1) also called reaction kinetic equation.
Rate constant chemical reaction k is determined by the nature of the reacting substances and depends on the temperature, on the presence of a catalyst, but does not depend on the concentration of the substances involved in the reaction.
Example 1 . 0.06 mol of substance A and 0.02 mol of substance B are placed in a reaction vessel with a volume of 2 l. At a certain temperature, the reaction A + 2B \u003d AB 2 proceeds. Find the value of the reaction rate constant at this temperature if, at given concentrations of substances A and B, the rate reaction is 6 10 -7 mol/(L sec).
Solution: Knowing the amounts of reactants and the volume of the system, we find the molar concentrations of the reactants:
FROM BUT= 0.06/2 = 0.03 = 3 10 -2 mol/l; FROM AT = 0,02/2 = 0.01 = 10 ―2 mol/l
We write the expression for the kinetic equation relating the reaction rate to the concentrations of the reactants:
V =k FROM BUT ·FROM AT 2
V 6.10 ―7
From here: k = ----- = ------- = 0,2 l 2 /(mol) 2 ∙sec
FROM BUT ·FROM AT 2 · 3 10 -2 (10 -2) 2
The law of mass action is valid only for the simplest interactions in their mechanism, occurring in gases or in dilute solutions. Complex reactions can be a set of parallel or sequential processes. The law of mass action is valid for each individual stage of the reaction, but not for the entire interaction as a whole. That stage of the process, the rate of which is minimal, limits the rate of the reaction in general. Therefore, the mathematical expression of the law of mass action, written for the slowest (limiting) stage of the process, is applicable simultaneously to the entire reaction as a whole.
If two or more substances are involved in the reaction, then the reaction rate may depend on the concentration of only one of them, participating in the slowest stage of the process, and not depend on the concentration of others.
The rate of heterogeneous chemical reactions. Many chemical processes of great importance in technology are heterogeneous reactions. One or more process components are in a condensed, usually solid phase. Solids concentrations are not written in the kinetic equation (law of action of masses). Conventionally, these concentrations are taken constant and equal to 1. This first feature of heterogeneous reactions. They go to the interface, which is their reaction space. That's why second A feature of the kinetics of these reactions is the effect of the reaction surface area on the reaction rate. So for the reaction:
Fe 2 O 3(K) + 3CO (G) → 2Fe + 3СО 2(G)
the kinetic equation can be written as: V = k∙С 3 SO ∙S, where FROM SO― molar concentration of carbon monoxide SO (G), the only gaseous component in the reacting starting materials, S is the surface area on which the reaction takes place. Solid Fe 2 O 3(K) is not written in the kinetic equation. The rates of heterogeneous chemical reactions have the dimension mol/l∙sec∙m 2
However, in most cases, the area of the reaction surface is practically impossible to measure and does not appear directly in the kinetic equation (the law of mass action). She is
""hides"" into the rate constant k and this is taken into account in the dimension of the rate constant.
Example 2 . For reaction: Si (TV) + 2H 2 O (G) SiO 2(TV) + 2H 2(G) write an expression for the kinetic equation.
Solution: This reaction is heterogeneous and proceeds at the phase boundary. Of the reactants, water participates in the reaction in gaseous form, in front of it the coefficient in the equation is 2 (…+ 2H 2 O (G) ). Silicon ( Si (TV) ) is a solid; therefore, its concentration is not taken into account in the kinetic equation. Therefore, the kinetic equation (the law of mass action) for this reaction can be: V = k C 2 H 2 O. The dimension of the rate constant in this case l/mol∙sec∙m 2 .
During the reaction, the concentration of the reagent in the reaction zone C S decreases compared to its concentration in the volume C V due to the consumption of the reagent. That's why the rate of a heterogeneous chemical reaction depends on the rate of supply of reagents to the chemical reaction zone,
That is third features of these reactions.
The greatest change in the concentration of the reagent occurs in a thin layer near the reaction surface, called diffusion about m layer. The transfer of matter here occurs mainly due to diffusion.
If the diffusion rate is much greater than the reaction rate ( V D >> V), then the reagents are fed into the reaction space, to the surface without problems, all the laws of the effect of concentration on the rate described above are observed. For such cases, there is an expression " kinetic reaction control". If the rates of a chemical reaction and diffusion are comparable, then mixed control. And, finally, when the diffusion rate is much less than the reaction rate ( V D << V ) then one speaks of diffusion control of the reaction.
AT 
In this case, the zero order of the reaction for all reagents can be observed. This means that in coordinates V―
C the rate does not depend on the concentrations of the reagents, but depends on the diffusion rate, surface area, and temperature, which are not included in the kinetic equation. Such a phenomenon can take place during the reaction on a solid surface in liquid media with high viscosity. However, most heterogeneous reactions have an order different from zero, often fractional. On fig. 2 shows graphical forms of possible dependences of the reaction rate on the concentrations of the reagents.
Dependence of the rate of reactions on the pressure in the system. In cases where there are gases among the reacting substances, the reaction rate depends on the pressure in the system. With an increase in pressure, the number of gas molecules per unit volume increases proportionally, which is equivalent to an increase in the concentration of this gas.
Example 3 How will the reaction rate change? 2NO + O 2 → 2NO 2 when the volume of a closed system is halved at a constant temperature?
Solution. A decrease in volume in a closed system is equivalent to a proportional increase in pressure, since, according to the Mendeleev-Claiperon law РW = νRT.(Here W is the volume of the system.)
The kinetic equation of this reaction has the form: V =k FROM 2 NO ·FROMO 2
When the volume of the system is halved and the associated pressure is doubled, the concentrations of the reactants also double: FROM" NO = 2C NO FROM"O 2 = 2CO 2
New reaction speed:
V" =k FROM" NO 2 ·FROM"O 2 = k (2 FROM NO ) 2 (2CO 2 ) = 8 k FROM NO 2 ·FROMO 2 = 8V
Conclusion. When the volume of a closed system is halved at a constant temperature, the rate of this reaction increases by 8 times.
