Formula for temperature coefficient of reaction. Temperature coefficient of the rate of a chemical reaction (van't Hoff rule)

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

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

a) Considering that the rate of a chemical reaction at a given temperature is inversely proportional to the duration of its occurrence, we substitute the data given in the problem statement into a formula that quantitatively expresses Van’t Hoff’s rule, we obtain:

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 occurrence, we substitute the data given in the problem statement into the formula that quantitatively expresses the van’t Hoff rule, we get:

Answer: a) at 200 0 C t2 = 9.8 s; b) at 80 0 C 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 reacting substances change?
Solution:
The reaction rate constant is a value that depends on the nature of the reacting substances, on temperature and on the presence of catalysts, and does not depend on the concentration of the reacting substances. 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 replacing one catalyst with another, the rate of a given chemical reaction will change or increase. If a catalyst is used, the rate of the chemical reaction will increase, and the value of the reaction rate constant will accordingly increase. A change in the value of the reaction rate constant will also occur when replacing one catalyst with another, which will increase or decrease the rate of this reaction in relation to the original catalyst.

b) When the concentration of reactants changes, the reaction rate values will change, but 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 states 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 increasing or decreasing the temperature, lowering or increasing it accordingly. Catalysts lower the activation energy, and inhibitors lower it.

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

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 leads the system from a less stable state to a more stable one, 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 releases heat?
Solution:
The difference between the activation energies of the forward and reverse reactions is equal to the thermal effect: H = E a(rev.) - E a(rev.) . This reaction occurs 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 occurring at 298 K increase if its activation energy is reduced by 4 kJ/mol?
Solution:
Let us denote the decrease in activation energy by Ea, and the reaction rate constants before and after the decrease in activation energy by k and k, respectively." Using the Arrhenius equation, we obtain:

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

Answer: 5 times.

Factors influencing the reaction

In the human body, thousands of enzymatic reactions take place in a living cell. However, in a multi-stage 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 t-RNA 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 monitor and regulate only the slowest ones. This method of regulating the rate of multi-stage synthesis is called the minimum principle. It allows you to significantly simplify and make the auto-regulation system in the cage more reliable.

Classifications of reactions used in kinetics: reactions, homogeneous, heterogeneous and microheterogeneous; reactions are simple and complex (parallel, sequential, conjugate, chain). Molecularity of an elementary reaction act. Kinetic equations. Order of reaction. Half-life

Microheterogeneous reactions –

The molecularity of a reaction is determined by the number of molecules that enter into a chemical interaction in an elementary reaction. On this basis, 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 of type A + B -> C or 2A -> C - are bimolecular, for example:
a) C + 0 2 -> C0 2; b) 2H 2 0 2 -> 2H 2 0 + 0 2, etc.

Trimolecular reactions are described by general equations like:

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

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

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

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

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

The order of the reaction is equal to the sum of the exponents of the powers of concentration 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 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 zero-order kinetics equations, 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 rate of dissolution does not depend on the amount (concentration) of the solute.

2. The hydrolysis reaction of sucrose: 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 the first-order kinetic equation: V = k*C cax, since under experimental conditions, including in the body, the concentration of water is a constant value C(H 2 0) - const.

3.
The decomposition reaction of hydrogen peroxide, which occurs with the participation of catalysts, both inorganic ions Fe 3+, Cu 2+ metal platinum, and biological enzymes, for example catalase, has the general form:

2H 2 0 2 -> 2H 2 0 + O i.e. it is bimolecular.

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

Dependence of reaction rate on temperature. Van't Hoff rule. Temperature coefficient of reaction rate and its features for biochemical processes.

γ-temperature coefficient of reaction rate.

The physical meaning of the value γ is that it shows how many times the reaction rate changes with a change in temperature for 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 transition state.

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

Steric factor A determines the probability of collision of two reacting particles in the active center of the molecule. This factor is especially important 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 directly occur at some points of the macromolecules will be effective , called active centers.

From the Arrhenius equation it follows that the lower the activation energy E and the higher the temperature T of the process, the higher the rate constant.

The rate of a chemical reaction increases with increasing temperature. You can estimate the increase in reaction rate with temperature using Van't Hoff's rule. According to the rule, increasing the temperature by 10 degrees increases the reaction rate constant by 2-4 times:

This rule does not apply at high temperatures, when the rate constant hardly changes with temperature.

Van't Hoff's rule allows you to quickly determine the shelf life of a drug. Increasing the temperature increases the rate of decomposition of the drug. This reduces the time it takes to determine the shelf life of the medicine.

