Activity and activity coefficient of the electrolyte. Ionic strength of the solution. Ionic strength rule.
Dissolved salt activity A can be determined from vapor pressure, solidification temperature, solubility data, 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+ = m + o + RT ln a + = m + o + RT log m+ + RT logg + ¢
m – = m – o + RT ln a -= m –o +RTln m– + RT lng – ¢ ,
Whereg + ¢ And g – ¢ - practical activity coefficients (activity coefficients at concentrations equal to the molality m ).
But the thermodynamic properties of various ions cannot be determined separately from experimental data without additional assumptions; we can only measure the average thermodynamic quantities for the ions into which the molecule of this substance decays.
Let the dissociation of the salt occur according to the equation
An+ IN n-= n+ A z + + n - Bz - .
With complete dissociationm + = n + m , m - = n - m . Using the Gibbs-Duhem equations, it can be shown that
A + n + ×A - n - ¤ A=const .
The standard states for finding activity values are defined as follows:
lim a + ® m + = n + m at m ® 0 ,
lim a – ® m – = n – m at m ® 0 .
Standard condition for A is chosen so thatconstwas equal to 1. Then
A + n + ×A -n-=A .
Since there are no methods for experimental determination of the values a + And A – separately, then the average ionic activity is introduced A ± , determined by the ratio
A ± n =A .
Thus, we have two quantities characterizing the activity of the dissolved salt. The first one- This molar activity , that is, the activity of the salt, determined independently of dissociation; it is found by the same experimental methods and according to the same formulas as the activity of the components in non-electrolytes. Second value- average ionic activity A ± .
Let's introduce now ion activity coefficients g + ¢ And g – ¢ , average ionic molality m ± And average ion activity factor g ± ¢ :
a + = g + ¢ m + ,a – = g – ¢ m – ,a ± = g ± ¢ m ± ,
Whereg ± ¢ =(g¢ + n + × g¢ - n - ) 1/ n ,m ± =(m + n + × m - n - ) 1/ n =(n + n + × n - n - ) 1/ nm .
So, the main quantities are related by the relations
a ± = g ± ¢ m ± = g ± ¢ ( n + n + × n - n - ) 1/ n m = L g ± ¢ m ,
Where L =(n + n + × n - n - ) 1/ nand for salts of each specific type of valency is a constant value.
Valueg ± ¢ 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 coefficients can be used:
g ± = - rational activity coefficient (practically not used);
g ± ¢ = - practical activity coefficient (average molal);
f ± =± (g ± ¢ )on the solution concentration ( With or m) has a minimum. If you represent the dependence in coordinates lgg ± ¢
Rice. 24. Dependence of the electrolyte activity coefficient on its concentration for salts of various valence types
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 force I(or ionic strength) of a solution is the half-sum of the products of the concentration of each ion and the square of its charge (valence) number, taken for all ions of a given solution.
- ion indices of all salts in solution; m i= n im .Lewis and Randall opened empirical law of ionic strength: average ionic activity coefficientg ± ¢ of a substance dissociating into ions is a universal function of the ionic strength of the solution, that is, 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 the given substance, but depend on the number and valence of its ions.
The law of ionic strength reflects the total interaction of the ions of the solution, taking into account their valency. This law is exact only at very low concentrations (m ≤ 0.01); even at moderate concentrations it is only approximately true. According to this law, in dilute solutions of strong electrolytes
lg g ± ¢ = - A .
By analogy with the average ionic molality, we can consider the average ionic activity:
calculated from the activities of individual ions. The average ionic activity and the average ionic molality are related to each other by the average ionic activity coefficient, that is: , where
Then the chemical potential of a real electrolyte solution has the expressions:
where is the activity of the electrolyte, A, is related to the average ionic activity:
The values of the average ionic activity coefficient are determined experimentally by various methods, which include lowering the freezing point, osmotic pressure, saturated vapor pressure of the solvent, and EMF measurements, which are discussed further. Knowing the average ionic molality and the average activity coefficient, one can calculate the average ionic activity and from it the chemical potential of the electrolyte in solution. In addition, for dilute solutions of electrolytes, a theory of interionic interactions was developed, which makes it possible to calculate the average ionic activity coefficients and the activity coefficients of individual ions in dilute solutions. This theory is called Debye-Hückel theories. According to it, the logarithm of the activity coefficient depends on ionic strength I electrolyte solution, which is defined as follows:
ionic strength based on molality:
ionic strength based on concentration:
the summation extending over all the ions in the solution.
For very dilute solutions ( I C< 0.01 моль дм –3) упомянутая зависимость имеет вид:
; ; 
where A is a constant, the value of which depends on the properties of the solvent and temperature, but does not depend on the concentration of the electrolyte or its nature. If the solvent is water and the temperature is 25°C, then A= 0.5092 (dm 3 mol –1) 1 / 2. This equation is called Debye Hückel's limit law. As can be seen from this equation, the activity coefficients of an electrolyte in very dilute solutions depend only on the ionic strength and charge of the ions, but do not depend on the individuality of the electrolyte. That is, with the same ionic strength, electrolytes, for example, MgCl 2 and Ca (OH) 2 should have the same activity coefficients. This agrees with reality, but only at values of ionic strength less than approximately 0.01 mol dm–3. At higher concentrations (and ionic strengths), the activity coefficients depend on the nature of the electrolyte, in particular on the radii of the ions into which the electrolyte decomposes. Up to an ionic strength of approximately 0.1 mol dm–3, they can be calculated from extended Debye Hückel's law:
; 
, 
Where IN is a constant depending on the properties of the solvent (at 25 °С IN= 0.3301 (dm 3 / 2 mol –1 / 2 Å –1 for a water solvent, Å is an angstrom, 10 –10 m), and r is the crystallographic radius of the ion. Unfortunately, the individual crystallographic radii of ions are in fact not exactly known, since only internuclear distances have been determined for crystal structures. Any of the modern systems of ion radii is based on an arbitrary choice of the radius of at least one ion, on the basis of which the relative radii of all other ions are calculated. On the other hand, the usual values of ion radii are such that the product INr in the denominator on the right side of the equation is approximately 1 for most ions. Based on this, the extended Debye-Hückel law is often used in the form.
