Chemical reactions proceed at different speeds: at a low speed - during the formation of stalactites and stalagmites, at an average speed - when cooking food, instantly - during an explosion. Reactions in aqueous solutions are very fast.
Determination of the rate of a chemical reaction, as well as elucidation of its dependence on the conditions of the process, is the task of chemical kinetics - the science of the laws governing the course of chemical reactions in time.
If chemical reactions occur in a homogeneous medium, for example, in a solution or in a gas phase, then the interaction of the reacting substances occurs in the entire volume. Such reactions are called homogeneous.
(v homog) is defined as the change in the amount of substance per unit time per unit volume:
where Δn is the change in the number of moles of one substance (most often the initial one, but it can also be the reaction product); Δt - time interval (s, min); V is the volume of gas or solution (l).
Since the ratio of the amount of substance to volume is the molar concentration C, then
Thus, the rate of a homogeneous reaction is defined as a change in the concentration of one of the substances per unit time:
if the volume of the system does not change.
If a reaction occurs between substances in different states of aggregation (for example, between a solid and a gas or liquid), or between substances that are unable to form a homogeneous medium (for example, between immiscible liquids), then it takes place only on the contact surface of substances. Such reactions are called heterogeneous.
It is defined as the change in the amount of substance per unit of time per unit of surface.
where S is the surface area of contact of substances (m 2, cm 2).
The change in the amount of a substance by which the reaction rate is determined is an external factor observed by the researcher. In fact, all processes are carried out at the micro level. Obviously, in order for some particles to react, they must first of all collide, and collide effectively: not to scatter like balls in different directions, but in such a way that the “old bonds” in the particles are destroyed or weakened and “new ones” can form. ”, and for this the particles must have sufficient energy.
The calculated data show that, for example, in gases, collisions of molecules at atmospheric pressure are in the billions per 1 second, that is, all reactions should have gone instantly. But it's not. It turns out that only a very small fraction of the molecules have the necessary energy to produce an effective collision.
The minimum excess energy that a particle (or pair of particles) must have in order for an effective collision to occur is called activation energy Ea.
Thus, on the way of all particles entering into the reaction, there is an energy barrier equal to the activation energy E a . When it is small, there are many particles that can overcome it, and the reaction rate is high. Otherwise, a "push" is required. When you bring a match to light a spirit lamp, you impart additional energy E a required for the effective collision of alcohol molecules with oxygen molecules (overcoming the barrier).
The rate of a chemical reaction depends on many factors. The main ones are: the nature and concentration of the reactants, pressure (in reactions involving gases), temperature, the action of catalysts and the surface of the reactants in the case of heterogeneous reactions.
Temperature
As the temperature rises, in most cases the rate of a chemical reaction increases significantly. In the 19th century Dutch chemist J. X. Van't Hoff formulated the rule:
An increase in temperature for every 10 ° C leads to an increase inreaction speed by 2-4 times(this value is called the temperature coefficient of the reaction).
With an increase in temperature, the average velocity of molecules, their energy, and the number of collisions increase slightly, but the proportion of "active" molecules participating in effective collisions that overcome the energy barrier of the reaction increases sharply. Mathematically, this dependence is expressed by the relation:
where v t 1 and v t 2 are the reaction rates, respectively, at the final t 2 and initial t 1 temperatures, and γ is the temperature coefficient of the reaction rate, which shows how many times the reaction rate increases with each 10 ° C increase in temperature.
However, to increase the reaction rate, raising the temperature is not always applicable, since the starting materials may begin to decompose, solvents or the substances themselves may evaporate, etc.
Endothermic and exothermic reactions
The reaction of methane with atmospheric oxygen is known to be accompanied by the release of a large amount of heat. Therefore, it is used in everyday life for cooking, heating water and heating. Natural gas supplied to homes through pipes is 98% methane. The reaction of calcium oxide (CaO) with water is also accompanied by the release of a large amount of heat.
What can these facts say? When new chemical bonds are formed in the reaction products, more energy than required to break the chemical bonds in the reactants. Excess energy is released in the form of heat and sometimes light.
CH 4 + 2O 2 \u003d CO 2 + 2H 2 O + Q (energy (light, heat));
CaO + H 2 O \u003d Ca (OH) 2 + Q (energy (heat)).
Such reactions should proceed easily (as a stone easily rolls downhill).
Reactions in which energy is released are called EXOTHERMIC(from the Latin "exo" - out).
For example, many redox reactions are exothermic. One of these beautiful reactions is an intramolecular oxidation-reduction occurring inside the same salt - ammonium dichromate (NH 4) 2 Cr 2 O 7:
(NH 4) 2 Cr 2 O 7 \u003d N 2 + Cr 2 O 3 + 4 H 2 O + Q (energy).
