Man, individual and personality are the key concepts of psychology, which are no less ...
Lewis and Randall introduced some mathematical corrections to the relations proposed by Arrhenius.
To bring theory into line with practice and preserve many convenient relations previously obtained on the basis of the Arrhenius theory, it was proposed to use instead of the concentrations activity... Then all thermodynamic relations, written in the form of equations for ideal solutions, but containing not concentrations, but activities, strictly agree with the results of experimental measurements.
G. Lewis and M. Randall proposed a method of using activities instead of concentrations, which made it possible to formally take into account all the variety of interactions in solutions without taking into account their physical nature.
In electrolyte solutions, both cations and anions of the solute are simultaneously present. It is physically impossible to introduce ions of only one kind into the solution. Even if such a process were feasible, it would cause a significant increase in the energy of the solution due to the introduced electric charge.
The connection between the activities of individual ions and the activity of the electrolyte as a whole is established based on the condition of electroneutrality. For this, the concepts are introduced average ionic activity and average ionic activity coefficient.
If an electrolyte molecule dissociates into n + cations and n - anions, then the average ionic activity of the electrolyte is a ±is equal to:
where and is the activity of cations and anions, respectively, n is the total number of ions ( n \u003d n + + n -).
Similarly, the average ionic activity coefficient of the electrolyte is recorded: characterizing the deviation of the real solution from the ideal
Activity can be thought of as the product of concentration and activity coefficient. There are three scales of expression of activities and concentrations: molality (molality, or practical scale), molarity from (molar scale) and molar fraction x (rational scale).
In the thermodynamics of electrolyte solutions, the molal concentration scale is usually used.
where is the coefficient depending on the valence type of the electrolyte.
((So, for a binary 1,1-charged electrolyte (, etc.)
For a 1.2-charge electrolyte (etc.) n + \u003d 2, n - \u003d 1, n \u003d 3 and
On a molar scale.))
There is a relationship between the average ionic activity coefficients on the molal and molar scales:
whereis the density of the pure solvent. (end of self-review)
G. Lewis and M. Randall introduced the concept of ionic strength of solutions:
where is the molal concentration of the ith ion; is the ion charge.
They formulated a rule of thumb constancy of ionic strength : in dilute solutions, the activity coefficient of a strong electrolyte of the same valence type is the same for all solutions with the same ionic strength, regardless of the nature of the electrolyte.
This rule is fulfilled at concentrations of no more than 0.02 M.
At higher values \u200b\u200bof the ionic strength, the nature of the interionic interaction becomes more complicated and deviations from this rule arise.
4. Non-equilibrium phenomena in electrolyte solutions. Faraday's laws
Let's digress from the logical narrative to move on to the material for laboratory work.
The patterns considered above were related to the conditions of thermodynamic equilibrium, when the parameters of the systems did not change over time. Electrochemical equilibrium can be disturbed by imposing an electric field on the cell, which causes a directed movement of charged particles (electric current), as well as by changing the concentration of a solute. In addition, chemical transformations of reactants can occur on the surface of the electrodes and in the solution. This mutual transformation of electrical and chemical forms of energy is called electrolysis.
The patterns of electrochemical reactions underlie the development of technologies for the most important processes, such as electrolysis and electroplating, the creation of current sources (galvanic cells and batteries), corrosion protection and electrochemical methods of analysis. In electrochemistry, reduction reactions are commonly called cathodic, and oxidation reactions are called anodic. The ratio between the amount of electricity and the masses of the reacted substances is expressed faraday's laws... (by yourself)
1st law . The mass of a substance that has undergone an electrochemical transformation is proportional to the amount of passed electricity (C):
where - electrochemical equivalent, equal to the mass of the reacted substance when passing a unit of the amount of electricity, r/ Cl.
2nd law. When passing the same amount of electricity, the masses of various substances participating in electrochemical reactions are proportional to their molar masses of equivalents ():
: = : .
The ratio is a constant value and equal faraday constant \u003d 96484 Cl / mol-eq. Thus, when passing through Cl, electricity undergoes an electrochemical transformation of 1 mol-equiv of any substance.
Both Faraday's laws are combined by the formula
where is the current strength, A and is the time, s.