Thermodynamics of electrolyte solutions
Basic concepts
Electrochemistry- a branch of physical chemistry that studies the laws of mutual transformation of chemical and electrical forms of energy, as well as systems where these transformations take place. Electrochemistry also studies the physicochemical properties of ionic conductors, processes and phenomena at the phase boundaries with the participation of charged particles - ions and electrons.
All conductors of electric current can be divided into electronic and ionic. Electronic conductors (conductors of the first kind) carry electric current by the movement of electrons. Ionic conductors (conductors of the second kind) conduct electric current due to the movement of ions.
electrolytes Substances (chemical compounds) are called substances (chemical compounds) that, in a solution or in a melt, spontaneously partially or completely decompose into ions - charged particles capable of independent existence. The transfer of electricity in electrolyte solutions is carried out by ions, i.e. electrolytes are type II conductors. Electrolytes are both solid and liquid. The number of ions of each sign, formed during the decomposition of the electrolyte, is determined by the stoichiometric coefficients in the equation for the chemical reaction of the dissociation of this electrolyte:
M n + A n - = n+ M z + + n-А z - , (1.1)
Where n+, n- And n = n+ + n-- the number of cations, the number of anions and the total number of charged particles in the electrolyte. Despite the presence of ions, the electrolyte solution remains electrically neutral.
The process by which a solute breaks down into ions in a solution is called electrolytic dissociation.
The fact that electrolytes decompose (dissociate) upon dissolution is evidenced by many phenomena discovered by many researchers in the study of electrolyte solutions. It was found that osmotic pressure, lowering the partial vapor pressure of a liquid over a solution, lowering the freezing point and some other properties are of greater importance for electrolyte solutions than for equimolecular solutions of non-electrolytes. All these quantities depend primarily on the number of particles of the solute per unit volume of the solution (colligative properties). Therefore, as Van't Hoff pointed out, their increased value for electrolyte solutions should be explained by an increase in the number of particles as a result of the dissociation of the solute into ions.
For a formal assessment of these deviations, van't Hoff proposed an isotonic coefficient:
Then, for electrolyte solutions:
_____________________________________________________________________
The classical theory of electrolytic dissociation was created by Arrhenius in 1887. She assumed that not all electrolyte molecules in solution decompose into ions. The ratio of the number of dissociated molecules to the initial number of undissociated electrolyte molecules (the fraction of dissociated molecules) in the equilibrium state is called degree of dissociation a, and 0 £ a £ 1. With a decrease in the concentration of the solution, the degree of dissociation of the electrolyte also increases in an infinitely dilute solution a= 1 for all electrolytes. The degree of dissociation also depends on the nature of the electrolyte and solvent, the temperature, and the presence of other electrolytes in the solution.
The higher the dielectric constant of the solvent, the greater the degree of electrolyte dissociation (approximate Kablukov-Nernst-Thomson rule).
The degree of dissociation and the isotonic coefficient are related by the equation 
, Where k is the number of ions into which the electrolyte decomposes.
Depending on the degree of dissociation, electrolytes are divided into strong ( a> 0.8) and weak ( a < 0,3). Иногда выделяют группу электролитов средней силы. В водных растворах сильными электролитами являются многие минеральные кислоты (HNO 3 , HCl, HClO 4 и др.), основания (NaOH, KOH, и др.), большинство солей (NaCl, K 2 SO 4 и др.).
Weak electrolytes are substances that decompose into ions only partially in solution. In aqueous solutions, weak electrolytes are some inorganic acids (H 2 CO 3, H 3 BO 3, etc.), bases (NH 4 OH, etc.), some salts (HgCl 2, etc.), most organic acids (CH 3 COOH, C 6 H 5 COOH, etc.), phenols (C 6 H 4 (OH) 2, etc.), amines (C 6 H 5 NH 2, etc.). Since the strength of the electrolyte depends on the nature of the solvent, the same substance in one solvent can be a strong electrolyte (for example, NaCl in water), and in another - a weak one (for example, NaCl in nitrobenzene).
Value a not convenient for characterizing the electrolyte, since it depends on the concentration . A more convenient characteristic of the ability of an electrolyte to dissociate is dissociation constant (TO diss), since the equilibrium between ions and molecules obeys the law of mass action. So, for a monovalent electrolyte AB, dissociating in solution into ions according to the scheme AB = A + + B - , the expression for the electrolytic dissociation constant TO diss looks like:
TO diss = . (1.2)
The dissociation constant depends on the nature of the solvent and temperature, but does not depend on the concentration of the electrolyte in the solution.
