Thermodynamic systems and processes. standard condition
A standard state of matter is a state of matter conditionally chosen as a standard for comparison. The standard state of a pure liquid or solid (crystalline) substance is its most stable physical state at a given temperature and normal atmospheric pressure. As a standard state for gases, a hypothetical state is taken in which the gas, being at a pressure of 1.013 10 5 Pa, obeys the laws of ideal gases, and its enthalpy is equal to the enthalpy of a real gas.
To determine the standard enthalpy of reaction, use the consequences of Hess's law:
Consequence 1: The standard enthalpy of a chemical reaction is equal to the difference between the standard enthalpies of formation of reaction products and reagents (taking into account stoichiometric coefficients):
The standard enthalpy (heat) of formation of a substance at a given temperature is the enthalpy of the reaction of formation of one mole of this substance from elements that are in the most stable standard state. According to this definition, the enthalpy of formation of the most stable simple substances in the standard state is 0 at any temperature. Standard enthalpies of formation of substances at a temperature of 298 K are given in reference books.
2 consequence. The standard enthalpy of a chemical reaction is equal to the difference between the enthalpies of combustion of the reactants and reaction products (taking into account stoichiometric coefficients):
The standard enthalpy (heat) of combustion of a substance is called the enthalpy of the reaction of complete oxidation of one mole of a substance.
3rd consequence: The enthalpy of a chemical reaction is equal to the difference between the energies of the broken and formed chemical bonds.
79. Dependence of the total vapor pressure on the composition of the liquid and vapor. 1 Konovalov's law. Distillation.
Imagine that a certain substance B is introduced into the equilibrium system liquid A - vapor. When a solution is formed, the mole fraction of the solvent X A becomes less than one; the equilibrium in accordance with the Le Chatelier-Brown principle shifts towards the condensation of substance A, i.e. in the direction of decreasing saturated vapor pressure P A. It is obvious that the smaller the mole fraction of component A in the solution, the lower the partial pressure of its saturated vapors over the solution. For some solutions, the following regularity, called Raoult's first law, holds true:
The partial pressure of the saturated vapor of a solution component is directly proportional to its mole fraction in the solution, and the proportionality coefficient is equal to the saturated vapor pressure over the pure component.
Since the sum of the mole fractions of all components of the solution is equal to one, for a binary solution consisting of components A and B it is easy to obtain the following ratio, which is also the formulation of Raoult's first law:
(2)
The relative decrease in the vapor pressure of the solvent over the solution is equal to the mole fraction of the solute and does not depend on the nature of the solute.
Solutions for which Raoult's law holds are called ideal solutions. Ideal at any concentration are solutions whose components are similar in physical and chemical properties (optical isomers, homologues, etc.) and whose formation is not accompanied by volumetric and thermal effects. In this case, the forces of intermolecular interaction between homogeneous and dissimilar particles are approximately the same, and the formation of a solution is due only to the entropy factor. Solutions, the components of which differ significantly in physical and chemical properties, obey Raoult's law only in the region of infinitesimal concentrations.
Vapor pressure of ideal and real solutions
If the components of a binary (consisting of two components) solution are volatile, then the vapor above the solution will contain both components (the relative content of the components in the vapor will, as a rule, differ from their content in the solution - the vapor is relatively richer in the component whose boiling point is lower). Consider a binary solution consisting of components A and B, which are infinitely soluble in each other. The total vapor pressure, according to Raoult's first law, is
Thus, for ideal binary solutions, the dependence of the total and partial pressure of saturated vapor on the composition of the solution, expressed in mole fractions of component B, is linear at any concentration (Fig. 3.3). Such systems include, for example, benzene-toluene, hexane-heptane systems, mixtures of isomeric hydrocarbons, etc.
Rice. 1 Dependence of partial and total vapor pressures
ideal solution on concentration
For real solutions, these dependences are curvilinear. If the molecules of a given component interact more strongly with each other than with the molecules of another component, then the true partial vapor pressures over the mixture will be greater than those calculated using Raoult's first law (positive deviations). If homogeneous particles interact with each other weaker than heterogeneous particles, the partial vapor pressures of the components will be less than the calculated ones (negative deviations). Real solutions with positive vapor pressure deviations are formed from pure components with heat absorption (ΔН solution > 0), solutions with negative deviations are formed with heat release (ΔН solution< 0).