In practice, as a rule, deviations from these laws are observed, arising from the occurrence of side electrochemical processes, chemical reactions, or mixed electrical conductivity. The efficiency of the electrochemical process is evaluated current output
where and is the mass of the practically obtained substance and calculated according to Faraday's law, respectively. Few reactions that run at 100% current efficiency are used in coulometers - devices designed to accurately measure the amount of electricity.
Average ionic activity, activity coefficient, concentration.
The total concentration of ions in a solution is the molar concentration of a dissolved electrolyte, taking into account its degree of dissociation into ions and the number of ions into which an electric stove molecule dissociates in solution.
For strong electrolytes, α \u003d 1, therefore, the total concentration of ions is determined by the molar concentration of the electrolyte and the number of ions into which the strong electrolyte molecule in solution decays.
So, in the case of the dissociation of a strong electrolyte - sodium chloride in an aqueous solution
NaCl → Na + + Cl -
at initial electrolyte concentration from(NaCl) \u003d 0.1 mol / L, the ion concentration turns out to be equal to the same value: c (Na +) \u003d 0.1 mol / L and c (Cl -) \u003d 0.1 mol / L.
For a strong electrolyte of a more complex composition, for example, aluminum sulfate Al 2 (SO 4) 3, the cation and anion concentrations are also easily calculated, taking into account the stoichiometry of the dissociation process:
Al 2 (SO 4) 3 → 2 Al 3+ + 3 SO 4 2-
If the initial concentration of aluminum sulfate from ref \u003d 0.1 mol / L, then s (A1 3+) \u003d 2 0.1 \u003d 0.2 mol / L and from(SO 4 2-) \u003d 3 · 0.1 \u003d \u003d 0.3 mol / l.
Activity and related to overall concentration from formal relationship
where f ˗ activity coefficient.
When from → 0 value a → c, so that f → 1, i.e., for extremely diluted solutions, the activity numerically coincides with the concentration, and the activity coefficient is equal to unity.
Lewis and Randall introduced some mathematical corrections to the relations proposed by Arrhenius.
G. Lewis and M. Randall proposed a method of using activities instead of concentrations, which made it possible to formally take into account all the variety of interactions in solutions without taking into account their physical nature.
In electrolyte solutions, both cations and anions of the solute are simultaneously present. It is physically impossible to introduce ions of only one kind into the solution. Even if such a process were feasible, it would cause a significant increase in the energy of the solution due to the introduced electric charge.
The connection between the activities of individual ions and the activity of the electrolyte as a whole is established based on the condition of electroneutrality. For this, the concepts are introduced average ionic activity and average ionic activity coefficient.
If the electrolyte molecule dissociates into n + cations and n - anions, then the average ionic activity of the electrolyte a ± is equal to:
,
where and is the activity of cations and anions, respectively, n is the total number of ions (n \u200b\u200b\u003d n + + n -).
Similarly, the average ionic activity coefficient of the electrolyte is recorded: characterizing the deviation of the real solution from the ideal
.
Activity can be thought of as the product of concentration and activity coefficient. There are three scales of expression of activities and concentrations: molality (molality, or practical scale), molarity from (molar scale) and mole fraction x(rational scale).
In the thermodynamics of electrolyte solutions, the molal concentration scale is usually used.
Ionic strength is the half-sum of the products of ionic endpoints in solution by the square of their valence.
I \u003d 1 / 2∑zi ^ 2 * mi, where zi is the charge of the ion, mi is the molality of the ion. According to the first approximation D-X (limiting law): logγ ± \u003d −A∣z + z - ∣√I, where I is the ionic strength of the solution,
z + z - charges of ions; A \u003d (1.825 * 10 ^ 6) / (ε T) ^ 3/2, where ε is the dielectric constant, T is the temperature. For water at 25 degrees, A \u003d 0.509.
Lewis-Randall pr-lo:
The average ionic coefficient of activity depends only on the ionic strength of the solution and does not depend on other ions in solution. Application area: 0.01-0.02 mol / kg
(When a strong el-that is added to the solution, which does not have common ions with our low-solute salt, the PR does not change, because it depends only on T and p. The solution will decrease, because I. )
The emergence of a potential jump at the interface between conductors of the I and II kind. Reversible electrodes and reversible electrochemical cells. Conditional record of a correctly open galvanic cell. Electromotive force (EMF) of a galvanic cell.