If With - the initial concentration of the electrolyte AB, and the degree of its dissociation is , then, according to the equation for the dissociation reaction of this electrolyte, in the state of equilibrium, the concentration of cations and anions will be equal to:
With A+ = With B- = a×s .
The concentration of undecayed electrolyte molecules will become equal to
With(1 – a).
Substituting these relations into equation (1.2), we obtain:
During the dissociation of the electrolyte according to the reaction 
two cations and one anion are formed and ; ; . Then
. (1.3,a)
For a given electrolyte dissociating into ions in a given solvent, at a given temperature, the dissociation constant is a constant value, independent of the concentration of the electrolyte solution.
The resulting equations, called the Ostwald dilution law, make it possible to estimate the degree of electrolyte dissociation.
For small values a, i.e. for weak electrolytes, it can be assumed that
(1 – a) @ 1. Then expression (1.3) becomes
As can be seen, the degree of dissociation is inversely proportional to the square root of the electrolyte concentration. With a decrease in the electrolyte concentration, for example, by a factor of 100, the degree of dissociation increases by a factor of 10.
The influence of temperature on the degree of dissociation is due to the fact that the dissociation constant depends on temperature (the equation of the isobar of a chemical reaction).
The introduction of foreign ions into a solution usually increases the degree of dissociation of a weak electrolyte. This phenomenon is called salt effect.
The Arrhenius theory makes it possible to qualitatively and quantitatively describe the phenomena associated with ionic equilibria. However, this theory does not take into account the interaction of ions with solvent dipoles and ion-ion interaction.
Expressions (1.2 - 1.4) are applicable for ideal solutions. The properties of solutions of real electrolytes differ significantly from the properties of ideal solutions. This is due to the increase in the number of particles in the electrolyte solution (due to dissociation) and the electrostatic interaction between the ions. The properties of real solutions can be described using instead of concentration activity. Activity(a) is the value that must be substituted into the expression for the chemical potential of an ideal solution in order to obtain the value of the chemical potential of a real electrolyte solution.
Activity is related to concentration by the following relationship: , (), where () is the activity coefficient, which takes into account the deviation of the properties of real electrolyte solutions from the properties of ideal solutions, c And m– molar and molal concentrations.
Thus, instead of expression (2) one gets:
, (1.5)
Where a i = с i ×g i ; with i ; gi- activity, concentration and activity coefficient of an individual ion or molecule.
Average ionic activity and average activity coefficient
The use of activity instead of ion concentration makes it possible to formally take into account the entire set of interactions (without taking into account their physical nature) that arise in electrolyte solutions. This method of describing interactions as applied to electrolyte solutions has a number of features.
The chemical potential of the dissolved salt ( m S) is equal to:
, (1.6)
Where a S is the activity of the salt; m S 0 is the standard value of the chemical potential corresponding to a S=1.
If the electrolyte dissociates into n + cations and n - anions, then, based on the condition of electrical neutrality, the chemical potential of the salt is related to the chemical potentials of cations and anions by the ratio:
m S= n+m++ n-m-; m S 0 = n+m+ 0 + n - m - 0; (1.7)
The chemical potential of an ion is related to the activity of the ion by the relation:
, (1.8)
Where m i - the chemical potential of the cation or anion.
From equations (1.5-1.7) it follows that:
= n+ + n- , (1.9)
. (1.10)
Due to the fact that both cations and anions of the solute are simultaneously present in electrolyte solutions (it is impossible to obtain a solution containing only cations or anions), it is impossible to estimate the activity and activity coefficient of an individual ion. Therefore, for electrolyte solutions, the concepts of average ionic activity and average ionic activity coefficient are introduced.
For an electrolyte that dissociates into n + cations and n - anions, the average ionic activity of the electrolyte a ± is equal to the geometric mean of the product of the activities of the cation and anion:
, (1.11)
Where a+ and a- are the activity of cations and anions, respectively; n = n+ + n-- the total number of ions formed during the dissociation of the electrolyte molecule.
For example, for a solution of Cu (NO 3) 2:
.
Similarly, the average electrolyte activity coefficient g ± and the average number of electrolyte ions in solution are calculated n ±:
; (1.12)
, (1.13)
where + and - are the activity coefficients of the cation and anion; n± - the average number of cations and anions in solution.
For example, for an electrolyte KCI=K + + CI - the average number of ions in the solution is n± = (1 1 1 1) 1 = 1, that is, there is one cation and one anion in the KCI solution. For the electrolyte Al 2 (SO 4) 3 = 2Al 3+ + 3SO 4 2- the average number of ions in the solution is n± \u003d (2 2 3 3) 1/5 \u003d 2.56. This means that the same average number of cations and anions (2.56) will appear in the calculations of the average activity, which differs from the actual number (2 cations, 3 anions).
Usually, the average ionic activity and the average ionic activity coefficient are determined experimentally (by the thermodynamic properties of solutions):
By increasing the boiling point of the solution;
By lowering the freezing point of the solution;
According to the vapor pressure of the solvent over the solution;
According to the solubility of poorly soluble compounds,
According to the EMF method of galvanic cells, etc.
The average ionic activity and the average ionic activity coefficient of an electrolyte for dilute solutions of strong electrolytes can be theoretically determined using the Debye-Hückel method.
