The formula for finding the reaction rate coefficient. Temperature dependence of the reaction rate

Van't Hoff's rule:

when the temperature rises by 10 degrees, the rate of a homogeneous chemical reaction increases by 2-4 times.

where V2 is the reaction rate at temperature T2, V1 is the reaction rate at temperature T1, is the temperature coefficient of the reaction (if it is equal to 2, for example, then the reaction rate will increase by 2 times when the temperature rises by 10 degrees).

From the van't Hoff equation temperature coefficient calculated by the formula:

The theory of active collisions generalizes the regularities the dependence of the speed of chem.r-and on temperature:

1. Not all molecules can react, but only those in a special active state

2.Activation of a molecule occurs as a result of a biomolecular collision.

3. When particles with approximately the same amount of energy collide, it is redistributed, as a result of which the energy of one of the molecules reaches a value corresponding to the activation energy.

4. Influence of temperature on the reaction rate: a shift in the equilibrium between ordinary and active molecules towards an increase in the concentration of the former.

Energy profile of the reaction (plot of potential energy versus reaction coordinate)

Activation energy Ea- the minimum additional energy that must be imparted to the molecule in excess of its average value in order to make chem. interaction.

Arrhenius equation sets the dependency of the rate constant chemical reaction k on temperature T.

Here A characterizes the frequency of collisions of reacting molecules, R is the universal gas constant.

7. Catalysis. Homogeneous and heterogeneous catalysis. Features of the catalytic activity of enzymes. Catalysis- a change in the rate of chemical reactions in the presence of substances that, after the completion of the reaction, remain unchanged in form and quantity. An increase in the rate of a reaction is called positive catalysis, decrease - negative catalysis (or inhibition). Catalysts name substances that cause positive catalysis; substances that slow down reactions inhibitors. Distinguish between homogeneous and heterogeneous catalysis. The acceleration of the reaction of disproportionation of hydrogen peroxide in an aqueous solution in the presence of dichromate ions is an example of homogeneous catalysis (the catalyst forms one phase with the reaction mixture), and in the presence of manganese(IV) oxide it is an example of heterogeneous catalysis (an aqueous solution of hydrogen peroxide-liquid phase, manganese oxide - solid). Catalysts of biochemical reactions are of a protein nature and are called enzymes. Enzymes differ from conventional catalysts in a number of ways: 1) they have a much higher catalytic efficiency; 2) high specificity, i.e. selectivity of action; 3) many enzymes exhibit catalytic activity with respect to only one substrate; 4) enzymes show maximum efficiency only in mild conditions, characterized by a small range of temperatures and pH values. Enzyme activity \u003d Zero-order reaction rate. 8. Chemical balance. Reversible and irreversible in the direction of the reaction. Chemical equilibrium: dynamic state in which the rates of the forward and reverse reactions are equal. Equilibrium constant: under constant external conditions in equilibrium, the ratio of the product of product concentrations to the product of reactant concentrations, taking into account stoichiometry, is a constant value, independent of the chemical composition of the system. K c is related to the Gibbs standard E by: Le Chatelier's principle: the impact of some factor (t, c, p) on the equilibrium system stimulates the shift of equilibrium in such a direction, which contributes to the restoration of the initial characteristics of the system. Thermodynamic equilibrium conditions: G 2 -G 1 \u003d 0S 2 -S 1 \u003d 0 Reversible p-tion: under these conditions, spontaneously flowing both in the forward and in the opposite direction .Run through conditions: - Slightly soluble precipitate - gas - low dissociating substance (water) - stable complex compound Irreversible district: under given conditions flows in one direction. The position of chemical equilibrium depends on the following reaction parameters: temperature, pressure and concentration. The influence that these factors have on a chemical reaction is subject to patterns, which was expressed in general terms in 1884 by the French scientist Le Chatelier. The modern formulation of Le Chatelier's principle is as follows:

9. The role of water and solutions in life. Thermodynamics of dissolution.Solution is a homogeneous system of variable composition of two or more substances in a state of equilibrium. Classification: 1) weigh(coarse-dispersed system): suspensions (solids in liquid) and emulsions (liquid in liquid) 2) colloids, sols(fine-dispersed systems). The value of solutions in life: many chemical processes proceed only if the substances involved in them are in a dissolved state. The most important biological fluids (blood, lymph, urine, saliva, sweat) are solutions of salts, proteins, carbohydrates, lipids in water. Assimilation of food is associated with the transition of nutrients into a dissolved state. Biochemical reactions in living organisms proceed in solutions. Biofluids are involved in the transport of nutrients (fats, amino acids, oxygen), drugs to organs and tissues, as well as in the excretion of metabolites from the body. In the liquid media of the body, the constancy of acidity, salt concentration and organic matter(concentration homeostasis). The most common solvent on our planet is water. Water features: surpasses all substances in its heat capacity; anomalous cooling behavior - water condenses, begins to sink, then rises (all other substances sink when compacted); can sublimate (sublimation of water) - sublimation (under certain conditions, ice can turn into steam without first turning into liquid water, i.e. without melting); water dissolves all substances (the only question is how much?); high dielectric constant of water (a value showing how many times the interaction force between two charges in a given substance is less than in vacuum); high critical temperature; water is ampholyte (not acid, not basic); participates in the creation of polymeric structures of the body (protein, lipids ...); basis of membrane transport. Dissolution thermodynamics: according to the 2nd law of thermodynamics at p, T=const substances can spontaneously dissolve in any solvent if, as a result of this process, the Gibbs energy of the system decreases, i.e. . G=( H - T S)<0 . (H- enthalpy factor, T S is the entropy factor of dissolution). When dissolving liquid and solid substances S>0. Dissolving gases in liquid S<0. The enthalpy change is the algebraic sum of the enthalpy change H cr as a result of the destruction of the crystal lattice and the change in enthalpy H sol due to solvation by solvent particles H sol = H kr + H Sol . When dissolving gases, the enthalpy H cr = 0, because no need to expend energy to destroy the crystal lattice. During dissolution, both entropy and enthalpy can change. 10 . Ideal Solution- the enthalpy of mixing is 0 (homogeneous mixtures of hydrocarbons; hypothetical solution, where the equality of all forces of intermolecular interaction.) Solubility constant or PR- this is the product of the concentrations of ions of a sparingly soluble electrolyte in a saturated solution at a given temperature - a constant value BaCO 3 \u003d Ba + CO 3, Ks \u003dDissolution and Precipitation Conditions Precipitation and dissolution - exchange reactions occurring in an electrolyte solution --- 1) The electrolyte will precipitate if the product of the concentration of its ions in the solution is greater than the solubility constant c (Ba) * c (CO 3)> Kpr 2) Its precipitate will dissolve if all vice versa 11. Coligative properties of solutions. Colligative properties of solutions- these are their properties that, under given conditions, turn out to be equal and independent of the chemical nature of the dissolved substance; properties of solutions that depend only on the number of kinetic units and on their thermal motion. Raoult's law and its consequences A vapor in equilibrium with a liquid is called saturated. The pressure of such a vapor over a pure solvent (p0) is called the pressure or saturated vapor pressure of a pure solvent. The vapor pressure of a solution containing a non-volatile solute is directly proportional to the mole fraction of the solvent in the solution: p = p0 χr-l, where p is the vapor pressure over the solution, PA; p0 is the vapor pressure over a pure solvent; χr-l is the molar fraction of the solvent. For electrolyte solutions, a slightly different form of the equation is used, which allows adding an isotonic coefficient to it: Δp = i p0 χv -va, where Δp is the actual change in pressure compared to a pure solvent; χv-va is the mole fraction of a substance in solution. From Raoult's law there are two consequences. According to one of them, the boiling point of the solution is higher than the boiling point of the solvent. This is due to the fact that the saturated vapor pressure of the solvent over the solution becomes equal to atmospheric pressure (liquid boiling condition) at a higher temperature than in the case of a pure solvent. The increase in boiling point Tboil is proportional to the molality of the solution:. Tkip = Ke cm where Ke is the ebullioscopic solvent constant, cm is the molal concentration. According to second investigation from Raoult's law, the freezing (crystallization) temperature of a solution is lower than the freezing (crystallization) temperature of a pure solvent. This is due to the lower vapor pressure of the solvent over the solution than over the solvent. The decrease in freezing point (crystallization) Тzam is proportional to the molality of the solution : Tzam = Kk cm where Kk is the cryoscopic constant of the solution Lowering the crystallization temperature of solutions. Condition crystallization is the equality of the saturated vapor pressure of the solvent over the solution to the vapor pressure over the solid solvent. Since the vapor pressure of a solvent over a solution is always lower than over a pure solvent, this equality will always be achieved at a temperature lower than the freezing point of the solvent. So, ocean water begins to freeze at a temperature of about minus 2 ° C. The difference between the crystallization temperature of the solvent and the temperature of the beginning of the crystallization of the solution is a decrease in the crystallization temperature. Increasing the boiling point of solutions Liquid boils at the temperature at which the total saturation vapor pressure becomes equal to the external pressure. the pressure of saturated vapors over a solution at any temperature will be less than over a pure solvent, and equality to its external pressure will be achieved at a higher temperature. Thus, the boiling point of a solution of a non-volatile substance T is always higher than the boiling point of a pure solvent at the same pressure T °. The increase in the boiling point of infinitely dilute solutions of non-volatile substances does not depend on the nature of the solute and is directly proportional to the molar concentration of the solution. The spontaneous passage of a solvent through a semi-permeable membrane separating a solution and a solvent or two solutions with different concentrations of a solute is called osmosis. Osmosis is due to the diffusion of solvent molecules through a semi-permeable barrier that allows only solvent molecules to pass through. Solvent molecules diffuse from a solvent into a solution or from a less concentrated solution to a more concentrated one. Osmosis is quantitatively characterized osmotic pressure, equal to the force per unit surface area, and forcing the solvent molecules to penetrate through a semipermeable partition. It is equal to the pressure of the solution column in the osmometer with height h. At equilibrium, the external pressure balances the osmotic pressure. In this case, the rates of forward and reverse transitions of molecules through a semipermeable partition become the same. Osmotic pressure increases with increasing solute concentration and temperature. Van't Hoff suggested that for the osmotic pressure one can apply the equation of state of an ideal gas: pV = nRT or p = (n/V) RT whence p = with RT, where p is the osmotic pressure (kPa), c is the molar concentration of the solution. Osmotic pressure is directly proportional to the molar concentration of the solute and temperature. Osmosis plays very important role in biological processes, ensuring the flow of water into cells and other structures. Solutions with the same osmotic pressure are called isotonic. If the osmotic pressure is higher than intracellular, then it is called hypertonic, if it is lower than intracellular, it is called hypotonic. The isotonic coefficient (also the van't Hoff factor; denoted i) is a dimensionless parameter that characterizes the behavior of a substance in solution. It is numerically equal to the ratio of the value of some colligative property of a solution of a given substance and the value of the same colligative property of a non-electrolyte of the same concentration, with other system parameters unchanged. Isoosmia-relative constancy of osmotic pressure in liquid media and tissues of the body, due to the maintenance of the concentrations of the substances contained in them at a given level: electrolytes, proteins. This is one of the most important physiological constants of the body, provided by the mechanisms of self-regulation (Homeostasis). HEMOLYSIS- destruction of red blood cells, accompanied by the release of hemoglobin from them. Physical reasons refers to the action of high and low temperatures, ultrasound, to chemical - hemolytic poisons, certain drugs, etc. Hemolysis can occur during transfusion of incompatible blood, the introduction of hypotonic solutions. Plasmolysis- when cells are placed in a hypertonic solution, water from the cells goes into a more concentrated solution and wrinkling of the cells is observed.

