Let us consider the general reverse reaction
Experimental studies show that in a state of equilibrium the following relationship holds:
(square brackets indicate concentration). The above relationship is a mathematical expression of the law of mass action, or the law of chemical equilibrium, according to which, in a state of chemical equilibrium at a certain temperature, the product of the concentrations of reaction products in powers, exponents
which are equal to the corresponding coefficients in the stoichiometric reaction equation, divided by a similar product of the concentrations of the reactants in the corresponding powers, represents a constant value. This constant is called the equilibrium constant. The expression of the equilibrium constant in terms of the concentrations of products and reagents is typical for reactions in solutions.
Note that the right side of the expression for the equilibrium constant contains only the concentrations of solutes. It should not include any terms related to the pure solids, pure liquids, or solvents participating in the reaction, since these terms are constant.
For reactions involving gases, the equilibrium constant is expressed in terms of the partial pressures of the gases, and not in terms of their concentrations. In this case, the equilibrium constant is denoted by the symbol.
The concentration of a gas can be expressed in terms of its pressure using the ideal gas equation of state (see Section 3.1):
From this equation it follows
where is the gas concentration, which can be denoted as [gas]. Since - is a constant value, we can write that at a given temperature
Let us express the equilibrium constant for the reaction between hydrogen and iodine in terms of the partial pressures of these gases.
The equation for this reaction has the form
Therefore, the equilibrium constant of this reaction is given by
Let us note that the concentrations or partial pressures of products, i.e., substances indicated on the right side of the chemical equation, always form the numerator, and the concentrations or partial pressures of reactants, i.e., substances indicated on the left side of the chemical equation, always form the denominator of the expression for the equilibrium constant.
Units of measurement for the equilibrium constant
The equilibrium constant can be a dimensional or dimensionless quantity, depending on the type of its mathematical expression. In the example above, the equilibrium constant is a dimensionless quantity because the numerator and denominator of the fraction have the same dimensions. Otherwise, the equilibrium constant has a dimension expressed in units of concentration or pressure.
What is the dimension of the equilibrium constant for the following reaction?
Therefore, it has a dimension (mol-dm-3)
So, the dimension of the equilibrium constant under consideration is or dm3/mol.
What is the dimension of the equilibrium constant for the following reaction?
The equilibrium constant of this reaction is determined by the expression
Therefore, it has dimension
So, the dimension of this equilibrium constant is: atm or Pa.
Heterogeneous equilibria
So far we have given examples only of homogeneous equilibria. For example, in the synthesis reaction of hydrogen iodide, both the product and both reactants are in a gaseous state.
As an example of a reaction leading to heterogeneous equilibrium, consider the thermal dissociation of calcium carbonate
The equilibrium constant of this reaction is given by
Note that this expression does not include any terms related to the two solids involved in the reaction. In the example given, the equilibrium constant represents the dissociation pressure of calcium carbonate. It shows that if calcium carbonate is heated in a closed vessel, then its dissociation pressure at a fixed temperature does not depend on the amount of calcium carbonate. In the next section, we will learn how the equilibrium constant changes with temperature. In the example under consideration, the dissociation pressure exceeds 1 atm only at a temperature higher. Therefore, in order for the dioxide
constant (from Latin constans, gen. constantis - constant, unchangeable) - one of the objects in a certain theory, the meaning of which within the framework of this theory (or, sometimes, narrower consideration) is always considered the same. K. are contrasted with such objects, the meanings of which change (by themselves or depending on changes in the meanings of other objects). The presence of K. when expressing plural. reflects the laws of nature and society. the immutability of certain aspects of reality, manifested in the presence of patterns. An important variety of K. is K., which is classified as physical. quantities, such as length, time, force, mass (for example, the rest mass of an electron), or more complex quantities, numerically expressible through the relationships between these quantities or their powers, such as volume, speed, work, etc. .P. (eg, acceleration of gravity at the Earth's surface). Those from K. of this kind, which are considered in modern times. physics (within the framework of its corresponding theories) that are significant for the entire observable part of the Universe, called. world (or universal) K.; Examples of such quantum parameters are the speed of light in vacuum, Planck’s quantum constant (i.e., the value of the so-called quantum of action), the gravitational constant, etc. Science drew attention to the great importance of world quantum constants in the 20–30s. 20th century At the same time, certain foreign scientists (English physicist and astronomer A. Eddington, German physicist Heisenberg, Austrian physicist A. March, etc.) tried to give them an idealistic approach. interpretation. Thus, Eddington saw in the system of world cosmos one of the manifestations of independence. existence of ideal mathematical forms expressing the harmony of nature and its laws. In fact, universal K. do not reflect an imaginary self. the existence (outside of things and knowledge) of the indicated forms, and (usually expressed mathematically) the fundamental laws of objective reality, in particular the laws associated with the structure of matter. Deep dialectical. The meaning of the world's principles is revealed in the fact that some of them (Planck's quantum constant, the