Calculate the average ionic activity coefficient. Activity and activity coefficient of electrolytes. Average ionic activity and average ionic activity coefficient. The solubility product rule allows

Thermodynamics of electrolyte solutions

Basic concepts

Electrochemistry- chapter physical chemistry, which 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 electricity the movement of electrons. Ionic conductors (conductors of the second kind) conduct electric current due to the movement of ions.

electrolytes substances are called chemical compounds), which 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 total number 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, a decrease partial pressure liquid vapor over solution, freezing point depression, 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:

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classical theory 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 a 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) arising 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 evaluate 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 (according to thermodynamic properties 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.

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, due to the development of research aqueous solutions proved (Izmailov et al.) that strong and weak electrolytes are two states 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 mass 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.

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:

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.

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:

where m i - the chemical potential of the cation or anion.

From equations (1.5-1.7) it follows that:

= n+ + n- , (1.9)

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 ±:

where + and - are the activity coefficients of the cation and anion; n± - the average number of cations and anions in solution.

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.

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 With (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 laws 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 imposing on the cell electric field, which causes a directed movement of charged particles (electric current), as well as by changing the concentration of a solute. In addition, chemical transformations of reactants can occur on the electrode surface and in solution. This mutual transformation of electrical and chemical forms of energy is called electrolysis.

Patterns of electro chemical 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 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 mass various substances involved in electrochemical reactions are proportional to their molar masses 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.

The average activity coefficient of a strong electrolyte.

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