Consider a reversible chemical reaction of a general form, in which all substances are in the same state of aggregation, for example, liquid:

aA + bB D cC + d D,

where A and B are the starting materials of the direct reaction; C and D are direct reaction products; a, b, c, and d- stoichiometric coefficients.

At the initial moment of time, when the concentration of substances A and B is the highest, the rate of the direct reaction will also be the highest and, according to the law of mass action, is equal to

u pr \u003d k 1 C A a C B in (6.1)

where k 1 is the rate constant of the direct reaction.

Over time, the concentration of substances A and B decreases, and, consequently, the rate of the direct reaction also decreases.

At the initial moment of time, the concentration of substances C and D is equal to zero, and, consequently, the rate of the reverse reaction is equal to zero, over time, the concentration of substances C and D increases, and, consequently, the rate of the reverse reaction also increases and it will be equal to

u arr \u003d k 2 C C with C D d (6.2)

where k 2 is the rate constant of the reverse reaction.

At the moment of reaching equilibrium, the concentrations take on the value of equilibrium, and the speeds are equal to each other u pr \u003d u arr, therefore

k 1 C A a C B c = k 2 C C c C D d (6.3)

Let's move the rate constants in one direction, and the concentrations in the other:

The ratio of two constants is a constant, and it is called the constant of chemical equilibrium:

The equilibrium constant shows how many times the rate of the forward reaction is greater or less than the rate of the reverse reaction.

Equilibrium constant is the ratio of the product of the equilibrium concentrations of the reaction products, taken to the power of their stoichiometric coefficients, to the product of the equilibrium concentrations of the starting materials, taken to the power of their stoichiometric coefficients.

The value of the equilibrium constant depends on the nature of the reacting substances and temperature, and does not depend on the concentration at the moment of equilibrium, since their ratio is always a constant value, numerically equal to the equilibrium constant. If a homogeneous reaction occurs between substances in solution, then the equilibrium constant is denoted by K C, and if between gases, then K P.

where Р С, Р D , Р А and Р В are the equilibrium pressures of the reaction participants.

Using the equation Clapeyron-Mendeleev, you can determine the relationship between K P and K C

Move the volume to the right side

p = RT, i.e. p = CRT (6.9)

We substitute equation (6.9) into (6.7), for each reagent and simplify

where Dn is the change in the number of moles of gaseous participants in the reaction

Dn = (s + d) - (a + c) (6.11)

Consequently,

K P \u003d K C (RT) D n (6.12)

From equation (6.12) it can be seen that K P = K C, if the number of moles of gaseous participants in the reaction does not change (Dn = 0) or there are no gases in the system.

It should be noted that in the case of a heterogeneous process, the concentration of the solid or liquid phase in the system is not taken into account.

For example, the equilibrium constant for a reaction of the form 2A + 3B \u003d C + 4D, provided that all substances are gases and has the form

and if D is solid, then

The equilibrium constant is of great theoretical and practical importance. The numerical value of the equilibrium constant makes it possible to judge the practical possibility and depth of a chemical reaction.

If K > 1, then this reaction proceeds with a significant yield of reaction products; if K > 10 4 , then the reaction is irreversible; if K< 1, то такая реакция нетехнологична; если K < 10 -4 , то такая реакция невозможна.

Knowing the equilibrium constant, one can determine the composition of the reaction mixture at the moment of equilibrium and calculate the yield constant of the reaction products. The equilibrium constant can be determined using experimental methods, by analyzing the quantitative composition of the reaction mixture at the moment of equilibrium, or by applying theoretical calculations. For many reactions under standard conditions, the equilibrium constant is a tabular value.

6.3. Factors affecting chemical equilibrium. Le Chatelier's principle

Under external action on the system, the chemical equilibrium is shifted, i.e., the equilibrium concentrations of the initial substances and reaction products change. If, as a result of an external influence, the equilibrium concentrations of the reaction products increase, then they speak of a shift of the equilibrium to the right (in the direction of the direct reaction). If, as a result of an external influence, the equilibrium concentrations of the starting substances increase, then one speaks of a shift of the equilibrium to the left (in the direction of the reverse reaction).