Elements of the theory of electrolyte solutions. Strong and weak electrolytes. Ionization constant of a weak electrolyte. Ostwald's breeding law. Ionic strength of the solution. Activity and activity coefficient of ions. Electrolytes in the body, saliva as an electrolyte.

electrolytes- These are substances with ionic or highly polar covalent bonds in aqueous solutions that undergo electrolytic dissociation, resulting in the formation of cations and anions.

Strong electrolytes- substances capable of dissociating completely. These include most salts, as well as some substances of a molecular structure (HCl).

Weak electrolytes dissociate to an insignificant degree, and their predominant form is molecular (H2S, organic acids).

Quantitatively, the ability of a molecular electrolyte to dissociate is determined by degree of ionization ( it depends on the electrolyte concentration ):

where Ntot is the total number of molecules in the solution; N ionization is the number of molecules decomposed into ions.

Ionization constant:

Where [A], [B] are decayed ions

- a substance that has not broken down into ions.

Ostwald's dilution law:

K= α 2 c/1- α ,

Where α is the degree of ionization

C - molar concentration

Ionic strength of solution:

I=0.5∑s i z i 2 ,

Where c i is the molar concentration of the ion in the solution, mol/l

z i is the ion charge.

Ion activity is its effective concentration.

Activity is related to molar concentration as follows:

where f is activity factor

electrolytes in the body: Na and Cl participate in maintaining the acid-base balance, osmotic balance in the body. Sa plays an important role in the construction of bone tissue and teeth, in the regulation of blood acidity and its coagulation, in the excitability of muscle and nervous tissue. TO It is located mainly in body fluids and soft tissues, where it is a necessary element for maintaining osmotic pressure and regulating blood pH. mg is a cofactor in many enzymatic reactions, is necessary at all stages of protein synthesis. in living organisms Fe is an important trace element that catalyzes the processes of oxygen exchange. Co is part of vitamin B 12, is involved in hematopoiesis, functions nervous system and liver, enzymatic reactions. Zn essential for the metabolism of vitamin E, is involved in the synthesis of various anabolic hormones in the body, including insulin, testosterone and growth hormone. Mn affects growth, blood formation and gonadal function.

Saliva as an electrolyte is a complex biochemical environment. The number of H + and OH ions "determines the pH of saliva, which is normally 6.9. The value of the pH value varies depending on the nature of the pathological process in the oral cavity. So. with infectious diseases saliva is acidic. Of the inorganic substances in saliva, anions of chlorine, bromine, iodine, and fluorine are contained. Anions of phosphates, fluorine contribute to an increase in electrochemical potentials, anion of chlorine - the transfer of ionic charges and is a depolarizer (a factor that accelerates anodic and cathodic processes). Microelements are determined in saliva: iron, copper, silver, manganese, aluminum, etc. - and macroelements: calcium, potassium, sodium, magnesium, phosphorus.

The increase in the reaction rate with increasing temperature is usually characterized by the temperature coefficient of the reaction rate, a number showing how many times the rate of a given reaction increases with an increase in the temperature of the system by 10 ° C. Temperature coefficient different reactions is different. At ordinary temperatures, its value for most reactions is in the range of 2 ... 4.

The temperature coefficient is determined in accordance with the so-called "van't Hoff rule", which is mathematically expressed by the equation

v 2 /v 1 = g ( T 2 – T 1)/10 ,

where v 1 and v 2 – reaction rates at temperatures T 1 and T 2; g is the temperature coefficient of the reaction.

So, for example, if g = 2, then for T 2 - T 1 = 50°С v 2 /v 1 = 2 5 = 32, i.e. the reaction accelerated by 32 times, and this acceleration does not depend on absolute values ​​in any way T 1 and T 2 but only on their difference.

activation energy, the difference between the values ​​of the average energy of particles (molecules, radicals, ions, etc.) entering into an elementary act of a chemical reaction and the average energy of all particles in the reacting system. For various chemical reactions E. and. varies widely - from a few to ~ 10 j./mol. For the same chemical reaction, the value of E. a. depends on the type of distribution functions of molecules in terms of the energies of their translational motion and internal degrees of freedom (electronic, vibrational, rotational). As a statistical value E. a. should be distinguished from the threshold energy, or energy barrier - the minimum energy that one pair of colliding particles must have for a given elementary reaction to occur.