Potential µ (cu2 + plate)\u003e µ (cu2 + solution) \u003d\u003e layer in solution before potential equalization \u003d\u003e emerging electronic layer at the interface l-tv \u003d\u003e there is a potential jump from Me and l- The phenomenon of the emergence of a potential jump at the interface underlies the operation of galv.el-tov.
The electrodes can be cationic or anionic reversible. By cation, type 1 electrodes with a metal plate and gas electrodes are reversible, which give a cation in solution. On the anion - 1st kind with a non-metallic plate, gas, which in solution give an anion, and electrodes of the 2nd kind. A galvanic cell is called reversible if, when a current is passed through it in the opposite direction, reverse chemical reactions occur in it. Such a galvanic cell is composed of two reversible electrodes. Conditional notation: on the left, an electrode with a more negative standard electrode potential is recorded; phase boundaries are indicated by a solid vertical line, the solution boundary is indicated by a single vertical dashed straight line, if there is a diffusion potential, or a double vertical dashed line, if it is absent. The exception is the hydrogen electrode, which is always on the left. An example of a properly open galvanic cell: Pt, H2 | HCl || CuSO4 | Cu | Pt EMF of a galvanic cell is equal to the difference between the electrode potentials of its constituent electrodes. According to the accepted form of recording a galvanic cell, its EMF is equal to the difference between the electrode potentials of the right and left electrodes: E \u003d Epr - Eleft\u003e 0
40. Give an example of a chemical galvanic cell composed of a gas electrode and an electrode of the second kind, an electrochemical circuit without liquid compounds - "without transfer." Write down the equations of electrode half-reactions and the equation of the chemical reaction, due to the energy of which electric energy is generated by this element.
An example of such a chain is the hydrogen-silver chloride element
Pt | (H 2) | HCl | AgCl | Ag, (I)
the cat consists of hydrogen and silver chloride electrodes immersed in a solution of hydrogen chloride. When working in such an element, e-reactions occur: 1 / 2H 2 (gas) ®H + (solution) + e; AgCl (tv) + e ®Ag (tv) + Cl - (solution)
So, the overall process is a chemical reaction: 1 / 2H 2 (gas) + AgCl (tv) ®Ag (tv) + H + (p-p) + Cl - (p-p);
The EMF of such a circuit is equal to the potential difference between the silver chloride and hydrogen electrodes. Given ur-ia we get
The difference between the standard potentials of silver chloride and hydrogen electrodes gives the standard EMF of the circuit E o, but m to the standard potential of the hydrogen e-da is taken equal to zero, then E o is equal to the standard potential of the silver chloride electrode. If hydrogen pressure \u003d 1, then
.
If hydrogen chloride is completely dissociated in solution, then the product of the activities of hydrogen and chlorine ions can be replaced by the average ionic activity, then
Gas electrodes, hydrogen electrode. Derivation and analysis of the equation expressing the dependence of the potential of the hydrogen electrode on the activity of hydrogen ions and the pressure of molecular hydrogen. The scope of the hydrogen electrode.
Gas electrodes are a plate of inert metal, washed with a gas, immersed in a solution containing ions of this gas. Example of an electrode: Pt, H2 | H + Half-reaction equation: H + + e → ½ H2 Nernst equation: 
<= ½ H2 Уравнение Нернста:
Hydrogen electrode. Conditional potential scale. Nernst equation for the potential of a hydrogen electrode. Dependence of the electrode potential on the pH of the solution and the pressure of molecular hydrogen. The scope of the hydrogen electrode.
Hydrogen electrolyte plate or wire made of Me, well absorbed by gas-forming hydrogen, saturated with hydrogen (at atmospheric pressure) and immersed in a water solution containing hydrogen ions.
Pt, H2 | H + Half-reaction equation: H + + e →<= ½ H2 Уравнение Нернста:
The use of water electrolyte in production is very inconvenient, because it is associated with the supply of gaseous H2. Advantage: a wide range of applicability. It can be used in a wide range of temperature, pressure, and pH, as well as in many non-aqueous or partially aqueous solutions. -rah.
