Should be replaced by activities.
For example, if for an ion, as well as for a component in a solution, the expression is true:
where with i- concentration i ion in an ideal solution, then for a real solution we will have:
where a i = c i f i is the activity of the i-th ion in solution,
fi - activity factor.
Then the interaction energy of an ion with surrounding ions per 1 mole of ions is equal to
f i →1 at с→0
Thus, the value of the activity coefficient, which mainly depends on the strength of the electrostatic interaction of ions, as well as a number of other effects, characterizes the degree of deviation of the properties of real electrolyte solutions from ideal solutions. According to the meaning of f i, this is the work of transferring an ion from an ideal solution to a real one.
Distinguish between the activity of the electrolyte and the activity of the ions. For any electrolyte, the dissociation process can be written as follows:
where n + and n - is the number of ions BUT with charge z+ and ions B with charge z- into which the original particle decays.
For the electrolyte solution as a whole, we can write:
m salt = m 0 salt + RT ln a salt, (9)
On the other hand, the chemical potential of the electrolyte is the sum of the chemical potentials of the ions, since the electrolyte decomposes into ions:
m salt = n + m + + n - m - , (10)
m + and m - refer to one mole of ions, m salt - to one mole of electrolyte. Let us substitute expression (10) into (9):
n + m + + n - m - = m 0 salt + RT ln a salt (11)
For each type of ions, we can write an equation like (9):
m + = m 0 + + RT ln a +
m - = m 0 - + RT ln a - (12)
We substitute equation (12) into the left side of equation (11) and swap the right and left sides.
m 0 s + RT ln aс = n + m 0 + + n + RT ln a+ + n - m 0 - + n - RT ln a - (13)
Combine all terms with m 0 on the left side:
(m 0 s - n + m 0 + - n - m 0 -) = n + RT ln a+ + n - RT·ln a- - RT·ln a salt (14)
If we take into account that by analogy with formula (10)
m 0 С \u003d n + m 0 + + n - m 0 - (15)
then m 0 С - n + m 0 + - n - m 0 - = 0 (16)
Equation (15) is similar to equation (10), but it refers to the standard state when ( a C = a + = a - = 1).
In equation (14), the right side is equal to zero, and it will be rewritten as follows:
RT ln a c = n + RT ln a+ + n - RT·ln a -
ln a c = ln a+ n + + ln a+n-
This is the relationship of the activity of the electrolyte in solution with the activities of the ions
where a C is the activity of the electrolyte, a+ and a- - activities of positive and negative ions.
For example, for binary electrolytes AB, the following is true:
Hence
It is impossible in principle to find experimentally the activities of individual ions, since one would have to deal with a solution of one kind of ions. It's impossible. Therefore, the concept of average ionic activity (), which is the geometric mean of the activity of individual ions, was introduced:
or substituting expression (17) we have:
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 C) and using equation (19) find the average ionic activity.
In all cases when it becomes necessary to substitute the value a+ or a- into some equation, these values are replaced by the average activity of a given electrolyte a± , for example,
a ± » a + » a -
As is known, activity is related to concentration by the ratio a= f?m. The average ionic activity coefficient () is determined by an expression similar to the expression for the average ionic activity
There are tabular values for different ways of expressing concentrations (molality, molarity, mole fractions). They have numerically different values. Experimentally, the values are determined by the cryoscopic method, the method of measuring vapor pressure, the method of measuring the EMF of galvanic cells, etc.
Similarly, the average ionic stoichiometric coefficient n ± is determined from the expression:
Average ionic molality () is defined as:
Then:
b) Concentrations of ions formed during complete dissociation Na2CO3, are equal to:
Since n + = 2, n - = 1, then .
Activity and activity coefficient of electrolytes. Ionic strength of the solution.
Disadvantages of the Arrhenius theory. Theory of electrolytes by Debye and Hueckel.
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 log g + ¢
m - \u003d m - o + RT ln a-= 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 only measure the average thermodynamic quantities for the ions into which the molecule of this substance decays.