Temperature dependence of the reaction rate constant. Most reactions are accelerated by heating. Temperature acts directly on the rate constant k . Let V 1 is the reaction rate at temperature T 1 , a V 2 is the rate of the same reaction at temperature T 2 (T 1 <Т 2 ) . In this case, Van't Hoff's empirical rule takes place.
where γ - temperature coefficient showing how many times the reaction rate will increase with an increase in temperature by 10 0 C. For most reactions at temperatures close to room temperature, γ is 2-4.
The van't Hoff equation is widely used, but it should be remembered that it is an empirical approximation, it can only be used for approximate calculations.
Example 4 At 100 0 C, some reaction ends in 20 minutes. Taking the temperature coefficient of the reaction rate γ \u003d 3.5, calculate how long the reaction will end at 60 0 С
Solution. The reaction rate, like the rate of any process, is inversely proportional to the time of the process. Consequently, V 2 /V 1 = τ 1 /τ 2 . Let T 1 , V 1 and τ 1 are the parameters of the slow (low-temperature) process, and T 2 , V 2 and τ 2 are the parameters of the high-temperature process. We substitute the available data into the van't Hoff equation:
V 2 /V 1 \u003d 3.5 (100 - 60) / 10 \u003d (3.5) 4 \u003d 150. Since V 2 /V 1 = τ 1 /τ 2 = 150,
τ 1 /τ 2 = τ 1 /20 τ 1 = 150 20 = 3000 min = 50 hours.
One of the methods to speed up a chemical reaction is catalysis, which is carried out with the help of substances (catalysts) that increase the rate of the reaction, but are not consumed as a result of its occurrence. As with an increase in temperature, the introduction of a catalyst increases reaction rate constant. The mechanism of action of the catalyst is reduced to a decrease in the activation energy of the reaction, i.e. to a decrease in the difference between the average energy of the active molecules (active complex) and the average energy of the molecules of the starting substances. The rate of a chemical reaction increases dramatically
Rice. 40. Dependence of the value of the reciprocal concentration of the reagent on time for a second-order reaction
Rice. Fig. 39. Dependence of the logarithm of the concentration of the reagent on the flow time for the reaction of the first order
Rice. 38. Change in the concentration of the starting substance over time in a first-order reaction
Rice. 37. Change in the concentration of the starting substance over time in a zero-order reaction
Mathematically, this linear dependence will be written as follows
where k is the rate constant, C 0 is the initial molar concentration of the reactant, C is the concentration at time t.
From it, you can derive a formula for calculating the rate constant of a zero-order chemical reaction.
Is the zero order rate constant measured in mol/L? s (mol l -1 s -1).
The half-life for a zero order reaction is proportional to the concentration of the starting material
For first-order reactions, the kinetic curve in the C,t coordinates is exponential and looks like this (Fig. 38) Mathematically, this curve is described by the following equation
C \u003d C 0 e - kt
In practice, for first-order reactions, the kinetic curve is most often plotted in the coordinates lnC, t. In this case, a linear dependence of lnС on time is observed (Fig. 39)
ln C \u003d lnC 0 - kt
|
Accordingly, the value of the rate constant and the half-life can be calculated using the following formulas
k = ln or k = 2.303lg
(when moving from a decimal logarithm to a natural one).
The first-order reaction rate constant has the dimension t -1 , i.e. 1/s and does not depend on concentration units. It shows the proportion of molecules that have reacted per unit of time from the total number of reagent molecules in the system. Thus, in the first-order reactions, the same fractions of the taken amount of the starting material are spent over the same time intervals.
The second distinctive feature of first-order reactions is that t ½ for them does not depend on the initial concentration of the reagent, but is determined only by the rate constant.
We will consider the form of the equation for the dependence of concentration on time for second-order reactions only for the simplest case, when 2 identical molecules, or molecules of different substances, participate in an elementary act, but their initial concentrations (C 0) are equal. In this case, a linear dependence is observed in the coordinates 1/C, t (Fig. 40). The mathematical equation of this dependence will be written as follows
and is measured in l?s -1? mol -1, i.e. its numerical value depends on the units in which the concentration of the substance is measured.
The half-life of second-order reactions is inversely proportional to the initial concentration of the reagent
This is due to the fact that the rate of second-order reactions strongly depends on the number of collisions between the molecules of the reacting substances per unit time, which, in turn, is proportional to the number of molecules per unit volume, i.e. substance concentration. Thus, the greater the concentration of a substance in the system, the more often the molecules collide with each other and the shorter the time period, half of them will have time to react.
Third-order reactions, as mentioned earlier, are extremely rare and are of no practical interest. Therefore, in this regard, we will not consider them.
General chemistry: textbook / A. V. Zholnin; ed. V. A. Popkova, A. V. Zholnina. - 2012. - 400 p.: ill.
Chapter 2. FUNDAMENTALS OF THE KINETICS OF CHEMICAL REACTIONS
Chapter 2. FUNDAMENTALS OF THE KINETICS OF CHEMICAL REACTIONS
The difference between breathing and burning is only in the speed of the process.
A.-L. Lavoisier
2.1. CHEMICAL KINETICS. SUBJECT AND BASIC CONCEPTS OF CHEMICAL KINETICS. SPEED REACTION
The direction, depth and fundamental possibility of the process is judged by the magnitude of the change in free energy (ΔG ≤0). However, this value does not indicate the real possibility of the reaction occurring under these conditions.