Standard water scale at k-th at all temperatures the potential of standard water power is selected for 0. It differs from the Nernst scale in that instead of single concentrations and pressures, single activity and volatility are selected ...
pH \u003d -lg \u003d\u003e E \u003d -0.059pH
Standard hydrogen electrode. Conditional electrode potential (electrode potential on a hydrogen scale). Communication of the EMF of a galvanic cell with conditional electrode potentials. Rule of EMF signs and electrode potentials.
Standard water-cell - water-cell the pressure of the supplied hydrogen k-th is 1 atm, and the activity of H2 ions in solution \u003d 1 at T \u003d 298K
Conditional electric potential (or electric potential on a hydrogen scale) E \u003d EMF of an element composed of a given electric and standard water electric, i.e. E \u003d EMF e-ta.
EMF connection: a) we find the difference in conventional electrical potential: E2-E1 \u003d L2Y M 2 -L1Y M 1 + (m2Y pt -m1Y pt) \u003d L2Y M 2 -L1Y M 1 + m2 Y M 1
b) compared with the level for EMF of a given element E \u003d E2-E1
Rule of signs: 1. Fundamental rule - EMF is positive if inside the galvanic cell positive electricity (cations) moves from left to right (Stockholm, international conference 1953)
2. conclusions... When discharging ions on the right the electrode is a recovery process (the electrode is charged positively), and the electrode itself is the positive pole of the GEM. (cathode); on the left electrode - oxidation process (negative pole, anode).
3. Compliance with EMF sign system of signs of the theory of chem. affinity a)
b) and, a spontaneous process
The total concentration of ions in a solution is the molar concentration of a dissolved electrolyte, taking into account its degree of dissociation into ions and the number of ions into which an electric stove molecule dissociates in solution.
For strong electrolytes, α \u003d 1, therefore, the total concentration of ions is determined by the molar concentration of the electrolyte and the number of ions into which the strong electrolyte molecule in solution decays.
So, in the case of the dissociation of a strong electrolyte - sodium chloride in an aqueous solution
NaCl → Na + + Cl -
at initial electrolyte concentration from(NaCl) \u003d 0.1 mol / L, the ion concentration turns out to be equal to the same value: c (Na +) \u003d 0.1 mol / L and c (Cl -) \u003d 0.1 mol / L.
For a strong electrolyte of a more complex composition, for example, aluminum sulfate Al 2 (SO 4) 3, the cation and anion concentrations are also easily calculated, taking into account the stoichiometry of the dissociation process:
Al 2 (SO 4) 3 → 2 Al 3+ + 3 SO 4 2-
If the initial concentration of aluminum sulfate from ref \u003d 0.1 mol / L, then s (A1 3+) \u003d 2 0.1 \u003d 0.2 mol / L and from(SO 4 2-) \u003d 3 · 0.1 \u003d \u003d 0.3 mol / l.
Activity and related to overall concentration from formal relationship
where f ˗ activity coefficient.
When from → 0 value a → c, so that f → 1, i.e., for extremely diluted solutions, the activity numerically coincides with the concentration, and the activity coefficient is equal to unity.
Lewis and Randall introduced some mathematical corrections to the relations proposed by Arrhenius.
G. Lewis and M. Randall proposed a method of using activities instead of concentrations, which made it possible to formally take into account all the variety of interactions in solutions without taking into account their physical nature.
In electrolyte solutions, both cations and anions of the solute are simultaneously present. It is physically impossible to introduce ions of only one kind into the solution. Even if such a process were feasible, it would cause a significant increase in the energy of the solution due to the introduced electric charge.
The connection between the activities of individual ions and the activity of the electrolyte as a whole is established based on the condition of electroneutrality. For this, the concepts are introduced average ionic activity and average ionic activity coefficient.
If the electrolyte molecule dissociates into n + cations and n - anions, then the average ionic activity of the electrolyte a ± is equal to:
,
where and is the activity of cations and anions, respectively, n is the total number of ions (n \u200b\u200b\u003d n + + n -).
Similarly, the average ionic activity coefficient of the electrolyte is recorded: characterizing the deviation of the real solution from the ideal
.
Activity can be thought of as the product of concentration and activity coefficient. There are three scales of expression of activities and concentrations: molality (molality, or practical scale), molarity from (molar scale) and mole fraction x(rational scale).
