Calculate how the temperature coefficient of the reaction will change. Dependence of reaction rate on temperature

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; in this case, 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 - increment sign (Δp = p2 - p1; Δt = t2 - t1).

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 a 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.

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.

As temperature increases, the rate of a chemical process usually increases. In 1879, the Dutch scientist J. van't Hoff formulated an empirical rule: with an increase in temperature by 10 K, the rate of most chemical reactions increases by 2-4 times.

Mathematical notation of the rule J. van't Hoff:

γ 10 = (k t+10)/k t, where k t is the reaction rate constant at temperature T; k t+10 - reaction rate constant at temperature T+10; γ 10 - Van't Hoff temperature coefficient. Its value ranges from 2 to 4. For biochemical processes, γ 10 varies from 7 to 10.

All biological processes take place in a certain temperature range: 45-50°C. The optimal temperature is 36-40°C. In the body of warm-blooded animals, this temperature is maintained constant due to the thermoregulation of the corresponding biosystem. When studying biological systems, temperature coefficients γ 2, γ 3, γ 5 are used. For comparison, they are reduced to γ 10.

The dependence of the reaction rate on temperature, in accordance with the Van't Hoff rule, can be represented by the equation:

V 2 /V 1 = γ ((T 2 -T 1)/10)

Activation energy. A significant increase in the reaction rate with increasing temperature cannot be explained only by an increase in the number of collisions between particles of reacting substances, since, in accordance with the kinetic theory of gases, with increasing temperature the number of collisions increases to an insignificant extent. The increase in reaction rate with increasing temperature is explained by the fact that a chemical reaction does not occur with any collision of particles of reacting substances, but only with the meeting of active particles that have the necessary excess energy at the moment of collision.

The energy required to convert inactive particles into active ones is called activation energy (Ea). Activation energy is the excess energy, compared to the average value, required for reacting substances to enter into a reaction upon their collision. Activation energy is measured in kilojoules per mole (kJ/mol). Typically E is between 40 and 200 kJ/mol.

The energy diagram of an exothermic and endothermic reaction is shown in Fig. 2.3. For any chemical process, initial, intermediate and final states can be distinguished. At the top of the energy barrier, the reactants are in an intermediate state called the activated complex, or transition state. The difference between the energy of the activated complex and the initial energy of the reactants is Ea, and the difference between the energy of the reaction products and the starting substances (reagents) is ΔH, the thermal effect of the reaction. The activation energy, unlike ΔH, is always a positive value. For an exothermic reaction (Fig. 2.3, a) the products are located at a lower energy level than the reactants (Ea< ΔН).

Rice. 2.3. Energy diagrams of reactions: A – exothermic B – endothermic

A B

Ea is the main factor determining the reaction rate: if Ea > 120 kJ/mol (higher energy barrier, fewer active particles in the system), the reaction proceeds slowly; and vice versa, if Ea< 40 кДж/моль, реакция осуществляется с большой скоростью.

For reactions involving complex biomolecules, one should take into account the fact that in an activated complex formed during the collision of particles, the molecules must be oriented in space in a certain way, since only the reacting region of the molecule, which is small in relation to its size, undergoes transformation.

If the rate constants k 1 and k 2 at temperatures T 1 and T 2 are known, the value of Ea can be calculated.

In biochemical processes, the activation energy is 2-3 times less than in inorganic ones. At the same time, the Ea of reactions involving foreign substances, xenobiotics, significantly exceeds the Ea of conventional biochemical processes. This fact is a natural bioprotection of the system from the influence of foreign substances, i.e. reactions natural to the body occur in favorable conditions with low Ea, and for foreign reactions Ea is high. This is a gene barrier that characterizes one of the main features of biochemical processes.

From qualitative considerations, it is clear that the rate of reactions should increase with increasing temperature, because at the same time, the energy of the colliding particles increases and the likelihood that a chemical transformation will occur during a collision increases. To quantitatively describe temperature effects in chemical kinetics, two main relationships are used - the Van't Hoff rule and the Arrhenius equation.

