where g is ttemperature coefficient, taking values from 2 to 4.
An explanation for 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 excess kinetic energy are capable of chemical reactions.
S. Arrhenius calculated the fraction of active (i.e., leading to a reaction) collisions of reacting particles a, depending on temperature: - a = exp(-E/RT). and brought out Arrhenius equation for the reaction rate constant:
k = koe-E/RT
where ko 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.
Van't Hoff's rule- an empirical rule that allows, as a first approximation, to estimate the effect of temperature on the rate of a chemical reaction in a small temperature range (usually from 0 °C to 100 °C). J. H. Van't Hoff, based on many experiments, formulated the following rule:
Activation energy in chemistry and biology - the minimum amount of energy that is required to be imparted to the system (in chemistry expressed in joules per mole) for a reaction to occur. The term was introduced by Svante August Arrhenius in. Typical notation for reaction energy Ea.
Activation entropy is considered as the difference between the entropy of the transition state and the ground state of the reactants. It is determined mainly by the loss of translational and rotational degrees of freedom of particles during the formation of an activated complex. Significant changes (vibrational degrees of freedom) can also occur if the activated complex is somewhat more tightly packed than the reactants.
The activation entropy of such a transition is positive.
Activation entropy depends on many factors. When, in a bimolecular reaction, two initial particles join together to form a transition state, the translational and rotational entropy of the two particles decreases to values corresponding to a single particle; a slight increase in vibrational entropy is not enough to compensate for this effect.
Activation entropies essentially vary more depending on structure than enthalpies. The activation entropies agree well in most cases with the Price and Hammett rule. This series also has the particular significance that the increase in the entropy of the silap can probably be accurately calculated from the known absolute entropies of the corresponding hydrocarbons
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Van't Hoff's rule. Arrhenius equation.
According to van't Hoff's rule of thumb, formulated around 1880, the rate of most reactions increases by 2-4 times with a 10-degree increase in temperature if the reaction is carried out at 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 minutes.
We already know that at any constant temperature the reaction rate is described by an empirical kinetic equation, which in most cases (except for reactions with a very complex mechanism) is the product of the rate constant and the concentration of the reactants in powers equal to the order of the reaction. The concentrations of reagents are practically independent of temperature, and the orders, as experience shows, are also independent. Consequently, rate constants are responsible for the sharp dependence of the reaction rate on temperature. The dependence of the rate constant on temperature is usually characterized temperature coefficient of reaction rate, which is the ratio of rate constants at temperatures differing by 10 degrees
and which, according to Van't Hoff's rule, is approximately 2-4.
Let us try to explain the observed high values of temperature coefficients of 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 and 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, on the speed of chaotic thermal motion of the 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 reaction rates with temperature. Indeed, according to the molecular kinetic theory of gases, the average speed of molecules is proportional to the square root of the absolute temperature, i.e., when the temperature of the system increases by 10 degrees, say, from 300 to 310 K, the average speed of molecules will increase only by 310/300 = 1.02 times - much less than required by Van't Hoff's rule.
Thus, an increase in the number of collisions alone cannot explain the temperature dependence of reaction rate constants. Obviously, there is another important factor at work here. To uncover it, let's turn to a more detailed analysis of the behavior of a large number of particles at different temperatures. Until now we have talked about the average speed of thermal movement 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, kinetic energy that deviates to a greater or lesser extent from the average value for a given temperature. This situation is depicted in Fig. (3.2), which
shows how the parts are distributed -
3.2. Distribution of particles by kinetic energy at different temperatures:
2-T 2; 3-T 3; Ti cy by kinetic energy at a certain temperature. Let us consider, for example, curve 1, corresponding to temperature Ti. The total number of particles in the system (let's denote it 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 higher energy, and the area to the left of the vertical corresponds to particles with energy 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 temperature Ti, the number of particles whose energy exceeds the value of 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 rate of a reaction is determined not by the total number of collisions of molecules per unit time, but by that part of it in which molecules whose kinetic energy exceeds a certain limit E a, called the activation energy of the reaction, take part. This becomes quite understandable if we remember that for the successful occurrence of an elementary act of reaction, it is necessary that during a collision the old bonds are broken and the conditions are created for the formation of new ones. Of course, this requires energy to be spent—the colliding particles need to 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 nonlinearly (in contrast to Van't Hoff's rule). Arrhenius found that in most cases the reaction rate constant obeys the equation LgK=lgA - , (3.14) which was named. Arrhenius equations E a - activation energy (see below) R is the molar gas constant equal to 8.314 J/mol۰K, T - absolute temperature A is a constant or very little temperature dependent value. It is called the frequency factor because it is related to the frequency of molecular collisions and the probability that a collision occurs when the molecules are oriented in a manner favorable to the reaction. As can be seen from (3.14), with increasing activation energy E a the rate constant