In the thermodynamics of electrolyte solutions, the molal concentration scale is usually used.
Activity and activity coefficient of electrolytes. Ionic strength of the solution.
Disadvantages of Arrhenius' theory. Debye and Gückel's theory of electrolytes.
Dissolved salt activity and can be determined by vapor pressure, solidification temperature, according to the data on solubility, by the EMF method. All methods for determining the activity of a salt lead to a value that characterizes the real thermodynamic properties of the dissolved salt as a whole, regardless of whether it is dissociated or not. However, in the general case, the properties of different ions are not the same, and it is possible to introduce and consider thermodynamic functions separately for ions of different types:
m + \u003d m + o + RT ln a + \u003d m + o + RT ln m + + RT ln g + ¢
m - \u003d m - o + RT ln a - \u003d m - o + RT ln m - + RT ln g - ¢
where g + ¢ and g - ¢ are practical activity coefficients (activity coefficients at concentrations equal to molality m).
But the thermodynamic properties of various ions cannot be determined separately from experimental data without additional assumptions; we can measure only the average thermodynamic values \u200b\u200bfor the ions into which the molecule of this substance decays.
Let the salt dissociation occur according to the equation:
А n + В n - \u003d n + А z + + n - B z -
With complete dissociation, m + \u003d n + m, m - \u003d n - m. Using the Gibbs-Duhem equations, one can show:
and + n + × and - n - ¤ and \u003d const
Standard states for finding the values \u200b\u200bof activities are defined as follows:
lim a + ® m + \u003d n + m as m ® 0, lim a - ® m - \u003d n - m as m ® 0
Standard state for and is chosen so that const is equal to 1. Then:
and + n + × and - n - \u003d and
Because no methods of experimental determination of values a +and and -separately, then enter the average ionic activity and ±, defined by the ratio:
and ± n = and
Thus, we have two quantities characterizing the activity of the dissolved salt... The first one is molar activity , i.e. salt activity, determined independently of dissociation; it is found by the same experimental methods and by the same formulas as the activity of the components in non-electrolytes. The second quantity is average ionic activity and ± .
We now introduce ion activity coefficients g + ¢ and g - ¢, average ionic molality m ± and average ionic activity coefficient g ± ¢:
a + = g + ¢ m +, a - = g - ¢ m -, m ± \u003d (m + n + × m - n -) 1 / n \u003d (n + n + × n - n -) 1 / n m
g ± ¢ \u003d (g ¢ + n + × g ¢ - n -) 1 / n
Obviously: a ± = (g ¢ + n + × g ¢ - n -) 1 / n (n + n + × n - n -) 1 / n m \u003d g ± \u200b\u200b¢ m ±
Thus, the main quantities are related by the ratios:
a ± = g ± ¢ m ± = g ± ¢ (n + n + × n - n - ) 1/ nm = Lg ± ¢ m
where L \u003d (n + n + × n - n -) 1 / n and for salts of each specific type of valence is a constant value.
The g ± ¢ value is an important characteristic of the deviation of the salt solution from the ideal state. In electrolyte solutions, as well as in non-electrolyte solutions, the following activities and activity factors can be used :
g ± \u003d - rational activity coefficient (practically not used);
g ± ¢ \u003d - practical activity coefficient (average molar);
f ± \u003d - average molar activity coefficient.
The main methods for measuring g ± ¢ are cryoscopic and EMF.
Numerous studies have shown that the curve of the dependence of g ± ¢ on the concentration of the solution (m) has a minimum. If the dependence is plotted in coordinates log g ± ¢ -, then for dilute solutions the dependence turns out to be linear. The slope of the straight lines corresponding to the limiting dilution is the same for salts of the same valence type.
The presence of other salts in the solution changes the activity coefficient of this salt. The total effect of a mixture of salts in a solution on the activity coefficient of each of them is covered by a general pattern, if the total concentration of all salts in a solution is expressed through ionic strength. Ionic power I (or ionic strength) of a solution is the half-sum of the products of the concentration of each ion by the square of its charge number (valence), taken for all ions of a given solution.
If we use molality as a measure of concentration, then the ionic strength of a solution is determined by the expression:
where i - indices of ions of all salts in solution; m i \u003d n i m.