Van't Hoff's rule is that when heated by 10 o C, the rate of most chemical reactions increases by 2 to 4 times. Mathematically, this means that the reaction rate depends on temperature in a power-law manner:

, (4.1)

where is the temperature coefficient of speed ( = 24). Van't Hoff's rule is very rough and is applicable only in a very limited temperature range.

Much more accurate is Arrhenius equation, describing the temperature dependence of the rate constant:

, (4.2)

Where R- universal gas constant; A- pre-exponential factor, which does not depend on temperature, but is determined only by the type of reaction; E A - activation energy, which can be characterized as a certain threshold energy: roughly speaking, if the energy of colliding particles is less E A, then during a collision the reaction will not occur if the energy exceeds E A, the reaction will occur. The activation energy does not depend on temperature.

Graphically dependency k(T) as follows:

At low temperatures, chemical reactions hardly occur: k(T) 0. At very high temperatures, the rate constant tends to the limiting value: k(T)A. This corresponds to the fact that all molecules are chemically active and every collision results in a reaction.

The activation energy can be determined by measuring the rate constant at two temperatures. From equation (4.2) it follows:

. (4.3)

More accurately, the activation energy is determined from the values of the rate constant at several temperatures. To do this, the Arrhenius equation (4.2) is written in logarithmic form

and record experimental data in ln coordinates k - 1/T. The tangent of the angle of inclination of the resulting straight line is equal to - E A / R.

For some reactions, the pre-exponential factor depends weakly on temperature. In this case, the so-called experienced activation energy:

. (4.4)

If the pre-exponential factor is constant, then the experimental activation energy is equal to the Arrhenius activation energy: E op = E A.

Example 4-1. Using the Arrhenius equation, estimate at what temperatures and activation energies the Van't Hoff rule is valid.

Solution. Let's imagine Van't Hoff's rule (4.1) as a power-law dependence of the rate constant:

Where B- constant value. Let us compare this expression with the Arrhenius equation (4.2), taking the value ~ for the temperature coefficient of velocity e = 2.718:

Let's take the natural logarithm of both sides of this approximate equality:

Having differentiated the resulting relationship with respect to temperature, we find the desired connection between activation energy and temperature:

If the activation energy and temperature approximately satisfy this relationship, then the van’t Hoff rule can be used to assess the effect of temperature on the reaction rate.

Example 4-2. The first order reaction at a temperature of 70 o C is 40% complete in 60 minutes. At what temperature will the reaction be 80% complete in 120 minutes if the activation energy is 60 kJ/mol?

Solution. For a first-order reaction, the rate constant is expressed in terms of the degree of conversion as follows:

where a = x/a- degree of transformation. Let us write this equation at two temperatures taking into account the Arrhenius equation:

Where E A= 60 kJ/mol, T 1 = 343 K, t 1 = 60 min, a 1 = 0.4, t 2 = 120 min, a 2 = 0.8. Let's divide one equation by another and take the logarithm:

Substituting the above values into this expression, we find T 2 = 333 K = 60 o C.

Example 4-3. The rate of bacterial hydrolysis of fish muscles doubles when moving from a temperature of -1.1 o C to a temperature of +2.2 o C. Estimate the activation energy of this reaction.

Solution. An increase in the rate of hydrolysis by 2 times is due to an increase in the rate constant: k 2 = 2k 1 . The activation energy in relation to the rate constants at two temperatures can be determined from equation (4.3) with T 1 = t 1 + 273.15 = 272.05 K, T 2 = t 2 + 273.15 = 275.35 K:

130800 J/mol = 130.8 kJ/mol.

4-1. Using Van't Hoff's rule, calculate at what temperature the reaction will end in 15 minutes, if at 20 o C it takes 2 hours. The temperature coefficient of rate is 3. (answer)

4-2. The half-life of the substance at 323 K is 100 minutes, and at 353 K it is 15 minutes. Determine the temperature coefficient of speed.(answer)

4-3. What should be the activation energy for the reaction rate to increase 3 times with an increase in temperature by 10 0 C a) at 300 K; b) at 1000 K? (answer)

4-4. The first order reaction has an activation energy of 25 kcal/mol and a pre-exponential factor of 5. 10 13 sec -1 . At what temperature will the half-life for this reaction be: a) 1 min; b) 30 days? (answer)

