electrolyte solutions. Activity, ionic strength, isotonic ratio

An electrolyte is a solution or melt of a solid or liquid substance capable of dissociating into ions. The process of decomposition of an electrolyte into ions is called electrolytic dissociation.

According to the ability to dissociate, electrolytes are conditionally divided into strong, medium and weak. For strong electrolytes  > 30%, for weak < 3%. Различие сильных и слабых электролитов состоит не столько в степени диссоциации, а в основном в поведении их в растворе, в степени отличия от идеальных растворов. К сильным электролитам относятся вещества HCl, HBr, HI, HNO 3 , H 2 SO 4 (разбавл.), HClO 4 , NaOH, KOH, Ba(OH) 2 , Ca(OH) 2 , почти все соли. К слабым электролитам относятся органические кислоты, HCN, HF, H 3 BO 4 , H 2 CO 3 , H 2 S, NH 4 OH, Fe(OH) 2 , Fe(OH) 3 , H 2 O, HgCl 2 , CdCl 2 . К электролитам средней силы относятся H 3 PO 4 , H 2 C 2 O 4 , H 2 SO 3 , H 2 Ca 2 O 3 .

Ionic strength of solution

The behavior of an ion in a strong electrolyte solution is characterized by a certain function of the electrolyte concentration, which takes into account various electrostatic interactions between ions. This function is called the ionic strength of the solution and is denoted I. The ionic strength of the solution is half the sum of the products of the concentration C of all ions in the solution and the square of their charge z:

If the solution contains only singly charged ions of a binary electrolyte, then the ionic strength of the solution is numerically equal to the molarity of the solution (for this, a factor of ½ is introduced into the formula. If the solution contains several electrolytes in different concentrations, then the contribution of all ions is taken into account when calculating the ionic strength. Weak electrolytes contribute a very small contribution to the ionic strength of a solution, so if they are present in a solution they are usually not included in the calculation of ionic strength.

With an increase in the ionic strength of the solution, the solubility of a sparingly soluble electrolyte in its saturated solution slightly increases. This phenomenon is called the salt effect.

Activity

Activity is a value that characterizes intermolecular and interionic interactions, as if reducing the concentration of ions in a solution. Activity is a quantity whose substitution into thermodynamic relations instead of concentration allows them to be used to describe the systems under consideration. Activity characterizes the active concentration of the electrolyte in the solution, reflects in total all the effects of the interaction of ions with each other and with solvent molecules. Activity is a measure of the actual behavior of a substance in solution. The activity is usually expressed in the same units as the concentration, for example in mol/L.

If we use activity values, then the laws of chemical equilibrium can be applied to strong electrolytes. Then, in the expression for the dissociation constant, there will be activities, and not concentrations of ions.

Activity factor

The activity coefficient characterizes the degree of deviation of the behavior of a real solution from an ideal one. The activity coefficient is equal to the ratio of activity to the concentration of the solution.

Activity and activity factor are calculated in two ways. Both of them make it possible to determine the activity of the electrolyte as a whole, and not of its individual ions. The first way is to compare the properties of a given solution with an ideal one. A graph of the dependence of the properties of the solution on concentration is constructed, and then the resulting graph is extrapolated for infinite dilution (it is assumed that with infinite dilution, the solution tends to ideal).

The second way to calculate activity and activity coefficient is related to the concept of ionic atmospheres. Based on these concepts, the electric potential of the ion is calculated with respect to the ionic atmosphere surrounding it, which decreases with distance from the central ion, gradually passing into the state of a pure solvent or an ideal solution. The change in the isobaric potential during the transfer of a solute from a real solution to an ideal one (transfer of a central ion from an ionic atmosphere to an ideal solution) is a function of the activity coefficient.

The activity coefficient is related to the ionic strength by the relationship:

, where z is the ion charge, f is the activity coefficient.