Rice. Fig. 2. Dependence of partial and total vapor pressures of ideal (dashed line) and real (solid line) binary solutions on composition for positive (left) and negative (right) deviations from Raoult's law.
Konovalov's first law
Konovalov's first law (1881) describes the fractional distillation process:
Saturated steam is enriched with a component compared to the equilibrium solution, the addition of which to the system increases the total vapor pressure
Distillation is the evaporation of a liquid, followed by cooling and condensation of vapors. Simple distillation - partial evaporation of a boiling liquid mixture by continuous removal and condensation of the resulting vapors in the refrigerator. The resulting condensate is called the distillate, and the unevaporated liquid is called the bottoms. Fractional distillation (or fractional distillation) is the separation of multicomponent liquid mixtures into fractions that differ in composition. It is based on the difference in the compositions of a multicomponent liquid and the vapor formed from it. It is carried out by partial evaporation of the volatile components of the initial mixture and their subsequent condensation. The first (low-temperature) fractions of the resulting condensate are enriched in low-boiling components, the rest of the liquid mixture is high-boiling. To improve the separation of fractions, a reflux condenser is used.
Chapter 9. Thermodynamic properties of individual substances. standard state of matter
9.1. Enthalpy reference system. Formulas for calculating enthalpies.
It is impossible to find the absolute values of enthalpies and internal energies by thermodynamic methods, but only their changes can be determined. At the same time, in thermodynamic calculations of chemically reacting systems, it is convenient to use a single frame of reference. In this case, since the enthalpy and internal energy are related by the relation , it is sufficient to introduce a frame of reference for only one enthalpy. In addition, in order to compare and systematize the thermal effects of chemical reactions, which depend on the physical state of the reacting substances and on the conditions for the occurrence of XP, the concept of the standard state of matter is introduced. On the recommendation of the commission on thermodynamics of the International Union of Pure and Applied Chemistry (IUPAC) in 1975, the standard state is defined as follows:
“The standard state for gases is the state of a hypothetical ideal gas at a pressure of 1 physical atmosphere (101325 Pa). For liquids and solids, the standard state is the state of a pure liquid or, respectively, a pure crystalline substance at a pressure of 1 physical atmosphere. For substances in solutions, the standard state is taken to be the hypothetical state in which the enthalpy of a one-molar solution (1 mol of substance in 1 kg of solvent) would be equal to the enthalpy of the solution at infinite dilution. The properties of substances in standard states are denoted by the superscript 0. (A pure substance is a substance consisting of identical structural particles (atoms, molecules, etc.)).
This definition refers to the hypothetical states of a gas and a solute, since in real conditions the states of gases differ to a greater or lesser extent from the ideal, and the states of solutions differ from the ideal solution. Therefore, when using the thermodynamic properties of substances in standard states for real conditions, corrections are introduced for the deviation of these properties from real ones. If these deviations are small, then corrections can be omitted.
In handbooks, thermodynamic quantities are usually given under standard conditions: pressure R 0 =101325Pa and temperature T 0 =0K or T 0 \u003d 298.15K (25 0 C). When creating tables of total enthalpies of substances, their standard state at a temperature T 0 =0K or T 0 = 298.15K.
Substances, which are clean chemical elements in the most stable phase condition at R 0 \u003d 101325 Pa and the temperature of the reference point of enthalpies T 0, take the value enthalpy equal to zero: 
. (For example, for substances in the gaseous state: O 2, N 2, H 2, Cl 2, F 2, etc., for C (graphite) and metals (solid crystals)).
For chemical compounds(CO 2, H 2 O, etc.) and for substances that, being pure chemical elements, not in the most stable state(O, N, etc.) enthalpy at R 0 =101325Pa and T 0 not equal to zero: 
.
Enthalpy chemical compounds at R 0 and T 0 relies equal to the thermal effect of formation them from pure chemical elements with these parameters, i.e. 