Arrhenius equation, temperature dependence of the rate constant To elemental chem. reactions:

where A is a pre-exponential factor (the dimension is the same as the dimension of k), E a-activation energy, usually accepting positive. values, T-abs. temperature, k-Boltzmann constant. It is customary to cite E a per molecule. and on the number of particles N A\u003d 6.02 * 10 23 (Avogadro's constant) and expressed in kJ / mol; in these cases, in the Arrhenius equation, the value k replace the gas constant R. Graph of 1nk versus 1 /kT(Arrhenius plot) - a straight line, the negative slope of which is determined by the activation energy E a and characterizes positive. temperature dependence To.

Catalyst A chemical that speeds up a reaction but is not part of the reaction products. The amount of catalyst, unlike other reagents, does not change after the reaction. It is important to understand that the catalyst is involved in the reaction. Providing a faster route for the reaction, the catalyst reacts with the starting material, the resulting intermediate compound undergoes transformations and is finally split into a product and a catalyst. Then the catalyst again reacts with the starting material, and this catalytic cycle is repeated many times (up to a million times) [ a source?] is repeated.

Catalysts are classified into homogeneous and heterogeneous. A homogeneous catalyst is in the same phase with the reactants, a heterogeneous catalyst forms an independent phase separated by an interface from the phase in which the reactants are located. Typical homogeneous catalysts are acids and bases. Metals, their oxides and sulfides are used as heterogeneous catalysts.

Reactions of the same type can proceed with both homogeneous and heterogeneous catalysts. So, along with acid solutions, solid Al 2 O 3 , TiO 2 , ThO 2 , aluminosilicates, zeolites with acidic properties are used. Heterogeneous catalysts with basic properties: CaO, BaO, MgO.

Heterogeneous catalysts, as a rule, have a highly developed surface, for which they are distributed on an inert carrier (silica gel, alumina, activated carbon, etc.).

For each type of reaction, only certain catalysts are effective. In addition to those already mentioned acid-base, there are catalysts redox; they are characterized by the presence of a transition metal or its compound (Co +3, V 2 O 5 + MoO 3). In this case, catalysis is carried out by changing the oxidation state of the transition metal.

Dispersed system- these are formations of two or more phases (bodies) that do not mix at all or practically and do not chemically react with each other. The first of the substances dispersed phase) is finely distributed in the second ( dispersion medium). If there are several phases, they can be separated from each other in a physical way(centrifuge, separate, etc.).

Usually dispersed systems are colloidal solutions, sols. Dispersed systems also include the case of a solid dispersed medium in which the dispersed phase is located.

Most general classification dispersed systems is based on the difference in the state of aggregation of the dispersion medium and the dispersed phase. Combinations of three types of aggregate state make it possible to distinguish nine types of dispersed systems. For brevity, they are usually denoted by a fraction, the numerator of which indicates the dispersed phase, and the denominator indicates the dispersion medium, for example, for the “gas in liquid” system, the designation G/L is adopted.

colloidal solutions. The colloidal state is characteristic of many substances if their particles have a size of 1 to 500 nm. It is easy to show that the total surface of these particles is huge. If we assume that the particles have the shape of a ball with a diameter of 10 nm, then with the total volume of these particles 1 cm 3 they will have

surface area of ​​about 10 m2. As mentioned earlier, the surface layer is characterized by surface energy and the ability to adsorb certain particles, including ions

from a solution. characteristic feature colloidal particles is the presence on their surface of a charge due to the selective adsorption of ions. A colloidal particle has a complex structure. It includes the nucleus, adsorbed ions, counterins and solvent. There are lyophilic (guid.

rophilic) colloids, in which the solvent interacts with the particle nuclei, ilnophobic (hydrophobic) colloids, in which the solvent does not interact with the nuclei

particles. The solvent is included in the composition of hydrophobic particles only as a solvate shell of adsorbed ions or in the presence of stabilizers (surfactants) having lyophobic and lyophilic parts.

Here are some examples of colloidal particles:

How. it can be seen that the core consists of an electrically neutral aggregate of particles with adsorbed ions of the elements that make up the core (in these examples, Ag +, HS-, Fe 3+ ions). A colloidal particle, in addition to the nucleus, has counterions and solvent molecules. Adsorbed ions and counterions form an adsorbed layer with the solvent. The total charge of the particle is equal to the difference between the charges of adsorbed ions and counterions. Around the particles there is a diffuse layer of ions, the charge of which is equal to the number of the colloidal particle. Colloidal particle and diffuse layers form an electrically neutral micelle

Micelles(diminutive of lat. mica- particle, grain) - particles in colloidal systems, consist of a very small nucleus insoluble in a given medium, surrounded by a stabilizing shell of adsorbed ions and solvent molecules. For example, an arsenic sulfide micelle has the structure:

((As 2 S 3) m nHS − (n-x)H + ) x- xH +

The average size micelles from 10 −5 to 10 −7 cm.