Degree of dissociation, isotonic coefficient

The degree of dissociation is a quantitative characteristic of the degree of dissociation of the solution. The degree of dissociation is equal to the ratio of the number of molecules decomposed into ions to the total number of molecules of the solute.

For strong electrolytes, the degree of dissociation in dilute solutions is high and depends little on the concentration of the solution. In weak electrolytes, the degree of dissociation is small and decreases with increasing solution concentration.

The degree of dissociation of weak electrolytes is calculated using the Ostwald equation. Let us denote the number of moles of the solute as C, and the degree of dissociation as . Then С mol dissociated in the solution and С mol of each substance was formed. Then the dissociation constant (the equilibrium constant of the dissociation process) will be:

where V is the dilution of the solution (the reciprocal of the concentration). Because for weak electrolytes   0, then the Ostwald equation can be written (assuming that 1 -   1): .

To determine the degree of dissociation, it is necessary to know the number of particles resulting from dissociation. This number can be determined by studying properties that depend on the number of particles in the solution (colligative properties), for example, by measuring the reduction in vapor pressure over the solution. The experimentally found quantitative characteristics of the colligative properties of the solution are greater than those calculated for the same solution from its molar concentration under the assumption that there is no dissociation. To characterize this difference, the isotonic coefficient i = p exp / r calc is introduced. Knowing the isotonic coefficient, it is easy to determine the number of particles in a solution and, consequently, the degree of dissociation.

47. Strong and weak electrolytes. Acids and bases. amphoteric electrolytes.

Amphoteric electrolytes

Amphoteric electrolytes are compounds that, depending on the conditions, are capable of exhibiting either acidic or basic properties. Ampholytes are weak electrolytes showing basic properties with a strong acid and acidic properties with a strong base. A striking example of an amphoteric electrolyte is aluminum hydroxide. Its precipitate can dissolve both in solutions of acids and alkalis.

The concept of amphotericity can be extended to simple substances. For example, aluminum dissolves in solutions of acids and alkalis. Amphoteric electrolytes also include substances in which acidic and basic properties are due to the joint presence of acidic and basic groups. These substances include amino acids (NH 2 RCOOH).

Medium solutions of strong and weak acids and bases (calculation of pH)

In solutions of strong acids and bases such as HCl, HNO 3 , NaOH, KOH, the molar concentration of hydrogen ions coincides and hydroxide ions coincide with the molar concentration of acid and base.

When calculating pH, the use of analytical concentrations is permissible only for very dilute solutions, in which the activities are practically equal to the concentrations of ions. If the pH of sufficiently concentrated solutions is calculated in terms of activities, then its values turn out to be somewhat overestimated.

There are various methods for determining the concentration of hydrogen ions. One of them is based on the use of acid-base indicators. The indicator changes its color depending on the medium of the solutions. Another method for calculating the concentration (titration) consists in adding an alkali solution of a known concentration to the test acid solution, or vice versa. At some point, a pH value is established at which acid and base are neutralized.

The pH of solutions of weak acids and bases is calculated using their dissociation constants. The concentrations of hydrogen ions and the acid residue into which the acid decomposes in weak monobasic acids are equal. In weak electrolytes, the concentration of undissociated molecules is approximately equal to the concentration of the acid itself. Therefore, the equilibrium constant is K sour = or Н +  = . The pH of solutions of weak bases is calculated in a similar way.

Theory of strong electrolytes

Strong electrolytes are electrolytes that are found in solution only in the form of ions. A strong electrolyte, even in the crystalline state, is in the form of ions, but in solutions the degree of dissociation is less than 100%. The electrical conductivity of solutions of strong electrolytes is less than one would expect with complete dissociation of the solute. These features of the properties of strong electrolytes are not described by the theory of electrolytic dissociation.