The average ionic activity and the average ionic activity coefficient depend not only on the concentration of the solution, but also on the charge of the ion. In the region of low concentrations, the average ionic activity coefficient is determined by the charge of the forming ions and does not depend on other properties of electrolytes. For example, in the region of low concentrations, g ± for solutions of KCl, NaNO 3 , HCl, etc. are the same.
In dilute solutions of strong electrolytes, the average activity coefficient g ± depends on the total concentration of all electrolytes present in the solution and ion charges, i.e. g ± depends on the ionic strength of the solution I.Ionic strength of solution calculated by the formula:
Where m i–molal (or molar) concentration i- that ion; z i is the charge of the ion. When calculating the ionic strength of a solution, it is necessary to take into account all the ions in the solution.
Exists solution ionic strength rule: in dilute solutions, the activity coefficient of a strong electrolyte is the same for all solutions with the same ionic strength, regardless of the nature of the electrolyte. This rule is valid at concentrations of not more than 0.02 mol/dm 3 . In solutions of medium and high concentrations, the ionic strength rule is transformed, since the nature of the interionic interaction becomes more complicated and the individual properties of electrolytes appear.
DEBYE-HUKKEL ELECTROLYTES.
One of the theories that quantitatively takes into account ion-ion interactions is Debye-Hückel theory, which explains quite well the properties of dilute solutions of strong electrolytes. The degree of dissociation for strong electrolytes is equal to one. Therefore, the dependence of electrical conductivity, osmotic pressure, and other properties of solutions on concentration is determined mainly by the action interionic forces And solvation effects. Solvation is understood as a set of energy and structural changes that occur in a solution during the interaction of solute particles with solvent molecules.
The Debye-Hückel theory is based on the following provisions: the electrostatic interaction of oppositely charged ions leads to the fact that around positive ions the probability of finding negative ions will be greater than positive ones. Thus, around each ion, as it were, there is an ionic atmosphere of oppositely charged ions. (The sphere in which the charge opposite in sign to the central ion predominates is called ionic atmosphere). The ionic atmosphere around the ion contains both positive and negative ions, however, on average, there is an excess of negative ions around each positive ion, and an excess of positive ions around a negative ion. The solution as a whole remains electrically neutral.
Chemical potential i th component in an ideal solution is equal to:
Where With i– concentration i th ion in solution. For a real solution:
Where a i = c i · f i- activity of the i-th ion in solution, f i– activity coefficient. Then the interaction energy of the central ion with the ionic atmosphere per 1 mole of ions is equal to
Thus, the value of the activity coefficient, which depends on the strength of the electrostatic interaction of ions, the degree of their solvation, and a number of other effects, characterizes the degree of deviation of the properties of real electrolyte solutions from the laws of ideal solutions.
1.3. Activity and activity coefficient of electrolytes.
AVERAGE IONIC ACTIVITY AND AVERAGE IONIC COEFFICIENT
ACTIVITIES. IONIC POWER. IONIC STRENGTH RULE.
Distinguish electrolyte activity And ion activity. For any electrolyte, the dissociation process can be written as follows:
where + and - - the number of ions A with charge z+ and ions B with charge z– into which the original particle decays. For example, during the dissociation of barium chloride:
.
The relationship between the activity of the electrolyte and the activities of the ions is expressed by the following relationship:
, (1.11)
Where A- electrolyte activity, A+ and A– - activities of positive and negative ions. For example, for binary electrolytes it is true:
.
Experimental methods for determining the activity of individual ions ( A+ and A-) does not exist. Therefore, the concept was introduced average ionic activity(
), which is the geometric mean of the activity of individual ions:
, (1.12)
Where 
.
The cryoscopic method and the method based on the determination of vapor pressure make it possible to determine the activity of the electrolyte as a whole ( A) and using equation (7.13) find the average ionic activity.
Average ionic activity coefficient(
) is determined by the expression
. (1.14)
Values 
mainly determined by the cryoscopic method and the EDS method.
Average ionic molality(
) is defined as
. (1.15)
If the concentration of a solution is expressed in terms of molality, then
Example 1.1. Find the relationship between the activity of the electrolyte, its molar concentration and the average ionic activity coefficient for solutions NaCl And Na 2 CO 3 molality m.
a) Concentrations of ions formed during complete dissociation NaCl, are equal m:
.
Since + = – = 1, then
.
For equal-valent electrolytes, the average molality will be equal to the total molality of the electrolyte:
,
b) Concentrations of ions formed during complete dissociation Na 2 CO 3 , are equal
.
Since + = 2, – = 1, then
.
WITH 
the average ionic activity coefficient depends on the concentration of the solution (Fig. 1). In the region of extremely dilute electrolyte solutions, this dependence is linear in the coordinates 
.
Rice. Fig. 1. Dependence of the average ionic 2. Dependence of the average coefficient
activity coefficient of ion activity on the ionic strength of the solution.
on electrolyte concentration. Curve 1 describes the experimental
dependence, curve 2 describes dependence
according to the Debye-Hückel limit law.
The presence of other salts in the solution changes the activity coefficient of the given salt and the stronger, the greater the charge of the added ions. The total concentration of all ions in a solution is expressed through ionic strength of the solution 
,
defined as half the sum of the products of the molality of all ions and the square of their charges :
, (1.16)
Where m i– concentration i-th ion; z i- charge i-th ion.
The dependence of the average activity coefficient of ions on the ionic strength of the solution has a complex character and is shown in fig. 2.