Coagulation- separation of a colloidal solution into two phases - a solvent and a gelatinous mass, or a thickening of the solution as a result of the enlargement of the particles of the solute

Peptization is the process of transition of a colloidal precipitate or gel into a colloidal solution under the action of a liquid or substances added to it that are well adsorbed by the precipitate or gel, in this case called peptizers (for example, peptization of fats under the action of bile).
Peptization - separation of aggregates of particles of gels (jelly) or loose sediments under the influence of certain substances - peptizers after coagulation of colloidal solutions. As a result of peptization, the precipitate (or gel) passes into a suspended state.

SOLUTIONS, single-phase systems consisting of two or more components. According to their state of aggregation, solutions can be solid, liquid or gaseous.

Solubility, the ability of a substance to form with another substance (or substances) homogeneous mixtures with a dispersed distribution of components (see Solutions). Usually, a solvent is considered a substance that exists in its pure form in the same state of aggregation as the resulting solution. If, before dissolution, both substances were in the same state of aggregation, the solvent is considered to be a substance present in the mixture in a significantly larger amount.

Solubility is determined by the physical and chemical affinity of the molecules of the solvent and the solute, the ratio of energies by the interaction of homogeneous and dissimilar components of the solution. As a rule, they are well soluble in each other, similar in physical. and chem. the properties of matter (the empirical rule "like dissolves in like"). In particular, substances consisting of polar molecules, and substances with an ionic bond type are well sol. in polar solvents (water, ethanol, liquid ammonia), and non-polar substances are well sol. in non-polar solvents (benzene, carbon disulfide).

The solubility of a given substance depends on temperature and pressure corresponds to general principle displacement of equilibria (see Le Chatelier-Brown principle). The concentration of a saturated solution under given conditions numerically determines the R. of a substance in a given solvent and is also called. solubility. Supersaturated solutions contain a larger amount of solute than corresponds to its solubility, the existence of supersaturated solutions is due to kinetic. difficulties of crystallization (see the Origin of a new phase). To characterize the solubility of poorly soluble substances, the product of PA activities is used (for solutions close in their properties to the ideal, the product of the solubility of PR).

The rate of most chemical reactions increases with increasing temperature. Since the concentration of reactants is practically independent of temperature, in accordance with the kinetic equation of the reaction, the main effect of temperature on the reaction rate is through a change in the reaction rate constant. As the temperature increases, the energy of the colliding particles increases and the probability that a chemical transformation occurs during the collision increases.

The dependence of the reaction rate on temperature can be characterized by the value of the temperature coefficient.

Experimental data on the effect of temperature on the rate of many chemical reactions at ordinary temperatures (273–373 K), in a small temperature range, showed that an increase in temperature by 10 degrees increases the reaction rate by 2–4 times (van't Hoff rule).

According to van't Hoff temperature coefficient of rate constant(Van't Hoff coefficient)is the increase in the rate of a reaction with an increase in temperature by 10degrees.

(4.63)

where and are the rate constants at temperatures and ; is the temperature coefficient of the reaction rate.

When the temperature rises to n tens of degrees, the ratio of the rate constants will be equal to

where n can be either an integer or a fractional number.

Van't Hoff's rule is an approximate rule. It is applicable in a narrow temperature range, since the temperature coefficient changes with temperature.

A more accurate dependence of the reaction rate constant on temperature is expressed by the semi-empirical Arrhenius equation

where A is a pre-exponential factor which does not depend on temperature, but is determined only by the type of reaction; E - the activation energy of a chemical reaction. The activation energy can be represented as a certain threshold energy that characterizes the height of the energy barrier on the reaction path. The activation energy also does not depend on temperature.

This dependence was established at the end of the 19th century. Dutch scientist Arrhenius for elementary chemical reactions.

Direct activation energy ( E 1) and reverse ( E 2) the reaction is related to the thermal effect of the reaction D H ratio (see Fig. 1):

E 1 – E 2=D N.

If the reaction is endothermic and D H> 0, then E 1 > E 2 and the activation energy of the forward reaction is greater than the reverse. If the reaction is exothermic, then E 1 < Е 2 .

Arrhenius equation (101) in differential form can be written:

It follows from the equation that more energy activation of E, the faster the reaction rate increases with temperature.

Separating variables k and T and considering E constant value, after integrating equation (4.66) we get:

Rice. 5. Graph ln k–1/T.

, (4.67)

where A is a pre-exponential factor having the dimension of the rate constant. If this equation is valid, then on the graph in coordinates, the experimental points are located on a straight line at an angle a to the abscissa axis and the slope () is equal to , which makes it possible to calculate the activation energy of a chemical reaction from the dependence of the rate constant on temperature according to the equation .

The activation energy of a chemical reaction can be calculated from the values ​​of the rate constants at two different temperatures using the equation

. (4.68)

The theoretical derivation of the Arrhenius equation is made for elementary reactions. But experience shows that the vast majority of complex reactions also obey this equation. However, for complex reactions, the activation energy and the pre-exponential factor in the Arrhenius equation do not have a definite physical meaning.

The Arrhenius equation (4.67) makes it possible to give a satisfactory description of a wide range of reactions in a narrow temperature range.

To describe the dependence of the reaction rate on temperature, the modified Arrhenius equation is also used

, (4.69)

which already includes three parameters : A, E and n.