The method is that the drugs are kept at an elevated temperature T for a certain time tT, the amount of decomposed drug m is found and recalculated to a standard storage temperature of 298K. Considering the process of drug decomposition to be a first-order reaction, the rate at the selected temperature T and T = 298 K is expressed:

Considering the mass of the decomposed drug to be the same for standard and real storage conditions, the decomposition rate can be expressed as:

Taking T=298+10n, where n = 1,2,3…,

The final expression for the shelf life of the drug is obtained under standard conditions of 298K:

Theory of active collisions. Activation energy. Arrhenius equation. Relationship between reaction rate and activation energy.

The theory of active collisions was formulated by S. Arrhenius in 1889. This theory is based on the idea that for a chemical reaction to occur, collisions between the molecules of the starting substances are necessary, and the number of collisions is determined by the intensity of the thermal motion of the molecules, i.e. depends on temperature. But not every collision of molecules leads to a chemical transformation: only an active collision leads to it.

Active collisions are collisions that occur, for example, between molecules A and B with a large amount of energy. The minimum amount of energy that the molecules of the starting substances must have in order for their collision to be active is called the energy barrier of the reaction.

Activation energy is the excess energy that can be imparted or transferred to one mole of a substance.

The activation energy significantly affects the value of the reaction rate constant and its dependence on temperature: the greater Ea, the smaller the rate constant and the more significantly the temperature change affects it.

The reaction rate constant is related to the activation energy by a complex relationship described by the Arrhenius equation:

k=Aе–Ea/RT, where A is the pre-exponential factor; Eа is the activation energy, R is the universal gas constant equal to 8.31 J/mol; T – absolute temperature;

e-base of natural logarithms.

However, the observed reaction rate constants are usually much smaller than those calculated from the Arrhenius equation. Therefore, the equation for the reaction rate constant is modified as follows:

(minus before all fractions)

The multiplier causes the temperature dependence of the rate constant to differ from the Arrhenius equation. Since the Arrhenius activation energy is calculated as the slope of the logarithmic dependence of the reaction rate on the inverse temperature, then doing the same with the equation , we get:

Features of heterogeneous reactions. The rate of heterogeneous reactions and its determining factors. Kinetic and diffusion areas of heterogeneous processes. Examples of heterogeneous reactions of interest to pharmacy.

HETEROGENEOUS REACTIONS, chem. reactions involving substances in decomposition. phases and collectively making up a heterogeneous system. Typical heterogeneous reactions: thermal. decomposition of salts with the formation of gaseous and solid products (for example, CaCO3 -> CaO + CO2), reduction of metal oxides with hydrogen or carbon (for example, PbO + C -> Pb + CO), dissolution of metals in acids (for example, Zn + + H2SO4 -> ZnSO4 + H2), interaction. solid reagents (A12O3 + NiO -> NiAl2O4). A special class includes heterogeneous catalytic reactions occurring on the surface of the catalyst; Moreover, the reactants and products may not be in different phases. Direction, during the reaction N2 + + ZH2 -> 2NH3 occurring on the surface of an iron catalyst, the reactants and the reaction product are in the gas phase and form a homogeneous system.

The features of heterogeneous reactions are due to the participation of condensed phases in them. This makes mixing and transport of reagents and products difficult; activation of reagent molecules at the interface is possible. The kinetics of any heterogeneous reaction is determined by the speed of the chemical itself. transformations, as well as by transfer processes (diffusion) necessary to replenish the consumption of reacting substances and remove reaction products from the reaction zone. In the absence of diffusion hindrances, the rate of a heterogeneous reaction is proportional to the size of the reaction zone; this is the specific reaction rate calculated per unit surface (or volume) of the reaction. zones, does not change over time; for simple (one-step) reactions it may be determined on the basis of the acting mass law. This law is not satisfied if the diffusion of substances proceeds slower than the chemical one. district; in this case, the observed rate of a heterogeneous reaction is described by the equations of diffusion kinetics.

The rate of a heterogeneous reaction is the amount of substance that reacts or is formed during a reaction per unit time per unit surface area of the phase.

Factors affecting the rate of a chemical reaction:

The nature of the reactants

Reagent concentration,

Temperature,

Presence of a catalyst.

Vheterogen = Δп(S Δt), where Vheterog is the reaction rate in a heterogeneous system; n is the number of moles of any of the substances resulting from the reaction; V is the volume of the system; t - time; S is the surface area of the phase on which the reaction occurs; Δ - sign of increment (Δp = p2 - p1; Δt = t2 - t1).

Task No. 1. Interaction with free oxygen leads to the formation of highly toxic nitrogen dioxide / /, although this reaction occurs slowly under physiological conditions and at low concentrations does not play a significant role in toxic damage to cells, however, pathogenic effects increase sharply with its overproduction. Determine how many times the rate of interaction of nitrogen oxide (II) with oxygen increases when the pressure in the mixture of initial gases doubles, if the reaction rate described by the equation ?