The influence of various factors on the shift in chemical equilibrium reflects Le Chatelier's principle (1884): if a system in stable chemical equilibrium is acted upon from the outside by changing the temperature, pressure or concentration, then the chemical equilibrium shifts in the direction in which the effect of the effect produced decreases.

It should be noted that the catalyst does not shift the chemical equilibrium, but only accelerates its onset.

Consider the influence of each factor on the shift of chemical equilibrium for a general reaction:

aA + bB = cC + d D±Q.

Effect of concentration change. According to the Le Chatelier principle, an increase in the concentration of one of the components of an equilibrium chemical reaction leads to a shift in the equilibrium towards an increase in the reaction in which the chemical processing of this component occurs. Conversely, a decrease in the concentration of one of the components leads to a shift in the equilibrium towards the formation of this component.

Thus, an increase in the concentration of substance A or B shifts the equilibrium in the forward direction; an increase in the concentration of substance C or D shifts the equilibrium in the opposite direction; a decrease in the concentration of A or B shifts the equilibrium in the opposite direction; a decrease in the concentration of substance C or D shifts the equilibrium in the forward direction. (Schematically, you can write: -C A or C B ®; -C C or C D ¬; ¯ C A or C B ¬; ¯ C C or CD ®).

The effect of temperature. The general rule that determines the effect of temperature on equilibrium has the following formulation: an increase in temperature contributes to a shift in equilibrium towards an endothermic reaction (- Q); lowering the temperature contributes to a shift in the equilibrium towards an exothermic reaction (+ Q).

Reactions that proceed without thermal effects do not shift the chemical equilibrium with a change in temperature. An increase in temperature in this case only leads to a more rapid establishment of equilibrium, which would be achieved in the given system even without heating, but over a longer time.

Thus, in an exothermic reaction (+ Q), an increase in temperature leads to a shift in the equilibrium in the opposite direction and, conversely, in an endothermic reaction (- Q), an increase in temperature leads to a shift in the forward direction, and a decrease in temperature in the opposite direction. (Schematically, you can write: at +Q -T ¬; ¯T ®; at -Q -T ®; ¯T ¬).

Influence of pressure. As experience shows, pressure has a noticeable effect on the displacement of only those equilibrium reactions in which gaseous substances participate, and in this case, the change in the number of moles of gaseous participants in the reaction (Dn) is not equal to zero. With an increase in pressure, the equilibrium shifts towards the reaction that is accompanied by the formation of a smaller number of moles of gaseous substances, and with a decrease in pressure - towards the formation of a larger number of moles of gaseous substances.

Thus, if Dn = 0, then pressure does not affect the shift in chemical equilibrium; if Dn< 0, то увеличение давления смещает равновесие в прямом направлении, уменьшение давления в сторону обратной реакции; если Dn >0, then an increase in pressure shifts the equilibrium in the opposite direction, and a decrease in pressure - in the direction of a direct reaction. (Schematically, it can be written: at Dn = 0 P does not affect; at Dn 0 -P ¬, ¯P ®). Le Chatelier's principle is applicable to both homogeneous and heterogeneous systems and gives a qualitative characteristic of an equilibrium shift.

A quantitative characteristic showing the direction of the reaction and the shift in the concentration of substances is called the equilibrium constant of a chemical reaction. The equilibrium constant depends on the temperature and the nature of the reactants.

Reversible and irreversible reactions

All reactions can be divided into two types:

• reversible, simultaneously flowing in two mutually opposite directions;
• irreversible flowing in the same direction with the total consumption of at least one initial substance.

In irreversible reactions, insoluble substances are usually formed in the form of a precipitate or gas. These reactions include:

• combustion:

  C 2 H 5 OH + 3O 2 → 2CO 2 + H 2 O;

• decomposition:

  2KMnO 4 → K 2 MnO 4 + MnO 2 + H 2 O;

• connection with the formation of a precipitate or gas:

  BaCl 2 + Na 2 SO 4 → BaSO 4 ↓ + 2NaCl.