speed of light in vacuum) are a kind of scales that delimit different classes of processes that proceed in fundamentally different ways; at the same time, such K. indicate the presence of a definition. connections between the phenomena of these classes. Thus, the connection between the laws of classical and relativistic mechanics (see Relativity theory) can be established from considering such a limiting transition of the equations of motion of relativistic mechanics into the equations of motion of classical. mechanics, which is associated with idealization, which consists in abandoning the idea of the speed of light in emptiness 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 transform into the equations of motion of classical theory. mechanics, etc. In addition to these most important K., defined purely physically and appearing in the formulations of many basic principles. laws of nature, those defined purely mathematically, K., as the numbers 0, are widely used there; 1; ? (ratio of circumference to diameter); e (base of natural logarithms); Euler's constant, etc. K. are no less often used, which are the results of well-known mathematical studies. operations on specified complexes. But the more difficult it is to express a frequently used complex through more simply defined complexes (or the simplest complexes such as 0 and 1) and known operations, the more independent is its participation in the formulations of those laws and relations in the more frequently it occurs, the more often special drugs are introduced for it. designation, calculate or measure it as accurately as possible. Some of the quantities occur occasionally and are Q. only within the framework of consideration of a certain problem, and they can even depend on the choice of conditions (parameter values) of the problem, becoming Q. only when these conditions are fixed. Such quantities are often denoted by the letters C or K (without associating these designations once and for all with the same quantity) or simply write that such and such a quantity = const. A. Kuznetsov, I. Lyakhov. Moscow. In cases where in mathematics or logic the role of the objects under consideration is played by functions, those of them are called the ones whose value 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. An example of a logical algebra function that is a K. is A/A (considered as a function of the “variable statement” A), since 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 “truth” conventionally identified with it). An example of a more complex function 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 appears as a K. (more precisely, as a function that is a K.). Any selected letter variables (for example, A, B, x, y, etc.) can be considered as arguments to this function, since she doesn't depend on them anyway. In other cases, such identification of a function that is a K. is not made with its meaning, i.e. distinguish between two arguments, one of which has a variable among its arguments, which the other does not. This allows, for example, to define a function as its table, and also simplifies the schematic. definition of certain operations on functions. Along with such codes, the values of which are numbers (maybe named) or are characterized by numbers, there are also other codes. For example, in set theory, an important code is the natural series N, i.e. the set of all non-negative integers. numbers. The value of a function, which is a 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 will be the set of all prime numbers. In addition to physical quantities and functions in the role of such objects, some of which turn out to be symbols, they often (especially in logic and semantics) consider signs and their combinations: words, sentences, terms, formulas, etc., and as meaning those of them whose meanings are not particularly discussed, their semantic meanings (if any). At the same time, new Ks are revealed. So, in arithmetic. The expression (term) 2+3–2 K contains not only the numbers 2 and 3 and the results of operations on them, but also the signs + and –, the meanings of which are the operations of addition and subtraction. These signs, being K. within the framework of theoretical considerations of ordinary school arithmetic and algebra cease to be K. when we enter the wider area of modern science. 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, during 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. Isolation of logical. K. plays a special role when applied to natural objects. language. In the role of logical K. in Russian language, for example, such conjunctions as “and”, “or”, etc., such quantifier words as “all”, “everyone”, “exists”, “some”, etc., such linking verbs, such 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 highlighting logical. K. in natural language is the recognition of the sameness 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 different from those identified by the principles are replaced by the corresponding variables. The smaller the number of schemes that can cover all the considered cases of reasoning, the simpler these schemes themselves are, and the more we are guaranteed against the possibility of erroneous reasoning based on them, the more justified is the choice of the logical logics 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, Leningrad–M., 1932; Born M., Mysterious number 137, in: Advances in Physics. Sciences, vol. 16, no. 6, 1936; Heisenberg W., Philos. problems of atomic physics, M., 1953; his, Planck's discovery and fundamentals. Philosopher questions of the doctrine of atoms, "Problems of Philosophy", 1958, No. 11; him, Physics and Philosophy, M., 1963; Sat. Art. in mathematics logic and its applications to certain issues of cybernetics, in the book: Tr. math. Institute, t. 51, M., 1958; Kuznetsov I.V., What is Werner Heisenberg right and what is wrong, “Questions of Philosophy”, 1958, No. 11; Uspensky V.?., Lectures on computable functions, M., 1960; Kaye, J. and Laby, T., Phys. Tables. and chem. permanent, trans. 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 knowledge, M., 1962, ch. 3; ?ddington A. St., New pathways in science, Camb., 1935; his, Relativity theory of protons and electrons, L., 1936; by him, 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.