Solution.

1. Doubling the pressure is equivalent to doubling the concentration ( With) And . Therefore, the interaction rates corresponding to and will take, in accordance with the law of mass action, the expressions: And

Answer. The reaction speed will increase 8 times.

Task No. 2. It is believed that the concentration of chlorine (a greenish gas with a pungent odor) in the air above 25 ppm is dangerous to life and health, but there is evidence that if the patient has recovered from acute severe poisoning with this gas, then no residual effects are observed. Determine how the rate of the reaction occurring in the gas phase will change if you increase by 3 times: concentration, concentration, 3) pressure / /?

Solution.

1. If we denote the concentrations and respectively by and , then the expression for the reaction rate will take the form: .

2. After increasing the concentrations by 3 times, they will be equal for and for . Therefore, the expression for the reaction rate will take the form: 1) 2)

3. An increase in pressure increases the concentration of gaseous reactants by the same amount, therefore

4. The increase in the reaction rate relative to the initial one is determined by the ratio, respectively: 1) , 2) , 3) .

Answer. The reaction rate will increase by: 1) , 2) , 3) times.

Problem No. 3. How does the rate of interaction of the starting substances change when the temperature changes from to if the temperature coefficient of the reaction is 2.5?

Solution.

1. The temperature coefficient shows how the reaction rate changes with every change in temperature (van't Hoff's rule): .

2. If the temperature change is: , then taking into account the fact that , we obtain: . From here, .

3. Using the table of antilogarithms we find: .

Answer. When the temperature changes (i.e. increases), the speed will increase by 67.7 times.

Problem No. 4. Calculate the temperature coefficient of the reaction rate, knowing that the rate increases by a factor of 128 as the temperature increases.

Solution.

1. The dependence of the rate of a chemical reaction on temperature is expressed by the empirical van’t Hoff rule:

.Solving the equation for , we find: , . Therefore =2

Answer. =2.

Problem No. 5. For one of the reactions, two rate constants were determined: at 0.00670 and at 0.06857. Determine the rate constant for the same reaction at .

Solution.

1. Based on two values of the reaction rate constants, using the Arrhenius equation, we determine the activation energy of the reaction: . For this case: Hence: J/mol.

2. Calculate the reaction rate constant at , using the rate constant at and the Arrhenius equation in the calculations: . For this case: and taking into account the fact that: , we get: . Hence,

Answer.

Calculation of the chemical equilibrium constant and determination of the direction of the equilibrium shift using Le Chatelier’s principle .

Task No. 6. Carbon dioxide / / unlike carbon monoxide / / does not violate the physiological functions and anatomical integrity of a living organism and their suffocating effect is due only to the presence in high concentrations and a decrease in the percentage of oxygen in the inhaled air. What is it equal to reaction equilibrium constant / /: at temperature, expressed through: a) partial pressures of reacting substances; b) their molar concentrations, knowing that the composition of the equilibrium mixture is expressed by volume fractions: , and , and the total pressure in the system is Pa?

Solution.

1. The partial pressure of a gas is equal to the total pressure multiplied by the volume fraction of gas in the mixture, therefore:

2. Substituting these values into the expression for the equilibrium constant, we obtain:

3. The relationship between and is established on the basis of the Mendeleev-Clapeyron equation for ideal gases and is expressed by the equality: , where is the difference between the number of moles of gaseous reaction products and gaseous starting substances. For this reaction: . Then: .

Answer. Pa. .

Task No. 7. In what direction will the equilibrium shift in the following reactions:

3. ;

a) with increasing temperature, b) with decreasing pressure, c) with increasing hydrogen concentration?

Solution.

1. Chemical equilibrium in the system is established at constant external parameters (etc.). If these parameters change, then the system leaves the state of equilibrium and the direct (to the right) or reverse reaction (to the left) begins to predominate. The influence of various factors on the shift in equilibrium is reflected in Le Chatelier's principle.

2. Let us consider the influence on the above reactions of all 3 factors influencing chemical equilibrium.

a) As the temperature increases, the equilibrium shifts towards the endothermic reaction, i.e. reaction that occurs with the absorption of heat. The 1st and 3rd reactions are exothermic / /, therefore, with increasing temperature, the equilibrium will shift towards the reverse reaction, and in the 2nd reaction / / - towards the forward reaction.

b) As the pressure decreases, the equilibrium shifts towards an increase in the number of moles of gases, i.e. towards greater pressure. In the 1st and 3rd reactions, the left and right sides of the equation will have the same number of moles of gases (2-2 and 1-1, respectively). Therefore, the change in pressure won't cause shifts in equilibrium in the system. In the 2nd reaction, there are 4 moles of gases on the left side and 2 moles on the right side, therefore, as the pressure decreases, the equilibrium will shift towards the reverse reaction.