Rice. 1. Precipitation of BaSO 4 .

Reversible reactions are possible only under certain constant conditions. The original substances give a new substance, which immediately breaks down into its constituent parts and is collected again. For example, as a result of the reaction 2NO + O 2 ↔ 2NO 2 nitric oxide (IV) easily decomposes into nitric oxide (II) and oxygen.

Equilibrium

After a certain time, the rate of the reversible reaction slows down. Chemical equilibrium is achieved - a state in which there is no change in the concentration of the starting substances and reaction products over time, since the rates of the forward and reverse reactions are equalized. Equilibrium is possible only in homogeneous systems, that is, all reacting substances are either liquids or gases.

Consider the chemical equilibrium on the example of the reaction of the interaction of hydrogen with iodine:

• direct reaction -

  H 2 + I 2 ↔ 2HI;

• back reaction -

  2HI ↔ H 2 + I 2 .

As soon as two reagents are mixed - hydrogen and iodine - hydrogen iodine does not yet exist, since simple substances only react. A large number of starting substances actively react with each other, so the rate of the direct reaction will be maximum. In this case, the reverse reaction does not proceed, and its rate is zero.

The rate of a direct reaction can be expressed graphically:

ν pr = k pr ∙ ∙ ,

where k pr is the rate constant of the direct reaction.

Over time, the reagents are consumed, their concentration decreases. Accordingly, the rate of the forward reaction decreases. At the same time, the concentration of a new substance, hydrogen iodide, increases. When accumulated, it begins to decompose, and the rate of the reverse reaction increases. It can be expressed as

ν arr = k arr ∙ 2 .

Hydrogen iodide is squared, since the coefficient of the molecule is two.

At some point, the rates of the forward and reverse reactions equalize. There is a state of chemical equilibrium.

Rice. 2. Graph of reaction rate versus time.

The equilibrium can be shifted either towards the starting materials or towards the products of the reaction. The displacement under the influence of external factors is called Le Chatelier's principle. Equilibrium is affected by temperature, pressure, concentration of one of the substances.

Constant calculation

In a state of equilibrium, both reactions proceed, but at the same time, the concentrations of substances are in equilibrium (equilibrium concentrations are formed), since the rates are balanced (ν pr \u003d ν arr).

Chemical equilibrium is characterized by the chemical equilibrium constant, which is expressed by the summary formula:

K p \u003d k pr / k arr \u003d const.

The reaction rate constants can be expressed in terms of the reaction rate ratio. Let's take the conditional equation of the reverse reaction:

aA + bB ↔ cC + dD.

Then the rates of the forward and reverse reactions will be equal:

• ν inc = k inc ∙ [A] p a ∙ [B] p b
• ν arr = k arr ∙ [C] p c ∙ [D] p d .

Accordingly, if

ν pr \u003d ν arr,

k ex ∙ [A] p a ∙ [B] p b = k arr ∙ [C] p c ∙ [D] p d .

From here we can express the ratio of constants:

k arr / k inc = [C] p c ∙ [D] p d / [A] p a ∙ [B] p b .

This ratio is equal to the equilibrium constant:

K p = [C] p c ∙ [D] p d / [A] p a ∙ [B] p b .

Rice. 3. The formula for the equilibrium constant.

The value shows how many times the rate of the forward reaction is greater than the rate of the reverse reaction.

What have we learned?

Reactions depending on the final products are classified into reversible and irreversible. Reversible reactions proceed in both directions: the starting materials form final products, which decompose into starting substances. During a reaction, the rates of the forward and reverse reactions are balanced. This state is called chemical equilibrium. It can be expressed as the ratio of the product of the equilibrium concentrations of the reaction products to the product of the equilibrium concentrations of the starting materials.

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In 1885, the French physicist and chemist Le Chatelier was deduced, and in 1887 by the German physicist Braun, the law of chemical equilibrium and the chemical equilibrium constant were substantiated, and their dependence on the influence of various external factors was studied.

