The reaction rate constant is a function of temperature; an increase in temperature generally increases the rate constant. The first attempt to take into account the effect of temperature was made by van't Hoff, who formulated the following rule of thumb:
With an increase in temperature for every 10 degrees, the rate constant of an elementary chemical reaction increases by 2-4 times.
The value showing how many times the rate constant increases with an increase in temperature by 10 degrees is temperature coefficient of reaction rate constantγ. Mathematically, the van't Hoff rule can be written as follows:
(II.30)
However, the van't Hoff rule is applicable only in a narrow temperature range, since the temperature coefficient of the reaction rate γ is itself a function of temperature; at very high and very low temperatures, γ becomes equal to unity (i.e., the rate of a chemical reaction ceases to depend on temperature).
Arrhenius equation
Obviously, the interaction of particles is carried out during their collisions; however, the number of collisions of molecules is very large, and if each collision led to a chemical interaction of particles, all reactions would proceed almost instantly. Arrhenius postulated that collisions of molecules would be effective (i.e., they would lead to a reaction) only if the colliding molecules had a certain amount of energy, the activation energy.
The activation energy is the minimum energy that molecules must have in order for their collision to lead to a chemical interaction.
Consider the path of some elementary reaction
A + B ––> C
Since the chemical interaction of particles is associated with the breaking of old chemical bonds and the formation of new ones, it is believed that any elementary reaction passes through the formation of some unstable intermediate compound, called an activated complex:
A ––> K # ––> B
The formation of an activated complex always requires the expenditure of a certain amount of energy, which is caused, firstly, by the repulsion of electron shells and atomic nuclei when the particles approach each other and, secondly, by the need to build a certain spatial configuration of atoms in the activated complex and redistribute the electron density. Thus, on the way from the initial state to the final state, the system must overcome a kind of energy barrier. The reaction activation energy is approximately equal to the excess of the average energy of the activated complex over the average energy level of the reactants. Obviously, if the direct reaction is exothermic, then the activation energy of the reverse reaction E "A is higher than the activation energy of the direct reaction E A. The activation energies of the direct and reverse reactions are related to each other through a change in internal energy during the reaction. The above can be illustrated using the energy chemical reaction diagrams (Fig. 2.5).
Rice. 2.5. Energy diagram of a chemical reaction. E ref is the average energy of the particles of the initial substances, E prod is the average energy of the particles of the reaction products.
Since temperature is a measure of the average kinetic energy of particles, an increase in temperature leads to an increase in the proportion of particles whose energy is equal to or greater than the activation energy, which leads to an increase in the reaction rate constant (Fig. 2.6):
Rice. 2.6. Energy distribution of particles. Here nE/N is the fraction of particles with energy E; E i - average particle energy at temperature T i (T 1< T 2 < T 3).
Let us consider the thermodynamic derivation of the expression describing the dependence of the reaction rate constant on temperature and the value of the activation energy - the Arrhenius equation. According to the van't Hoff isobar equation,
Since the equilibrium constant is the ratio of the rate constants of the forward and reverse reactions, expression (II.31) can be rewritten as follows:
(II.32)
Representing the change in the enthalpy of the reaction ΔHº as the difference between two values E 1 and E 2, we obtain:
(II.33)
(II.34)
Here C is some constant. Postulating that C = 0, we obtain the Arrhenius equation, where E A is the activation energy:
After indefinite integration of expression (II.35), we obtain the Arrhenius equation in integral form:
(II.36)
(II.37)
Rice. 2.7. Dependence of the logarithm of the rate constant of a chemical reaction on the reciprocal temperature.
Here A is the constant of integration. From equation (II.37) it is easy to show the physical meaning of the pre-exponential factor A, which is equal to the rate constant of the reaction at a temperature tending to infinity. As can be seen from expression (II.36), the logarithm of the rate constant depends linearly on the reciprocal temperature (Fig. 2.7); the value of the activation energy E A and the logarithm of the pre-exponential factor A can be determined graphically (the tangent of the slope of the straight line to the abscissa axis and the segment cut off by the straight line on the y-axis).
