Electrochemistry

Ion activity. Ionic strength of the solution. Dependence of the ion activity coefficient on the ionic strength of the solution. Debye-Hückel theory.

Activity (ions) - effective concentration, taking into account the electrostatic interaction between ions in solution. Activity differs from concentration by some amount. The ratio of activity (a) to the concentration of a substance in solution (c, in g-ion / l) is called the activity coefficient: γ \u003d a / c.

Ionic strength of solution - measure of intensity electric field created by ions in solution. Half the sum of the products of the concentration of all ions in a solution and the square of their charge. The formula was first derived by Lewis:

where cB - molar concentrations individual ions (mol/l), zB ion charges

The summation is carried out over all types of ions present in the solution. If two or more electrolytes are present in the solution, then the total total ionic strength of the solution is calculated. For electrolytes in which multiply charged ions are present, the ionic strength usually exceeds the molarity of the solution.

The ionic strength of the solution has great importance in the Debye-Hückel theory of strong electrolytes. The basic equation of this theory (Debye-Hückel limiting law) shows the relationship between the ion activity coefficient ze and the ionic strength of the solution I in the form: solvent constant and temperature.

The ratio of activity (a) to the total concentration of a substance in solution (c, in mol / l), that is, the activity of ions at a concentration of 1 mol / l, is called activity factor :

In infinitely diluted aqueous solutions non-electrolyte activity coefficient equal to one. Experience shows that as the electrolyte concentration increases, the values ​​of f decrease, pass through a minimum, and then increase again and become significantly large units in strong solutions. Such behavior of the dependence of f on concentration is determined by two physical phenomena.

The first is especially pronounced at low concentrations and is due to the electrostatic attraction between oppositely charged ions. Attractive forces between ions prevail over repulsive forces, i.e. in solution, a short-range order is established, in which each ion is surrounded by ions of the opposite sign. The consequence of this is an increase in the bond with the solution, which is reflected in a decrease in the activity coefficient. Naturally, the interaction between ions increases with increasing their charges.

With increasing concentration, the activity of electrolytes is increasingly influenced by the second phenomenon, which is due to the interaction between ions and water molecules (hydration). In this case, in relatively concentrated solutions, the amount of water becomes insufficient for all ions and gradual dehydration begins, i.e. the connection of ions with the solution decreases, therefore, the activity coefficients increase.

Some regularities concerning activity coefficients are known. So, for dilute solutions (up to approximately m = 0.05), the relation 1 - f = k√m is observed. In somewhat more dilute solutions (m ≈ 0.01), the values ​​of f do not depend on the nature of the ions. This is due to the fact that the ions are located at such distances from each other, at which the interaction is determined only by their charges.

At higher concentrations, along with the charge, the activity value begins to be affected by the radius of the ions.

To assess the dependence of activity coefficients on concentration in solutions where several electrolytes are present, G. Lewis and M. Randall introduced the concept of ionic strength I, which characterizes the intensity of the electric field acting on ions in a solution. The ionic strength is defined as half the sum of the terms obtained by multiplying the molalities of each ion, mi, by the square of its valence, Zi:

I = 1/2∑miZi. (IX.18)

DEBYE-HUKKEL THEORY , statistical theory of dilute solutions of strong electrolytes, which allows you to calculate the coefficient. ion activity. It is based on the assumption of complete dissociation of the electrolyte into ions, which are distributed in the solvent, considered as a continuous medium. Each ion by the action of its electric charge polarizes the environment and forms around itself a certain predominance of ions of the opposite sign - the so-called. ionic atmosphere. In the absence of external electric field ionic atmosphere has a spherical. symmetry and its charge is equal in magnitude and opposite in sign to the charge of the center that creates it. and she. Potential j total electric. fields, center being created. ion and its ionic atmosphere at a point located at a distance r from the center. ion, m.b. calculated if the ionic atmosphere is described by a continuous distribution of charge density r near the center. and she. For the calculation, the Poisson equation is used (in the SI system):

n2j = -r/ee0,

where n2 is the Laplace operator, e is the dielectric. solvent permeability, e0 - electric. constant (vacuum permittivity). For each i-th kind of ions, r is described by the function of the Boltzmann distribution; then, in the approximation that considers ions as point charges (the first approximation of D.-H.T.), the solution to the Poisson equation takes the form: where z is the charge number center. ion, rd - so-called. Debye screening radius (radius of the ionic atmosphere). At distances r > rd, the potential j becomes negligible, i.e., the ionic atmosphere shields the electric. center field. and she.