The essence of chemical equilibrium

Equilibrium is a state that means things are always moving. Products are decomposed into reagents, and reagents are combined into products. Things move, but concentrations remain the same. The reaction is written with a double arrow instead of an equals sign to show that it is reversible.

Classic patterns

Back in the last century, chemists discovered certain patterns that provide for the possibility of changing the direction of the reaction in the same container. Knowing how chemical reactions work is incredibly important for both laboratory research and industrial production. At the same time, the ability to control all these phenomena is of great importance. It is human nature to intervene in many natural processes, especially reversible ones, in order to later use them for their own benefit. From knowledge of chemical reactions will be more useful if you are fluent in the levers of controlling them.

The law of mass action in chemistry is used by chemists to correctly calculate the rates of reactions. It gives a clear idea that none will be completed if it takes place in a closed system. The molecules of the resulting substances are in constant and random motion, and a reverse reaction may soon occur, in which the molecules of the starting material will be restored.

In industry, open systems are most often used. Vessels, apparatus and other containers where chemical reactions take place remain unlocked. This is necessary so that during these processes it is possible to extract the desired product and get rid of useless reaction products. For example, coal is burned in open furnaces, cement is produced in open furnaces, blast furnaces operate with a constant supply of air, and ammonia is synthesized by continuously removing ammonia itself.

Reversible and irreversible chemical reactions

Based on the name, one can give the appropriate definitions: irreversible reactions are those that are brought to an end, do not change their direction and proceed along a given trajectory, regardless of pressure drops and temperature fluctuations. Their distinguishing feature is that some products may leave the reaction sphere. Thus, for example, it is possible to obtain gas (CaCO 3 \u003d CaO + CO 2), a precipitate (Cu (NO 3) 2 + H 2 S \u003d CuS + 2HNO 3) or others will also be considered irreversible if a large amount is released during the process thermal energy, for example: 4P + 5O 2 \u003d 2P 2 O 5 + Q.

Almost all reactions that occur in nature are reversible. Regardless of such external conditions as pressure and temperature, almost all processes can proceed simultaneously in different directions. As the law of mass action in chemistry says, the amount of heat absorbed will be equal to the amount released, which means that if one reaction was exothermic, then the second (reverse) will be endothermic.

Chemical equilibrium: chemical equilibrium constant

Reactions are the "verbs" of chemistry - the activities that chemists study. Many reactions go to their completion and then stop, which means that the reactants are completely converted into products, with no way to return to their original state. In some cases, the reaction is indeed irreversible, for example, when combustion changes both physical and chemical. However, there are many other circumstances in which it is not only possible, but also continuous, since the products of the first reaction become reactants in the second.

The dynamic state in which the concentrations of reactants and products remain constant is called equilibrium. It is possible to predict the behavior of substances with the help of certain laws that are applied in industries seeking to reduce the cost of producing specific chemicals. The concept of chemical equilibrium is also useful in understanding processes that maintain or potentially threaten human health. The chemical equilibrium constant is the value of a reaction factor that depends on ionic strength and temperature and is independent of the concentrations of reactants and products in solution.

Calculation of the equilibrium constant

This value is dimensionless, that is, it does not have a certain number of units. Although the calculation is usually written for two reactants and two products, it works for any number of reaction participants. The calculation and interpretation of the equilibrium constant depends on whether the chemical reaction is associated with a homogeneous or heterogeneous equilibrium. This means that all reacting components can be pure liquids or gases. For reactions that reach heterogeneous equilibrium, as a rule, not one phase is present, but at least two. For example, liquids and gases or and liquids.

The value of the equilibrium constant

For any given temperature, there is only one value for the equilibrium constant, which only changes if the temperature at which the reaction occurs changes in one direction or another. Some predictions about a chemical reaction can be made based on whether the equilibrium constant is large or small. If the value is very large, then the equilibrium favors the reaction to the right and more products are obtained than there were reactants. The reaction in this case can be called "total" or "quantitative".