For example, the reaction of interaction of nitrous oxide with oxygen proceeds instantly at room temperature:
At the same time, 2H 2 (g) + O 2 (g) \u003d 2H 2 O (g), Δ °G\u003d -286.8 kJ / mol - a reaction characterized by a significantly large decrease in free energy, under normal conditions, the interaction does not occur, but at 700 ° C or in the presence of a catalyst, the process proceeds instantly. Consequently, thermodynamics does not answer the question of the conditions and rate of the process. This shows the limitations of the thermodynamic approach. To describe a chemical reaction, it is also necessary to know the regularities of its course in time, which are studied by kinetics.
Kinetics is a branch of chemistry that studies the rate, mechanism of chemical reactions and the influence of various factors on them.
Depending on whether the reaction components are in one or more phases, the kinetics of homogeneous and heterogeneous reactions are distinguished. According to the reaction mechanism, they are divided into simple and complex, therefore, the kinetics of simple and complex reactions are distinguished.
The basic concept of reaction kinetics is the rate of a chemical reaction. Determining the rate of chemical reactions is of biological and national economic importance.
The rate of a chemical reaction is determined by the amount of a substance that has reacted per unit time per unit volume (in the case of homogeneous reactions, when the reactants are in the same phase) or per unit interface(in the case of heterogeneous reactions, when the reactants are in different phases).
The reaction rate is characterized by a change in the concentration of any of the initial or final reaction products as a function of time. The equation describing the dependence of the reaction rate (v) on concentration (With) reactants are called kinetic. The reaction rate is often expressed in mol/l-s, in biochemistry in mg/100 ml-s, or in mass fraction, in %/100 ml-s. Distinguish between the average reaction rate in a time interval and the true reaction rate at a certain point in time. If in the time interval t1 and t2 the concentration of one of the starting substances or reaction products is equal to c 1 and c 2, respectively, then the average reaction rate (v) in the time interval t1 and t2 can be expressed:
Since in this case we are talking about a decrease in the concentration of the starting substance, i.e. the change in the concentration of a substance is taken in this case with a minus sign (-). If the reaction rate is estimated by a change (increase) in the concentration of one of the reaction products, then with a plus sign (+):
According to equation (2.2) determine average speed chemical reaction. True (instantaneous) speed reactions are determined graphically. Build a graph of the dependence of the concentration of the starting substance or reaction product (Ca) on time (t) - the kinetic curve of the reaction of Ca - f(t) for a non-linear process (Fig. 2.1).
At any point in time (eg. t1) the true reaction rate is equal to the tangent of the slope of the tangent to the kinetic curve at the point corresponding to a given moment in time. According to the graph, the instantaneous reaction rate will be calculated by the formula:
In biochemistry, to describe the kinetics of enzymatic reactions, Michaelis-Menten equation, which shows the dependence of the rate of the reaction catalyzed by the enzyme on the concentration of the substrate and the enzyme. The simplest kinetic scheme for which the Michaelis equation is valid: E+ S↔ES→E+ P:
Rice. 2.1. Kinetic curve
where Vm- maximum reaction rate; K m - Michaelis constant, equal to the concentration of the substrate, at which the reaction rate is half of the maximum; S- substrate concentration.
The study of the rate of a chemical reaction provides information about its mechanism. In addition to the concentration, the reaction rate depends on the nature of the reactants, external conditions, and the presence of a catalyst.
2.2. MOLECULARITY AND ORDER OF THE REACTION. HALF-LIFE
In kinetics, chemical reactions differ in terms of molecularity and reaction order. Reaction molecularity is determined by the number of particles (atoms, molecules or ions) simultaneously participating in the elementary act of chemical transformation. One, two or three molecules can take part in the elementary act of the reaction. The probability of collision of more particles is very small. On this basis, monomolecular, bimolecular and trimolecular reactions are distinguished. Experimentally, the molecularity of a reaction can only be determined for elementary (simple) reactions proceeding in one stage in accordance with the stoichiometric equation. Most of these reactions require a large activation energy (150-450 kJ/mol).
Most reactions are complex. The set of elementary steps that make up a complex reaction is called reaction mechanism
tions. Therefore, to characterize the reaction kinetics, the concept is introduced reaction order, which is determined by the stoichiometric equation.
The sum of the stoichiometric indicators of all the initial substances included in the reaction equation (2.5) (a+ b), determines the general order of the reaction. The indicator with which this reagent enters the equation is called the order of the reaction with respect to the substance (particular order of the reaction), for example, the indicator a- reaction order for substance A, b- for substance B. The reaction order and molecularity are the same only for simple reactions. The order of the reaction is determined by those substances that affect the rate of the reaction.
Monomolecular reactions include decomposition and isomerization reactions.
Reactions whose rate equation includes the concentration of one reactant to the first power are called first-order reactions.
The kinetic equation includes substances whose concentration changes during the reaction. The concentrations of substances that are in significant excess do not change during the reaction.
Water in the sodium carbonate hydrolysis reaction is in significant excess and is not included in the kinetic equation.
In heterogeneous systems, the collision of particles occurs at the interface, so the mass of the solid phase does not affect the reaction rate and is therefore not taken into account in the expression for the reaction rate.
Bimolecular reactions include dimerization reactions and substitution reactions that proceed through the stage activated complex.
Reactions whose rate is proportional to the product of the concentrations of two substances to the first power or the square of the concentration of one substance are called second-order reactions.
Trimolecular reactions are rare, and four-molecular reactions are not known.
Third-order reactions do not occur among biochemical processes.
Reactions whose rate does not depend on the concentration of the starting substances are called zero-order reactions (v = k).
An example of zero-order reactions is catalytic reactions, the rate of which depends only on the concentration of the catalyst. Enzymatic reactions are a special case of such reactions.