Example 1.2. Determine the ionic strength of a solution containing 0.01 mol per 1000 g of water 
and 0.1 mol 
.
Solution. The ionic strength of such a solution is
Example 1.3. Determine the ionic strength of the solution 
with molality m
= 0,5.
Solution. By equation (7.16) we get
For solutions of strong electrolytes, ionic strength rule : in solutions with the same ionic strength, the average activity coefficients of the ions are equal. The theory of strong electrolytes leads to the following relation, which relates the average activity coefficients of ions to the ionic strength of the solution in the region of highly dilute electrolytes:
, (1.17)
Where A = f (D, T) is a constant depending on the permittivity of the solvent ( D) and temperature ( T).
Equation (1.17) is applicable only for very large dilutions ( I≤ 0.01, fig. 2) why it got the name limiting Debye-Hückel law. In weakly mineralized waters for calculation 
at 25°C the following equation is used:
. (1.18)
For aqueous solutions of binary electrolytes at 25 o C, the following is true:
. (1.19)
It is known that in highly dilute solutions of electrolytes, the activity coefficients of ions mainly take into account corrections to their concentrations (molalities) due to electrostatic (ion–ion) interaction. At the same time, according to the Coulomb law, these interactions also depend on the magnitude of the charges and radii of the ions. Therefore, it is natural to accept, as was first done by D. McInnes, that the activity coefficients of ions with the same charges and radii in solutions with the same ionic strength will be the same. This assumption has been called McInnes rule.
McInnes suggested taking potassium and chlorine ions as standards, as having the same charges and radii of hydrated ions. Having defined the values 
And 
, one can then calculate the activity coefficients of all other ions based on the law of ionic strength.
SUBJECT2
Specific and equivalent electrical conductivity, their dependence on concentration for strong and weak electrolytes. Ion mobility. Kohlrausch's law of independence of movement of ions, limiting ionic electrical conductivity. Abnormal mobility of hydroxyl and hydroxonium ions. Experimental applications of the electrical conductivity method.
2.1. SPECIFIC ELECTRICAL CONDUCTIVITY OF ELECTROLYTE SOLUTIONS.
When an electric field is applied to an electrolyte solution, the solvated ions, which were previously in random thermal motion, begin an ordered movement (migration) towards oppositely charged electrodes. With an increase in the speed of movement of ions, the resistance of the medium increases and after a while the speed of movement of the ions becomes constant.
Ion movement speed i-th type is determined by the gradient of the potential (strength) of the electric field E(V / cm) and the resistance of the medium, depending on the temperature, the nature of the ion and the solvent:
, (2.1)
Where U(B) - potential difference between the electrodes, l(cm) is the distance between them, u i(cm 2 V -1 s -1) - the absolute speed of movement of ions under these conditions (i.e., the speed of movement of ions at E= 1 V/cm).
A measure of the ability of a substance to conduct an electric current when an external electric field is applied is electrical conductivity (electrical conductivity)L. In practice, this ability is often characterized by the reciprocal - conductor resistance. So, the total resistance of the conductor R(ohm) length l(cm) and cross section S(cm 2) equals
, (2.2)
where ρ is the coefficient of proportionality, called resistivity. From (8.2) it follows that the resistivity is the resistance of a conductor 1 cm long and 1 cm 2 in cross section, its dimension is:
. (2.2)
Electrical conductivity electrolyte æ - the reciprocal of the resistivity:
æ 
[Ohm -1 cm -1]. (2.3)
It characterizes the electrical conductivity of an electrolyte layer 1 cm thick with a cross-sectional area of 1 cm 2 . Then
æ 
. (2.4)
The electrical conductivity of an electrolyte solution is determined by the number of ions that carry electricity and the rate of their migration.
Let between electrodes located at a distance l(cm) and to which the potential difference is applied U(B), there is an electrolyte solution (Fig. 3). For ions i-th type: concentration C i(mol-eq / cm 3) and migration rate υ i(cm/s).
Rice. 3. Scheme of charge transfer through the electrolyte solution.
H 
through the cross section S solution (Fig. 3) migrates in 1 s ( C i υ
i S) mole equivalents of ions i-th species that will transfer ( 
) To 
the amount of electricity where
F– Faraday number(96485 C/mol-eq). The amount of electricity (C) transferred by all ions in 1 s (i.e., the current strength I in A) is equal to:
(2.5)
Or, taking into account (8.1),
. (2.6)
Ohm's law
(æ S), (2.7)
æ. (2.8)
Then, from equations (8.6) and (8.8), for the electrical conductivity we obtain
æ
. (2.9),
i.e., the specific electrical conductivity of the electrolyte is proportional to the concentrations of ions and their absolute velocities. For a binary electrolyte solution of concentration WITH(mol-equiv / cm 3) with the degree of dissociation α we have
æ
, (2.10)
Where u+ and u‑ ‑ absolute velocities of cations and anions.
With an increase in the temperature of the electrolyte, the velocities of the movement of ions and the electrical conductivity increase:
æ 2 = æ 1 
, (2.11)
Where B- temperature coefficient (for strong acids 0.016; for strong bases 0.019; for salts 0.022).