In the absence of an external electric field, the ionic atmosphere has spherical symmetry, and its charge is equal in magnitude and opposite in sign to the charge of the central ion that creates it. In this theory, almost no attention is paid to the formation of pairs of oppositely charged ions by direct interaction between them.

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Department of Electrochemical Production Technology

Calculation of activity coefficients

Guidelines for implementation in the discipline "Introduction to the theory of electrolyte solutions"

for students studying

direction 240100 - chemical technology and biotechnology (profile - technology of electrochemical production)

Yekaterinburg

Compiled by:

Professor, dr chem. Sciences

professor, doctor of chem. Sciences,

Scientific editor professor dr chem. Sci. Irina Borisovna Murashova

Calculation of activity coefficients: Guidelines for performing settlement work on the discipline "Introduction to the theory of electrolyte solutions" /,. Ekaterinburg: USTU-UPI 2009.12s.

AT guidelines bases of calculation of coefficients of activity are stated. The possibility of calculating this value on the basis of various theoretical models is shown.

Bibliography: 5 titles. 1 Tab.

Prepared by the department "Technology of electrochemical production".

Variants of assignments for term paper

Bibliographic list

INTRODUCTION

Theoretical ideas about the structure of solutions were first formulated in the Arrhenius theory of electrolytic dissociation:

1. Electrolytes are substances that, when dissolved in appropriate solvents (for example, water), decompose (dissociate) into ions. The process is called electrolytic dissociation. Ions in solution are charged particles that behave like molecules. ideal gas, that is, they do not interact with each other.

2. Not all molecules decompose into ions, but only a certain fraction of b, which is called the degree of dissociation

Where n is the number of decayed molecules, N is the total number of solute molecules. 0<б<1

3. The law of mass action applies to the process of electrolytic dissociation.

The theory does not take into account the interaction of ions with water dipoles, that is, the ion-dipole interaction. However, it is this type of interaction that determines the physical foundations for the formation of ions, explains the causes of dissociation and the stability of ionic systems. The theory does not take into account the ion-ion interaction. Ions are charged particles and therefore act on each other. Neglecting this interaction leads to a violation of the quantitative relations of the Arrhenius theory.

Because of this, later the theory of solvation and the theory of interionic interaction arose.

Modern ideas about the mechanism of formation of electrolyte solutions. Balance electrodes

The process of formation of ions and the stability of electrolyte solutions (ionic systems) cannot be explained without taking into account the forces of interaction between ions and solvent molecules (ion-dipole interaction) and ion-ion interaction. The entire set of interactions can be formally described using instead of concentrations (Ci) ion activities (ai)

where fi is the activity coefficient of the i-th kind of ions.

Depending on the form of expression of concentrations, there are 3 scales of activity networks and activity coefficients: molar c-scale (mol/l or mol/m3); m is the molar scale (mol/kg); N is a rational scale (the ratio of the number of moles of a solute to the total number of moles in the volume of a solution). Accordingly: f, fm, fN, a, am, aN.

When describing the properties of electrolyte solutions, the concepts of salt activity are used

(2)

and average ionic activity

where , a and are the stoichiometric coefficients of the cation and anion, respectively;

C is the molar concentration of the solute;

- average activity coefficient.

The main provisions of the theory of solutions of strong electrolytes by Debye and Hueckel:

1. Only electrostatic forces act between ions.

2. When calculating the Coulomb interaction, it is assumed that the permittivity of the solution and the pure solvent are equal.

3. The distribution of ions in a potential field obeys the Boltzmann statistics.

In the theory of strong electrolytes by Debye and Hueckel, two approximations are considered when determining the activity coefficients.

In the first approximation, when deriving the expression for the average activity coefficient, it is assumed that the ions are material points (ion size ) and the forces of electrostatic interaction act between them:

, (4)

Activity coefficient in a rational scale (N is the concentration expressed in mole fractions);

T - temperature;

e is the permittivity of the medium (solvent);

- ionic strength of the solution, mol/l, k - the number of types of ions in the solution;

.