As a rule, several reagents (substrate, coenzyme, cofactor) are involved in biochemical processes. Sometimes not all of them are known. Therefore, the course of the process is judged by one substance. In this case, the quantitative characteristic of the course of reactions in time is half-life (time) reagent - the time during which the amount or concentration of the starting substance is halved (by 50%) or half of the reaction products are formed. In this way, in particular, the decay of radionuclides is characterized, since their half-life does not depend on the initial amount.
By analyzing the dependence of the half-life of the reaction on the initial concentration, it is possible to determine the order of the reaction (the Ostwald-Noyes method). The constancy of the half-life (at a given temperature) characterizes many decomposition reactions and, in general, first-order reactions. As the reagent concentration increases, the half-life decreases for second-order reactions and increases for zero-order reactions.
2.3. REACTION RATE CONSTANT, ITS DEFINITION. LAW OF MASS ACTION
The rate of homogeneous reactions depends on the number of encounters of reacting particles per unit time per unit volume. The probability of collision of interacting particles is proportional to the product of the concentrations of the reacting substances. Thus, the reaction rate is directly proportional to the product of the concentrations of the reactants, taken in powers equal to the stoichiometric coefficients of the corresponding substances in the reaction equation. This pattern is called law of acting masses(the law of the rate of a chemical reaction), which is
fundamental law of chemical kinetics. The law of mass action was established by the Norwegian scientists K. Guldberg and P. Wage in 1867.
For example, for a reaction proceeding in a general form, according to the scheme
the kinetic equation will be valid:
where v- the rate of a chemical reaction; with A and with B- concentration of substances BUT and AT[mol/l]; v a and vb- order indicators for reagents A and B; k- rate constant of a chemical reaction - a coefficient that does not depend on the concentration of reactants.
Chemical reaction rate constant (k) is the rate of a chemical reaction under conditions where the product of the concentrations of the reactants is 1 mol/l. In this case v = k.
For example, if in the reaction H 2 (g) + I 2 (g) \u003d 2НI (g) c (H 2) and c (I 2) are equal to 1 mol / l or if c (H 2) is 2 mol / l , and c(I 2) 0.5 mol/l, then v= k.
The units of the equilibrium constant are determined by the stoichiometry of the reaction. It is incorrect to compare the rate constants of reactions of different orders with each other, since they are quantities that are different in meaning and have different dimensions.
2.4. MECHANISM OF CHEMICAL REACTIONS. CLASSIFICATION OF COMPLEX REACTIONS
The reaction mechanism considers all collisions of individual particles that occur simultaneously or sequentially. The mechanism gives a detailed stoichiometric picture of each reaction step, i.e. understanding the mechanism means establishing the molecularity of each reaction step. Studying the mechanism of chemical reactions is a very difficult task. After all, we cannot conduct direct observations of the course of the interaction of molecules. The results obtained sometimes depend on the size and shape of the vessel. In some cases, the same results can be explained using different mechanisms.
The reaction of gaseous hydrogen with iodine H 2 (g) + I 2 (g) \u003d 2HI (g) was considered a classic example of a bimolecular reaction of the second
order, but in 1967 N.N. Semenov, G. Eyring and J. Sullivan showed that it has a complex character and consists of 3 elementary reactions: I 2 = 2I; 2I = I 2 ; 2I + H 2 = 2HI. Although the reaction can formally be classified as a trimolecular reaction, its rate is described by a kinetic equation resembling a second-order reaction equation:
In complex reactions, the molecularity and order of the reaction, as a rule, do not match. An unusual - fractional or negative - order of the reaction clearly indicates its complex mechanism.
The kinetic equation for the reaction of carbon monoxide oxidation with oxygen 2CO (g) + O 2 (g) \u003d CO 2 (g) has a negative (minus the first) order in CO:
as the carbon monoxide concentration increases, the reaction rate decreases.
According to the mechanism of the reaction, it can be divided into several types.
successive reactions call complex reactions, in each of which the product (X 1) of the first elementary stage reacts with the product of the second stage, the product (X 2) of the second stage enters the third, etc., until the final product is formed:
where S- substrate (initial reagent); k 1 , k 2 , k 3 ... - rate constant 1, 2, etc. reaction steps; P- final product.
The stages of successive reactions proceed at different rates. The stage with the lowest rate constant is called the limiting stage. It determines the kinetic regularity of the reaction as a whole. Substances formed in intermediate stages are called intermediate products or intermediates which are the substrates of subsequent stages. If an intermediate is slowly formed and quickly decomposes, then its concentration does not change for a long time. Almost all metabolic processes are sequential reactions (for example, glucose metabolism).
Parallel reactions are reactions that have the same initial reagents, which correspond to different products. FROM the rate of parallel reactions is equal to the sum of the rates of individual reactions. This rule also applies to bimolecular parallel chemical reactions.
Series-parallel reactions called reactions that have the same initial reagents that can react in two ways (mechanisms) or more, including with a different number of intermediate stages. This case underlies the phenomenon catalysis, when the intermediate of one of the paths will increase the speed of other paths.
Competing reactions called complex reactions in which the same substance BUT reacts simultaneously with one or more reagents B 1 , B 2 etc., participates in simultaneously occurring reactions: BUT+ B 1 → X 1; BUT+ B 2 → X 2 . These reactions compete with each other for the reactant BUT.
Conjugated reactions complex reactions are called in which one reaction occurs only in the presence of another. In coupled reactions, the intermediate serves as a connecting link between the primary and secondary processes and causes both to occur.