Knowing the activation energy of the reaction and the rate constant at any temperature T 1, using the Arrhenius equation, you can calculate the value of the rate constant at any temperature T 2:
(II.39)
The dependence of the reaction rate on temperature is approximately determined by the van't Hoff rule of thumb: for every 10 degrees change in temperature, the rate of most reactions changes by a factor of 2-4.
Mathematically, Van't Hoff's rule is expressed as follows:
where v(T2) and v(T1) are the reaction rates, respectively, at temperatures T2 and T1 (T2> T1);
γ is the temperature coefficient of the reaction rate.
The value of γ for an endothermic reaction is higher than for an exothermic one. For many reactions, γ is in the range 2-4.
The physical meaning of the value of γ is that it shows how many times the reaction rate changes with a change in temperature for every 10 degrees.
Since the reaction rate and the rate constant of a chemical reaction are directly proportional, expression (3.6) is often written in the following form:
(3.7)
where k(T2), k(T1) are reaction rate constants, respectively
at temperatures T2 and T1;
γ is the temperature coefficient of the reaction rate.
Example 8 By how many degrees should the temperature be raised to increase the rate of the reaction by 27 times? The temperature coefficient of the reaction is 3.
Solution. We use expression (3.6):
We get: 27 = , = 3, DT = 30.
Answer: 30 degrees.
The reaction rate and the time it takes are inversely related: the larger v, the
less than t. Mathematically, this is expressed by the relation
Example 9 At a temperature of 293 K, the reaction proceeds in 2 minutes. How long will this reaction take at a temperature of 273 K if γ = 2.
Solution. Equation (3.8) implies:
.
We use equation (3.6) because 
We get:
min.
Answer: 8 min.
Van't Hoff's rule is applicable to a limited number of chemical reactions. The effect of temperature on the rate of processes is often determined by the Arrhenius equation.
Arrhenius equation . In 1889, the Swedish scientist S. Arreius, on the basis of experiments, derived an equation that is named after him
where k is the reaction rate constant;
k0 - pre-exponential factor;
e is the base of the natural logarithm;
Ea is a constant, called the activation energy, determined by the nature of the reactants:
R is the universal gas constant, equal to 8.314 J/mol×K.
The values of Ea for chemical reactions are in the range of 4 - 400 kJ/mol.
Many reactions are characterized by a certain energy barrier. To overcome it, activation energy is needed - some excess energy (compared to the harmful energy of molecules at a given temperature), which molecules must have in order for their collision to be effective, i.e., would lead to the formation of a new substance. As the temperature rises, the number of active molecules increases rapidly, which leads to a sharp increase in the reaction rate.
In the general case, if the reaction temperature changes from T1 to T2, equation (3.9) after taking the logarithm will take the form:
. (3.10)
This equation allows you to calculate the activation energy of the reaction when the temperature changes from T1 to T2.
The rate of chemical reactions increases in the presence of a catalyst. The action of a catalyst lies in the fact that it forms unstable intermediate compounds (activated complexes) with the reagents, the decomposition of which leads to the formation of reaction products. At the same time, the activation energy decreases, and molecules become active, the energy of which was insufficient to carry out the reaction in the absence of a catalyst. As a result, the total number of active £ molecules increases and the reaction rate increases.
The change in the reaction rate in the presence of a catalyst is expressed by the following equation:
, (3.11)
where vcat, and Ea(cat) - the rate and activation energy of a chemical reaction in the presence of a catalyst;
v and Ea are the rate and activation energy of a chemical reaction without a catalyst.