If the value of the equilibrium constant is small, then it favors the reaction to the left, where the amount of reactants was greater than the number of products formed. If this value tends to zero, we can assume that the reaction does not occur. If the values ​​of the equilibrium constant for the direct and reverse reactions are almost the same, then the amount of reactants and products will also be almost the same. This type of reaction is considered to be reversible.

Consider a specific reversible reaction

Take two such chemical elements as iodine and hydrogen, which, when mixed, give a new substance - hydrogen iodide.

For v 1 we take the rate of the direct reaction, for v 2 - the rate of the reverse reaction, k - the equilibrium constant. Using the law of mass action, we obtain the following expression:

v 1 \u003d k 1 * c (H 2) * c (I 2),

v 2 = k 2 * c 2 (HI).

When mixing iodine (I 2) and hydrogen (H 2) molecules, their interaction begins. At the initial stage, the concentration of these elements is maximum, but by the end of the reaction, the concentration of a new compound, hydrogen iodide (HI), will be maximum. Accordingly, the reaction rates will also be different. At the very beginning, they will be maximum. Over time, there comes a moment when these values ​​are equal, and this is the state called chemical equilibrium.

The expression of the chemical equilibrium constant, as a rule, is denoted using square brackets: , , . Since at equilibrium the speeds are equal, then:

k 1 \u003d k 2 2,

so we get the equation of the chemical equilibrium constant:

k 1 /k 2 = 2 / = K.

Le Chatelier-Brown principle

There is the following regularity: if a certain effect is made on a system that is in equilibrium (change the conditions of chemical equilibrium by changing temperature or pressure, for example), then the balance will shift in order to partially counteract the effect of the change. In addition to chemistry, this principle also applies in slightly different forms to the fields of pharmacology and economics.

Chemical equilibrium constant and ways of its expression

The equilibrium expression can be expressed in terms of the concentration of products and reactants. Only chemicals in the aqueous and gaseous phases are included in the equilibrium formula because the concentrations of liquids and solids do not change. What factors affect chemical equilibrium? If a pure liquid or solid is involved in it, it is considered that it has K \u003d 1, and accordingly ceases to be taken into account, with the exception of highly concentrated solutions. For example, pure water has an activity of 1.

Another example is solid carbon, which can be formed by the reaction of two molecules of carbon monoxide to form carbon dioxide and carbon. Factors that can affect the balance include the addition of a reactant or product (changes in concentration affect the balance). The addition of a reactant can bring equilibrium to the right in the chemical equation, where more forms of the product appear. The addition of product can bring equilibrium to the left as more reactant forms become available.

Equilibrium occurs when a reaction proceeding in both directions has a constant ratio of products and reactants. In general, the chemical equilibrium is static, since the quantitative ratio of products and reactants is constant. However, a closer look reveals that equilibrium is actually a very dynamic process, as the reaction moves in both directions at the same rate.

Dynamic equilibrium is an example of a steady state function. For a system at steady state, the currently observed behavior continues into the future. Therefore, once the reaction reaches equilibrium, the ratio of product to reactant concentrations will remain the same even though the reaction continues.

How easy is it to talk about complex things?

Concepts such as chemical equilibrium and chemical equilibrium constant are quite difficult to understand. Let's take an example from life. Have you ever been stuck on a bridge between two cities and noticed that the traffic in the other direction is smooth and measured while you are hopelessly stuck in traffic? This is not good.

What if the cars were measured and at the same speed moving on both sides? Would the number of cars in both cities remain constant? When the speed of entry and exit to both cities is the same, and the number of cars in each city is stable over time, this means that the whole process is in dynamic equilibrium.