2.2. EQUIVALENT ELECTRICAL CONDUCTIVITY.
Specific conductivity of solutions depends on the nature of the electrolyte, the nature of the solvent, the temperature, the concentration of ions in the solution, etc. Although the electrical conductivity is an inconvenient quantity for understanding the properties of electrolytes, it can be measured directly and then converted to equivalent electrical conductivity λ. The equivalent electrical conductivity is the electrical conductivity of such a volume of solution V (cm 3 ), which contains 1 mole equivalent of a solute and is enclosed between two parallel electrodes of the corresponding area, located at a distance of 1 cm from each other:
æ V
= æ / C, (2.12)
Where WITH- concentration of the solution (mol-equiv / cm 3).
Equivalent electrical conductivity (Ohm -1 cm 2 (mol-equiv) -1) is easy to calculate if the specific electrical conductivity and concentration of the solution are known.
The following equation is used to describe the temperature dependence of the equivalent electrical conductivity:
, (2.13)
where and are empirical coefficients. The increase in electrical conductivity with increasing temperature is mainly due to a decrease in the viscosity of the electrolyte solution. Typically, with an increase in temperature by 1 K, the electrical conductivity increases by 1.5 - 2%.
The equivalent electrical conductivity of electrolyte solutions increases with dilution and in the range of limiting dilutions reaches the limiting value λ ∞ , called electrical conductivity at infinite dilution or ultimate electrical conductivity. This value corresponds to the electrical conductivity of a hypothetically infinitely dilute solution characterized by complete dissociation of the electrolyte and the absence of electrostatic interaction forces between ions.
Equations (2.10) and (2.11) imply that
The product of the Faraday number and the absolute speed of the ion is called mobility and she:
. (2.15)
where λ + and λ - are the cation and anion mobilities, respectively. Ion mobilities are measured in the same units as the equivalent electrical conductivity (cm 2 Ohm -1 mol-eq -1), so they are sometimes called ionic conductivities or electrical conductivities of ions.
With an infinite dilution (α = 1), we obtain
, (8.17)
Where 
And 
- limiting mobility of ions.
The value of the limiting electrical conductivity of an infinitely dilute electrolyte solution is the sum of two independent terms, each of which corresponds to a certain type of ion. This relation was established by Kohlrausch and is called the law of independent motion of ions (Kohlrausch law): the equivalent electrical conductivity at infinite dilution is equal to the sum of the limiting ion mobilities. The essence of this law is as follows: In an extremely dilute electrolyte solution, cations and anions carry current independently of each other.
Kohlrausch's law helped to calculate the values of λ ∞ for many weak electrolytes, for which it was impossible to determine these values from experimental data by extrapolating them to zero concentration (or to infinite dilution) as is done in the case of strong (and average) electrolytes. The limiting ion mobilities, as well as the equivalent electrical conductivity, increase with temperature. Their values, for example, at 25 ° C lie in the range from 30 to 80 and from 40 to 80 (cm 2 Ohm -1 mol-eq -1) for singly charged cations and anions, respectively.
Ions HE- And H+ Abnormally high mobility is observed:
198 and 
350 (cm 2 Ohm -1 mol-equiv -1) at 25 o C,
which is explained by a special - relay - mechanism of their movement (Fig. 4).
R 
is. 4. Relay-race mechanism for ion movement HE- And H + .
Based on the equivalent electrical conductivity of the electrolyte solution and the limiting ion mobilities, the degree of dissociation of a weak electrolyte can be calculated:
, (2.18).
For strong electrolytes that dissociate completely, calculate to 
conductivity factor:
, (2.19)
which takes into account the influence of the electrostatic interaction of ions on the speed of their movement.
Taking into account the new concept - ion mobility - for electrical conductivity, we can write:
æ 
, (2.20)
Note that modern scientific and educational literature also uses the concept molar electrical conductivity λ m, which is easily related to the value of λ, knowing the number of mole equivalents ( Z) in 1 mole of a substance:
. (2.22)
2.2. DEPENDENCE OF SPECIFIC AND EQUIVALENT ELECTRICAL CONDUCTIVITIES ON CONCENTRATION
FOR WEAK AND STRONG ELECTROLYTES.
E 
equivalent electrical conductivity weak and strong electrolytes increases with dilution (Fig. 5 b). For weak electrolytes, this is mainly due to the fact that with increasing dilution, the degree of electrolyte dissociation increases and tends to 1 in the limit. The increase in the equivalent electrical conductivity of strong electrolytes is mainly due to a change in the ion mobilities. The mobility of ions is the less, the greater the concentration of the solution. In the region of highly dilute solutions, the ion mobilities reach their limiting value.
Rice. 5. Dependence of specific ( A) and equivalent ( b)
conductivity on the concentration of the electrolyte solution.
Electrical conductivity for strong electrolytes, the higher the concentration of ions and the greater their absolute velocities (mobilities). Acids have the highest electrical conductivity, then bases, followed by salts, the electrical conductivity of solutions of such weak electrolytes as acetic acid or ammonia is very low.
The curves of dependences of specific electrical conductivity on concentration have maxima (Fig. 5 A). In dilute solutions of weak and strong electrolytes, the increase in electrical conductivity with concentration is due to an increase in the number of ions that carry electricity. A further increase in concentration is accompanied by an increase in the viscosity of the solution, which reduces the ion velocity and electrical conductivity. Moreover, for weak electrolytes in concentrated solutions, the degree of dissociation and, consequently, the total number of ions decreases markedly. For weak electrolytes, the speed of ion movement is almost independent of concentration, and in the general case, their electrical conductivity varies slightly with concentration.