. So, at T 0 \u003d 0K: 
and at T 0 \u003d 298.15K: 
.
The enthalpy of any substance at a temperature T will be equal to the amount of heat that must be supplied in the isobaric process so that from pure chemical elements at a temperature T 0 get a given substance and heat it from temperature T 0 to temperature T, i.e. the formula for calculating the enthalpy of any substance is:
, or in a more compact notation we have:
,
where the superscript "o" means that the substance is in the standard state at R 0 =101325Pa; 
is the enthalpy of formation of a substance at a temperature T 0 from pure chemical elements; 
=
is the excess enthalpy associated with the heat capacity of the substance, 
- total enthalpy, taking into account the enthalpy of formation of the substance.
For T 0 = 0:
,
For T= 298.15 K:
Scheme for calculating enthalpy at temperature T can be represented as:
The reference book for various individual substances presents the values: 
and excess enthalpy 
for different temperatures T.
Since the excess enthalpy 
in the tables of individual substances is not given, then to the left side of the expression for 
at T 0 \u003d 298.15K, it is necessary to add and subtract the heat of formation of a substance 
at a temperature T 0 = 0K. Then we get the excess enthalpy 
, which is given in the tables, and an additional term 
, equal to the difference in the heats of formation at temperatures T 0 =298K and T 0=0K; those. . Then we have:
Total enthalpies calculated using the ratios for T 0 = 0K and T 0 \u003d 298.15K have the same numerical values \u200b\u200bfor a given substance at a given temperature T.
Reduced Gibbs energy and its relationship with other thermodynamic quantities
Reduced Gibbs energy for 1 mole of a substance in the standard state 
is introduced by the following relation:
[J/molK] (1)
where 
- molar Gibbs free energy at standard pressure, J/mol; 
is the enthalpy of formation of a substance at T\u003d 0 K from simple chemical elements: 
is a state function and depends only on temperature.
Take the derivative of () with respect to temperature at p=const:
(2)
In equation (2), the derivative of the Gibbs energy with respect to temperature is
, (3)
and the value 
is by definition equal to
(4)
Substituting (3) and (4) into (2) we get
(5)
(6)
The first derivative of the reduced Gibbs energy with respect to temperature gives the excess enthalpy. For practical problems, it is much more convenient to take the derivative with respect to the temperature logarithm, given that dT=Td ln T. Then we have
(7)
We write expression (6) as 
(8)
The second derivative of 
by temperature at R=const gives heat capacity
=
(9)
or 
(10)
Dependencies (6), (7), (9) and (10) for ( 
)/T and 
are used to obtain temperature approximations of the thermodynamic properties of individual substances. The molar entropy at standard pressure is also expressed in terms of the reduced Gibbs energy:
(11)
Representation of the thermodynamic properties of individual substances in the reference literature
In the reference book edited by V.P. Glushko for the 1st mole of each individual substance in the standard state, depending on the temperature, tables of values are given in the interval t 0 from 100K to 6000K:
- isobaric heat capacity, J/molK;
is the reduced Gibbs energy, J/molK;
- entropy, J/molK;
- excess enthalpy, kJ/mol;
, where K 0 is the equilibrium constant of XP decay of a given substance AT into gaseous atoms, a dimensionless quantity. Substance decay formula: 
, where 
- number of atoms 
in a molecule of matter AT.
For example: 
.
Values are given:
- thermal effect of the decomposition reaction of substance B into gaseous atoms at T 0 = 0K, kJ / mol;
- enthalpy of formation of a substance from pure chemical elements (heat effect of formation) at T 0 =0K, kJ/mol;
- enthalpy of formation of a substance at T 0 =298.15K, kJ/mol;
M - relative molecular weight, dimensionless value;
- the nuclear component of the entropy of a substance, which depends on the isotopic composition of the substance and does not change during XP, J/molK. The value does not affect Practical functions are given in the handbook without taking into account 
.
The handbook provides approximations of the reduced Gibbs energy as a function of temperature in the form of a polynomial for each individual substance.