Equation (4.69) is widely used for reactions occurring in solutions. For some reactions, the dependence of the reaction rate constant on temperature differs from the dependences given above. For example, in third-order reactions, the rate constant decreases with increasing temperature. In chain exothermic reactions, the reaction rate constant increases sharply at a temperature above a certain limit (thermal explosion).

4.5.1. Examples of problem solving

Example 1 The rate constant of some reaction with increasing temperature changed as follows: t 1 = 20°C;

k 1 \u003d 2.76 10 -4 min. -one ; t 2 \u003d 50 0 С; k 2 = 137.4 10 -4 min. -1 Determine the temperature coefficient of the rate constant of a chemical reaction.

Solution. The van't Hoff rule makes it possible to calculate the temperature coefficient of the rate constant from the relation

g n= =2 ¸ 4, where n = = =3;

g 3 \u003d \u003d 49.78 g \u003d 3.68

Example 2 Using the van't Hoff rule, calculate at what temperature the reaction will end in 15 minutes, if it took 120 minutes at a temperature of 20 0 C. The temperature coefficient of the reaction rate is 3.

Solution. Obviously, the shorter the reaction time ( t), the greater the rate constant of the reaction:

3n = 8, n ln3 = ln8, n== .

The temperature at which the reaction will end in 15 minutes is:

20 + 1.9 × 10 \u003d 39 0 C.

Example 3 The rate constant of the reaction of saponification of acetic-ethyl ester with an alkali solution at a temperature of 282.4 K is equal to 2.37 l 2 / mol 2 min. , and at a temperature of 287.40 K it is equal to 3.2 l 2 / mol 2 min. Find the temperature at which the rate constant of this reaction is 4?

Solution.

1. Knowing the values ​​of the rate constants at two temperatures, we can find the activation energy of the reaction:

= = 40.8 kJ/mol.

2. Knowing the value of the activation energy, from the Arrhenius equation

,

Questions and tasks for self-control.

1. What quantities are called "Arrhenius" parameters?

2. What is the minimum amount of experimental data needed to calculate the activation energy of a chemical reaction?

3. Show that the temperature coefficient of the rate constant depends on temperature.

4. Are there deviations from the Arrhenius equation? How can the dependence of the rate constant on temperature be described in this case?

Kinetics of complex reactions

Reactions, as a rule, do not proceed through the direct interaction of all initial particles with their direct transition into reaction products, but consist of several elementary stages. This primarily applies to reactions in which, according to their stoichiometric equation, more than three particles take part. However, even reactions of two or one particle often do not proceed by a simple bi- or monomolecular mechanism, but by a more complex path, that is, through a number of elementary stages.

Reactions are called complex if the consumption of starting materials and the formation of reaction products occur through a series of elementary stages that can occur simultaneously or sequentially. At the same time, some stages take place with the participation of substances that are neither starting substances nor reaction products (intermediate substances).

As an example of a complex reaction, we can consider the reaction of chlorination of ethylene with the formation of dichloroethane. Direct interaction must go through a four-membered activated complex, which is associated with overcoming a high energy barrier. The speed of such a process is low. If atoms are formed in the system in one way or another (for example, under the action of light), then the process can proceed according to a chain mechanism. The atom easily joins at the double bond to form a free radical - . This free radical can easily tear off an atom from a molecule to form the final product - , as a result of which the free atom is regenerated.

As a result of these two stages, one molecule and one molecule are converted into a product molecule - , and the regenerated atom interacts with the next ethylene molecule. Both stages have low activation energies, and this way provides a fast reaction. Taking into account the possibility of recombination of free atoms and free radicals, the complete scheme of the process can be written as:

With all the variety, complex reactions can be reduced to a combination of several types of complex reactions, namely parallel, sequential and series-parallel reactions.

The two stages are called successive if the particle formed in one stage is the initial particle in another stage. For example, in the above scheme, the first and second stages are sequential:

.

The two stages are called parallel, if the same particles take part as initial in both. For example, in the reaction scheme, the fourth and fifth stages are parallel:

The two stages are called series-parallel, if they are parallel with respect to one and sequential with respect to the other of the particles participating in these stages.

An example of series-parallel steps are the second and fourth steps of this reaction scheme.

TO characteristics The fact that the reaction proceeds according to a complex mechanism includes the following signs:

Mismatch of reaction order and stoichiometric coefficients;

Changing the composition of products depending on temperature, initial concentrations and other conditions;

Speeding up or slowing down the process when added to reaction mixture small amounts of substances;

Influence of the material and dimensions of the vessel on the reaction rate, etc.

In the kinetic analysis of complex reactions, the principle of independence is used: “If several simple reactions occur simultaneously in the system, then the main postulate chemical kinetics applied to each of them as if the given reaction were the only one. This principle can also be formulated as follows: "The value of the rate constant of an elementary reaction does not depend on whether other elementary reactions proceed simultaneously in a given system."

The principle of independence is valid for most reactions that proceed according to a complex mechanism, but is not universal, since there are reactions in which some simple reactions affect the course of others (for example, conjugated reactions.)

Important in the study of complex chemical reactions is the principle microreversibility or detailed balance:

if chemical equilibrium is established in a complex process, then the rates of the forward and reverse reactions must be equal for each of the elementary stages.