To calculate the activity coefficient in the molal scale, the ratio is used

Molar concentration of the dissolved substance, mol/kg;

Molar mass of solvent, kg/mol.

The calculation of the average activity coefficient in the first approximation is valid for dilute solutions of strong electrolytes.

In the second approximation, Debye and Hueckel took into account that the ions have a finite size equal to a. The size of an ion is the minimum distance that ions can approach each other. The size values ​​of some ions are presented in the table.

Table 1. Values ​​of parameter a characterizing the size of ions

		F-, Cl-, Br-, I-, CN-, NO2-, NO3-, OH-, CNS-
		IO3-, HCO3-, H2PO4-, HSO3-, SO42-
		PO43-, Fe(CN)63-
Rb+, Cs+, NH4+, Tl+, Ag+
Ca2+, Cu2+, Zn2+, Sn2+, Mn2+, Fe2+, Ni2+, Co2+
Pb2+, Sr2+, Ba2+, Ra2+, Cd2+, Hg2+,
Fe3+, Al3+, Cr3+, Sc3+, Y3+, La3+, In3+, Ce3+,

As a result of thermal motion, the ions in the electrolyte solution are located around the ion, arbitrarily chosen as the central one, in the form of a sphere. All ions of the solution are equivalent: each is surrounded by an ionic atmosphere and, at the same time, each central ion is part of the ionic atmosphere of another ion. A hypothetical ionic atmosphere has an equal and opposite charge with respect to the charge of the central ion. The radius of the ionic atmosphere is denoted as .

If the sizes of the cation and anion are close, then the second approximation of Debye and Hueckel can be used to determine the average activity coefficient:

, (6)

where , . (7)

The expressions for the activity coefficients of the cation and anion are:

and

From the known activity coefficients of individual ions, the average ionic activity coefficient can be calculated: .

The theory of Debye and Hueckel is applicable to dilute solutions. The main disadvantage of this theory is that only the forces of the Coulomb interaction between ions are taken into account.

Calculation of activity coefficients according to Robinson-Stokes and Ikeda.

In deriving the equation for the average activity coefficient, Robinson and Stokes learned from the fact that ions in solution are in a solvated state:

where - the activity of the solvent depends on the osmotic coefficient (c), ;

The number of solvent molecules associated with one solute molecule; bi is the hydration number of the i-th ion.

Ikeda proposed a simpler formula for calculating the molar average ionic activity coefficient

The Robinson-Stokes equation makes it possible to calculate the activity coefficients of 1-1 valence electrolytes up to a concentration of 4 kmol/m3 with an accuracy of 1%.

Determination of the mean ionic activity coefficient of an electrolyte in a mixture of electrolytes.

For the case when there are two electrolytes B and P in the solution, Harned's rule is often fulfilled:

, (10)

where is the average ionic activity coefficient of electrolyte B in the presence of electrolyte P

Average ionic activity coefficient B in the absence of P,

- total molality of the electrolyte, which is calculated as the sum of the molar concentrations of electrolytes B and P,

Here hB and hP are the number of solvent molecules associated with one electrolyte molecule B and P, respectively, and are the osmotic coefficients of electrolytes B and P.

Topics of term papers in the discipline

for part-time students

option number	Electrolyte	Concentration, mol/m3	Temperature, 0C

Activity components of the solution is the concentration of the components, calculated taking into account their interaction in the solution. The term "activity" was proposed in 1907 by the American scientist Lewis as a quantity, the use of which will help to describe the properties of real solutions in a relatively simple way.

Instruction

There are various experimental methods for determining the activity of solution components. For example, by increasing the boiling point of the test solution. If this temperature (denoted as T) is higher than the boiling point of the pure solvent (To), then the natural logarithm of the activity of the solvent is calculated by the following formula: lnA = (-? H / RT0T) x? T. Where, ?H is the heat of evaporation of the solvent in the temperature range between To and T.

You can determine the activity of the components of the solution by lowering the freezing point of the test solution. In this case, the natural logarithm of the solvent activity is calculated using the following formula: lnA = (-?H/RT0T) x?T, where, ?H is the freezing heat of the solution in the range between the freezing point of the solution (T) and the freezing point of the pure solvent (To ).