Approximation ( T) depending on the temperature is represented as a polynomial:
where x = T 10 -4 K; φ , φ n (n=-2, -1, 0, 1, 2, 3) – approximation coefficients for the temperature range T min T T max ,( T min = 500K, T max =6000K).
Using the approximation coefficients φ , φ n the excess enthalpy and heat capacity of a substance can be calculated:
as well as the molar entropy: 
For a complete assignment of all thermodynamic properties of individual substances of chemically reacting systems at a temperature T for calculations on a computer when choosing T 0 = 298.15K, you must enter the following values:
those. 13 parameters in total, where .
When choosing T 0
= 0K value 
and 
should be excluded from the list. Then there are 11 parameters left: 
(7 odds) 
. Thus, in thermodynamic calculations of rocket and aircraft engines, it is advisable to choose the temperature of the enthalpy reference point T 0 = 0K.
9.4. Calculation of the Gibbs free energy and entropy of matter at a pressure different from the pressure under standard conditions
Molar enthalpy 
, heat capacity 
and internal energy 
depend only on temperature:
Molar entropy 
, Gibbs free energy 
, Helmholtz free energy 
depend on temperature and pressure.
Let's establish a connection between the quantities: 
and their values in the standard state 
which are determined using reference materials.
Let us first obtain an expression for the Gibbs free energy. From the combined expression of the 1st and 2nd laws of thermodynamics for a simple, closed TS and for reversible processes for 1 mole of a substance, we have:
At T=
const( dT= 0) we get 
, where 
. Where after integration for the final process in the pressure range from R 0 to R we have
, or 
(1)
where 
-molar Gibbs free energy at R 0 \u003d 1 physical atm, 
- the same with pressure 
. Dependence (1) is valid for gaseous and condensed substances at T= const.
For an ideal gas, 
. Consequently, 
and the integral in (1) will be equal to 
. Denoting through 
dimensionless pressure; where R 0 = 101325Pa; ~ tilde, we obtain for an ideal gas a formula for calculating the Gibbs free energy at pressure p≠r 0:
If the substance is in a gas mixture, then for i th component of a mixture of ideal gases, we have:
where is the normalized partial pressure 
and normalized mixture pressure 
related by the ratio 
, taking into account the molar fraction 
i-th gas, 
, and the pressure of the gas mixture is determined by the Dalton law 
.To get the formula for calculation 
, expressed in terms of mole fractions, we represent formula (3) as:
Let us denote the Gibbs molar free energy i th gas at mixture pressure. Then we get
The molar Gibbs free energies of condensed substances do not depend on pressure, since their volumes can be neglected in comparison with the volumes of gaseous components. Then the formula for calculating 
condensed substances will take the form:
where X i– mole fraction i-th substance relative to the phase in which it is located (to the number of moles of its phase), 
is the molar Gibbs free energy of a pure condensed matter, at p=
p 0 =101325Pa.
The effect of pressure on entropy can be determined from the expression for the Gibbs molar free energy for i th component of an ideal gas at pressure p ≠p 0
from which it follows that
(7)
After substituting (8) into (7) and taking into account that 
, we get:
For the i-th component of the condensed matter, by analogy with expression (9), one can obtain a formula for calculating the entropy at p ≠p 0
Value 
- taken from the handbook R 0
=101325 Pa.
9.5. Calculation of Gibbs free energy for real gases and solutions. Volatility and activity
When calculating the Gibbs molar free energy for real gases and solutions, you can use the formulas obtained for ideal gases and solutions. At the same time, partial pressures p i are replaced by the value of volatility f i [Pa] and mole fractions x i- on activity a i. Volatility is the pressure, determined from the equation of state for real gases, which has the same effect on the system as in the case of an ideal gas. Actually f i is the corrected pressure, which characterizes the deviation of the thermodynamic system from the ideal state described by the equation of state for an ideal gas.
Thus, for real gases, the value of the Gibbs molar free energy will be determined by the expression
where 
, 
composition). As the state of a real gas approaches the state of an ideal gas, volatility 
tends to partial pressure 
. For an ideal gas f i =
p i(at low pressures).