For strong electrolytes in the region of dilute solutions, there are practically no interionic interactions, but the number of ions is small - the electrical conductivity is low. With increasing concentration, the number of ions per unit volume increases, which leads to an increase in electrical conductivity. However, further increasing interaction between ions leads to a decrease in the mobility of ions and the increase in electrical conductivity slows down. Finally, the interaction between ions with increasing concentration begins to increase so strongly that it leads to a decrease in electrical conductivity.
From the standpoint of the Debye-Hückel theory, the decrease in the mobility of ions with increasing concentration is due to the effects of deceleration of the movement of ions due to the electrostatic interaction between the ion and the ionic atmosphere.
The effect of electrophoretic inhibition due to the deceleration of the movement of the central ion by the oncoming movement of the ionic atmosphere and has a hydrodynamic nature. Since the ions are hydrated, the movement of the central ion occurs not in a stationary medium, but in a medium moving towards it. A moving ion is under the influence of an additional retarding force (electrophoretic braking force), which leads to a decrease in the speed of its movement.
The effect of relaxation inhibition. The ionic atmosphere has spherical symmetry as long as there is no external electric field. As soon as the central ion begins to move under the action of an electric field, the symmetry of the ionic atmosphere is broken. The movement of the ion is accompanied by the destruction of the ionic atmosphere in the new position of the ion and its formation in another, new one. This process takes place at a finite rate over a period of time called relaxation time. As a result, the ionic atmosphere loses its central symmetry and behind the moving ion there will always be some excess charge of the opposite sign, which causes a decrease in its speed.
The density of the ionic atmosphere increases with an increase in the electrolyte concentration, which leads to an increase in the braking effects. The theory of electrophoretic and relaxation effects was developed by L. Onsager. It quantitatively allows taking into account the influence of these effects on the value of the equivalent electrical conductivity of the electrolyte solution:
where constants ( IN 1 λ∞) and IN 2 characterize the influence of relaxation and electrophoretic effects, respectively. In solutions with WITH→ 0, these effects practically do not appear and 
.
2.4. EXPERIMENTAL APPLICATIONS OF THE ELECTRICAL CONDUCTIVITY METHOD.
2.4.1. Determination of the dissociation constant and degree of dissociation
weak electrolytes.
The degree of dissociation of a weak electrolyte can be found from relation (8.18):
.
Dissociation constant TO D weak electrolyte is related to the degree of dissociation by the equation
. (2.24)
Taking into account (8.18), we obtain
. (2.25)
The value λ ∞ is calculated according to the Kohlrausch law (Equation 2.17).
2.4.2. Determination of the solubility product
insoluble compounds.
Electrolyte solubility (S) is its concentration in a saturated solution (mol/l), and solubility product (ETC) is the product of the activities of the cation and anion of a sparingly soluble salt.
A saturated solution of a sparingly soluble salt is a very dilute solution (α → 1 and λ → λ ∞). Then
(æ 1000) / C. (2.26)
By finding the value of λ ∞ from tabular data and measuring the electrical conductivity of the solution, we can calculate the concentration of the saturated solution (in mol-eq/l), which is the solubility of the salt
C= (æ 1000) / λ∞ = S (2.27).
Since æ of sparingly soluble solutions (æ R) is often commensurate with the electrical conductivity of water (æ B), then in the equations the specific electrical conductivity of the solution is often calculated as the difference: æ = æ R - æ B.
For sparingly soluble salts, the activities of the cation and anion practically coincide with their concentrations, therefore
ETC =
(2.28),
Where i is the stoichiometric coefficient of the ion in the dissociation equation; n is the number of types of ions into which the electrolyte dissociates; C i is the ion concentration related to the electrolyte concentration WITH ratio
.
Since = 1, then
,
and the solubility product
. (2.29)
So, for a poorly soluble (binary) monovalent electrolyte dissociating according to the scheme
,
(mol/l) 2 .
THEME 3
Electrode processes. The concept of electromotive forces (EMF) and potential jumps. Electrochemical circuits, galvanic elements. Normal hydrogen electrode, standard electrode potential. Thermodynamics of a galvanic cell. Classification of electrochemical circuits and electrodes.
Electrolytes are chemical compounds that completely or partially dissociate into ions in solution. Distinguish between strong and weak electrolytes. Strong electrolytes dissociate into ions in solution almost completely. Some inorganic bases are examples of strong electrolytes. (NaOH) and acids (HCl, HNO3), as well as most inorganic and organic salts. Weak electrolytes dissociate only partially in solution. The proportion of dissociated molecules from the number of initially taken ones is called the degree of dissociation. Weak electrolytes in aqueous solutions include almost all organic acids and bases (for example, CH3COOH, pyridine) and some organic compounds. At present, in connection with the development of research on non-aqueous solutions, it has been proved (Izmailov et al.) that strong and weak electrolytes are two states of chemical elements (electrolytes), depending on the nature of the solvent. In one solvent, a given electrolyte can be a strong electrolyte, in another it can be a weak one.