Example 10. The activation energy of a certain reaction in the absence of a catalyst is 75.24 kJ/mol, with a catalyst - 50.14 kJ/mol. How many times does the reaction rate increase in the presence of a catalyst if the reaction proceeds at a temperature of 298 K? Solution. We use equation (3.11). Substituting data into the equation
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Van't Hoff's rule. Arrhenius equation.
According to Van't Hoff's empirical rule, formulated around 1880, the rate of most reactions increases by a factor of 2-4 with a 10 degree increase in temperature if the reaction is carried out at a temperature close to room temperature. For example, the half-life of gaseous nitric oxide (V) at 35°C is about 85 minutes, at 45°C it is about 22 minutes. and at 55°C - about 8 min.
We already know that at any constant temperature the reaction rate is described by an empirical kinetic equation representing in most cases (with the exception of a reaction with a very complex mechanism) the product of the rate constant and the concentration of the reactants in powers equal to the orders of the reaction. The concentrations of reagents practically do not depend on temperature, orders, as experience shows, do the same. Consequently, the rate constants are responsible for the sharp dependence of the reaction rate on temperature. The temperature dependence of the rate constant is usually characterized by reaction rate temperature coefficient, which is the ratio of the rate constants at temperatures that differ by 10 degrees
and which, according to the van't Hoff rule, is approximately 2-4.
Let us try to explain the observed high values of the temperature coefficients of the reaction rates using the example of a homogeneous reaction in the gas phase from the standpoint of the molecular-kinetic theory of gases. In order for the molecules of interacting gases to react with each other, their collision is necessary, in which some bonds are broken, while others are formed, as a result of which a new molecule appears - the molecule of the reaction product. Consequently, the reaction rate depends on the number of collisions of reactant molecules, and the number of collisions, in particular, depends on the rate of chaotic thermal motion of molecules. The speed of molecules and, accordingly, the number of collisions increase with temperature. However, only an increase in the speed of molecules does not explain such a rapid increase in the rates of reactions with temperature. Indeed, according to the molecular kinetic theory of gases, the average velocity of molecules is proportional to the square root of the absolute temperature, i.e., with an increase in the temperature of the system by 10 degrees, say, from 300 to 310K, the average velocity of molecules will increase only by 310/300 = 1.02 times - much less than the van't Hoff rule requires.
Thus, the dependence of the reaction rate constants on temperature cannot be explained by the increase in the number of collisions alone. Obviously, there is another important factor at work here. To reveal it, let us turn to a more detailed analysis of the behavior of a large number of particles at various temperatures. So far, we have been talking about the average speed of the thermal motion of molecules and its change with temperature, but if the number of particles in the system is large, then, according to the laws of statistics, individual particles can have a speed and, accordingly, a kinetic energy that deviates to a greater or lesser extent from the average value for a given temperature. This situation is shown in Fig. (3.2), which
shows how parts are distributed -
3.2. Distribution of particles by kinetic energy at different temperatures:
2-T 2; 3-T 3 ; Ti ts in kinetic energy at a certain temperature. Consider, for example, curve 1 corresponding to the temperature Ti. The total number of particles in the system (we denote it by N 0) is equal to the area under the curve. The maximum number of particles, equal to Ni, has the most probable kinetic energy E 1 for a given temperature. Particles whose number is equal to the area under the curve to the right of the vertical E 1 will have a higher energy, and the area to the left of the vertical corresponds to particles with energies less than E The more the kinetic energy differs from the average, the fewer particles have it. Let us choose, for example, some energy E a greater than E 1 ). At a temperature Ti, the number of particles whose energy exceeds the value E a is only a small part of the total number of particles - this is the blackened area under curve 1 to the right of the vertical E a. However, at a higher temperature T 2, more particles already have an energy exceeding E a (curve 2), and with a further increase in temperature to T 3 (curve 3), the energy E a turns out to be close to the average, and such a reserve of kinetic energy will already have about half of all molecules. The reaction rate is determined not by the total number of collisions of molecules per unit time, but by that part of it, in which molecules take part, the kinetic energy of which exceeds a certain limit E a, called the activation energy of the reaction. This becomes quite understandable if we remember that in order for an elementary reaction to proceed successfully, it is necessary that the collision should break the old bonds and create conditions for the formation of new ones. Of course, this requires the expenditure of energy - it is necessary that the colliding particles have a sufficient supply of it. The Swedish scientist S. Arrhenius found that the increase in the rate of most reactions with increasing temperature occurs non-linearly (in contrast to the van't Hoff rule). Arrhenius found that in most cases the reaction rate constant obeys the equation LgK=lgA - , (3.14) which was named Arrhenius equations. Еа - activation energy (see below) R - molar gas constant, equal to 8.314 J / mol۰K, T - absolute temperature A is a constant or very little dependent on temperature value. It is called the frequency factor because it is related to the frequency of molecular collisions and the probability that the collision occurs at an orientation of the molecules favorable for the reaction. As can be seen from (3.14), as the activation energy E increases, the rate constant TO
decreases. Therefore, the rate of a reaction decreases as its energy barrier increases (see below). Ticket number 2 1) MAIN CLASSES OF INORGANIC COMPOUNDS: Bases, oxides, acids, salts. 2) Be - beryllium. Chemical properties: beryllium is relatively unreactive at room temperature. In compact form, it does not react with water and water vapor even at red heat and is not oxidized by air up to 600 °C. When ignited, beryllium powder burns with a bright flame, producing oxide and nitride. Halogens react with beryllium at temperatures above 600 °C, while chalcogens require even higher temperatures. Physical properties: Beryllium is a relatively hard, but brittle, silvery-white metal. It has a high modulus of elasticity - 300 GPa (for steels - 200-210 GPa). In air, it is actively covered with a resistant oxide film. Magnesium (Mg). Physical properties: Magnesium is a silver-white metal with a hexagonal lattice, space group P 63 / mmc, lattice parameters a = 0.32029 nm, c = 0.52000 nm, Z = 2. Under normal conditions, the surface of magnesium is covered with a strong protective film of magnesium oxide MgO , which is destroyed when heated in air to about 600 ° C, after which the metal burns with a dazzling white flame to form magnesium oxide and nitride Mg3N2. Chemical properties: Mixture of powdered magnesium with potassium permanganate KMnO4 - explosive Hot magnesium reacts with water: Mg (decay) + H2O = MgO + H2; Alkalis do not act on magnesium, it dissolves easily in acids with the release of hydrogen: Mg + 2HCl = MgCl2 + H2; When heated in air, magnesium burns to form an oxide; a small amount of nitride can also form with nitrogen: 2Mg + O2 = 2MgO; 3Mg + N2 = Mg3N2 Ticket number 3. Solubility- the ability of a substance to form homogeneous systems with other substances - solutions in which the substance is in the form of individual atoms, ions, molecules or particles. saturated solution- a solution in which the solute has reached its maximum concentration under given conditions and is no longer soluble. The precipitate of a given substance is in equilibrium with the substance in solution. unsaturated solution- a solution in