Activity a i(dimensionless quantity) is the corrected mole fraction x i, which characterizes the deviation of the condensed system from the ideal state. As the real solution approaches the ideal state, the activity a i tends to the molar fraction x i. For weak solutions a i =x i . Thus, for real solutions
The described method for calculating the Gibbs free energy was proposed by the American physical chemist Lewis G.N. (1875-1946).
In thermodynamics, the concepts of fugacity coefficients are also used 
and activities 
. For ideal gases and solutions 
.
9.6. Third law of thermodynamics, and by isothermal expansion of the working fluid, since the working fluid ceases to give off heat to the environment, because states Calculation of pressure drop in system ship's gas outlet, when using a shore gas outlet for ...
Thermodynamics of real processes
Document... system called free enthalpy. For more details on this feature, see the following chapter ... states shielding for this substance flow. Formulas(222) and (223) are valid forsystems... specific thermodynamicproperties ...
In systems with chemical processes, the main reason for the change in thermodynamic parameters is chemical reactions. Since chemical transformations are very diverse, the problem of choosing the origin of energy values, for example, thermodynamic potentials, arises. To this end, in thermodynamics, concepts such as standard states and standard conditions. Given that in chemical reactions the elements do not rotate into each other, the totality of all chemical elements in the form of simple substances that are in more stable forms at 25 ° C is taken as the reference zero. This selected a set of simple substances forms a basis for carrying out thermodynamic calculations, and each simple substance included in the basis is the basis substance. To perform thermodynamic calculations, the parameters of the substance in the standard state are used.
The standard state is chosen in accordance with the IUPAC recommendation as follows:
1) the temperature of a substance in the standard state is equal to the temperature of the system: T \u003d T (system);
2) the pressure above the substance or the pressure of the gaseous substance in the standard state (P 0) is 1 bar:
P= P 0 = 1 bar
(1 bar = 10 5 Pa). (Pascals have been recommended for use by IUPAC since 1982.) Previously, one atmosphere was used as the standard state (1 atm = 101325 Pa). Although the differences in units are small, it is recommended to pay attention to the pressure units.
3) For liquid and solid substances, real states are taken at P 0 \u003d 1 bar and temperature T. (Sometimes substances in hypothetical states are also taken into consideration - for example, water in the form of a gas at a pressure of 1 bar at a temperature below 100 ° C or in the form ice at 25°C.)
Thermodynamic quantities characterizing substances in the standard state are called standard, and a superscript is used to designate them, for example.
As used, 298.15 K (25°C).
The standard enthalpy and Gibbs energy of formation of substance A is usually understood as the change in enthalpy and Gibbs energy in the reaction:
Where are the basic substances.
The index f comes from the English word formation. It is used to denote the reaction of the formation of a substance from simple basic substances. If the substances and A are under standard conditions, then one speaks of the standard enthalpy, standard entropy and standard Gibbs energy of formation under standard conditions:
For basic substances in any standard states take =0 kJ/mol and =0 kJ/mol. Usually, the calculation of thermodynamic parameters at any temperature is based on the use of standard states under standard conditions, for which kJ/mol and kJ/mol are also assumed. The tables usually give the values of the standard enthalpies of formation of compounds from simple basic substances under standard conditions with designations per mole of formed substance A.
Chemical reactions are used not only to obtain final products. It is very often important to know how much heat can be obtained by burning a particular type of fuel, how much work can be obtained during various chemical reactions. Of great importance is also the preliminary solution of the question of the fundamental possibility of the occurrence of a particular reaction. All this can be done by carrying out special calculations based on knowledge of the thermodynamic parameters of the substances involved in the chemical process. Since chemical transformations are very diverse, and more than 100 chemical elements can participate in reactions, the problem arises of choosing the origin of thermodynamic quantities. For this purpose, thermodynamics widely uses the concepts standard states and standard conditions.
An important feature of chemical reactions is that during the course of the reaction, various chemical elements do not turn into each other. This means that to set the reference point for thermodynamic quantities, one can take all chemical elements in standard states, exactly the same both in relation to the starting materials and in relation to the reaction products.