A living cell needs energy for its existence. The universal source of energy in living organisms is adenosine triphosphoric acid (ATP). This compound performs the function of an energy accumulator, since when it interacts with water, i.e. hydrolysis, adenosine diphosphoric (ADP) and phosphoric (P) acids are formed and energy is released. That is why ATP is called macro-ergic compound, and the P-O-P bond that breaks during its hydrolysis is macroergic. macroergic bond a chemical bond is called, upon rupture of which, as a result of the hydrolysis reaction, significant energy is released:
As is known, the breaking of any bond (including macroergic) always requires the expenditure of energy. In the case of ATP hydrolysis, in addition to the process of breaking the bond between phosphate groups, for which Δ G>0, the processes of hydration, isomerization and neutralization of the products formed during hydrolysis occur. As a result of all these processes, the total change in the Gibbs energy has a negative
meaning. Consequently, it is not the breaking of the bond that is macroergic, but the energy result of its hydrolysis.
In order for endergonic reactions to occur in living systems (ΔG > 0), it is necessary that they be coupled with exergonic reactions (ΔG<0). Такое сопряжение возможно, если обе реакции имеют какое-либо общее промежуточное соединение, и на всех стадиях сопряженных реакций суммарный процесс характеризуется отрицательным значением изменения энергии Гиббса (∑ΔG сопр.р <0). Например, синтез сахарозы является эндэргонической реакцией и самопроизвольно происходить не может:
However, the conjugation of this reaction with the exergonic reaction of ATP hydrolysis, accompanied by the formation of a common intermediate compound glucose-1-phosphate, leads to the fact that the overall process has ∑ΔG<0:
chain reactions are called chemical and nuclear reactions in which the appearance of an active particle (a free radical or atom in chemical processes, a neutron in nuclear processes) causes a large number (chain) of successive transformations of inactive molecules or nuclei. Chain reactions are common in chemistry. Many photochemical reactions, oxidation processes (combustion, explosion), polymerization, cracking proceed according to the chain mechanism. The theory of chain reactions was developed by academician H.H. Semenov, S.N. Hinshelwood (England) and others. The main stages of chain reactions are: nucleation (initiation), continuation (elongation) and chain termination (termination). There are two types of chain reactions: straight chain reactions and branched chain reactions. A feature of chain reactions is that one primary act of activation leads to the transformation of a huge number of molecules of the starting substances. Biochemical reactions of free radical oxidation are chain reactions.
Periodic (self-oscillatory) reactions called complex multi-stage autocatalytic reactions involving several substances, in which there is a periodic fluctuation in the concentrations of the oxidized and reduced forms. Vibrational reactions were discovered by B.P. Belousov, studied by A.M. Zhabotinsky and others. The frequency and form of oscillations depend on the concentrations of the starting substances, acids
ness, temperature. An example of such reactions can be the interaction of bromomalonic acid with potassium bromate in an acidic medium, the catalyst is a salt of cerium (III). Periodic reactions are of great importance for biological objects, where reactions of this kind are widespread.
Solid phase combustion reactions(reactions of self-propagating high-temperature synthesis, SHS) were discovered in 1967 at the Institute of Chemical Physics of the USSR Academy of Sciences by A.G. Merzhanov and I.G. Borovinskaya. The essence of the SHS method lies in the fact that after local initiation of the interaction reaction of reagents, the combustion reaction front spontaneously propagates throughout the system due to heat transfer from hot products to the starting materials, initiating the interaction reaction in them. Thus, the combustion process is carried out, which is both the cause and the consequence of the reaction. The mechanism of SHS reactions is quite complex and includes the processes reaction diffusion. The term "reactive diffusion" defines a set of phenomena that occur during the interaction of two chemically different components capable of forming chemical compounds in the form of solid phases. The products of chemical interaction form a continuous layer, which differs in its structure from the initial components, but does not interfere with further interaction.
2.5. THE THEORY OF ACTIVE IMPACTS. ENERGY OF ACTIVATION. DEPENDENCE OF THE REACTION RATE ON THE NATURE OF REACTING SUBSTANCES AND TEMPERATURE
In order for an elementary act of chemical interaction to take place, the reacting particles must collide with each other. However, not every collision results in a chemical interaction. The latter occurs when the particles approach at distances at which the redistribution of the electron density and the emergence of new chemical bonds are possible. Interacting particles must have enough energy to overcome the repulsive forces that arise between their electron shells.
transition state- the state of the system, in which the destruction and creation of a connection are balanced. In a transitional state, the system
stays for a short (10 -15 s) time. The energy required to bring the system into a transition state is called activation energy. In multistep reactions that include several transition states, the activation energy corresponds to the highest energy value. After overcoming the transition state, the molecules fly apart again with the destruction of old bonds and the formation of new ones or with the transformation of the original bonds. Both options are possible, as they occur with the release of energy. There are substances that can reduce the activation energy for a given reaction.
Active molecules A 2 and B 2 upon collision combine into an intermediate active complex A 2 ... B 2 with weakening and then breaking of the A-A and B-B bonds and strengthening of the A-B bonds.
The "activation energy" of the HI formation reaction (168 kJ/mol) is much less than the energy required to completely break the bond in the initial H 2 and I 2 molecules (571 kJ/mol). Therefore, the reaction path through the formation active (activated) complex energetically more favorable than the path through the complete breaking of bonds in the original molecules. The vast majority of reactions occur through the formation of intermediate active complexes. The provisions of the active complex theory were developed by G. Eyring and M. Polyani in the 30s of the XX century.
Activation energy represents the excess of the kinetic energy of the particles relative to the average energy required for the chemical transformation of the colliding particles. Reactions are characterized by different values of activation energy (E a). In most cases, the activation energy of chemical reactions between neutral molecules ranges from 80 to 240 kJ/mol. For biochemical processes, the values of E and are often lower - up to 20 kJ / mol. This is explained by the fact that the vast majority of biochemical processes proceed through the stage of enzyme-substrate complexes. Energy barriers limit the reaction. Due to this, in principle, possible reactions (at G<0) практически всегда не протекают
or slow down. Reactions with an activation energy above 120 kJ/mol are so slow that they are difficult to see.