Calculate the activity using the method of studying the equilibrium of a chemical reaction with a gas phase. Suppose you are undergoing a chemical reaction between a melt of some metal oxide (denoted by the general formula MeO) and a gas. For example: MeO + H2 = Me + H2O - that is, the metal oxide is reduced to pure metal, with the formation of water in the form of water vapor.

In this case, the equilibrium constant of the reaction is calculated as follows: Кр = (pH2O x Ameo) / (рН2 x Ameo), where p is the partial pressure of hydrogen and water vapors, respectively, A are the activities of the pure metal and its oxide, respectively.

Calculate the activity by calculating the electromotive force of a galvanic cell formed by an electrolyte solution or melt. This method is considered one of the most accurate and reliable for determining activity.

The turnover of capital is the speed at which funds pass through the various stages of production and circulation. The greater the velocity of capital circulation, the more profit the organization will receive, which indicates the growth of its business activity.

Instruction

Asset turnover in turnover is calculated by dividing the amount of revenue by the average annual value of assets.

where A is the average annual value of assets (total capital) -
B - revenue for the analyzed period (year).

The found indicator will indicate how many turnovers are made by the funds invested in the property of the organization for the analyzed period. With the growth of the value of this indicator, the business activity of the company increases.

Divide the duration of the analyzed period by the turnover of assets, thereby you will find the duration of one turnover. When analyzing, it should be taken into account that the lower the value of this indicator, the better for the organization.

Use tables for clarity.

Calculate the coefficient of fixing current assets, which is equal to the average sum of current assets for the analyzed period, divided by the organization's revenue.

This ratio indicates how much working capital is spent on 1 ruble of sold products.

Now calculate the duration of the operating cycle, which is equal to the duration of the turnover of raw materials, plus the duration of the turnover of finished products, plus the duration of the turnover of work in progress, as well as the duration of the turnover of receivables.

This indicator should be calculated for several periods. If a trend towards its growth is noticed, this indicates a deterioration in the state of the company's business activity, because. at the same time, the turnover of capital slows down. Therefore, the company's need for cash increases, and it begins to experience financial difficulties.

Remember that the duration of the financial cycle is the duration of the operating cycle minus the duration of the accounts payable turnover.

The lower the value of this indicator, the higher the business activity.

The coefficient of stability of economic growth also affects the turnover of capital. This indicator is calculated according to the formula:

(Chpr-D)/ Sk

where Npr - net profit of the company;
D - dividends;
Sk - own capital.

This indicator characterizes the average growth rate of the organization. The higher its value, the better, as it indicates the development of the enterprise, the expansion and growth of opportunities to increase its business activity in subsequent periods.

Helpful advice

The concept of "activity" is closely related to the concept of "concentration". Their relationship is described by the formula: B \u003d A / C, where A is activity, C is concentration, B is “activity coefficient”.

Any physical or mental activity requires energy, so the calculation of the daily calorie intake per day for a woman or man should take into account not only gender, weight, but also lifestyle.

We spend energy daily on metabolism (metabolism at rest) and on movement (exercise). Schematically it looks like this:

Energy \u003d E basal metabolism + E physical activity

Basal metabolic energy, or basal metabolic rate (BRM)- Basal Metabolic Rate (BMR) - this is the energy needed for the life (metabolism) of the body without physical activity. The basic metabolic rate is a value that depends on the weight, height and age of the person. The taller a person, and the greater his weight, the more energy is needed for metabolism, the higher the basic metabolic rate. Conversely, lower, thinner people will have a lower basal metabolic rate.

For men
= 88.362 + (13.397 * weight, kg) + (4.799 * height, cm) - (5.677 * age, years)
For women
= 447.593 + (9.247 * weight, kg) + (3.098 * height, cm) - (4.330 * age, years)
For example, a woman with a weight of 70 kg, a height of 170 cm, 28 years old, requires for basic metabolism (basal metabolism)
= 447,593 + (9.247 * 70) + (3,098 *170) - (4.330 *28)
\u003d 447.593 + 647.29 + 526.66–121.24 \u003d 1500.303 kcal

You can also check the table: Daily energy consumption of the adult population without physical activity according to the norms of the physiological needs of the population in basic nutrients and energy.

A physically inactive person spends 60–70% of daily energy on basal metabolism, and the remaining 30–40% on physical activity.