In the previous section, it was shown that the values of the energy parameters of chemical processes generally depend on the reaction path. These are, for example, the heat of the process or the work of the process. But nevertheless, there are conditions when the heat and work of the process are uniquely determined by setting the final and initial states. Wherein processes must occur at a constant volume or pressure. The temperature of the system at the end of the process must be the same as the temperature at the beginning of the process. In such cases, the scheme for carrying out thermodynamic calculations looks especially simple, as follows from Fig. 11.1.
Change in thermodynamic parameter in a reaction
starting substances -» final substances
is equal to the difference between the corresponding parameters for the formation of final and initial substances. For example, the enthalpy change in a reaction is
Similarly, the change in the reaction and other quantities is calculated. For entropy, the absolute values of substances are used
Designation of thermodynamic quantities in fig. 11.1 is provided with additional indices. Index "o" indicates that the value under consideration characterizes the standard state of matter.
The index "g" comes from the English word reaction and will be widely used in the future to characterize quantities that change in reactions. Index "f" (formation) indicates a change in the considered value in the reaction of the formation of a compound from simple substances. However, the use of the index "r" (or "f") has another important function: a change in some thermodynamic quantity, written as A g M, characterizes
Rice. 11.1. Scheme for calculating the thermodynamic parameters of chemical reactions rate of change M in a response with a change by one for a very large system, when the changes do not affect the properties of the system. In other words, quantities with the index "r" (or "f") characterize the differential properties of the system:
and for example
while keeping the system parameters unchanged (except for the value?). So, AM is the change in the value of M, a A x M - the rate of change of the value of M with the depth of the reaction. The value of A x M characterizes the tangent of the slope of the curve of the dependence of M on ?,.
The values necessary for calculations are taken directly from thermodynamic tables, which are created on the basis of experimental and theoretical data.
As a single reference zero, a set of all chemical elements in the form of simple substances that are in the most stable forms at 25 ° C is currently used. For example, carbon is taken in the form of graphite, bromine is taken in the form of a liquid. Exceptions are made for phosphorus and tin. For phosphorus, white phosphorus (compound P 4) is taken as the basic substance, and for tin, white tin ((3-tin), since these substances are more accessible. Selected a set of simple substances forms a basis for thermodynamic calculations, and each simple substance included in the basis is basic substance.
To perform thermodynamic calculations, the parameters of the substance are used in standard states, which, in accordance with the IUPAC recommendation (for use since 1982), are selected as follows:
1. The temperature of a substance in the standard state is equal to the temperature of the system:
2. Pressure over a substance in the standard state or pressure of a gaseous substance in the standard state (p°) equals 1 bar:
Until 1982, a pressure of one atmosphere was used as the pressure in the standard state (1 atm = 101325 Pa). Although the possible differences in the reference data are small, it is still recommended to pay attention to the system of units used for pressure in the standard state.
- 3. For gaseous substances, hypothetical states in the form of ideal gases are chosen as standard states.
- 4. For liquid and solid substances, real states are taken at p°= 1 bar and temperature T.
- 5. Sometimes hypothetical states of matter are introduced into consideration, for example, water in the form of a gas at a pressure of 1 bar and a temperature below 100 °C, or in the form of ice at 25 °C.
- 6. Thermodynamic quantities characterizing substances in standard states are called standard.
It is said that substances in standard states at a temperature T° = 298.15 K are found under standard conditions. Please note that you should not confuse standard states and standard conditions: standard conditions possible at any temperature, standard conditions refer only to temperature 25 °C.
It should be noted that other standard states are sometimes used in practice, if this seems more convenient. For solid and liquid substances, the concept of the standard state is often used at any pressure, and not just at p°= 1 bar. To designate standard values related to such standard conditions, we will use the superscript "*" (for example, AN*).
For mixtures and solutions, the state of an ideal mixture or solution with a concentration of a substance equal to unity (molarity or molality) is used as a standard.
Sometimes states with T= Dsystems) and V= And ' = 1 l.