Let the dissociation of salt occur according to the equation:
A n + B n - \u003d n + A z + + n - B z -
With complete dissociation m + \u003d n + m, m - \u003d n - m. Using the Gibbs-Duhem equations, one can show:
a+ n + × a- n - ¤ a= const
The standard states for finding activity values are defined as follows:
lim a+ ® m + = n + m as m ® 0 , lim a- ® m - = n - m for m ® 0
Standard condition for a is chosen so that const is equal to 1. Then:
a+ n + × a-n-= a
Because no methods for experimental determination of values a + and a - separately, then the average ionic activity is introduced a± , determined by the ratio:
a ± n = a
That., we have two quantities characterizing the activity of the dissolved salt. The first of these is molar activity , i.e. salt activity, 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. The second value is average ionic activity a ± .
Let's introduce now ion activity coefficients g + ¢ and g - ¢, average ionic molality m ± and average ionic activity coefficient g ± ¢ :
a + = g + ¢m + , a - = g - ¢m - , m ± = (m + n + ×m - n -) 1/ n = (n + n + ×n - n -) 1/ n m
g ± ¢ = (g¢ + n + ×g¢ - n -) 1/ n
Obviously: a ± = (g¢ + n + ×g¢ - n -) 1/ n (n + n + ×n - n -) 1/ n m = g ± ¢ m ±
Thus, the main quantities are related by the relations:
a ± = g ± ¢ m ± = g ± ¢ (n + n + × n - n - ) 1/ nm = Lg ± ¢ m
where L = (n + n + ×n - n -) 1/ n and for salts of each specific type of valency is a constant value.
The value g ± ¢ 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± = - average molar activity coefficient.
The main methods for measuring the value of g ± ¢ are cryoscopic and the EMF method.
Numerous studies have shown that the dependence curve of g ± ¢ on the solution concentration (m) has a minimum. If the dependence is depicted in the coordinates lg 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 strength 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.
If we use molality as a measure of concentration, then the ionic strength of a solution is given by:
where i- indices of ions of all salts in solution; m i=n i m.
Lewis and Randall opened 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 the 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 the given substance, but depend on the number and valency 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 accurate only at very low concentrations (m ≤ 0.02); even at moderate concentrations it is only approximately true.
In dilute solutions of strong electrolytes:
lgg ± ¢ = - BUT
FAULTS OF THE ARRENIUS 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 motion - in a state similar to gaseous.
However, the idea of a random distribution of ions in a solution is not true, 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 to 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 the electrostatic energy and the energy of the chaotic motion of ions. These energies are comparable in magnitude, so the actual distribution of ions in the electrolyte is intermediate between disordered and ordered. This is the peculiarity of electrolytes and the difficulties that arise in the creation of the theory of electrolytes.
Around each ion, a peculiar ionic atmosphere is formed, in which ions of the opposite (compared to the central ion) sign predominate. The Arrhenius theory did not take this circumstance into account, and many of the conclusions of this theory turned out to be in conflict with experiment.
As one of the quantitative characteristics of an electrolyte, the Arrhenius theory proposes 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 should be the same, regardless of the method of its measurement (by measuring electrical conductivity, osmotic pressure, or EMF). However, in practice, the values of a obtained by different methods coincide only for dilute solutions of weak electrolytes; for strong electrolytes, the greater the discrepancy, the greater the concentration of the electrolyte, and in the region of high concentrations a becomes greater than 1. Consequently, a cannot have the physical meaning that was attributed to it by the Arrhenius theory.
The second quantitative characteristic according to the Arrhenius theory is the dissociation constant; it must 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.
That., the theory of electrolytic dissociation is applicable only to dilute solutions of weak electrolytes.
THE THEORY OF DEBYE AND HUCKEL ELECTROLYTES .
The main provisions of the modern theory of electrolyte solutions were formulated in 1923 by Debye and Hueckel. For the statistical theory of electrolytes the starting position is the following: ions are distributed in the volume of the solution not randomly, but in accordance with the law of the Coulomb interaction. Around each individual ion exists ion atmosphere (ion cloud) - a sphere consisting of ions of the opposite sign. The ions that make up the sphere continuously exchange 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 Hueckel, distinguishes real electrolyte solutions from ideal ones.
Using the equations of electrostatics, one can derive formula for 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 = 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 was obtained for the activity coefficient:
lg f± = - A |z + ×z - | (one)
Coefficient A depends on T and D: inversely proportional to (DT) 3/2.