constant (from lat. constans, genus n. constantis - constant, unchanged), - such an object in a certain theory, the meaning of which within this theory (or, sometimes, narrower consideration) is always considered the same. K. are opposed to such objects, the values ​​of which change (by themselves or depending on the change in the values ​​of other objects). The presence of K. in the expression of many. laws of nature and society reflects relates. the immutability of certain aspects of reality, manifested in the presence of patterns. An important variety of K. is K., related to the number of physical. quantities, such as length, time, force, mass (for example, the rest mass of an electron), or more complex quantities expressed numerically in terms of the ratios between these K. or their powers, such as volume, speed, work, etc. .P. (e.g., the acceleration of gravity at the Earth's surface). Those from K. of this kind, to-rye are considered in modern. physics (within the framework of its respective theories) relevant to the entire observable part of the universe, called. world (or universal) K.; Examples of such quantum are the speed of light in a vacuum, Planck's quantum constant (i.e., the value of the so-called quantum of action), the gravitational constant, and others. 20th century At the same time, some foreign scientists (English physicist and astronomer A. Eddington, German physicist Heisenberg, Austrian physicist A. March, etc.) tried to give them idealistic. interpretation. So, Eddington saw in the system of world k. one of the manifestations of self-sufficiency. the existence of ideal mathematical forms expressing the harmony of nature and its laws. In fact, universal K. reflect not an imaginary self-sufficiency. being (outside of things and cognition) of the indicated forms, and (usually expressed mathematically) fundamental regularities of objective reality, in particular, regularities associated with the structure of matter. deep dialectic. the meaning of world quantum mechanics is revealed in the fact that some of them (Planck's quantum constant, the speed of light in a vacuum) are a kind of scale that delimits various classes of processes that proceed in fundamentally different ways; at the same time, such K. indicate the presence of a certain. connections between the phenomena of these classes. So, the connection between the laws of classical. and relativistic mechanics (see Relativity theory) can be established from the consideration of such a limiting transition of the equations of motion of relativistic mechanics to the equations of motion of the classical. mechanics, which is associated with idealization, which consists in the rejection of the idea of ​​the speed of light in a vacuum as a finite K. and in understanding the speed of light as infinitely large; with another idealization, which consists in considering the quantum of action as an infinitesimal quantity, the equations of motion of quantum theory pass into the equations of motion of the classical. mechanics, etc. In addition to these most important K., determined purely physically and appearing in the formulations of many basic. laws of nature are widely used in the same place and such, defined purely mathematically, K., as the number 0; one; ? (the ratio of the circumference to the diameter); e (base of natural logarithms); Euler's constant, and others. No less frequently used are also K., which are the results of well-known mathematical. operations on the specified K. But the more difficult it is to express the frequently used K. through more simply defined K. (or such simplest K. as 0 and 1) and known operations, the more independent is its participation in the formulation of those laws and relations, in to-rykh it occurs, the more often a special is introduced for it. designation, calculate or measure it as accurately as possible. Some of the quantities occur sporadically and are K. only within the framework of the consideration of a certain problem, and they may even depend on the choice of conditions (values ​​of parameters) of the problem, becoming K. only when these conditions are fixed. Such K. are often denoted by the letters C or K (without linking these designations once and for all with the same K.) or they simply write that such and such a value \u003d const. A. Kuznetsov, I. Lyakhov. Moscow. In cases where functions play the role of the objects under consideration in mathematics or logic, K. are called such of them, the value of which does not depend on the values ​​of the arguments of these functions. For example, K. is the difference x–x as a function of x, because for all (numerical) values ​​of the variable x, the value of the function x–x is the same number 0. for all possible values ​​of its argument A, it has (within the framework of the usual, classical algebra of logic) the same value 1 (which is characterized by the logical value "true" conditionally identified with it). An example of a more complex