Another thing is the backlash. They are similar to rolling a stone uphill. It is still not possible to obtain methane from CO 2 and water, and strong heating is required to obtain quicklime CaO from calcium hydroxide Ca (OH) 2. Such a reaction occurs only with a constant influx of energy from the outside:
Ca (OH) 2 \u003d CaO + H 2 O - Q (energy (heat))
This suggests that the breaking of chemical bonds in Ca(OH) 2 requires more energy than can be released during the formation of new chemical bonds in CaO and H 2 O molecules.
Reactions in which energy is absorbed are called ENDOTHERMIC(from "endo" - inside).
Reactant concentration
A change in pressure with the participation of gaseous substances in the reaction also leads to a change in the concentration of these substances.
In order for a chemical interaction to occur between particles, they must effectively collide. The greater the concentration of reactants, the more collisions and, accordingly, the higher the reaction rate. For example, acetylene burns very quickly in pure oxygen. This develops a temperature sufficient to melt the metal. On the basis of a large amount of experimental material, in 1867 the Norwegians K. Guldenberg and P. Waage, and independently of them in 1865, the Russian scientist N. I. Beketov formulated the basic law of chemical kinetics, which establishes the dependence of the reaction rate on the concentration of reacting substances.
The rate of a chemical reaction is proportional to the product of the concentrations of the reactants, taken in powers equal to their coefficients in the reaction equation.
This law is also called the law of mass action.
For the reaction A + B \u003d D, this law will be expressed as follows:
For the reaction 2A + B = D, this law is expressed as follows:
Here C A, C B are the concentrations of substances A and B (mol / l); k 1 and k 2 - coefficients of proportionality, called the rate constants of the reaction.
The physical meaning of the reaction rate constant is easy to establish - it is numerically equal to the reaction rate in which the concentrations of the reactants are 1 mol / l or their product is equal to one. In this case, it is clear that the rate constant of the reaction depends only on temperature and does not depend on the concentration of substances.
Law of acting masses does not take into account the concentration of reactants in the solid state, since they react on surfaces and their concentrations are usually constant.
For example, for the combustion reaction of coal, the expression for the reaction rate should be written as follows:
i.e., the reaction rate is only proportional to the oxygen concentration.
If the reaction equation describes only the overall chemical reaction, which takes place in several stages, then the rate of such a reaction can depend in a complex way on the concentrations of the starting substances. This dependence is determined experimentally or theoretically based on the proposed reaction mechanism.
The action of catalysts
It is possible to increase the reaction rate by using special substances that change the reaction mechanism and direct it along an energetically more favorable path with a lower activation energy. They are called catalysts (from Latin katalysis - destruction).
The catalyst acts as an experienced guide, guiding a group of tourists not through a high pass in the mountains (overcoming it requires a lot of effort and time and is not accessible to everyone), but along the detour paths known to him, along which you can overcome the mountain much easier and faster.
True, on a detour you can get not quite where the main pass leads. But sometimes that's exactly what you need! This is how catalysts, which are called selective, work. It is clear that there is no need to burn ammonia and nitrogen, but nitric oxide (II) finds use in the production of nitric acid.
Catalysts- These are substances that participate in a chemical reaction and change its speed or direction, but at the end of the reaction remain unchanged quantitatively and qualitatively.
Changing the rate of a chemical reaction or its direction with the help of a catalyst is called catalysis. Catalysts are widely used in various industries and in transport (catalytic converters that convert nitrogen oxides in car exhaust gases into harmless nitrogen).
There are two types of catalysis.
homogeneous catalysis, in which both the catalyst and the reactants are in the same state of aggregation (phase).
heterogeneous catalysis where the catalyst and reactants are in different phases. For example, the decomposition of hydrogen peroxide in the presence of a solid manganese (IV) oxide catalyst:
The catalyst itself is not consumed as a result of the reaction, but if other substances are adsorbed on its surface (they are called catalytic poisons), then the surface becomes inoperable, and catalyst regeneration is required. Therefore, before carrying out the catalytic reaction, the starting materials are thoroughly purified.
For example, in the production of sulfuric acid by the contact method, a solid catalyst is used - vanadium (V) oxide V 2 O 5:
In the production of methanol, a solid "zinc-chromium" catalyst is used (8ZnO Cr 2 O 3 x CrO 3):
Biological catalysts - enzymes - work very effectively. By chemical nature, these are proteins. Thanks to them, complex chemical reactions proceed at a high speed in living organisms at low temperatures.
Other interesting substances are known - inhibitors (from the Latin inhibere - to delay). They react with active particles at a high rate to form inactive compounds. As a result, the reaction slows down sharply and then stops. Inhibitors are often specifically added to various substances in order to prevent unwanted processes.
For example, hydrogen peroxide solutions are stabilized with inhibitors.
The nature of the reactants (their composition, structure)
Meaning activation energy is the factor through which the influence of the nature of the reacting substances on the reaction rate is affected.