Lewis and Randall discovered empirical law of ionic strength : the average ionic activity coefficient g ± ¢ of a substance dissociating into ions is a universal function of the ionic strength of a solution, i.e. in a solution with a given ionic strength, all substances dissociating into ions have activity coefficients that do not depend on the nature and concentration of a given substance, but depend on the number and valence of its ions.
The ionic strength law reflects the total interaction of the ions in the solution, taking into account their valence. This law is accurate only at very low concentrations (m ≤ 0.02); even at moderate concentrations, it is only approximately correct.
In dilute solutions of strong electrolytes:
lgg ± ¢ = - AND
DISADVANTAGES OF ARRENIUS'S THEORY .
In the theory of electrolytes, the question of the distribution of ions in solution is very important. According to the original theory of electrolytic dissociation, based on the physical theory of Van't Hoff solutions, it was believed that ions in solutions are in a state of random movement - in a state similar to a gaseous one.
However, the idea of \u200b\u200ba random distribution of ions in a solution does not correspond to reality, since it does not take into account the electrostatic interaction between ions. Electric forces manifest themselves at relatively large distances, and in strong electrolytes, where dissociation is large, and the concentration of ions is significant and the distances between them are small, the electrostatic interaction between ions is so strong that it cannot but affect the nature of their distribution. There is a tendency towards an ordered distribution, similar to the distribution of ions in ionic crystals, where each ion is surrounded by ions of the opposite sign.
The distribution of ions will be determined by the ratio of electrostatic energy and the energy of chaotic movement of ions. These energies are comparable in magnitude; therefore, the actual distribution of ions in the electrolyte is intermediate between disordered and ordered. This is the originality of electrolytes and the difficulties arising in the creation of the theory of electrolytes.
A kind of ionic atmosphere is formed around each ion, in which ions of the opposite (in comparison with the central ion) sign prevail. Arrhenius's theory did not take this circumstance into account, and many of the conclusions of this theory turned out to be in contradiction with experiment.
As one of the quantitative characteristics of the electrolyte, Arrhenius's theory suggests the degree of electrolytic dissociation a, which determines the fraction of ionized molecules in a given solution. In accordance with its physical meaning, a cannot be greater than 1 or less than 0; under given conditions, it must be the same, regardless of the method of its measurement (by measuring electrical conductivity, osmotic pressure or EMF). However, in practice, the a values \u200b\u200bobtained by different methods coincide only for dilute solutions of weak electrolytes; for strong electrolytes, the larger the electrolyte concentration, the larger the electrolyte concentration, and in the region of high concentrations a becomes greater than 1. Therefore, a cannot have the physical meaning that was attributed to it by the Arrhenius theory.
The second quantitative characteristic according to Arrhenius's theory is the dissociation constant; it should be constant for a given electrolyte at given T and P, regardless of the concentration of the solution. In practice, only for dilute solutions of very weak electrolytes, Kdis remains more or less constant upon dilution.
Thus, the theory of electrolytic dissociation is applicable only to dilute solutions of weak electrolytes.
DEBAY AND HUKKEL ELECTROLYTES THEORY .
The main provisions of the modern theory of electrolyte solutions were formulated in 1923 by Debye and Gückel. For the statistical theory of electrolytes the starting point is the following position : ions are distributed in the volume of the solution not randomly, but in accordance with the law of the Coulomb interaction. Around every single ion there is ionic atmosphere (ion cloud) - a sphere consisting of ions of the opposite sign. The ions that make up the sphere are constantly exchanging places with other ions. All ions of the solution are equivalent, each of them is surrounded by an ionic atmosphere, and at the same time, each central ion is part of the ionic atmosphere of some other ion. The existence of ionic atmospheres is the characteristic feature that, according to Debye and Gückel, distinguishes real solutions of electrolytes from ideal ones.
Using the equations of electrostatics, you can derive formula for the electric potential of the ionic atmosphere, from which the equations for the average activity coefficients in electrolytes follow:
D is the dielectric constant of the solution; e - electron charge; z i - ion charge; r - coordinate (radius).
c \u003d is a value that depends on the concentration of the solution, D and T, but does not depend on the potential; has the dimension of inverse length; characterizes the change in the density of the ionic atmosphere around the central ion with increasing distance r from this ion.