K. from the algebra of logic is the function (AB? BA). In some cases, a function whose value is constant is identified with this value itself. In this case, the value of the function already appears as a K. (more precisely, as a function that is a K.). Arguments to this function can be any selected literal variables (eg, A, B, x, y, etc.), because anyway, it doesn't depend on them. In other cases, such an identification of a function, which is a key, is not made with its value, i.e. distinguish between such two K., one of which has a variable among its arguments, which the other does not. This makes it possible, for example, to define a function as its table, and also simplifies the schematic. definition of certain operations on functions. Along with such constants, the values ​​of which are numbers (possibly named) or are characterized by numbers, there are also other constants. the set of all integers is non-negative. numbers. The value of the function, which is K., can also be an object of any nature. For example, considering functions of such a variable A whose values ​​are subsets of the natural series, one can determine one of these functions whose value for all values ​​of the variable A is the set of all prime numbers. In addition to the physical quantities and functions in the role of such objects, some of which turn out to be K., often (especially in logic and semantics) consider signs and their combinations: words, sentences, terms, formulas, etc., and as meaning those of them, the meanings of which are not specifically mentioned, their semantic meanings (if any). At the same time, new K are revealed. So, in arithmetic. expression (term) 2 + 3–2 K. are not only the numbers 2 and 3 and the results of operations on them, but also the signs + and -, the values ​​of which are the operations of addition and subtraction. These signs, being K. within the theoretical consideration of ordinary school arithmetic and algebra cease to be K. when we enter the wider area of ​​modern. algebra or logic, where the + sign in some cases has the meaning of the operation of ordinary addition of numbers, in other cases (for example, in the algebra of logic) - addition modulo 2 or Boolean addition, in other cases - another operation. However, with narrower considerations (for example, when constructing a specific algebraic or logical system), the meanings of the signs of operations are fixed and these signs, in contrast to the signs of variables, become K. The selection of a logical. K. plays a special role when applied to objects from nature. language. In the role of logical K. in Russian. the language includes, for example, such unions as "and", "or", etc., such quantifier words as "all", "every", "exists", "some", etc., such linking verbs, as "is", "essence", "is", etc., as well as such more complex phrases as "if ... then", "if and only if", "there is only one", "the one that" , "such that", "equivalent to that", etc. By means of selection logical. K. in nature. The language is the recognition of the similarity of their role in a huge number of cases of inferences or other reasoning, which makes it possible to combine these cases into one or another single scheme (logical rule), in which objects that differ from those distinguished by K. are replaced by the corresponding variables. The smaller the number of schemes that manage to cover all the cases of reasoning under consideration, the simpler these schemes themselves are, and the more we are guaranteed against the possibility of erroneous reasoning on them, the more justified is the choice of the logical ones appearing in these schemes. TO. A. Kuznetsov. Moscow. Lit.: Eddington?., Space, time and gravity, trans. from English, O., 1923; Jeans, D., The universe around us, trans. from English, L.–M., 1932; Born M., Mysterious number 137, in Sat.: Uspekhi nat. Sciences, vol. 16, no. 6, 1936; Heisenberg W., Philos. problems of atomic physics, M., 1953; his own, Planck's Discovery and DOS. philosophy questions of the doctrine of atoms, "Problems of Philosophy", 1958, No 11; his own, Physics and Philosophy, M., 1963; Sat. Art. by math. logic and its applications to certain issues of cybernetics, in: Tr. math. in-ta, t. 51, M., 1958; Kuznetsov IV, What Werner Heisenberg is right and what is wrong, "Problems of Philosophy", 1958, No 11; Uspensky V. ?., Lectures on computable functions, Moscow, 1960; Kay J. and Laby T., Tables of nat. and chem. permanent, per. from English, 2nd ed., M., 1962; Kurosh A. G., Lectures on General Algebra, M., 1962; Svidersky V.I., On the dialectics of elements and structure in the objective world and in cognition, M., 1962, ch. 3; ?ddington A. St., New pathways in science, Camb., 1935; his own, Relativity theory of protons and electrons, L., 1936; his own, The philosophy of physical science, N. Y.–Camb., 1939; Louis de Broglie, physicien et penseur, P., ; March?., Die physikalische Erkenntnis und ihre Grenzen, 2 Aufl., Braunschweig, 1960.