Calculating the degree of dissociation from the saturation vapor pressure above the solution, from the increase in boiling point and decrease in freezing point, assumes that the solution is ideal. The application of the theory of ideal electrolytes to real ones is associated with a number of deviations. In addition, electrolyte ions interact with solution molecules. Solvation of an ion is the formation around an ion of any charge of a shell of solvent molecules. Interionic interaction also takes place in electrolyte solutions, as a result of which an ion cloud of oppositely charged ions is formed around each ion - an ionic atmosphere. Thus, in real solutions there are no free ions, therefore, the law of mass action cannot be applied to them.

The distance between ions in solutions of strong electrolytes is so small that if the kinetic energy of thermal motion is insufficient to overcome the forces of mutual attraction between the ions, the formation of an ion pair is possible. An ion pair is in some respects similar to an undissociated molecule. The content of ion pairs reaches several percent in very concentrated solutions.

pH=-lg;<7 – кисл, >7 - main.

When a precipitate of a strong electrolyte is formed between the precipitate and

solution establishes chemical equilibrium. A small part of the molecules

Substances constantly pass in the form of ions into solution. Simultaneously from

solution, the same number of ions pass into the precipitate of the substance:

2- ⇔ BaSO4 (tv).

If we take into account that the concentration of BaSO4 in a saturated solution is constant,

then, applying the law of mass action, we can write:

In a saturated solution of a sparingly soluble electrolyte, the product

concentration of its ions at a constant temperature is constant

and is called solubility product (PR or L).

ETC = K1= ⋅x [In+]y. (1.41)

The solubility product rule can only be applied to difficult

soluble substances, in saturated solutions, in which the concentration

ions are very small.

The concept of the solubility product is a special case of the general

the concept of the constancy of the product of ion activity in a saturated solution

electrolyte.

The solubility product PR allows you to control the process

sediment formation. If the ionic product of IP (the product of concentrations

precipitate-forming ions) is less than PR, then no precipitate is formed, because

the concentration of ions in the solution is below the equilibrium. If IP > PR, then

sediment. Precipitation continues until the ionic

products and solubility products. There is balance and

further sedimentation stops.

Solubility can be determined from the solubility product

precipitation S (P). If the precipitate is formed by ions of the same charge and has

composition of MA, then in the solution above the precipitate, the molecules break up into the same

the number of M+ cations and A- anions. The solubility of the precipitate can be represented

as concentrations of either M+ or A-, because they are equal to the concentration

dissolved MA molecules:

MA(tv) ⇔ M+ + A-; PR = [M+]⋅[A-];

[M+] = [A-]; PR \u003d [M +] 2.

S= M+ = ETC

S= ETC(1.42) .

In the general case, for a precipitate, the composition of MnAm is the product of solubility and

solubility are related by the equations:

= ; (1.43)

ETC= S m+n⋅(mm⋅ nn) . (1.44)

The solubility of the precipitate is influenced by various factors. Solubility

electrolyte precipitation increases if the concentration in the solution is lowered

one of its ions (bind into a slightly dissociated compound)

At a low ionic strength of the solution, when the activity coefficients

salt solubility approaches the product of activities.

The solubility product rule allows:

Calculate the concentration of ions of a sparingly soluble salt in

saturated solution,

Calculate the concentration of the reagent - precipitant required for

almost complete deposition

Assess the possibility of sediment formation under given conditions, etc.

Degree of hydrolysis

Under degree of hydrolysis refers to the ratio of the part of the salt undergoing hydrolysis to the total concentration of its ions in solution. Denoted α (or hhydr);
α = (c hydr/ c total) 100%
where c hydr - the number of moles of hydrolyzed salt, c total - the total number of moles of dissolved salt.
The degree of salt hydrolysis is the higher, the weaker the acid or base that forms it.

Is an quantitative characteristic of hydrolysis.

, where Ka- dissociation constant of a weak acid formed during hydrolysis

for a salt formed by a strong acid and a weak base:

, where kb- dissociation constant of the weak base formed during hydrolysis

for a salt formed from a weak acid and a weak base:

In this section, absolute activity, activity coefficient, average activity coefficient and osmotic coefficient are entered. The last two coefficients are useful in tabulating the dependences of the thermodynamic properties of solutions on their composition, but their theoretical expressions are rather cumbersome.