Let's return to the ammonia production process, expressed by the equation:
N 2 (g) + 3H 2 (g) → 2NH 3 (g)
Being in a closed volume, nitrogen and hydrogen combine and form ammonia. How long will this process last? It is logical to assume that until any of the reagents runs out. However, in real life this is not entirely true. The fact is that some time after the reaction has begun, the resulting ammonia will begin to decompose into nitrogen and hydrogen, i.e., a reverse reaction will begin:
2NH 3 (g) → N 2 (g) + 3H 2 (g)
In fact, in a closed volume, two reactions, directly opposite to each other, will take place at once. Therefore, this process is written by the following equation:
N 2 (g) + 3H 2 (g) ↔ 2NH 3 (g)
A double arrow indicates that the reaction is going in two directions. The reaction of nitrogen and hydrogen combining is called direct reaction. Ammonia decomposition reaction - backlash.
At the very beginning of the process, the rate of direct reaction is very high. But over time, the concentrations of the reagents decrease, and the amount of ammonia increases - as a result, the rate of the forward reaction decreases, and the rate of the reverse reaction increases. There comes a time when the rates of forward and reverse reactions are compared - chemical equilibrium or dynamic equilibrium occurs. At equilibrium, both forward and reverse reactions occur, but their rates are the same, so no changes are noticeable.
Equilibrium constant
Different reactions proceed in different ways. In some reactions, a fairly large number of reaction products are formed before equilibrium occurs; in others - much less. Thus, we can say that a particular equation has its own equilibrium constant. Knowing the equilibrium constant of a reaction, it is possible to determine the relative amounts of reactants and reaction products at which chemical equilibrium occurs.
Let some reaction be described by the equation: aA + bB = cC + dD
- a, b, c, d - coefficients of the reaction equation;
- A, B, C, D - chemical formulas of substances.
Equilibrium constant:
[C] c [D] d K = ———————— [A] a [B] b
Square brackets indicate that the formula involves molar concentrations of substances.
What does the equilibrium constant say?
For the synthesis of ammonia at room temperature K = 3.5·10 8. This is a fairly large number, indicating that chemical equilibrium will occur when the ammonia concentration is much greater than the remaining starting materials.
In actual ammonia production, the technologist’s task is to obtain the highest possible equilibrium coefficient, i.e., so that the direct reaction proceeds to completion. How can this be achieved?
Le Chatelier's principle
Le Chatelier's principle reads:
How to understand this? Everything is very simple. There are three ways to upset the balance:
- changing the concentration of the substance;
- changing the temperature;
- changing the pressure.
When the ammonia synthesis reaction is in equilibrium, it can be depicted as follows (the reaction is exothermic):
N 2 (g) + 3H 2 (g) → 2NH 3 (g) + Heat
Changing concentration
Let's introduce additional nitrogen into a balanced system. This will upset the balance:
The forward reaction will begin to proceed faster because the amount of nitrogen has increased and more of it reacts. After some time, chemical equilibrium will occur again, but the nitrogen concentration will be greater than the hydrogen concentration:
But, it is possible to “skew” the system to the left side in another way - by “lightening” the right side, for example, by removing ammonia from the system as it forms. Thus, the direct reaction of ammonia formation will again predominate.
Changing the temperature
The right side of our “scales” can be changed by changing the temperature. In order for the left side to “outweigh”, it is necessary to “lighten” the right side - reduce the temperature:
Changing the pressure
It is possible to upset the equilibrium in a system using pressure only in reactions with gases. There are two ways to increase pressure:
- reducing the volume of the system;
- introduction of inert gas.
As pressure increases, the number of molecular collisions increases. At the same time, the concentration of gases in the system increases and the rates of forward and reverse reactions change - the equilibrium is disturbed. To restore balance, the system “tries” to reduce the pressure.
During the synthesis of ammonia, two molecules of ammonia are formed from 4 molecules of nitrogen and hydrogen. As a result, the number of gas molecules decreases - the pressure drops. As a consequence, in order to reach equilibrium after increasing pressure, the rate of the forward reaction increases.
Summarize. According to Le Chatelier's principle, ammonia production can be increased by:
- increasing the concentration of reagents;
- reducing the concentration of reaction products;
- reducing the reaction temperature;
- increasing the pressure at which the reaction occurs.