In order for a reaction to occur, the molecules must be oriented in a certain way and have sufficient energy upon collision. The probability of proper orientation in a collision is characterized by activation entropyΔ S a . The redistribution of the electron density in the active complex is favored by the condition that, upon collision, the molecules A 2 and B 2 are oriented, as shown in Fig. 2.2, a, while with the orientation shown in Fig. 2.2, b, the probability of a reaction is still much less - in fig. 2.2, c.
Rice. 2.2. Favorable (a) and unfavorable (b, c) orientations of A 2 molecules
and B 2 on collision
The equation characterizing the dependence of the rate and reaction on temperature, activation energy and activation entropy has the form:
where k- reaction rate constant; A - in the first approximation, the total number of collisions between molecules per unit time (second) per unit volume; e is the base of natural logarithms; R- universal gas constant; T- absolute temperature; E a- activation energy; Δ S a- change in entropy of activation.
Equation (2.8) was derived by Arrhenius in 1889. The pre-exponential factor A is proportional to the total number of collisions between molecules per unit time. Its dimension coincides with the dimension of the rate constant and, therefore, depends on the total order of the reaction. The exponent is equal to the fraction of active collisions from their total number, i.e. the colliding molecules must have enough
exact interaction energy. The probability of their desired orientation at the moment of impact is proportional to e ΔSa/R
When discussing the law of mass action for velocity (2.6), it was specially stipulated that the rate constant is a constant value that does not depend on the concentrations of reagents. It was assumed that all chemical transformations proceed at a constant temperature. At the same time, it is well known that the rate of chemical transformation can change significantly with a decrease or increase in temperature. From the point of view of the law of mass action, this change in velocity is due to the temperature dependence of the rate constant, since the concentrations of reactants change only slightly due to thermal expansion or contraction of the liquid.
The most well known fact is that the rate of reactions increases with increasing temperature. This type of temperature dependence of the velocity is called normal (Fig. 2.3, a). This type of dependence is characteristic of all simple reactions.
Rice. 2.3. Types of temperature dependence of the rate of chemical reactions: a - normal; b - abnormal; c - enzymatic
However, chemical transformations are now well known, the rate of which decreases with increasing temperature. An example is the gas-phase reaction of nitrogen (II) oxide with bromine (Fig. 2.3, b). This type of temperature dependence of the velocity is called anomalous.
Of particular interest to physicians is the temperature dependence of the rate of enzymatic reactions, i.e. reactions involving enzymes. Almost all reactions occurring in the body belong to this class. For example, during the decomposition of hydrogen peroxide in the presence of the enzyme catalase, the rate of decomposition depends on temperature. In the range 273–320 °K, the temperature dependence has a normal character. As the temperature increases, the speed increases, and as the temperature decreases, it decreases. When the temperature rises above
320 °K, a sharp anomalous drop in the peroxide decomposition rate is observed. A similar picture takes place for other enzymatic reactions (Fig. 2.3, c).
From the Arrhenius equation for k it is clear that, since T included in the exponent, the rate of a chemical reaction is very sensitive to changes in temperature. The dependence of the rate of a homogeneous reaction on temperature can be expressed by the van't Hoff rule, according to which with an increase in temperature for every 10 °, the reaction rate increases by 2-4 times; the number showing how many times the rate of a given reaction increases with an increase in temperature by 10 ° is called reaction rate temperature coefficient- γ.
where k- rate constant at temperature t°C Knowing the value of γ, one can calculate the change in the reaction rate with a change in temperature from T1 before T2 according to the formula:
As the temperature rises in an arithmetic progression, the speed increases exponentially.
For example, if γ = 2.9, then with an increase in temperature by 100 ° the reaction rate increases by a factor of 2.9 10, i.e. 40 thousand times. Deviations from this rule are biochemical reactions, the rate of which increases tenfold with a slight increase in temperature. This rule is valid only in a rough approximation. Reactions involving large molecules (proteins) are characterized by a large temperature coefficient. The rate of protein denaturation (ovalbumin) increases 50 times with a temperature increase of 10 °C. After reaching a certain maximum (50-60 °C), the reaction rate decreases sharply as a result of thermal denaturation of the protein.
For many chemical reactions, the law of mass action for velocity is unknown. In such cases, the following expression can be used to describe the temperature dependence of the conversion rate:
pre-exponent A with does not depend on temperature, but depends on concentration. The unit of measure is mol/l s.
The theoretical dependence makes it possible to pre-calculate the velocity at any temperature if the activation energy and the pre-exponential are known. Thus, the effect of temperature on the rate of chemical transformation is predicted.
2.6. REVERSIBLE AND IRREVERSIBLE REACTIONS. STATE OF CHEMICAL EQUILIBRIUM. REACTION ISOTHERM EQUATION
A chemical reaction does not always "come to an end", in other words, the starting materials are not always completely converted into reaction products. This is because as the reaction products accumulate, conditions can be created for the reaction to proceed in the opposite direction. Indeed, if, for example, iodine vapor is mixed with hydrogen at a temperature of ~200 ° C, then the following reaction will occur: H 2 + I 2 = 2HI. However, it is known that hydrogen iodine, even when heated to 180 ° C, begins to decompose into iodine and hydrogen: 2HI \u003d H 2 + I 2.
Chemical reactions that can go in opposite directions under the same conditions are called reversible. When writing the equations of reversible reactions, two oppositely directed arrows are put instead of the equal sign. A reaction proceeding from left to right is called straight(forward reaction rate constant k1), from right to left - reverse(reverse reaction rate constant k2).