Common abbreviations
d - gas, gaseous state of matter
g - liquid, liquid state of matter
t - solid state of matter (in this manual, t is equivalent to the crystalline state, since the non-crystalline state of a solid is not considered within the program)
aq is the dissolved state, and the solvent is water (from the word aqueous- water)
EMF - electromotive force
Comments
Standard state in thermodynamics. The standard states are as follows:
for a gaseous substance, pure or in a gas mixture, the hypothetical state of a pure substance in the gas phase, in which it has the properties of an ideal gas and standard pressure R°. In this manual, it is accepted R° \u003d 1.01325 × 10 5 Pa (1 atm).
for a pure liquid or solid phase, as well as for a liquid solution solvent - the state of a pure substance in the corresponding state of aggregation under standard pressure R°.
for a solute in a solid or liquid solution, the hypothetical state of that substance in a solution with a standard concentration FROM°, which has the properties of an infinitely dilute solution (for a given substance) under standard pressure R°. Standard concentration accepted FROM° \u003d 1 mol / dm 3.
Choice of stoichiometric coefficients. The stoichiometric coefficients of a chemical reaction show the molar ratio in which these substances react with each other. For example, in the reaction A + B \u003d Z, the stoichiometric coefficients of the reactants are equal (in absolute value), from which it follows that 1 mol A reacts without residue with 1 mol B to form 1 mol Z. The meaning of this entry will not change if choose any other equal coefficients. For example, the equation 2A + 2B = 2Z corresponds to the same stoichiometric ratio between the reactants. Therefore, in the general case, the coefficients n i any reaction are defined up to an arbitrary common factor. However, in different sections of physical chemistry, different conventions are adopted regarding the choice of this factor.
In thermochemistry, in the reactions of the formation of substances from simple substances, the coefficients are chosen so that the coefficient 1 stands in front of the formed substance. For example, for the formation of hydrogen iodide:
1/2H 2 + 1/2I 2 = HI
In chemical kinetics, the coefficients are chosen to match, if possible, the reaction orders for the respective reactants. For example, the formation of HI is first order in H 2 and first order in I 2 . Therefore, the reaction is written as:
H 2 + I 2 ® 2HI
In the thermodynamics of chemical equilibria, the choice of coefficients is generally arbitrary, but depending on the type of reaction, preference may be given to one or another choice. For example, to express the equilibrium constant of acid dissociation, it is customary to choose the coefficient in front of the acid symbol equal to 1. In particular, for the acid dissociation of hydrogen iodide, choose
HI H + + I –
(coefficient before HI is 1).
Concentration designations. With the same symbol, the concentration or content of a component in a mixture can have a different meaning. The concentration can be equilibrium (one that is reached at equilibrium), current (one that exists at a given time or at a given stage of the process) and gross or "analytical". These concentrations may vary. For example, if you prepare a solution of acetic anhydride (CH 3 CO) 2 O in water, taking 1 mol of 100% acetic anhydride and diluting it with water to 1 liter, then the resulting solution will have a gross or analytical concentration FROM\u003d 1 mol / l (CH 3 CO) 2 O. In fact, acetic anhydride undergoes irreversible hydrolysis to acetic acid (CH 3 CO) 2 O + H 2 O ® 2CH 3 COOH, therefore its current concentration decreases from 1 mol / l to initial time to an equilibrium concentration of approximately 0 mol/l at the end of the reaction. On the other hand, based on the complete hydrolysis of the anhydride, we can say that the total concentration of the solution is 2 mol/l CH 3 COOH (regardless of the stage of the hydrolysis process). However, the reaction product is subject to acid dissociation of CH 3 COOH CH 3 COO - + H +, so that the real concentrations in the solution, including the real concentration of CH 3 COOH, are not equal to any of the gross ones. The real concentrations of CH 3 COOH, CH 3 COO - and H + at equilibrium are called equilibrium. Chemists often use the same notation FROM for all these kinds of concentrations, assuming that the meaning of the designation is clear from the context. If you want to emphasize the difference, then the following notation is usually used for molar concentrations : FROM is the gross or analytical concentration, [A] is the current or equilibrium concentration of component A, and (sometimes) [A]e is the equilibrium concentration of component A. This index makes the writing of equilibrium constants, such as