concentration constant

When calculating equilibria in real systems, it is necessary to take into account the presence of foreign substances and their influence on the behavior of the initial substances and products of the reaction under study. This effect can be expressed both in the electrostatic interaction of ions and in chemical interaction with the formation of slightly dissociated or poorly soluble products. In both cases, a shift in the equilibrium of the reaction under study is observed. The concentration constant is expressed in terms of total concentrations, and not the activities of the starting materials and reaction products. In the case when foreign substances do not enter into competing chemical reactions, the concentration constant can be expressed in terms of equilibrium concentrations. For convenience of study, the concentration constant expressed in terms of equilibrium concentrations is often called the real constant, and the concentration constant expressed in terms of total concentrations is called the conditional constant.

The state of equilibrium is characterized by a real (concentration) constant

if the differences from ideality are due only to electrostatic interactions A, B, C and D with foreign ions.

The activity and equilibrium concentration of any ion are functionally related to each other by a simple relationship. For example, for ion A

a A = γ A [A]

Proportionality factor γ , called the activity coefficient, characterizes the degree of deviation of the system from the ideal due to the electrostatic interactions of the ions involved in the reaction under study with foreign (or own, if their concentration is high) ions. In an ideal system a A = [A] and the activity coefficient is equal to one. This means that there are no electrostatic interactions.

The value of the activity coefficient depends on the charge and ionic strength created by all ions in the solution:

Here I- ionic strength; [i] is the equilibrium concentration of the ion; z i- its charge.

The activity coefficients of individual ions can be theoretically estimated using the Debye-Hückel formulas

If a I< 0.01 (1-3)

If a I< 0.1 (1-4)

Here BUT and AT - constants depending on the temperature and dielectric constant of the solvent (for water at 20°С A = 0.5 and B = 0.3); a - distance of maximum approach of ions; these values ​​are usually given in reference tables. Since fluctuations in the values ​​of a do not affect the final result too much, it is recommended to take a constant value a = 3 A. Therefore,

The activity coefficient of an individual ion cannot be measured experimentally, since it is impossible to obtain a solution containing only positive or only negative ions.

For the A m B n electrolyte, only the average activity coefficient can be experimentally determined, which is related to the activity coefficients of individual ions γ A and γ B by the relations:

for binary electrolyte AB

for electrolyte type A m B n

The average activity coefficient can also be calculated theoretically using the Debye-Hückel formulas

If a I< 0.01

If a I< 0.1

Here a, a and b have the same meanings as in formulas (1-3) and (1-4), therefore

At low ionic strengths (I< 0.1) величины средних коэффициентов активности, рассчитанные по формулам Дебая - Хюккеля и найденные экспериментально, удовлетворительно совпадают. Это говорит о правомочности использования в этих условиях формул (1-3) - (1-4) для расчета величин γ ± и активности электролитов. Эти же формулы используются и для расчета коэффициентов активности индивидуальных ионов, хотя правильность таких расчетов нельзя проверить экспериментально.

For a more accurate calculation of the activity coefficients, it is proposed to introduce additional terms into the Debye-Hückel formulas. For example, the Davis equation makes it possible to calculate the activity coefficients of electrolytes and individual ions for ionic strengths of 0.2 - 0.5 with an error not exceeding 10%. The Davis equation for the activity coefficient of an individual ion has the form:

and for the average activity coefficient of the electrolyte A m B n:

The values ​​of the activity coefficients of individual ions at different ionic strengths and the average activity coefficients for electrolyte solutions of different concentrations, calculated using the Debye-Hückel formulas, are given in reference books.

Knowing the activity coefficients, one can estimate the activity of an ion or electrolyte in a solution. To facilitate the calculations, the following assumptions can be used:

1. The activity coefficients of ions of the same charge, regardless of the radius of the ions, are approximately equal. Therefore, reference books sometimes give average values ​​of the activity coefficients for one-, two-, three-, and four-charged ions.

2. The activity coefficients of neutral particles in dilute electrolyte solutions are assumed to be equal to one.

3. Very dilute electrolyte solutions, such as a saturated solution of a sparingly soluble electrolyte, can be considered ideal.

Often, when calculating complex equilibria, the activity coefficients are taken equal to unity. This assumption is justified for a number of reasons. First, the values ​​of the activity coefficients found using the Debye-Hückel formulas may in these cases turn out to be very far from the true ones. Secondly, the influence of chemical factors on equilibrium is much greater than that of electrostatic forces, so neglecting the latter when calculating complex equilibria does not introduce a noticeable error into the results.