For aqueous solutions of 1-1 charging electrolytes at 298 K, assuming the equality of the permittivities of the solution and solvent (78.54), we can write:
lg f±=-A=-A=-0.51
Thus, the theory of Debye and Hueckel makes it possible to obtain the same equation for the activity coefficient as was found empirically for dilute electrolyte solutions. The theory, therefore, is in qualitative agreement with experience. In 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, because it is considered to be completely dissociated (a = 1). The theory of Debye and Hueckel 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 statistics of Maxwell-Boltzmann.
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. Interaction between ions is exhausted by Coulomb forces. The imposition of thermal motion forces leads to such a distribution of ions in solution, which is characterized by a statistical spherical ionic atmosphere. This assumption is valid only for dilute solutions. With increasing 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. When calculating, it is assumed that the dielectric constants of the solution and pure solvent are equal; this is true only in the case of dilute solutions.
Thus, all the assumptions of Debye and Hueckel lead to the fact that their theory can only be applied to dilute electrolyte solutions with low valence ions. Equation (1) corresponds to this limiting case and expresses the so-called limiting law Debye and Hueckel or first approximation of the theory of Debye and Hueckel .
The limiting Debye-Hückel law gives the correct values for the activity coefficients 1-1 of the charging electrolyte, especially in very dilute solutions. The convergence of theory with experiment worsens as the concentration of the electrolyte increases, the charges of the ions increase, and the permittivity of the solvent decreases, i.e. with an increase in the interaction forces between the ions.
The first attempt to improve the theory of Debye and Hueckel 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 dimensions of the ions, endowing each electrolyte with a certain average diameter a(this also changes assumption 4). By assigning certain sizes to the ions, Debye and Hueckel 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±= - (2)
where A retains its former value; a provisionally 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 a close to 1.
Retaining the main provisions of the second approximation of the theory, Hueckel took into account the decrease in the dielectric constant with increasing concentration of solutions. Its decrease is caused by the orientation of the dipoles of the solvent around the ion, as a result of which their response to the effect of an external field decreases. The Hückel equation looks like this:
lg f±=-+C I (3)
where C is an empirical constant. With a successful selection of the values of B and C, the Hueckel formula agrees well with experience and is widely used in calculations. With a successive decrease in ionic strength, equation (3) successively transforms into the formula of the second approximation of the Debye and Hueckel theory (equation (2)), and then into the limiting Debye-Huckel law (equation (1)).
In the process of developing the Debye-Hückel theory and consistently rejecting the accepted assumptions, the convergence with experience improves and the area of its applicability expands, but this is achieved at the cost of transforming theoretical equations into semi-empirical ones.
Electrolytes are chemical compounds that fully 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, this electrolyte can be a strong electrolyte, in another - 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 one, 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 its dissociation into ions is not formally taken into account) 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.
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
BUTn+ AT n-= n+ BUT 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 relation
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 valency 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 ± ¢ = - BUT .
The EMF method can be used to determine the average ionic activity coefficients.
Method 1 - calculated. For this purpose, elements without wrapping are used. Let it be necessary to determine in an aqueous solution of HBr with concentration . We compose a galvanic cell without transfer, the circuit of which
Pt(H2) | HBR | AgBr TV, Ag| Pt
It is known that V.
Electrode reaction equations:
H 2 - 2e + 2H 2 O \u003d 2 H 3 O +
AgBr + e = Ag + Br -
Final reaction: H 2 + 2H 2 O + 2AgBr = 2H 3 O + + 2Ag + 2 Br -
Let's write down the Nernst equation for the given total reaction taking place in the galvanic cell:
At a pressure of 1 atm, this expression is simplified:
The reaction HBr + H 2 O = H 3 O + + Br - goes almost to the end, i.e. , a .
Hence,
Hence, the logarithm of the average ionic activity coefficient is equal to
Using formula (42), it is easy to calculate the value of the average ionic activity coefficient, having data on the initial acid concentration and on the values of standard conditional electrode potentials. It should be noted that these values (of standard electrode potentials) are given in reference books at a solution temperature of 298 K.
Method 2 - graphic. If it is necessary to calculate the activity coefficients at a temperature other than 298 K, proceed as follows. Make up a galvanic cell without transfer, for example this
A series of experiments is carried out in which the EMF of such a galvanic cell is measured, but the electrolyte concentration in each experiment is different. This concentration is set by the researcher, i.e. she is famous. For example, the electromotive force ( E, C) the specified galvanic cell was measured at a temperature of 313 K in a series of experiments with different values of the concentration of hydrochloric acid, mol/l.