If the activation energy is low (< 40 кДж/моль), то это означает, что значительная часть столкновений между частицами реагирующих веществ приводит к их взаимодействию, и скорость такой реакции очень большая. Все реакции ионного обмена протекают практически мгновенно, ибо в этих реакциях участвуют разноименно заряженные ионы, и энергия активации в данных случаях ничтожно мала.
If the activation energy is high(> 120 kJ/mol), this means that only a negligible part of the collisions between interacting particles leads to a reaction. The rate of such a reaction is therefore very slow. For example, the progress of the ammonia synthesis reaction at ordinary temperature is almost impossible to notice.
If the activation energies of chemical reactions have intermediate values (40120 kJ/mol), then the rates of such reactions will be average. Such reactions include the interaction of sodium with water or ethyl alcohol, the decolorization of bromine water with ethylene, the interaction of zinc with hydrochloric acid, etc.
Contact surface of reactants
The rate of reactions occurring on the surface of substances, i.e., heterogeneous, depends, other things being equal, on the properties of this surface. It is known that powdered chalk dissolves much faster in hydrochloric acid than an equal mass piece of chalk.
The increase in the reaction rate is primarily due to increase in the contact surface of the starting substances, as well as a number of other reasons, for example, a violation of the structure of the "correct" crystal lattice. This leads to the fact that the particles on the surface of the formed microcrystals are much more reactive than the same particles on a “smooth” surface.
In industry, for carrying out heterogeneous reactions, a “fluidized bed” is used to increase the contact surface of the reactants, the supply of starting materials and the removal of products. For example, in the production of sulfuric acid with the help of a "fluidized bed", pyrite is roasted.
Reference material for passing the test:
Mendeleev table
Solubility table
The effect of pressure on the reaction rate depends on order reactions. If the temperature remains unchanged and the composition of the initial gas mixture is given, then according to the equation of state for each of the concentrations, we can write: p a=aR m T, pb=bR m T. Here A, b,…, are molar concentrations, and p a, pb, ..., - partial pressures of the corresponding gases. If the total number of moles per unit volume is z, then in exactly the same way one can write p=zR m T, Where R- total pressure. Hence , , …etc. Values ... etc. are relative volumetric concentrations. Denoting them with A, IN... etc., we get: p a=Ap,
Where ; pb =Bp, . Consider monomolecular the process described by the equation:
in this case, the rate of transformation of the substance is directly proportional to the pressure: ~ p.
For bimolecular reactions:
i.e. ~ p 2. Accordingly, for trimolecular reactions we get:
Where k is the reaction rate constant.
2.2. Activation energy. Arrhenius law
The number of mutual collisions of the reacting molecules increases ~ , which contributes to the growth of the reaction rate. For example, for many reactions, an increase in temperature by only 10°C leads to an increase in the rate constant by a factor of 2–4.
Example. The half-life of hydrogen iodide according to the equation 2HJ→H 2 +J 2 . At T = 373K half-life is 314000 years, at T\u003d 666K, it decreases to 1.3 hours, and at T=973K t 1/2 = 0.12sec.
Arrhenius: for a chemical reaction to take place, a preliminary weakening or breaking of the internal bonds of a stable molecule is necessary, for which a certain amount of energy must be expended E . The greater the thermal energy of the colliding molecules, the greater the likelihood of rearrangement of internal bonds and the creation of new molecules. At E= const the frequency of collisions ending in a reaction will grow much faster than .
The energy required to overcome the energy barrier that prevents the approach of reacting molecules and the formation of reaction products is called activation energy E a. Thus, the elementary act of a chemical reaction occurs only in the collision of those molecules whose kinetic energy is greater than E a.
Activation energy E a usually higher than the average energy of thermal motion of molecules. The lower the activation energy, the more often collisions of molecules will occur, leading to the formation of reaction products, the higher will be the rate of the chemical reaction. Increase T leads to an increase in the number of molecules with excess energy, exceeding E a. This explains the increase in the rate of a chemical reaction with increasing temperature (Fig. 2.1).
Rice. 2.1. Heat of combustion Q and activation energy E=u max- u 1
In the simplest cases, the rate constants of chemical reactions can be determined on the basis of the general relations of the molecular kinetic theory (see, for example, ).
Denote by p A And p c the number of molecules A and B in 1 cm 3 . The reaction rate will be equal to the number Z such collisions of molecules A and B per unit time, the energy of which is greater than the activation energy E . For an ideal gas Z is determined on the basis of the Maxwell-Boltzmann energy distribution law:
Here, is the average effective diameter of the colliding molecules, is the reduced molecular weight, R m = 8.315∙10 7 erg/deg - universal gas constant, m A, m B - molecular weights.