The absolute activity A of the ionic or neutral component, widely used by Guggenheim, is determined from the ratio

It has the advantage that it vanishes in the absence of a component, while the chemical potential then vanishes to minus infinity. In addition, it is dimensionless. Absolute activity has the further advantage that it can be treated like ordinary activity, and is not dependent on any secondary standard state that might be assumed for some solution or solvent at a certain temperature and pressure.

For the dissolved component, the value of A, can be further written as follows:

where is the molality, or the number of moles of a solute per unit mass of the solvent (usually expressed in gram molecules or gram ions per kilogram of solvent), Y is the activity coefficient of the component, a constant proportionality factor that does not depend on the composition and electrical state, but is determined by the dissolved component and dependent on temperature and pressure. For condensed phases, the pressure dependence is often neglected.

Other concentration scales can be used, however, the activity factor and the constant factor change in such a way that it does not depend on the concentration scale used. Another generally accepted concentration scale is molarity, or the number of moles per unit volume of a solution (usually expressed in moles per liter and denoted by M), and is associated with this scale by the ratio

where the molarity of the component is the activity coefficient, and a constant proportionality coefficient, similar to

Molarity is related to molarity according to the equation

where is the density of the solution, is the molecular weight of the component or g / g-ion), and the sum does not include the solvent indicated by the subscript

The popularity of molality among experimenters working in physical chemistry is apparently due to the fact that it is easy to obtain directly from the masses of components in solution, without a separate determination of density. The concentration in the molar scale is more convenient for the analysis of transport processes in solutions. In addition, molality is especially inconvenient if molten salt enters the concentration range under consideration, since the molality becomes infinite in this case. You can use the mole fraction scale, but then you have to decide how to consider the dissociated electrolyte. The mass fraction has the advantage that it depends only on the masses of the components and, moreover, does not depend on the scale of atomic weights, which, as is known, has changed even in recent years. However, the mass fraction scale does not allow one to simply consider the interrelated properties of solutions (decrease in freezing point, increase in boiling point, decrease in vapor pressure), as well as the properties of dilute electrolyte solutions. The only one of these scales that changes with temperature when a given solution is heated is the molar concentration.

The secondary standard states required to find or are calculated from the condition of converting to unity a certain combination of activity coefficients as the solution is infinitely diluted, i.e.

for all such combinations in which the values satisfy equation (13-3). In particular, the activity coefficient of any neutral non-dissociated component

approaches unity as the concentrations of all solutes tend to zero. If we assume that the activity coefficients are dimensionless, then they have dimensions inverse to those of . Taking into account the conditions (13-5) and (13-6) for determining the secondary standard states, we can say that they are related by the relation

where is the density of the pure solvent

For the ionic component, it depends on the electrical state of the phase. Since they are assumed to be independent of the electrical state, we conclude that depends on this state. A similar statement applies to the activity coefficient. In contrast, the Guggenheim accepts that it does not depend, but no. depends on the electrical state. This brings us to the unacceptable situation where y must depend on the composition in a constant electrical state. However, for solutions of various compositions, the definition of a constant electrical state has not yet been given.

To further illustrate the nature of these activity coefficients, consider a solution of one electrolyte A dissociating into cations with a charge number of anions with a charge number - (there is only one electrolyte, so the superscript A y is omitted). Then the stoichiometric concentration of the electrolyte can be represented as

Equation (12-3) can be used to express the chemical potential A as follows:

Since A is neutral, according to condition (14-5) it is necessary that at Therefore, such a definition of the secondary standard state leads to the following combination of quantities

This limiting process allows us to find further the product

At any non-zero value using Equation (14-10).

Summarizing these ideas, we come to the following conclusions:

one can uniquely define an expression of the form

for such works, the indicators of which satisfy the Guggenheim condition

Thus, the choice of the secondary standard state in accordance with the condition (14-5) makes it possible to separately determine the corresponding products of the type

These conclusions follow from the fact that the corresponding products of electrochemical potentials and absolute activities

do not depend on the electrical state in the case of neutral combinations of ions.