How to find from these data the value of the average ionic activity coefficient in a solution of hydrochloric acid of any concentration, for example, 0.023 mol / l.
At a temperature of 313 K, reference books do not contain data on the values of standard electrode potentials, so the value of the standard EMF must be found graphically.
The Nernst equation for the final reaction occurring in a given galvanic cell will have the form (14):
We write the equation in a form convenient for further calculations:
On the left side of Eq. (43) are the values given by the experimental condition () and measured in the experiment ( E) . The one on the right in the equation contains two unknown quantities - the standard emf ( E about) and the average ionic activity coefficient in a solution of hydrogen chloride, which must be determined ().
There is a method that allows, under certain conditions, to make on the right side of the equation not two unknown quantities, but one. If we consider such a state in which the average ionic activity coefficient in the electrolyte solution can be taken equal to unity, then its logarithm will be equal to zero and then there will be only one unknown on the right side of the equation - the standard EMF of a galvanic cell at the temperature of the study.
It is known that the average ionic activity coefficients tend to unity in highly dilute solutions when the concentration is 0. As follows from the limit law of the Debye-Hückel theory, the logarithm of the average ionic activity coefficient is proportional to the square root of the ionic strength of the solution (or the square root of the electrolyte concentration) . That is why, with the graphical method of finding the standard EMF of a galvanic cell, the dependence of the left side of equation (30) on the square root of the concentration of the electrolyte solution is built (Fig. 12).
By plotting the experimental values at different values on a graph, a dependence is obtained, which is then extrapolated to a zero value. This is how the standard EMF of a galvanic cell is found at a temperature other than 298 K.
Then return to equation (43). Calculate (i.e. the square root of the concentration at which you need to find the average ionic activity coefficient - point a in Fig. 12). According to the graph (Fig. 12), the value is determined (point b in Fig. 12). Knowing , using equation (43) it is not difficult to calculate the required value of the average ionic activity coefficient.
To compare experimentally determined average ionic activity coefficients with those calculated according to the Debye-Hückel theory, we use the formulas of the limiting law of the theory and the second approximation of this theory.
In the case of the limit law of the Debye-Hückel theory
where are the charges of the cation and anion;
Ionic strength of the solution;
Constant depending on the permittivity of the solvent and temperature.
For aqueous solutions at different temperatures, the value of the constant h is equal to:
Temperature, K 298 303 313 323 Constant h, (l/mol) 0.5 0.512 0.517 0.528 0.539
Equation (45) is valid up to an ionic strength of 0.01 mol/l.
The second approximation of the Debye-Hückel theory is expressed by the following equation
where is the distance of closest approach of the electrical centers of the ions;
AT is an empirical parameter that depends on temperature.
For an aqueous solution at 298 K AT\u003d 3.29 × 10 9 m -1 × mol -0.5 kg 0.5.
If we take the distance of closest approach equal to = 0.304 nm, then we can calculate the average activity coefficients using the Güntelberg equation:
Equation (46) is valid up to an ionic strength of 0.1 mol/l.
OPTIONS OF TASKS FOR COURSE WORK
Depending on the preparedness of students and at the discretion of the teacher, a complete assignment for a term paper may include a combination of two to three options for fragments of assignments listed below.
Option A. Present theoretical material on the topic of the course work. Compose a correctly open galvanic cell without transfer from the proposed electrodes, write down the electrode and final reactions. Write down the Nernst equation for the EMF of such a galvanic cell.
Option B. Present the theoretical material and investigate the temperature dependence of the EMF of a galvanic cell. Calculate according to the EMF data the thermodynamic characteristics of the reaction taking place in the galvanic cell and compare them with the reference data.
Option C. Present the theoretical material and, on the basis of experimental data, determine the average ionic activity coefficients of the electrolyte of the investigated galvanic cell using the EMF method and compare them with those calculated according to the Debye-Hückel theory.
Option D. Present the theoretical material and determine the value of the ionization constant of a weak acid or weak base independently (or on the basis of the experimental data of potentiometric titration given in the task). Compare the obtained data with reference data.
Option E. Present the theoretical material and determine independently (or on the basis of the experimental data given in the task) the method of measuring the EMF and pH-metrically the value of the ionization constant of a weak acid or a weak base. Compare the obtained data with reference data.