In most cases, the experimental values are much smaller than the theoretical ones. Therefore, the so-called probabilistic or steric coefficient is introduced into the calculation formula R. As a result, the formula for calculating the rate of a bimolecular reaction, called Arrhenius formula, takes the following form:
Comparing the resulting formula with equation (2.8) for second-order reactions, we can obtain an expression for the rate constant of this reaction:
The strong influence of temperature on the reaction rate is explained mainly by the Arrhenius factor. Therefore, in approximate calculations, the pre-exponential factor is often assumed to be independent of T.
An analysis of formula (2.12) shows that with increasing T, the growth rate W first increases, reaches a certain maximum value, and then decreases, in other words, the curve W with respect to T has an inflection point. Equating to zero the second derivative of W with respect to T, we find the temperature corresponding to the inflection point:
It is easy to see that this temperature is rather high. For example, at E=20000cal/(g-mol) Tp=5000K. When using formula (2.12) for numerical calculations, one should take into account the dimensions of the quantities included in it.
Formula (2.12) can be written as follows:
where is the pre-exponential factor, i.e. the total number of collisions at n A =n B =1 molecule/cm 3 . Sometimes R are also included in the pre-exponential factor.
For estimated calculations of the order of the reaction rate, the value k 0 can be taken for temperature T\u003d 300K equal to 10 -10 cm 3 / (molecule ∙ sec) (for d cf »4 ∙ 10 -8 and m A \u003d m B »30).
The rate of a chemical reaction is equal to the change in the amount of a substance per unit time in a unit of the reaction space Depending on the type of chemical reaction (homogeneous or heterogeneous), the nature of the reaction space changes. The reaction space is usually called the area in which the chemical process is localized: volume (V), area (S).
The reaction space of homogeneous reactions is the volume filled with reagents. Since the ratio of the amount of a substance to a unit volume is called concentration (c), the rate of a homogeneous reaction is equal to the change in the concentration of the starting substances or reaction products over time. Distinguish between average and instantaneous reaction rates.
The average reaction rate is:
where c2 and c1 are the concentrations of the initial substances at times t2 and t1.
The minus sign "-" in this expression is put when finding the speed through the change in the concentration of reagents (in this case, Dс< 0, так как со временем концентрации реагентов уменьшаются); концентрации продуктов со временем нарастают, и в этом случае используется знак плюс «+».
The reaction rate at a given moment of time or the instantaneous (true) reaction rate v is equal to:
The reaction rate in SI has the unit [mol×m-3×s-1], other units of quantity [mol×l-1×s-1], [mol×cm-3×s-1], [mol ×cm –3×min-1].
The rate of a heterogeneous chemical reaction v called, the change in the amount of the reactant (Dn) per unit time (Dt) per unit area of the phase separation (S) and is determined by the formula:
or through the derivative:
The unit of the rate of a heterogeneous reaction is mol/m2 s.
Example 1. Chlorine and hydrogen are mixed in a vessel. The mixture was heated. After 5 s, the concentration of hydrogen chloride in the vessel became equal to 0.05 mol/dm3. Determine the average rate of formation of hydrochloric acid (mol/dm3 s).
Solution. We determine the change in the concentration of hydrogen chloride in the vessel 5 s after the start of the reaction:
where c2, c1 - final and initial molar concentration of HCl.
Dc (HCl) \u003d 0.05 - 0 \u003d 0.05 mol / dm3.
Calculate the average rate of formation of hydrogen chloride, using equation (3.1):
Answer: 7 \u003d 0.01 mol / dm3 × s.
Example 2 The following reaction takes place in a vessel with a volume of 3 dm3:
C2H2 + 2H2®C2H6.
The initial mass of hydrogen is 1 g. After 2 s after the start of the reaction, the mass of hydrogen becomes 0.4 g. Determine the average rate of formation of C2H6 (mol / dm "× s).
Solution. The mass of hydrogen that entered into the reaction (mpror (H2)) is equal to the difference between the initial mass of hydrogen (mref (H2)) and the final mass of unreacted hydrogen (tk (H2)):
tpror. (H2) \u003d tis (H2) - mk (H2); tpror (H2) \u003d 1-0.4 \u003d 0.6 g.
Let's calculate the amount of hydrogen:
= 0.3 mol.
We determine the amount of C2H6 formed:
According to the equation: from 2 mol of H2, ® 1 mol of C2H6 is formed;
According to the condition: from 0.3 mol of H2, ® x mol of C2H6 is formed.
n(С2Н6) = 0.15 mol.
We calculate the concentration of the formed С2Н6:
We find the change in the concentration of C2H6:
0.05-0 = 0.05 mol/dm3. We calculate the average rate of formation of C2H6 using equation (3.1):
Answer: \u003d 0.025 mol / dm3 × s.
Factors affecting the rate of a chemical reaction . The rate of a chemical reaction is determined by the following main factors:
1) the nature of the reacting substances (activation energy);
2) the concentration of reacting substances (the law of mass action);
3) temperature (van't Hoff rule);
4) the presence of catalysts (activation energy);
5) pressure (reactions involving gases);
6) the degree of grinding (reactions occurring with the participation of solids);
7) type of radiation (visible, UV, IR, X-ray).