In reversible reactions, the rate of the direct reaction initially has a maximum value, and then decreases due to a decrease in the concentration of the starting substances. Conversely, the reverse reaction at the initial moment has a minimum rate, which increases as the concentration of the reaction products increases. Finally, there comes a moment when the rates of the forward and reverse reactions become equal. The state in which the rate of the reverse reaction becomes equal to the rate of the forward reaction is called chemical balance.
The state of chemical equilibrium of reversible processes is quantitatively characterized by equilibrium constant. At the moment the state of chemical equilibrium is reached, the rates of the forward and reverse reactions are equal to (kinetic condition).
where K - equilibrium constant, which is the ratio of the rate constants of the forward and reverse reactions.
On the right side of the equation are those concentrations of interacting substances that are established at equilibrium - equilibrium concentrations. This equation is a mathematical expression of the law of mass action in chemical equilibrium. It should be especially noted that, in contrast to the law of mass action for the reaction rate in this equation, the exponents a, b, d, f and etc. are always equal to the stoichiometric coefficients in the equilibrium reaction.
The numerical value of the equilibrium constant of a given reaction determines its yield. Reaction yield called the ratio of the amount of product actually obtained to the amount that would have been obtained if the reaction had proceeded to the end (usually expressed as a percentage). So, at K >> 1, the reaction yield is high, and vice versa, at K<<1 выход реакции очень мал.
The equilibrium constant is related to standard Gibbs energy reactions by the following ratio:
Using equation (2.12), one can find the value of the Gibbs energy of the reaction in terms of equilibrium concentrations:
This equation is called chemical reaction isotherm equation. It allows you to calculate the change in the Gibbs energy during the course of the process and determine the direction of the reaction:
at ∆G<0 - реакция идет в прямом направлении, слева направо;
At ΔG = 0 - the reaction has reached equilibrium (thermodynamic condition);
when ΔG>0 - the reaction goes in the opposite direction.
It is important to understand that the equilibrium constant does not depend on the concentrations of substances. The converse statement is true: in a state of equilibrium, the concentrations themselves take on such values that the ratio of their products in powers of stoichiometric coefficients
is constant at a given temperature. This statement corresponds to the law of mass action and can even be used as one of its formulations.
As mentioned above, reversible reactions do not proceed to the end. However, if one of the products of a reversible reaction leaves the reaction sphere, then the essentially reversible process proceeds almost to the end. If electrolytes are involved in a reversible reaction and one of the products of this reaction is a weak electrolyte, precipitate or gas, then in this case the reaction also proceeds almost to the end. irreversible reactions called such reactions, the products of which do not interact with each other with the formation of starting substances. Irreversible reactions, as a rule, "reach the end", i.e. until the complete consumption of at least one of the starting substances.
2.7. LE CHATELIER PRINCIPLE
The state of chemical equilibrium under constant external conditions can theoretically be maintained indefinitely. In reality, with a change in temperature, pressure or concentration of reagents, the equilibrium can “shift” in one direction or another of the process.
Changes occurring in the system as a result of external influences are determined by the principle of mobile equilibrium - Le Chatelier's principle.
An external impact on a system that is in a state of equilibrium leads to a shift in this equilibrium in the direction in which the effect of the produced impact is weakened.
With regard to the three main types of external influence - changes in concentration, pressure and temperature - Le Chatelier's principle is interpreted as follows.
With an increase in the concentration of one of the reacting substances, the equilibrium shifts towards the consumption of this substance, with a decrease in concentration, the equilibrium shifts towards the formation of this substance.
The influence of pressure is very similar to the effect of changing the concentrations of reactants, but it affects only gas systems. Let us formulate a general proposition on the effect of pressure on chemical equilibrium.
With an increase in pressure, the equilibrium shifts towards a decrease in the amount of gaseous substances, i.e. in the direction of decreasing pressure; when the pressure decreases, the equilibrium shifts in the direction of increasing
quantities of gaseous substances, i.e. towards increasing pressure. If the reaction proceeds without changing the number of molecules of gaseous substances, then the pressure does not affect the equilibrium position in this system.
When the temperature changes, both the forward and reverse reactions change, but to different degrees. Therefore, to clarify the effect of temperature on chemical equilibrium, it is necessary to know the sign of the thermal effect of the reaction.
As the temperature rises, the equilibrium shifts towards an endothermic reaction, and as the temperature decreases, it shifts towards an exothermic reaction.
As applied to biosystems, Le Chatelier's principle states that in a biosystem, for each action, a counteraction of the same strength and nature is formed, which balances biological regulatory processes and reactions and forms an associated level of their disequilibrium.
In pathological processes, the existing closedness of the regulatory circuit is violated. Depending on the level of disequilibrium, the quality of intersystem and interorgan relations changes, they become more and more non-linear. The structure and specificity of these relationships is confirmed by the analysis of the relationship between the indicators of the lipid peroxidation system and the level of antioxidants, between harmonic indicators in conditions of adaptation and pathology. These systems are involved in maintaining antioxidant homeostasis.
2.8. QUESTIONS AND TASKS FOR SELF-CHECKING OF PREPAREDNESS FOR LESSONS AND EXAMS
1. What reactions are called homogeneous and which are heterogeneous? Give one example of each type of reaction.
2. What reactions are called simple and which are complex? Give two examples of simple and complex reactions.
3. In what case can the molecularity and the order of the kinetic equation coincide numerically?
4. The speed of some reaction does not change over time. Will the half-life of this reaction change over time, and if so, how? Give an explanation.
5. In what case can the true (instantaneous) rate and the average reaction rate (in a sufficiently large time interval) coincide?
6. Calculate the rate constant of the reaction A + B → AB, if at concentrations of substances A and B equal to 0.5 and 0.1 mol/l, respectively, its rate is 0.005 mol/l min.
7. The half-life of some first-order reaction is 30 minutes. What part of the original amount of the substance will remain after an hour?