How to calculate the total amount of energy expended by the body per day

Recall that total energy is the sum of basal metabolic energy (or basal metabolic rate) and energy that goes into movement (physical activity).
To calculate the total energy expenditure, taking into account physical activity, there is Physical activity coefficient.

What is Physical Activity Factor (CFA)

Physical activity coefficient (CFA) \u003d Physical Activity Level (PAL) is the ratio of total energy expenditure at a certain level of physical activity to the basal metabolic rate, or, more simply, the value of the total energy expended divided by the base metabolic rate.

The more intense the physical activity, the higher the coefficient of physical activity will be.

• People who move very little have CFA = 1.2. For them, the total energy expended by the body will be calculated: E \u003d BRM * 1.2
• People who do light exercise 1-3 days a week have a CFA of 1.375. So the formula: E \u003d BRM * 1.375
• People who perform moderate exercise, namely 3-5 days a week, have a CFA of 1.55. Formula for calculation: E \u003d BRM * 1.55
• People who do heavy exercise 6-7 days a week have a CFA of 1.725. Formula for calculation: E \u003d BRM * 1.725
• People who do very hard exercise twice a day, or hard workers, have a CFA of 1.9. Accordingly, the formula for calculating: E ​​\u003d BRM * 1.9

So, in order to calculate the total amount of energy spent per day, it is necessary to multiply the basal metabolic rate according to age and weight (basal metabolic rate) by the coefficient of physical activity according to the physical activity group (Physical activity level).

What is energy balance? And when will I lose weight?

Energy balance is the difference between the energy that enters the body and the energy that the body spends.

Equilibrium in the energy balance is when the energy supplied to the body with food is equal to the energy expended by the body. In this situation, the weight remains stable.
Accordingly, a positive energy balance is when the energy received from the consumed food is greater than the energy needed for the life of the body. In a state of positive energy balance, a person gains extra pounds.

Negative energy balance is when less energy is received than the body has expended. To lose weight, you need to create a negative energy balance.

For more accurate calculations based on the law of mass action, activities are used instead of equilibrium concentrations.

This value was introduced to take into account the mutual attraction of ions, the interaction of a solute with a solvent, and other phenomena that change the mobility of ions and are not taken into account by the theory of electrolytic dissociation.

Activity for infinitely dilute solutions is equal to the concentration:

For real solutions, due to the strong manifestation of interionic forces, the activity is less than the concentration.

Activity can be considered as a value characterizing the degree of bonding of electrolyte particles. Thus, activity is an effective (acting) concentration that manifests itself in chemical processes as a really acting mass, in contrast to the total concentration of a substance in a solution.

Activity coefficient. Numerically, the activity is equal to the concentration multiplied by the coefficient, called the activity coefficient.

The activity coefficient is a value reflecting all the phenomena present in a given system that cause changes in the mobility of ions, and is the ratio of activity to concentration: . At infinite dilution, the concentration and activity become equal, and the value of the activity coefficient is equal to one.

For real systems, the activity factor is usually less than unity. Activities and activity coefficients related to infinitely dilute solutions are marked with an index and denoted, respectively.

An equation applied to real solutions. If we substitute the value of activity instead of the value of the concentration of a given substance in the equation characterizing the equilibrium of the reaction, then the activity will express the effect of this substance on the state of equilibrium.

The substitution of activity values ​​instead of concentration values ​​into the equations following from the mass action law makes these equations applicable to real solutions.

So, for the reaction we get:

or, if we substitute the values:

In the case of applying the equations arising from the law of mass action to solutions of strong electrolytes and to concentrated solutions of weak electrolytes or to solutions of weak electrolytes in the presence of other electrolytes, it is necessary to substitute activities instead of equilibrium concentrations. For example, the electrolytic dissociation constant of an electrolyte type is expressed by the equation:

In this case, the electrolytic dissociation constants determined using activities are called true or thermodynamic electrolytic dissociation constants.

Values ​​of activity coefficients. The dependence of the activity coefficient on various factors is complex and its determination encounters some difficulties, therefore, in a number of cases (especially in the case of solutions of weak electrolytes), where great accuracy is not required, analytical chemistry is limited to applying the law of mass action in its classical form.

The values ​​of the activity coefficients of some ions are given in table. one.

TABLE 1. Approximate values ​​of the average activity coefficients f at different ionic strengths of the solution