The dependence of the rate of a chemical reaction on concentration is expressed by the basic law of chemical kinetics - the law of mass action.
Law of acting masses . In 1865, Professor N. N. Beketov for the first time expressed a hypothesis about the quantitative relationship between the masses of the reactants and the reaction time: "... attraction is proportional to the product of the acting masses." This hypothesis was confirmed in the law of mass action, which was established in 1867 by two Norwegian chemists K. M. Guldberg and P. Waage. The modern formulation of the law of mass action is as follows: at a constant temperature, the rate of a chemical reaction is directly proportional to the product of the concentrations of the reactants, taken in powers equal to the stoichiometric coefficients in the reaction equation.
For the reaction aA + bB = mM + nN, the kinetic equation of the law of mass action has the form:
, (3.5)
where is the reaction rate;
k- coefficient of proportionality, called the rate constant of a chemical reaction (at = 1 mol/dm3 k is numerically equal to ); - concentration of reagents involved in the reaction.
The rate constant of a chemical reaction does not depend on the concentration of reagents, but is determined by the nature of the reactants and the conditions for the reactions to occur (temperature, the presence of a catalyst). For a particular reaction proceeding under given conditions, the rate constant is a constant value.
Example 3 Write the kinetic equation of the law of mass action for the reaction:
2NO (g) + C12 (g) = 2NOCl (g).
Solution. Equation (3.5) for a given chemical reaction has the following form:
.
For heterogeneous chemical reactions, the equation of the law of mass action includes the concentrations of only those substances that are in the gas or liquid phases. The concentration of a substance in the solid phase is usually constant and is included in the rate constant.
Example 4 Write the kinetic equation of the law of action of masses for reactions:
a) 4Fe(t) + 3O2(g) = 2Fe2O3(t);
b) CaCO3 (t) \u003d CaO (t) + CO2 (g).
Solution. Equation (3.5) for these reactions will have the following form:
Since calcium carbonate is a solid substance, the concentration of which does not change during the reaction, i.e., in this case, the reaction rate at a certain temperature is constant.
Example 5 How many times will the rate of the reaction of oxidation of nitric oxide (II) with oxygen increase if the concentrations of the reagents are doubled?
Solution. We write the reaction equation:
2NO + O2= 2NO2.
Let us denote the initial and final concentrations of the reagents as c1(NO), cl(O2) and c2(NO), c2(O2), respectively. In the same way, we denote the initial and final reaction rates: vt, v2. Then, using equation (3.5), we obtain:
.
By condition c2(NO) = 2c1 (NO), c2(O2) = 2c1(O2).
We find v2 =k2 ×2cl(O2).
Find how many times the reaction rate will increase:
Answer: 8 times.
The effect of pressure on the rate of a chemical reaction is most significant for processes involving gases. When the pressure changes by n times, the volume decreases and the concentration increases n times, and vice versa.
Example 6 How many times will the rate of a chemical reaction between gaseous substances reacting according to the equation A + B \u003d C increase if the pressure in the system is doubled?
Solution. Using equation (3.5), we express the reaction rate before increasing the pressure:
.
The kinetic equation after increasing the pressure will have the following form:
.
With an increase in pressure by a factor of 2, the volume of the gas mixture, according to the Boyle-Mariotte law (pY = const), will also decrease by a factor of 2. Therefore, the concentration of substances will increase by 2 times.
Thus, c2(A) = 2c1(A), c2(B) = 2c1(B). Then
Determine how many times the reaction rate will increase with increasing pressure.
In life, we are faced with different chemical reactions. Some of them, like the rusting of iron, can go on for several years. Others, such as the fermentation of sugar into alcohol, take several weeks. Firewood in the stove burns out in a couple of hours, and gasoline in the engine burns out in a split second.
To reduce equipment costs, chemical plants increase the rate of reactions. And some processes, such as food spoilage, metal corrosion, need to be slowed down.
The rate of a chemical reaction can be expressed as change in the amount of matter (n, modulo) per unit time (t) - compare the speed of a moving body in physics as a change in coordinates per unit time: υ = Δx/Δt . So that the rate does not depend on the volume of the vessel in which the reaction takes place, we divide the expression by the volume of reacting substances (v), i.e., we obtain change in the amount of a substance per unit time per unit volume, or change in the concentration of one of the substances per unit time:
n 2 − n 1
υ = –––––––––– = –––––––– = Δс/Δt (1)
(t 2 − t 1) v Δt v
where c = n / v is the concentration of the substance,
Δ (pronounced "delta") is the generally accepted designation for a change in magnitude.