8. Give the concept of the general order of the reaction and the order of the reaction by substance.
9.Methods for determining the reaction rate.
10.Basic law of chemical kinetics.
11. Give the concept of the mechanism of chemical reactions.
12. Simple and complex reactions.
13. Conjugated reactions. What factors affect the rate constant of a chemical reaction?
14. Is the reaction rate really proportional to the product of the concentrations of the reactants to the power of their stoichiometric coefficients?
15. What experimental data are required to determine the order of reactions?
16. Write the kinetic equation for the reaction H 2 O 2 + 2HI → I 2 + + 2H 2 O if equal volumes of 0.02 mol / l H 2 O 2 solution and 0.05 mol / l HI solution are mixed. Rate constant 0.05 l/mol s.
17. Write the kinetic equation for the reaction H 2 O 2 + 2HI → I 2 + + 2H 2 O, given that it is characterized by the first order of the reaction in terms of the concentrations of both starting substances.
18. Prove that the rate of a chemical reaction is maximum at a stoichiometric ratio of components.
19. List possible explanations for the effect of temperature on the reaction rate.
2.9. TESTS
1. According to the van't Hoff rule, with an increase in temperature by 10 °, the rate of many reactions:
a) decreases by 2-4 times;
b) decreases by 5-10 times;
c) increases by 2-4 times;
d) increases by 5-10 times.
2. The number of elementary acts of interaction per unit of time determines:
a) the order of the reaction;
b) reaction rate;
c) molecularity of the reaction;
d) half-life.
3. What factors increase the rate of a reaction?
a) the nature of the reactants;
b) temperature, concentration, catalyst;
c) only a catalyst;
d) only concentration;
d) temperature only.
4. How many times will the reaction rate 2A(g) + B(g) increase?→A 2 B (g) with an increase in the concentration of substance A by 2 times?
a) the speed will not change;
b) will increase 18 times;
c) increase by 8 times;
d) will increase by 4 times;
d) doubled.
5. Elementary reaction A(tv) + 2B(g)→AB 2 (d). Indicate the correct kinetic equation for this reaction:
a)k[A][B] 2 ;
b)k[A][B];
c) to [B];
d) to [B] 2;
e) to [A].
6. How to change the pressure in the system in order to increase the reaction rate A (tv) + 2B (g)→AB 2 (d) 9 times?
a) increase the pressure by 9 times;
b) reduce the pressure by 9 times;
c) increase the pressure by 3 times;
d) reduce the pressure by 3 times.
7. What is the temperature coefficient of the reactionγ 10 , if, when the reaction mixture is cooled by 30 °, the reaction rate decreases by 8 times?
a) 16;
b) 8;
at 6;
d) 4;
D 2.
8. Which reaction is faster?
a) E act= 40 kJ/mol;
b) E act = 80 kJ/mol;
in) E act = 160 kJ/mol;
G) E act \u003d 200 kJ / mol.
The probability of the formation of new molecules when 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 for overcoming this energy barrier is the kinetic energy of the thermal motion of 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 the activation energy are considered to be constant values that do not depend on 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 the total number of collisions of molecules A and B in a gas can be calculated from 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; is the average molecular weight of 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 a mixture of equal volumes of 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; n E >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 cross section of elastic collisions (s) and the average velocity of the molecules () is 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 the 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.
reaction rate constant- - the rate of a chemical reaction under conditions when the product of the concentrations of the reactants is 1 mol / l. General chemistry: textbook / A. V. Zholnin The reaction rate constant is the coefficient of proportionality in the differential kinetic ... ... Chemical terms
reaction rate constant- - [A.S. Goldberg. English Russian Energy Dictionary. 2006] Topics energy in general EN reaction constant …
reaction rate constant- reakcijos greičio konstanta statusas T sritis chemija apibrėžtis Reakcijos, kurios reaguojančiųjų medžiagų koncentracijos lygios vienetui, greitis. atitikmenys: engl. rate constant; reaction constant rus. reaction rate constant; specific ... ... Chemijos terminų aiskinamasis žodynas
reaction rate constant- reakcijos spartos konstanta statusas T sritis Standartizacija ir metrologija apibrėžtis Reakcijos, kurios reaguojančių medžiagų koncentracijos yra lygios vienetui, sparta. atitikmenys: engl. reaction rate constant vok. Reaktionskonstante, f rus.… … Penkiakalbis aiskinamasis metrologijos terminų žodynas
A chemical reaction has its main kinetic characteristic; coefficient of proportionality in the kinetic equation relating the reaction rate to the concentrations of the reactants and their stoichiometric coefficients. For monomolecular ... ... Big Encyclopedic Dictionary
catalytic reaction rate constant- - [A.S. Goldberg. English Russian Energy Dictionary. 2006] Energy topics in general EN catalytic coefficient … Technical Translator's Handbook
Chemical reaction, its main kinetic characteristic; coefficient of proportionality in the kinetic equation relating the reaction rate to the concentrations of the reactants and their stoichiometric coefficients. For monomolecular ... ... encyclopedic Dictionary
chemical reaction rate constant- change in the amount (concentration) of a substance that enters into a reaction or is formed during the process, per unit of time at a given temperature and concentrations of all components equal to one: d[A] / dt = ... ... Encyclopedic Dictionary of Metallurgy
Chem. reactions, its main kinetic. characteristic; coefficient proportionality in kinetic. urnia, linking the reaction rate with the concentrations of the reacting in in and their stoichiometric. coefficients. For monomolecular reactions To. has dimensions of... Natural science. encyclopedic Dictionary
Relative rate constants of the reaction CH 3 I + Cl - in different solvents at 25 ° C (according to Parker)- Solvent Relative rate constant CH3OH 1 HCONH2 12.5 HCONHCH3 … Chemical reference