V) As the concentration of reaction components increases, the equilibrium shifts towards their consumption. In the first reaction, hydrogen is present in the products, and increasing its concentration will enhance the reverse reaction, during which it is consumed. In the 2nd and 3rd reactions, hydrogen is among the starting substances, so an increase in its concentration shifts the equilibrium towards the reaction that occurs with the consumption of hydrogen.

Answer.

a) As the temperature increases, the equilibrium in reactions 1 and 3 will shift to the left, and in reaction 2 - to the right.

b) Reactions 1 and 3 will not be affected by a decrease in pressure, but in reaction 2 the equilibrium will be shifted to the left.

c) An increase in temperature in reactions 2 and 3 will entail a shift of equilibrium to the right, and in reaction 1 - to the left.

1.2. Situational tasks No. 7 to 21 to consolidate the material (done in a protocol notebook).

Task No. 8. How will the rate of glucose oxidation in the body change when the temperature decreases from to if the temperature coefficient of the reaction rate is 4?

Problem No. 9.Using the approximate Van't Hoff rule, calculate how much the temperature needs to be increased in order for the reaction rate to increase 80 times? Take the temperature velocity coefficient equal to 3.

Task No. 10. To practically stop the reaction, rapid cooling of the reaction mixture is used (“reaction freezing”). Determine how many times the reaction rate will change when the reaction mixture is cooled from 40 to , if the temperature coefficient of the reaction is 2.7.

Task No. 11. The isotope used to treat some tumors has a half-life of 8.1 days. After what time will the content of radioactive iodine in the patient’s body decrease by 5 times?

Task No. 12. The hydrolysis of some synthetic hormone (pharmaceutical) is a first-order reaction with a rate constant of 0.25 (). How will the concentration of this hormone change after 2 months?

Task No. 13. The radioactive half-life is 5600 years. In a living organism, a constant amount is maintained due to metabolism. In the remains of the mammoth, the content was the same as the original. Determine when the mammoth lived?

Problem No. 14. The half-life of an insecticide (a pesticide used to control insects) is 6 months. A certain amount of it entered the reservoir, where the concentration mol/l was established. How long will it take for the insecticide concentration to drop to the mol/l level?

Task No. 15. Fats and carbohydrates oxidize at a noticeable rate at a temperature of 450 - 500 °, and in living organisms - at a temperature of 36 - 40 °. What is the reason for the sharp decrease in temperature required for oxidation?

Problem No. 16. Hydrogen peroxide decomposes in aqueous solutions into oxygen and water. The reaction is accelerated by both an inorganic catalyst (ion) and a bioorganic catalyst (catalase enzyme). The activation energy of the reaction in the absence of a catalyst is 75.4 kJ/mol. The ion reduces it to 42 kJ/mol, and the enzyme catalase - to 2 kJ/mol. Calculate the ratio of reaction rates in the absence of a catalyst in the presence of catalase. What conclusion can be drawn about the activity of the enzyme? The reaction takes place at a temperature of 27 °C.

Problem No. 17 Penicillin decay rate constant for walkie-talkie J/mol.

1.3. Control questions

1. Explain what the terms mean: reaction rate, rate constant?

2. How are the average and true rates of chemical reactions expressed?

3. Why does it make sense to talk about the rate of chemical reactions only for a given point in time?

4. Formulate the definition of a reversible and irreversible reaction.

5. Define the law of mass action. In the equalities expressing this law, is the dependence of the reaction rate on the nature of the reactants reflected?

6. How does the reaction rate depend on temperature? What is activation energy called? What are active molecules?

7. On what factors does the rate of homogeneous and heterogeneous reactions depend? Give examples.

8. What is the order and molecularity of chemical reactions? In what cases do they not match?

9. What substances are called catalysts? What is the mechanism of the accelerating action of the catalyst?

10. What is the concept of “catalyst poisoning”? What substances are called inhibitors?

11. What is called chemical equilibrium? Why is it called dynamic? What concentrations of reactants are called equilibrium?

12. What is called the chemical equilibrium constant? Does it depend on the nature of the reacting substances, their concentration, temperature, pressure? What are the features of the mathematical notation for the equilibrium constant in heterogeneous systems?

13. What is the pharmacokinetics of drugs?

14. The processes occurring with the drug in the body are quantitatively characterized by a number of pharmacokinetic parameters. Give the main ones.

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

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

Answer: E a(ex.)< Е а(обр.) .

Answer: 5 times.