The most common case for a complex reaction to occur is when the reaction proceeds through several simple steps proceeding at different rates. The difference in rates leads to the fact that the kinetics of obtaining the reaction product can be determined by the laws of only one reaction. For example, for parallel reactions, the rate of the entire process is determined by the rate of the fastest stage, and for sequential reactions, the slowest one. Therefore, when analyzing the kinetics of parallel reactions with a significant difference in the constants, the rate of the slow stage can be neglected, and when analyzing sequential reactions, it is not necessary to determine the rate of the fast reaction.

In sequential reactions, the slowest reaction is called limiting. The limiting stage has the smallest rate constant.

If the values ​​of the rate constants of the individual stages of a complex reaction are close, then a complete analysis of the entire kinetic scheme is required.

The introduction of the concept of a rate-determining stage in many cases simplifies the mathematical side of considering such systems and explains the fact that sometimes the kinetics of complex, multi-stage reactions is well described by simple equations, for example, of the first order.

Factors affecting the course of the reaction

In the human body, thousands of enzymatic reactions take place in a living cell. However, in a multistage chain of processes, the difference between the rates of individual reactions is quite large. Thus, the synthesis of protein molecules in a cell is preceded by at least two more stages: the synthesis of transfer RNA and the synthesis of ribosomes. But the time during which the concentration of tRNA molecules doubles is 1.7 minutes, protein molecules - 17 minutes, and ribosomes - 170 minutes. The rate of the overall process of the slow (limiting) stage, in our example, the rate of ribosome synthesis. The presence of a limiting reaction provides high reliability and flexibility in controlling thousands of reactions occurring in the cell. It is enough to keep under observation and regulate only the slowest of them. This method of controlling the rate of multi-stage synthesis is called the minimum principle. It allows to significantly simplify and make more reliable the system of autoregulation in the cell.

Classifications of reactions used in kinetics: reactions, homogeneous, heterogeneous and microheterogeneous; simple and complex reactions (parallel, sequential, conjugated, chain). Molecularity of the elementary act of the reaction. Kinetic equations. Reaction order. Half life

Microheterogeneous reactions -

The molecularity of the reaction is determined by the number of molecules that enter into chemical interaction in the elementary act of the reaction. On this basis, the reactions are divided into monomolecular, bimolecular and trimolecular.

Then reactions of type A -> B will be monomolecular, for example:

a) C 16 H 34 (t ° C) -> C g H 18 + C 8 H 16 - hydrocarbon cracking reaction;

b) CaC0 3 (t ° C) -> CaO + C0 2 - thermal decomposition of calcium carbonate.
Reactions like A + B -> C or 2A -> C - are bimolecular, for example:
a) C + 0 2 -> C0 2; b) 2Н 2 0 2 -> 2Н 2 0 + 0 2 etc.

Trimolecular reactions are described by general equations of the type:

a) A + B + C D; b) 2A + B D; c) 3A D.

For example: a) 2Н 2 + 0 2 2Н 2 0; b) 2NO + H 2 N 2 0 + H 2 0.

The reaction rate depending on the molecularity will be expressed by the equations: a) V = k C A - for a monomolecular reaction; b) V \u003d to C A C in or c) V \u003d to C 2 A - for a bimolecular reaction; d) V \u003d k C C in C e) V \u003d k C 2 A C in or e) V \u003d k C 3 A - for a trimolecular reaction.

Molecularity is the number of molecules that react in one elementary chemical act.

It is often difficult to establish the molecularity of a reaction, so a more formal sign is used - the order of a chemical reaction.

The reaction order is equal to the sum of the exponents of concentrations in the equation expressing the dependence of the reaction rate on the concentration of the reactants (kinetic equation).

The order of the reaction most often does not coincide with the molecularity due to the fact that the reaction mechanism, i.e., the "elementary act" of the reaction (see the definition of the sign of molecularity), is difficult to establish.

Let us consider a number of examples illustrating this position.

1. The rate of dissolution of crystals is described by the equations of zero-order kinetics, despite the monomolecular nature of the reaction: AgCl (TB) -> Ag + + CI", V = k C (AgCl (TB p = k" C (AgCl (ra)) - p - density and is a constant value, i.e., the dissolution rate does not depend on the amount (concentration) of the dissolved substance.

2. The reaction of sucrose hydrolysis: CO + H 2 0 -> C 6 H 12 0 6 (glucose) + C 6 H 12 0 6 (fructose) is a bimolecular reaction, but its kinetics is described by a first-order kinetic equation: V \u003d k * C cax , since under experimental conditions, including in the body, the concentration of water is a constant value С(Н 2 0) - const.

3.
The decomposition reaction of hydrogen peroxide, proceeding with the participation of catalysts, both inorganic ions Fe 3+, Cu 2+ of metallic platinum, and biological enzymes, such as catalase, has general form:

2H 2 0 2 -\u003e 2H 2 0 + O e, i.e., is bimolecular.

Dependence of reaction rate on concentration. Kinetic equations of reactions of the first, second and zero orders. Experimental methods for determining the rate and rate constant of reactions.

The dependence of the reaction rate on temperature. Van't Hoff rule. The temperature coefficient of the reaction rate and its features for biochemical processes.

γ is the temperature coefficient of the reaction rate.