If substances have different coefficients in the equation, the reaction rate for each of them, calculated by this formula, will be different. For example, 2 moles of sulfur dioxide reacted completely with 1 mole of oxygen in 10 seconds in 1 liter:
2SO 2 + O 2 \u003d 2SO 3
The oxygen velocity will be: υ \u003d 1: (10 1) \u003d 0.1 mol / l s
Sour gas speed: υ \u003d 2: (10 1) \u003d 0.2 mol / l s- this does not need to be memorized and spoken in the exam, an example is given in order not to get confused if this question arises.
The rate of heterogeneous reactions (involving solids) is often expressed per unit area of contacting surfaces:
Δn
υ = –––––– (2)
Δt S
Reactions are called heterogeneous when the reactants are in different phases:
- a solid with another solid, liquid or gas,
- two immiscible liquids
- gas liquid.
Homogeneous reactions occur between substances in the same phase:
- between well-miscible liquids,
- gases,
- substances in solutions.
Conditions affecting the rate of chemical reactions
1) The reaction rate depends on the nature of the reactants. Simply put, different substances react at different rates. For example, zinc reacts violently with hydrochloric acid, while iron reacts rather slowly.
2) The reaction rate is greater, the higher concentration substances. With a highly dilute acid, the zinc will take significantly longer to react.
3) The reaction rate increases significantly with increasing temperature. For example, in order to burn fuel, it is necessary to set it on fire, that is, to increase the temperature. For many reactions, an increase in temperature by 10°C is accompanied by an increase in the rate by a factor of 2–4.
4) Speed heterogeneous reactions increases with increasing surfaces of reactants. Solids for this are usually crushed. For example, in order for iron and sulfur powders to react when heated, iron must be in the form of small sawdust.
Note that formula (1) is implied in this case! Formula (2) expresses the speed per unit area, therefore it cannot depend on the area.
5) The reaction rate depends on the presence of catalysts or inhibitors.
Catalysts Substances that speed up chemical reactions but are not themselves consumed. An example is the rapid decomposition of hydrogen peroxide with the addition of a catalyst - manganese (IV) oxide:
2H 2 O 2 \u003d 2H 2 O + O 2
Manganese (IV) oxide remains on the bottom and can be reused.
Inhibitors- substances that slow down the reaction. For example, to extend the life of pipes and batteries, corrosion inhibitors are added to the water heating system. In automobiles, corrosion inhibitors are added to the brake fluid.
A few more examples.
When writing the kinetic reaction equation for gaseous systems, instead of the concentration (C), the pressure (P) of the reagents is written, since the change in pressure in the system is similar to the change in concentration. An increase in pressure in the system causes a decrease in the volume of the system by the same factor, while the concentration of reagents per unit volume increases in the same way. With a decrease in pressure, the volume of the system increases, while the concentration per unit volume decreases accordingly.
Examples and problem solving.
Example 1
The rate of which reaction is greater if 9 g of water vapor was formed per unit of time in a unit volume as a result of the first reaction, 3.65 g of hydrogen chloride as a result of the second reaction?
The reaction rate is measured by the number of moles of a substance that is formed per unit volume per unit time. Molar mass of water Molar mass of hydrogen chloride 
then the rate of the first reaction,
mol/l×s,
and the rate of the second reaction
will 
mol/l.
The rate of formation of water vapor is greater because the number of moles of formation of water vapor is greater than the number of moles of formation of hydrogen chloride.
Example 2
The reaction between substances A and B is expressed by the equation: A + 2B®C. The initial concentration of substance A is 0.3 mol/l, and that of substance B is 0.5 mol/l. The rate constant is 0.4. Determine the reaction rate after some time, when the concentration of substance A decreases by 0.1 mol/l.
The concentration of substance A decreased by 0.1 mol/l. Therefore, based on the reaction equation, the concentration of substance B decreased by 0.2 mol / l, since substance B has a coefficient of 2. Then the concentration of substance A after a while will become equal to 0.3-0.1 \u003d 0.2 mol / l, and the concentration of B is 0.5-0.2 \u003d 0.3 mol / l.
Determine the reaction rate:
mol/l×s
Example 3
How will the reaction rate change: if the concentration of NO is increased by 3 times? According to the law of mass action, we write the expression for the reaction rate:
.
With an increase in the concentration of NO by 3 times, the reaction rate will be:
The reaction rate will increase by 9 times.
Example 4
Determine how the reaction rate will change 
if you increase the pressure in the system by 2 times.
A 2-fold increase in pressure in the system will cause a 2-fold decrease in the volume of the system, while the concentrations of the reactants will increase by 2 times.
According to the law of mass action, we write the initial reaction rate 
and when the pressure is doubled:
, .
The reaction rate will increase by 8 times.
Example 5
Calculate the initial concentrations of substances A and B in the system A + 3B \u003d 2C, if the equilibrium concentration of substances A is 0.1 mol / l, substances B is 0.2 mol / l, substances C - 0.7 mol / l.