On the other hand, the differences and ratios taken in different phases are uniquely determined, but depend on the electrical states of the phases. Their absolute values in a separate phase are not determined, since the primary standard state (for example, at 0 °C and 1 atm) does not contain information about the electrical standard state. Accordingly, the secondary standard state also includes only neutral combinations of components. Consequently, the values for the ionic components are not determined in the only possible way, and this difficulty could be overcome by assigning an arbitrary value to the value for one ionic component in each solvent at each temperature. However, in any application, the equations can be written in such a way that only the products of the quantities also y corresponding to neutral combinations of ions are always required.

Let's return to the solution of one electrolyte. By definition, the average activity factor on the molar scale is given by

The above discussion shows that this average activity coefficient is uniquely determined and does not depend on the electrical state of the solution. If we also determine from the relation

then equality (14-10) can be written in the form

For solutions of one electrolyte, it is the average activity coefficient that is measured and tabulated

Of course, the thermodynamic properties of solutions of one electrolyte can be studied by non-electrochemical means and without detailed consideration of its dissociation. For example, by measuring vapor pressures or freezing points, one can also obtain the dependence of the chemical potential on concentration. This is the merit of thermodynamics, that it allows one to study the macroscopic characteristics of the system, without resorting to molecular concepts, if the various components are rapidly balanced with each other.

If we applied equality (14-2) to electrolyte A without taking into account its dissociation, we would get

This expression differs from equality (14-15) primarily in the absence of the factor v. Thus, should differ from and should have a concentration dependence that is significantly different from the dependence. Specifically, we have

Therefore, at and equality (14-5) is not applicable to determine the secondary standard state for in equality (14-16). We come to the conclusion that at

infinite dilution, it is essential to know the state of aggregation of the solute. This information must be taken into account when choosing the components of the solution, if we wish to use the condition (14-5) to determine the secondary standard state. Except for this need to choose another secondary standard state, it is quite legitimate from a strictly thermodynamic point of view to treat the electrolyte as undissociated, although rarely if this is done. Thus, by the activity coefficient we mean the average ionic activity coefficient of the electrolyte.

Similar representations can be developed for the molar concentration scale. In this scale, the average activity coefficient of the electrolyte is determined from the ratio

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, 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 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 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.

In connection with the electrostatic interaction in solution, even for dilute solutions of strong electrolytes, concentrations in thermodynamic equations must be replaced by activities. For example, if for an ion, as well as for a component in a solution, the expression is true

where from i– concentration i ion in an ideal solution, then for a real solution we will have:

where a i = c i f i - activity of the i-th ion in solution,

f i - activity coefficient.

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  + and  - - 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:

 salt =  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:

 salts =     +     , (10)

 + and   refer to one mole of ions,  salts to one mole of electrolyte. Let us substitute expression (10) into (9):

    +     =  0 salt + RT ln a salt (11)

For each type of ions, we can write an equation like (9):

  =  0  + RT ln a 

  =  0  + RT ln a  (12)

We substitute equation (12) into the left side of equation (11) and swap the right and left sides.

 0 s +RT·ln a c \u003d    0  +  + RT ln a + –  0 – +  RT·ln a  (13)

Combine all terms with  0 on the left side

( 0 s -   0  -   0 ) =  RT ln a +  RT·ln a RT ln a salt (14)

If we take into account that by analogy with formula (10)

 0 С =   0  +   0  (15)

then  0 С -   0  -   0  = 0 (16)

Equation (15) is similar to equation (10), but it refers to the standard state when ( but C = but + =but- = 1). In equation (14), the right side is equal to zero, and it will be rewritten as follows:

RT ln a c \u003d   RT ln a +   RT·ln a 

ln a c = ln a  + ln a  

, (17)

This is the relationship of the activity of the electrolyte in solution with the activities of the ions

where but C - electrolyte activity, but+ and but– - activities of positive and negative ions. For example, for binary electrolytes AB, the following is true:

, Consequently

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 was introduced ( ), which is the geometric mean of the activity of individual ions:

, where
. (18)

or substituting expression (17) we have:

,
(19)

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 ( but C) and using equation (19) find the average ionic activity.