In electrolyte solutions, as a rule, more significant deviations from ideality are observed than in a solution of non-electrolytes of the same concentration. This is explained by the electrostatic interaction between ions: the attraction of ions with charges of different signs and the repulsion of ions with charges of the same sign. In solutions of weak electrolytes, the forces of electrostatic interaction between ions are less than in solutions of strong electrolytes of the same concentration. This is due to the partial dissociation of weak electrolytes. In solutions of strong electrolytes (even in dilute solutions), the electrostatic interaction between ions is strong and they must be considered as ideal solutions and the activity method should be used.
Consider a strong electrolyte M X+, AX-; it completely dissociates into ions
M X+ A X- = v + M X+ + v - A X- ; v = v + + v -
In connection with the requirement of electrical neutrality of the solution, the chemical potential of the considered electrolyte (in general) μ 2 related to the chemical potentials of the ions μ - μ + ratio
μ 2 \u003d v + μ + + v - μ -
The chemical potentials of the constituents of the electrolyte are related to their activities by the following equations (according to expression II. 107).
(VII.3)
Substituting these equations into (VI.2), we obtain
Let's choose the standard state μ 2 0 so that between the standard chemical potentials μ 2 0 ; µ + 2 ; μ - 0 a relation similar in form to equation VII.2 was valid
(VII.5)
Taking into account equation VII.5, relation VII.4 after canceling the same terms and the same factors (RT) brought to mind
Or 
(VII.6)
Due to the fact that the activities of individual ions are not determined from experience, we introduce the concept of the average activity of electrolyte ions as the geometric mean of the activities of the cation and anion of the electrolyte:
; 
(VII.7)
The average activity of electrolyte ions can be determined from experience. From equations VII.6 and VII.7 we obtain.
The activities of cations and anions can be expressed by the relations
a + = y + m + , a - = y - m -(VII.9)
Where y + And y-- activity coefficients of the cation and anion; m + And m-- molality of the cation and anion in the electrolyte solution:
m+=mv+ And m - = m v -(VII.10)
Substituting values a + And a- from VII.9 and VII.7 we get
(VII.11)
Where y ±- average activity coefficient of the electrolyte
(VII.12)
m ±- average molality of electrolyte ions
(VII.13)
Average activity coefficient of the electrolyte y ± is the geometric mean of the activity coefficients of the cation and anion, and the average concentration of electrolyte ions m ± is the geometric mean of the cation and anion concentrations. Substituting values m + And m- from equation (VII.10) we obtain
m±=mv±(VII.14)
Where 
(VII.15)
For a binary univalent MA electrolyte (for example NaCl), y+=y-=1, v ± = (1 1 ⋅ 1 1) = 1 And m±=m; the average molality of electrolyte ions is equal to its molality. For a binary divalent electrolyte MA (for example MgSO4) we also get v ±= 1 And m±=m. For electrolyte type M 2 A 3(For example Al 2 (SO 4) 3) 
And m ±= 2.55 m. Thus, the average molality of electrolyte ions m ± not equal to the molality of the electrolyte m.
To determine the activity of the components, you need to know the standard state of the solution. As a standard state for the solvent in the electrolyte solution, a pure solvent is chosen (1-standard state):
x1; a 1 ; y 1(VII.16)
For a standard state for a strong electrolyte in a solution, a hypothetical solution is chosen with an average concentration of electrolyte ions equal to unity and with the properties of an extremely dilute solution (2nd standard state):
Average activity of electrolyte ions a ± and the average activity coefficient of the electrolyte y ± depend on the way the electrolyte concentration is expressed ( x ± , m, s):
(VII.18)
Where x ± = v ± x; m ± = v ± m; c ± = v ± c(VII.19)
For a strong electrolyte solution
(VII.20)
Where M1- molecular weight of the solvent; M2- molecular weight of the electrolyte; ρ - density of the solution; ρ 1 is the density of the solvent.
In electrolyte solutions, the activity coefficient y±x is called rational, and the activity coefficients y±m And y±c- practically average electrolyte activity coefficients and denote
y±m ≡ y± And y±c ≡ f±
Figure VII.1 shows the dependence of the average activity coefficients on the concentration for aqueous solutions of some strong electrolytes. With an electrolyte molality of 0.0 to 0.2 mol/kg, the average activity coefficient y ± decreases, and the stronger, the higher the charge of the ions that form the electrolyte. When changing the concentrations of solutions from 0.5 to 1.0 mol/kg and above, the average activity coefficient reaches a minimum value, increases and becomes equal to or even greater than unity.
The average activity coefficient of a dilute electrolyte can be estimated using the ionic strength rule. The ionic strength I of a solution of a strong electrolyte or a mixture of strong electrolytes is determined by the equation:
Or (VII.22)
In particular, for a monovalent electrolyte, the ionic strength is equal to the concentration (I = m); for a one-bivalent or two-univalent electrolyte (I = 3 m); for binary electrolyte with ionic charge z I= m z 2.
According to the rule of ionic strength in dilute solutions, the average activity coefficient of the electrolyte depends only on the ionic strength of the solution. This rule is valid at a solution concentration of less than 0.01 - 0.02 mol / kg, but approximately it can be used up to a concentration of 0.1 - 0.2 mol / kg.
The average activity coefficient of a strong electrolyte.
Between activity a 2 strong electrolyte in solution (if we do not formally take into account its dissociation into ions) and the average activity of electrolyte ions y ± in accordance with equations (VII.8), (VII.11) and (VII.14) we obtain the relation
(VII.23)
Consider several ways to determine the average activity coefficient of the electrolyte y ± according to the equilibrium properties of the electrolyte solution.