which the concentration of a solute is less than in a saturated solution, and in which, under given conditions, some more of it can be dissolved. Supersaturated solutions- solutions characterized by the fact that the content of a dissolved substance in them is greater than its normal solubility under given conditions. Henry's law- the law according to which, at a constant temperature, the solubility of a gas in a given liquid is directly proportional to the pressure of this gas over the solution. The law is suitable only for ideal solutions and low pressures. Henry's law is usually written as follows: Where p is the partial pressure of the gas above the solution, c is the gas concentration in the solution in fractions of a mole, k is the Henry coefficient. Extraction(from late Latin extractio - extraction), extraction, the process of separating a mixture of liquid or solid substances using selective (selective) solvents (extractants). Ticket number 4. 1)Mass fraction is the ratio of the mass of the solute to the total mass of the solution. For binary solution ω(x) = m(x) / (m(x) + m(s)) = m(x) / m where ω(x) - mass fraction of the dissolved substance X m(x) - mass of dissolved substance X, g; m(s) is the mass of the solvent S, g; m \u003d m (x) + m (s) - mass of the solution, g. 2)Aluminum- an element of the main subgroup of the third group of the third period of the periodic system of chemical elements of D. I. Mendeleev, with atomic number 13. Finding in nature: Natural aluminum consists almost entirely of a single stable isotope, 27Al, with traces of 26Al, a radioactive isotope with a half-life of 720,000 years, formed in the atmosphere when argon nuclei are bombarded by cosmic ray protons. Receipt: It consists in the dissolution of aluminum oxide Al2O3 in a melt of Na3AlF6 cryolite, followed by electrolysis using consumable coke oven or graphite electrodes. This method of obtaining requires large amounts of electricity, and therefore was in demand only in the 20th century. Aluminothermy- a method for obtaining metals, non-metals (as well as alloys) by reducing their oxides with metallic aluminum. Ticket number 5. SOLUTIONS OF NON-ELECTROLYTES, binary or multicomponent pier. systems, the composition of which can change continuously (at least within certain limits). Unlike electrolyte solutions, there are no charged particles in any noticeable concentrations in non-electrolyte solutions (mol. solutions). solutions of non-electrolytes can be solid, liquid and gaseous. Raoult's first law Raoult's first law relates the saturation vapor pressure over a solution to its composition; it is formulated as follows: The partial pressure of the saturated vapor of a solution component is directly proportional to its mole fraction in the solution, and the coefficient of proportionality is equal to the saturated vapor pressure over the pure component. Raoult's second law The fact that the vapor pressure of a solution differs from the vapor pressure of a pure solvent significantly affects the crystallization and boiling processes. From Raoult's first law, two consequences are derived regarding the decrease in the freezing point and the increase in the boiling point of solutions, which, in their combined form, are known as the second Raoult's law. Cryoscopy(from the Greek kryos - cold and scopeo - look) - measurement of the decrease in the freezing point of a solution compared to a pure solvent. Van't Hoff's rule - For every 10 degrees increase in temperature, the rate constant of a homogeneous elementary reaction increases two to four times Hardness of water- a set of chemical and physical properties of water associated with the content of dissolved salts of alkaline earth metals in it, mainly calcium and magnesium. Ticket number 6. SOLUTIONS OF ELECTROLYTES, contain appreciable concentrations of ions-cations and anions formed as a result of the electrolytic dissociation of the molecules of the dissolved matter. Strong electrolytes- chemical compounds whose molecules in dilute solutions are almost completely dissociated into ions. Weak electrolytes- chemical compounds, the molecules of which, even in highly dilute solutions, are not completely dissociated into ions, which are in dynamic equilibrium with undissociated molecules. electrolytic dissociation- the process of decomposition of the electrolyte into ions when it is dissolved in a polar solvent or when melted. Ostwald dilution law- ratio expressing the dependence of the equivalent electrical conductivity of a dilute solution of a binary weak electrolyte on the concentration of the solution: P-elements 4 groups- carbon, silicon, germanium, tin and lead. Ticket number 7. 