TO decreases. Consequently, the rate of a reaction decreases as its energy barrier increases (see below). Dependence of the rate of a chemical reaction on temperature. In heterogeneous systems, reactions occur at the interface. In this case, the concentration of the solid phase remains almost constant and does not affect the reaction rate. The rate of a heterogeneous reaction will depend only on the concentration of the substance in the liquid or gaseous phase. Therefore, the concentrations of solids are not indicated in the kinetic equation; their values are included in the values of the constants. For example, for a heterogeneous reaction the kinetic equation can be written EXAMPLE 4. The kinetic order of the reaction between chromium and aluminum is 1. Write the chemical and kinetic equations of the reaction. The reaction between aluminum and chlorine is heterogeneous, the kinetic equation can be written EXAMPLE 5. Kinetic equation of the reaction looks like Determine the dimension of the rate constant and calculate the rate of silver dissolution at a partial pressure of oxygen Pa and a potassium cyanide concentration of 0.055 mol/l. The dimension of the constant is determined from the kinetic equation given in the problem statement: Substituting the problem data into the kinetic equation, we find the rate of silver dissolution: EXAMPLE 6. Kinetic equation of the reaction looks like How will the reaction rate change if the concentration of mercuric chloride (M) is halved, and the concentration of oxalate –
ions to double? After changing the concentration of the starting substances, the reaction rate is expressed by the kinetic equation Comparing and, we find that the reaction rate increased by 2
times. As the temperature increases, the rate of a chemical reaction increases markedly. The quantitative dependence of the reaction rate on temperature is determined by the Van't Hoff rule. To characterize the dependence of the rate of a chemical reaction (rate constant) on temperature, the temperature coefficient of reaction rate (), also called the Van't Hoff coefficient, is used. The temperature coefficient of the reaction rate shows how many times the reaction rate will increase with an increase in the temperature of the reactants by 10 degrees. Mathematically, the dependence of the reaction rate on temperature is expressed by the relation Where –
temperature coefficient of speed; –
T; T; ––
reaction rate constant at temperature T+ 10; ––
reaction rate at temperature T+ 10. For calculations it is more convenient to use the equations as well as logarithmic forms of these equations The increase in reaction rate with increasing temperature explains activation theory.
According to this theory, when particles of reacting substances collide, they must overcome repulsive forces, weaken or break old chemical bonds and form new ones. They must expend a certain energy for this, i.e. overcome some kind of energy barrier. A particle that has excess energy sufficient to overcome the energy barrier is called active particles.
Under normal conditions, there are few active particles in the system, and the reaction proceeds at a slower rate. But inactive particles can become active if you give them additional energy. One way to activate particles is by increasing the temperature. As the temperature rises, the number of active particles in the system increases sharply and the reaction rate increases. The dependence of the rate of a chemical reaction on temperature is determined by the Van't Hoff rule. Dutch chemist Van't Hoff Jacob Hendrick, the founder of stereochemistry, became the first Nobel Prize winner in chemistry in 1901. It was awarded to him for his discovery of the laws of chemical dynamics and osmotic pressure. Van't Hoff introduced ideas about the spatial structure of chemical substances. He was confident that progress in fundamental and applied research in chemistry could be achieved using physical and mathematical methods. Having developed the theory of reaction rates, he created chemical kinetics. So, the kinetics of chemical reactions is the study of the rate of occurrence, what chemical interaction occurs during the reaction process, and the dependence of reactions on various factors. Different reactions have different rates of occurrence. Chemical reaction rate directly depends on the nature of the chemicals entering the reaction. Some substances, such as NaOH and HCl, can react in a fraction of a second. And some chemical reactions last for years. An example of such a reaction is the rusting of iron. The rate of the reaction also depends on the concentration of the reactants. The higher the concentration of reagents, the higher the reaction rate. During the reaction, the concentration of reagents decreases, therefore, the reaction rate slows down. That is, at the initial moment the speed is always higher than at any subsequent moment. V = (C end – From start)/(t end – t start) Reagent concentrations are determined at certain time intervals. An important factor on which the rate of reactions depends is temperature. All molecules collide with others. The number of impacts per second is very high. But, nevertheless, chemical reactions do not occur at great speed. This happens because during the reaction the molecules must assemble into an activated complex. And only active molecules whose kinetic energy is sufficient for this can form it. With a small number of active molecules, the reaction proceeds slowly. As the temperature increases, the number of active molecules increases. Consequently, the reaction rate will be higher. Van't Hoff believed that the rate of a chemical reaction is a natural change in the concentration of reacting substances per unit time. But it is not always uniform. Van't Hoff's rule states that with every 10° increase in temperature, the rate of a chemical reaction increases by 2-4 times