In all cases when it becomes necessary to substitute the value but+ or but- into some equation, these values are replaced by the average activity of a given electrolyte but , for example,

but   but +  but –

As is known, activity is related to concentration by the ratio a=f∙m. Average ionic activity coefficient ( ) is determined by an expression similar to the expression for the average ionic activity

. (20)

There are table values for different ways of expressing concentrations (molality, molarity, mole fractions). For them has numerically different values. Experimental values 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   is determined from the expression

(21)

Average ionic molality (
) is defined as

. (22)

If the concentration of a solution is expressed in terms of molality, then

and, substituting the expressions

m + \u003d ν + m, m - \u003d ν - m,

where m is the molality of the solution, we will have

. (23)

Example 7.1. Find the relationship between the activity of an electrolyte, its molal 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
.

Lewis and Randall introduced some mathematical corrections to the ratios proposed by Arrhenius.

To bring the theory in line with practice and preserve many of the convenient relationships previously obtained on the basis of the Arrhenius theory, it was proposed to use instead of concentrations activity. Then all thermodynamic relations written in the form of equations for ideal solutions, but containing activities rather than concentrations, are in strict agreement 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 the whole 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 only one kind of ions 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 relationship between the activities of individual ions and the activity of the electrolyte as a whole is established based on the condition of electrical neutrality. For this, the concepts 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 a ± is equal to:

where and are the activity of cations and anions, respectively, n is the total number of ions ( n= n + + n-).

Similarly, the average ionic activity coefficient of the electrolyte is written, which characterizes the deviations of the real solution from the ideal

Activity can be represented as the product of concentration and activity coefficient. There are three scales for expressing activities and concentrations: molality (molal or practical scale), molarity from (molar scale) and molar fraction X (rational scale).

In the thermodynamics of electrolyte solutions, the molar concentration scale is commonly used.

where is the coefficient depending on the valence type of the electrolyte.

((So, for a binary 1,1-charge electrolyte (, etc.)

For a 1,2-charge electrolyte (etc.) n + = 2, n - = 1, n = 3 and

On the molar scale.))

There is a relationship between the average ionic activity coefficients in the molar and molar scales:

whereis the density of the pure solvent. (end of independent review)

G. Lewis and M. Randall introduced the concept of ionic strength of solutions:

where is the molar concentration of the th ion; is the charge of the ion.

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 not exceeding 0.02 M.

At higher values of 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 regularities considered above referred to the conditions of thermodynamic equilibrium, when the parameters of the systems did not change in time. The electrochemical equilibrium can be disturbed by applying an electric field to the cell, which causes the directed movement of charged particles (electric current), as well as by changing the concentration of the solute. In addition, chemical transformations of reactants can occur on the electrode surface and in solution. This mutual transformation of electrical and chemical forms of energy is called electrolysis.

The laws 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 usually called cathodic, and oxidation reactions are called anodic. The ratio between the amount of electricity and the masses of reacted substances is expressed as Faraday's laws. (on one's own)

1st law . The mass of a substance that has undergone an electrochemical transformation is proportional to the amount of electricity passed (C):

where - electrochemical equivalent, equal to the mass of the reacted substance when passing a unit amount of electricity, G/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 ():

: = : .

Ratio is a constant value and equal to Faraday constant\u003d 96484 C / mol-equiv. Thus, when passing electricity, CL undergoes an electrochemical transformation of 1 mol-eq 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 are the mass of practically obtained substance and calculated according to Faraday's law, respectively. The few reactions that take place with 100% current efficiency are used in coulometers, instruments designed to accurately measure the amount of electricity.