The quantity 1 / c is called characteristic length ; it can be identified with the radius of the ionic atmosphere. It is of great importance in the theory of electrolyte solutions.
The following expression is obtained for the activity coefficient:
lg f ± \u003d - A | z + × z - | (1)
The coefficient A depends on T and D: it is inversely proportional to (DT) 3/2.
For aqueous solutions of 1-1 charging electrolytes at 298 K, assuming the equality of the dielectric constants of the solution and the solvent (78.54), we can write:
lg f ± \u003d - A \u003d - A \u003d - 0.51
Thus, the theory of Debye and Gückel allows obtaining the same equation for the activity coefficient, which was empirically found for dilute electrolyte solutions. Theory, therefore, is in qualitative agreement with experience. When developing this theory, the following assumptions were made :
1. The number of ions in the electrolyte can be determined from the analytical concentration of the electrolyte, since it is considered completely dissociated (a \u003d 1). The theory of Debye and Gückel is therefore sometimes called the theory of complete dissociation. However, it can also be applied in cases where a ¹ 1.
2. The distribution of ions around any central ion obeys the classical Maxwell-Boltzmann statistics.
3. The intrinsic dimensions of the ions can be neglected in comparison with the distances between them and with the total volume of the solution. Thus, ions are identified with material points, and all their properties are reduced only to the magnitude of the charge. This assumption is valid only for dilute solutions.
4. The interaction between ions is exhausted by the Coulomb forces. The superposition of forces of thermal motion leads to such a distribution of ions in the solution, which is characterized by a statistical spherical ionic atmosphere. This assumption is valid only for dilute solutions. With an increase in concentration, the average distance between ions decreases, and along with electrostatic forces, other forces appear that act at a closer distance, primarily the Van der Waals forces. It becomes necessary to take into account the interaction not only between a given ion and its environment, but also between any two neighboring ions.
5. In the calculations it is assumed that the dielectric constants of the solution and the pure solvent are equal; this is true only in the case of dilute solutions.
Thus, all the assumptions of Debye and Gückel lead to the fact that their the theory can only be applied to dilute solutions of electrolytes with low valence ions... Equation (1) corresponds to this limiting case and expresses the so-called limit law Debye and Gückel or first approximation of the theory of Debye and Gückel .
The Debye-Gückel limit law gives the correct values \u200b\u200bof the activity coefficients 1-1 of the charging electrolyte, especially in very dilute solutions. The convergence of theory with experiment deteriorates with an increase in the concentration of the electrolyte, an increase in ion charges, and a decrease in the dielectric constant of the solvent, i.e. with an increase in the forces of interaction between ions.
The first attempt to improve the theory of Debye and Gückel and expand the scope of its application was made by the authors themselves. In second approximation they abandoned the concept of ions as material points (Assumption 3) and tried to take into account the finite sizes of ions, endowing each electrolyte with a certain average diameter and (this also changes assumption 4). By assigning certain sizes to the ions, Debye and Gückel took into account the forces of non-Coulomb origin, which prevent the ions from approaching at a distance less than a certain value.
In the second approximation, the average activity coefficient is described by the equation:
lg f ± \u003d - (2)
where A retains its previous value; and conventionally named average effective ion diameter , has the dimension of length, in fact - an empirical constant; B \u003d c /, B changes slightly with T. For aqueous solutions, the product B and close to 1.
Retaining the main provisions of the second approximation of the theory, Gückel took into account the decrease in the dielectric constant with increasing concentration of solutions. Its decrease is caused by the orientation of the solvent dipoles around the ion, as a result of which their response to the effect of the external field decreases. The Gückel equation looks like this:
lg f ± \u003d - + C I (3)
where C is an empirical constant. With a successful selection of the values \u200b\u200bof B and C, the Gückel formula is in good agreement with experience and is widely used in calculations. With a sequential decrease in the ionic strength, equation (3) successively transforms into the formula for the second approximation of the theory of Debye and Gückel (equation (2)), and then into the limiting Debye-Gückel law (equation (1)).
In the process of the development of the Debye-Gückel theory and the consistent rejection of the accepted assumptions, the convergence with experiment improves and the area of \u200b\u200bits applicability expands, but this is achieved at the cost of transforming theoretical equations into semi-empirical ones.