We find the concentration of substance A spent on the reaction, making up the proportion according to the reaction equation:
2 mol/l C obtained from 1 mol/l A,
0.7 mol/l C®x mol/l × A.
mol/l A.
Therefore, the initial concentration of substance A is equal to:
0.1 + 0.35 = 0.45 mol/l.
Find the concentration of substance B consumed in the reaction.
We compose the proportion according to the reaction equation:
2 mol/l C obtained from 3 mol/l B
0.7 mol/l C ® x mol/l B
x \u003d mol / l A.
Then the initial concentration of substance B is equal to:
mol/l.
Example 6
At a temperature of 40 0 C, 0.5 mol / l of substance A was formed. How many mol / l A is formed if the temperature is raised to 80 0 C? The temperature coefficient of the reaction is 2.
According to the van't Hoff rule, we write the expression for the reaction rate at 80 0 С:
.
Substituting the problem data into the equation, we get:
At 80 0 C, 8 mol/l of substance A is formed.
Example 7
Calculate the change in the rate constant of a reaction with an activation energy of 191 kJ/mol as the temperature increases from 330 to 400 K.
Let's write the Arrhenius equation for the condition of the problem:
where R is the universal gas constant equal to 8.32 J/k(K×mol).
from where the change in rate constant will be:
Control tasks
61. The rate of a chemical reaction
2NO(g) + O2(g) = 2NO2(g)
at concentrations of reactants =0.3 mol/l and =0.15 mol/l was 1.2 10-3 mol/(l s). Find the value of the reaction rate constant.
62. By how many degrees should the temperature of the system be raised so that the reaction rate in it increases by 30 times (= 2.5)?
63. How many times should the concentration of carbon monoxide in the system be increased
2CO \u003d CO2 + C,
to increase the rate of the reaction by 4 times?
64. How many times should the pressure be increased so that the rate of the reaction of NO2 formation according to the reaction
increased 1000 times?
65. The reaction proceeds according to the equation
2NO(g) + Cl2(g) = 2NOCl(g).
The concentrations of the starting materials before the start of the reaction were: =0.4 mol/l; \u003d 0.3 mol / l. How many times will the reaction rate change compared to the initial one at the moment when half of the nitric oxide has time to react?
66. How many times will the rate constant of a chemical reaction increase with an increase in temperature by 40, if \u003d 3.2?
67. Write an expression for the rate of a chemical reaction occurring in a homogeneous system according to the equation
and determine how many times the rate of this reaction will increase if:
a) the concentration A will decrease by 2 times;
b) concentration A will increase by 2 times;
c) the concentration of B will increase by 2 times;
d) the concentration of both substances will increase by 2 times.
68. How many times should the concentration of hydrogen in the system be increased
N2 + 3H2= 2NH3,
to increase the reaction rate by 100 times?
69. Calculate the temperature coefficient of the reaction rate if its rate constant at 100 C is 0.0006, and at 150 C it is 0.072.
70. The reaction between nitric oxide (II) and chlorine proceeds according to the equation
2NO + Cl2= 2NOCl.
How will the reaction rate change with increasing:
a) the concentration of nitric oxide by 2 times;
b) chlorine concentration by 2 times;
c) the concentration of both substances is 2 times?
CHEMICAL EQUILIBRIUM
Examples of problem solving
Chemical equilibrium is such a state of the system in which the rates of forward and reverse chemical reactions are equal, and the concentrations of the reactants do not change over time.
The quantitative characteristic of chemical equilibrium is the equilibrium constant. The equilibrium constant at a constant temperature is equal to the ratio of the product of the equilibrium concentrations of the reaction products to the product of the equilibrium concentrations of the starting materials, taken in powers of their stoichiometric coefficients, and is a constant value.
In the general case, for a homogeneous reaction mA+ nB« pC+qD
the equilibrium constant is:
This equation is expressed by the law of mass action for a reversible reaction.
When external conditions change, a shift in chemical equilibrium occurs, which is expressed in a change in the equilibrium concentrations of the initial substances and reaction products. The direction of equilibrium shift is determined by the Le Chatelier principle: if an external influence is exerted on a system in equilibrium, then the equilibrium is shifted in the direction that weakens the external influence.
Chemical equilibrium can be shifted by the influence of changes in the concentration of reactants, temperature, pressure.
With an increase in the concentration of the starting substances, the equilibrium will shift in accordance with the Le Chatelier principle towards the reaction products, and with an increase in the concentrations of the products, towards the starting substances.
With a change in temperature (its increase), the equilibrium shifts towards an endothermic reaction (D H > 0), which proceeds with the absorption of heat, i.e. the rate of the forward reaction increases and the equilibrium shifts towards the reaction products. In the case of an exothermic reaction (D H > 0), with an increase in temperature, the rate of the reverse reaction will increase, which will ensure the absorption of heat, and the equilibrium will shift towards the starting materials.