The physical meaning of the value of γ is that it shows how many times the reaction rate changes with a temperature change of every 10 degrees.

15. The concept of the theory of active collisions. Energy profile of the reaction; activation energy; Arrhenius equation. The role of the steric factor. The concept of the theory of the transition state.

The relationship of the rate constant, activation energy and temperature is described by the Arrhenius equation: k T \u003d k 0 *Ae ~ E / RT, where k t and k 0 are the rate constants at temperature T and T e e is the base of the natural logarithm, A is the steric factor.

The steric factor A determines the probability of collision of two reacting particles in the active center of the molecule. This factor is especially importance for biochemical reactions with biopolymers. In acid-base reactions, the H + ion must react with the terminal carboxyl group - COO. However, not every collision of the H + ion with a protein molecule will lead to this reaction. Only those collisions that are directly carried out at certain points of the macromolecules will be effective called active centers.

It follows from the Arrhenius equation that the higher the rate constant, the lower the value of the activation energy E and the higher the temperature T of the process.

Problem 336.
At 150°C, some reaction is complete in 16 minutes. Taking the temperature coefficient of the reaction rate equal to 2.5, calculate how long this reaction will end if it is carried out: a) at 20 0 °С; b) at 80°C.
Solution:
According to the van't Hoff rule, the dependence of velocity on temperature is expressed by the equation:

v t and k t - the rate and rate constant of the reaction at a temperature of t°C; v (t + 10) and k (t + 10) the same values ​​at temperature (t + 10 0 C); - the temperature coefficient of the reaction rate, the value of which for most reactions lies in the range of 2 - 4.

a) Given that the rate of a chemical reaction at a given temperature is inversely proportional to the duration of its course, we substitute the data given in the condition of the problem into a formula that quantitatively expresses the van't Hoff rule, we get:

b) Since this reaction proceeds with a decrease in temperature, then at a given temperature the rate of this reaction is directly proportional to the duration of its course, we substitute the data given in the condition of the problem into a formula that quantitatively expresses the van't Hoff rule, we get:

Answer: a) at 200 0 С t2 = 9.8 s; b) at 80 0 С t3 = 162 h 1 min 16 s.

Problem 337.
Will the value of the reaction rate constant change: a) when replacing one catalyst with another; b) when the concentrations of reactants change?
Solution:
The reaction rate constant is a value that depends on the nature of the reactants, on the temperature and on the presence of catalysts, and does not depend on the concentration of the reactants. It can be equal to the reaction rate in the case when the concentrations of the reactants are equal to unity (1 mol/l).

a) When one catalyst is replaced by another, the rate of a given chemical reaction will change, or it will increase. If a catalyst is used, the rate of a chemical reaction will increase, and the value of the reaction rate constant will increase accordingly. A change in the value of the reaction rate constant will also occur when one catalyst is replaced by another, which will increase or decrease the rate of this reaction relative to the original catalyst.

b) When the concentration of the reactants changes, the values ​​of the reaction rate will change, and the value of the reaction rate constant will not change.

Problem 338.
Does the thermal effect of a reaction depend on its activation energy? Justify the answer.
Solution:
The thermal effect of the reaction depends only on the initial and final state of the system and does not depend on the intermediate stages of the process. Activation energy is the excess energy that molecules of substances must have in order for their collision to lead to the formation of a new substance. The activation energy can be changed by raising or lowering the temperature, respectively lowering or increasing it. Catalysts lower the activation energy, while inhibitors lower it.

Thus, a change in the activation energy leads to a change in the reaction rate, but not to a change in the heat of the reaction. The thermal effect of a reaction is a constant value and does not depend on a change in the activation energy for a given reaction. For example, the reaction for the formation of ammonia from nitrogen and hydrogen is:

This reaction is exothermic, > 0). The reaction proceeds with a decrease in the number of moles of reacting particles and the number of moles of gaseous substances, which brings the system from a less stable state to a more stable one, the entropy decreases,< 0. Данная реакция в обычных условиях не протекает (она возможна только при достаточно низких температурах). В присутствии катализатора энергия активации уменьшается, и скорость реакции возрастает. Но, как до применения катализатора, так и в присутствии его тепловой эффект реакции не изменяется, реакция имеет вид:

Problem 339.
For which reaction, direct or reverse, is the activation energy greater if the direct reaction proceeds with the release of heat?
Solution:
The difference between the activation energies of the direct and reverse reactions is equal to the thermal effect: H \u003d E a (pr.) - E a (arr.) . This reaction proceeds with the release of heat, i.e. is exothermic,< 0 Исходя из этого, энергия активации прямой реакции имеет меньшее значение, чем энергия активации обратной реакции:
E a(ex.)< Е а(обр.) .

Answer: E a(ex.)< Е а(обр.) .

Problem 340.
How many times will the rate of a reaction proceeding at 298 K increase if its activation energy is reduced by 4 kJ/mol?
Solution:
Let us denote the decrease in the activation energy by Ea, and the rate constants of the reaction before and after the decrease in the activation energy, respectively, by k and k. Using the Arrhenius equation, we obtain:

E a is the activation energy, k and k" are the reaction rate constants, T is the temperature in K (298).
Substituting the data of the problem into the last equation and, expressing the activation energy in joules, we calculate the increase in the reaction rate:

Answer: 5 times.