1) Electrolytic dissociation- this is the disintegration of a substance into ions under the action of polar solvent molecules. pH = -lg. buffer solutions- These are solutions when acids or alkalis are added to which their pH changes slightly. Carbonic acid forms: 1) medium salts (carbonates), 2) acidic (hydrocarbonates). Carbonates and hydrocarbonates are thermally unstable: CaCO3 \u003d CaO + CO2 ^, Ca (HCO3) 2 \u003d CaCO3v + CO2 ^ + H2O. Sodium carbonate (soda ash) is one of the main products of the chemical industry. In aqueous solution, it hydrolyzes according to the reaction Na2CO3 > 2Na+ + CO3-2, CO3-2 + H + -OH- - HCO3- + OH-. Sodium bicarbonate (baking soda) is widely used in the food industry. Due to hydrolysis, the solution also has an alkaline environment. NaHCO3 > Na+ + HCO3-, HCO3- + H-OH - H2CO3 + OH-. Soda ash and drinking soda interact with acids Na2CO3 + 2HCl - 2NaCl + CO2 ^ + H2O, 2Na+ + CO3-2 + 2H+ + 2Cl- - 2Na+ + 2Cl- + CO2^ + H2O, CO3-2 + 2H+ - CO2^ + H2O; NaHCO3 + CH3COOH - CH3COOHa + CO2^ + H2O, Na+ + HCO3- + CH3COOH - CH3COO- + Na+ + CO2^ + H2O, HCO3- + CH3COOH - CH3COO- + CO2^ + H2O. Ticket number 8. 1)_ion-exchange in solutions: Na2CO3 + H2SO4 → Na2SO4 + CO2 +H2O 2Na + CO3 + 2H + SO4 → 2Na + SO4 + CO2 + H2O CO3 + 2H → CO2 + H2O With gas evolution: Na2CO3 + 2HCl = CO2 + H2O + 2NaCl 2) Chemical properties of nitrogen. Only with such active metals as lithium, calcium, magnesium, nitrogen interacts when heated to relatively low temperatures. Nitrogen reacts with most other elements at high temperatures and in the presence of catalysts. Nitrogen compounds with oxygen N2O, NO, N2O3, NO2 and N2O5 are well studied. Physical properties of nitrogen. Nitrogen is slightly lighter than air; density 1.2506 kg/m3 (at 0°С and 101325 n/m2 or 760 mm Hg), mp -209.86°С, tbp -195.8°С. Nitrogen liquefies with difficulty: its critical temperature is rather low (-147.1°C) and its critical pressure is high, 3.39 MN/m2 (34.6 kgf/cm2); the density of liquid nitrogen is 808 kg/m3. Nitrogen is less soluble in water than oxygen: at 0°C, 23.3 g of nitrogen dissolves in 1 m3 of H2O. Better than water, nitrogen is soluble in some hydrocarbons. Ticket number 9. Hydrolysis (from Greek hydro - water, lysis - decomposition) means the decomposition of a substance by water. Salt hydrolysis is the reversible interaction of salt with water, leading to the formation of a weak electrolyte. Water, although to a small extent, dissociates: H 2 O H + + OH -. Sodium chloride H2O H+ + OH–, Na+ + Cl– + H2O Na+ + Cl– + H+ + OH–, NaCl + H2O (no reaction) Neutral Sodium carbonate + HOH + OH–, 2Na+ + + H2O + OH–, Na2CO3 + H2O NaHCO3 + NaOH Alkaline Aluminum chloride Al3+ + HOH AlOH2+ + H+, Al3+ + 3Cl– + H2O AlОH2+ + 2Cl– + H+ + Cl–, AlCl3 + H2O AlOHCl2 + HCl acidic The effect of temperature on the number of molecular collisions can be shown using a model. In the first approximation, the effect of temperature on the reaction rate is determined by the van't Hoff rule (formulated by J. Kh. van't Hoff based on an experimental study of many reactions): where g - ttemperature coefficient, taking values from 2 to 4. The explanation of the dependence of the reaction rate on temperature was given by S. Arrhenius. Not every collision of reactant molecules leads to a reaction, but only the strongest collisions.
Only molecules with an excess of kinetic energy are capable of a chemical reaction. S. Arrhenius calculated the proportion of active (i.e. leading to a reaction) collisions of reacting particles a, depending on temperature: - a = exp(-E/RT). and brought Arrhenius equation for the reaction rate constant: where k o and E d depend on the nature of the reagents. E is the energy that must be given to molecules in order for them to interact, called activation energy.
k \u003d k o e -E / RT