. Mathematically, van't Hoff's rule looks like this: Where V 2 t 2, A V 1
– reaction rate at temperature t 1 ; ɣ
- temperature coefficient of reaction rate. This coefficient is the ratio of rate constants at temperature t+10 And t. So, if ɣ
= 3, and at 0 o C the reaction lasts 10 minutes, then at 100 o C it will last only 0.01 seconds. The sharp increase in the rate of a chemical reaction is explained by an increase in the number of active molecules with increasing temperature. Van't Hoff's rule is applicable only in the temperature range of 10-400 o C. Reactions in which large molecules participate do not obey Van't Hoff's rule. The law of mass action establishes the relationship between the masses of reacting substances in chemical reactions at equilibrium. The law of mass action was formulated in 1864-1867. K. Guldberg and P. Waage. According to this law, the rate at which substances react with each other depends on their concentration. The law of mass action is used in various calculations of chemical processes. It makes it possible to solve the question in which direction the spontaneous course of the reaction under consideration is possible at a given ratio of the concentrations of the reacting substances, what yield of the desired product can be obtained. Van't Hoff's rule is an empirical rule that allows, as a first approximation, to estimate the effect of temperature on the rate of a chemical reaction in a small temperature range (usually from 0 °C to 100 °C). Van't Hoff, based on many experiments, formulated the following rule: With every 10 degree increase in temperature, the rate constant of a homogeneous elementary reaction increases two to four times. The equation that describes this rule is: V = V0 * Y(T2 − T1) / 10 where V is the reaction rate at a given temperature (T2), V0 is the reaction rate at temperature T1, Y is the temperature coefficient of the reaction (if it is equal to 2, for example, then the reaction rate will increase 2 times when the temperature increases by 10 degrees). It should be remembered that Van't Hoff's rule has a limited scope of applicability. Many reactions do not obey it, for example, reactions occurring at high temperatures, very fast and very slow reactions. Van't Hoff's rule also does not apply to reactions involving bulky molecules, such as proteins in biological systems. The temperature dependence of the reaction rate is more correctly described by the Arrhenius equation. V = V0 * Y(T2 − T1) / 10 Activation energy in chemistry and biology, the minimum amount of energy that must be supplied to the system (in chemistry expressed in joules per mole) for a reaction to occur. The term was introduced by Svante August Arrhenius in 1889. A typical designation for the reaction energy is Ea. Activation energy in physics is the minimum amount of energy that electrons of a donor impurity must receive in order to enter the conduction band. In the chemical model known as the Theory of Active Collisions (TAC), there are three conditions necessary for a reaction to occur: Molecules must collide. This is an important condition, but it is not sufficient, since a collision does not necessarily cause a reaction. Molecules must have the necessary energy (activation energy). During a chemical reaction, the interacting molecules must pass through an intermediate state, which may have more energy. That is, the molecules must overcome an energy barrier; if this does not happen, the reaction will not begin. The molecules must be correctly oriented relative to each other. At low (for a certain reaction) temperature, most molecules have energy less than the activation energy and are unable to overcome the energy barrier. However, in a substance there will always be individual molecules whose energy is significantly higher than the average. Even at low temperatures, most reactions continue to occur. Increasing the temperature allows you to increase the proportion of molecules with sufficient energy to overcome the energy barrier. This increases the reaction speed. Mathematical description The Arrhenius equation establishes the relationship between activation energy and reaction rate: k is the reaction rate constant, A is the frequency factor for the reaction, R is the universal gas constant, T is the temperature in kelvins. As the temperature rises, the probability of overcoming the energy barrier increases. General rule of thumb: a 10K increase in temperature doubles the reaction rate Transition state The relationship between the activation energy (Ea) and the enthalpy (entropy) of the reaction (ΔH) in the presence and absence of a catalyst. The highest point of energy represents an energy barrier. In the presence of a catalyst, less energy is required to start a reaction. A transition state is a state of a system in which the destruction and creation of a connection are balanced. The system is in a transition state for a short time (10-15 s). The energy that must be expended to bring the system into a transition state is called activation energy. In multistep reactions that include several transition states, the activation energy corresponds to the highest energy value. After overcoming the transition state, the molecules scatter again with the destruction of old bonds and the formation of new ones or with the transformation of the original bonds. Both options are possible, since they occur with the release of energy (this is clearly visible in the figure, since both positions are energetically lower than the activation energy). There are substances that can reduce the activation energy for a given reaction. Such substances are called catalysts. Biologists call such substances enzymes. Interestingly, catalysts thus speed up the reaction without participating in it themselves.
Chemical reaction rate
Van't Hoff's rule
Question 18. Van't Hoff's rule.
Question 19. Activation energy.