4-5. In which of the two cases does the reaction rate constant increase more times: when heated from 0 o C to 10 o C or when heated from 10 o C to 20 o C? Justify your answer using the Arrhenius equation. (answer)

4-6. The activation energy of some reaction is 1.5 times greater than the activation energy of another reaction. When heated from T 1 to T 2 the rate constant of the second reaction increased by a once. How many times did the rate constant of the first reaction increase when heated from T 1 to T 2 ?(answer)

4-7. The rate constant of a complex reaction is expressed in terms of the rate constants of the elementary stages as follows:

Express the activation energy and pre-exponential factor of the complex reaction in terms of the corresponding quantities related to the elementary stages.(answer)

4-8. In an irreversible 1st order reaction in 20 minutes at 125 o C, the degree of conversion of the starting substance was 60%, and at 145 o C the same degree of conversion was achieved in 5.5 minutes. Find the rate constants and activation energy for this reaction.(answer)

4-9. The 1st order reaction at a temperature of 25 o C is completed by 30% in 30 minutes. At what temperature will the reaction be 60% complete in 40 minutes if the activation energy is 30 kJ/mol? (answer)

4-10. The 1st order reaction at a temperature of 25 o C is 70% complete in 15 minutes. At what temperature will the reaction be 50% complete in 15 minutes if the activation energy is 50 kJ/mol? (answer)

4-11. The first order reaction rate constant is 4.02. 10 -4 s -1 at 393 K and 1.98 . 10 -3 s -1 at 413 K. Calculate the pre-exponential factor for this reaction. (answer)

4-12. For the reaction H 2 + I 2 2HI, the rate constant at a temperature of 683 K is equal to 0.0659 l/(mol. min), and at a temperature of 716 K - 0.375 l/(mol. min). Find the activation energy of this reaction and the rate constant at a temperature of 700 K.(answer)

4-13. For the reaction 2N 2 O 2N 2 + O 2 the rate constant at a temperature of 986 K is 6.72 l/(mol. min), and at a temperature of 1165 K - 977.0 l/(mol. min). Find the activation energy of this reaction and the rate constant at a temperature of 1053.0 K. (answer)

4-14. Trichloroacetate ion in ionizing solvents containing H + decomposes according to the equation

H + + CCl 3 COO - CO 2 + CHCl 3

The stage that determines the rate of the reaction is the monomolecular cleavage of the C-C bond in the trichloroacetate ion. The reaction proceeds in first order, and the rate constants have the following values: k= 3.11. 10 -4 s -1 at 90 o C, k= 7.62. 10 -5 s -1 at 80 o C. Calculate a) activation energy, b) rate constant at 60 o C. (answer)

4-15. For the reaction CH 3 COOC 2 H 5 + NaOH * CH 3 COONa + C 2 H 5 OH, the rate constant at a temperature of 282.6 K is equal to 2.307 l/(mol. min), and at a temperature of 318.1 K - 21.65 l /(mol min). Find the activation energy of this reaction and the rate constant at a temperature of 343 K.(answer)

4-16. For the reaction C 12 H 22 O 11 + H 2 O C 6 H 12 O 6 + C 6 H 12 O 6 the rate constant at a temperature of 298.2 K is equal to 0.765 l/(mol. min), and at a temperature of 328.2 K - 35.5 l/(mol min). Find the activation energy of this reaction and the rate constant at a temperature of 313.2 K.(answer)

4-17. The substance decomposes in two parallel paths with rate constants k 1 and k 2. What is the difference in activation energies of these two reactions if at 10 o C k 1 /k 2 = 10, and at 40 o C k 1 /k 2 = 0.1? (answer)

4-18. In two reactions of the same order, the difference in activation energies is E 2 - E 1 = 40 kJ/mol. At a temperature of 293 K the ratio of the rate constants is k 1 /k 2 = 2. At what temperature do the rate constants become equal? (answer)

4-19. The decomposition of acetone dicarboxylic acid in an aqueous solution is a first order reaction. The rate constants of this reaction were measured at different temperatures:

Calculate the activation energy and pre-exponential factor. What is the half-life at 25 o C?