If substances in the gaseous state participate in the reaction, then the chemical equilibrium can be shifted by changing the pressure. An increase in pressure is tantamount to an increase in the concentration of the reactants. With increasing pressure, the equilibrium shifts towards the reaction with a smaller number of moles of gaseous substances, and with a decrease in pressure, towards the reaction with a large number of moles of gaseous substances.
Example 1
Calculate the initial concentrations of substances A and B in the homogeneous system A + 3B - 2C, if the equilibrium concentrations are A = 0.1 mol / l, B = 0.2 mol / l, C = 0.7 mol / l.
It is known that the initial concentration of a substance is equal to the sum of the equilibrium concentration and the concentration that went into the reaction, i.e. reacted:
To find, you need to know how much substance A reacted.
We calculate by making up the proportion according to the reaction equation:
2 mol/l C obtained from 1 mol/l A
0.7 mol/l C ––––––––x mol/l A,
x \u003d (0.7 × 1) / 2 \u003d 0.35 mol / l
We calculate the initial concentration of substance B:
Let's calculate the proportion:
2 mol/l C obtained from 3 mol/l B
0.7 mol/l C ––––––––––––x mol/l B
x \u003d (0.7 × 3) / 2 \u003d 1.05 mol / l
Then the initial concentration B is equal to:
Example 2.
Calculate the equilibrium concentrations of substances in the system A + B "C + D", provided that the initial concentrations of substances: A \u003d 1 mol / l, B \u003d 5 mol / l. The equilibrium constant is 1.
Suppose that by the time of equilibrium of substance A, x moles have reacted. Based on the reaction equation, the equilibrium concentrations will be:
;
since according to the equation of the reaction of substance B, the reaction took as much as the reaction of substance A.
We substitute the values of the equilibrium concentrations into the equilibrium constant and find x.
Then: 
Example 3
An equilibrium has been established in the system: 2AB + B 2 “2AB; D H > 0.
In which direction will the equilibrium shift as the temperature decreases?
This direct reaction is endothermic, i.e. goes with the absorption of heat, therefore, when the temperature in the system decreases, the equilibrium in accordance with the Le Chatelier principle will shift to the left, towards the reverse reaction, which is exothermic.
Example 4.
The equilibrium of the system A + B "AB was established at the following concentrations of substances: C (A) \u003d C (B) \u003d C (AB) \u003d 0.01 mol / l. Calculate the equilibrium constant and the initial concentrations of substances. 72. Initial concentrations of nitric oxide (II) and chlorine in the system
2NO + Cl2 2NOCl
are respectively 0.5 mol/l and 0.2 mol/l. Calculate the equilibrium constant if 20 nitric oxide (II) oxides have reacted by the time equilibrium is reached.
73. At a certain temperature, the equilibrium concentrations of the reagents of a reversible chemical reaction
2A(g)+B(g) 2C(g)
were [A]=0.04 mol/l, [B]=0.06 mol/l, [C]=0.02 mol/l. Calculate the equilibrium constant and the initial concentrations of substances A and B.
74. At a certain temperature, the equilibrium concentrations in the system
were respectively: = 0.04 mol/l, = 0.06 mol/l,
0.02 mol/l. Calculate the equilibrium constant and initial con-
concentration of sulfur oxide (IV) and oxygen.
75. When the system is in equilibrium
the concentrations of the substances involved were: = 0.3 mol/l; = =0.9 mol/l; = 0.4 mol/l. Calculate how the rates of the forward and reverse reactions will change if the pressure is increased by 5 times. In which direction will the equilibrium shift?
76. Calculate the equilibrium constant of the reversible reaction
2SO2(g) + O2(g) 2SO3(g),
if the equilibrium concentration \u003d 0.04 mol / l, and the initial concentrations of substances \u003d 1 mol / l, \u003d 0.8 mol / l.
77. System equilibrium
CO + Cl2 COCl2,
was established at the following concentrations of reactants: [CO] = = [Сl2] = = 0.001 mol/l. Determine the equilibrium constant and the initial concentrations of carbon monoxide and chlorine.
78. The initial concentrations of carbon monoxide (II) and water vapor are equal and amount to 0.03 mol/l. Calculate the equilibrium concentrations of CO, H2O and H2 in the system
CO + H2O CO2 + H2,
if the equilibrium concentration of CO2 turned out to be equal to 0.01 mol / l. Calculate the equilibrium constant.
79. Determine the equilibrium concentration of hydrogen in the system
if the initial concentration of HJ was 0.05 mol/l, and the equilibrium constant K=0.02.
80. System equilibrium constant
CO + H2O CO2 + H2
at a certain temperature is 1. Calculate the percentage composition of the mixture at equilibrium if the initial concentrations of CO and H2O are 1 mol/L each.
