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, which 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 mass action law 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
In solutions of strong electrolytes, as a result of their almost complete dissociation, a high concentration of ions is created, which is determined by the formula
[ion] = n C M,
where n is the number of ions of a given type, formed during the dissociation of one electrolyte molecule.
To take into account the interaction between ions in a solution of a strong electrolyte, the concept of "activity" is introduced. Activity - it is the effective concentration of an ion, according to which the ion manifests itself in chemical reactions. Ion concentration and activity a related by the ratio
a =[ion] × f,
where f– activity coefficient.
In highly dilute solutions of strong electrolytes f= 1, a =[and he].
The dissociation constant of a strong electrolyte dissociating according to the equation KA Û K + + Аˉ, is written like this:
K dis = = ×,
where are the activities of the cation and anion; – activity coefficients of the cation and anion; a 2 , f 2 – activity and activity coefficient of the electrolyte in solution. This dissociation constant is called thermodynamic.
Electrolyte activity KA(cation and anion are singly charged) is related to the activities of ions by the relation
a 2 = = (FROM M) 2 × .
For electrolyte KA average ionic activity a± and average ionic activity coefficient f± are related to the activities and activity coefficients of cations and anions by the relations:
a ± = ; f ± = .
For electrolyte K m A n similar expressions look like:
a ± = ; f ± = .
In dilute electrolyte solutions, the average ionic activity coefficient can be calculated from the equation ( Debye-Hückel limit law):
lg f ± = – 0,5z + ×,
where z+, are ion charges; I is the ionic strength of the solution.
Ionic strength of solution I half the sum of the product of the concentrations of each ion and the square of its charge is called:
The values of the activity coefficients of ions depending on the ionic strength of the solution are given in Table. 4 applications.
The presence of interaction between ions in solutions of strong electrolytes leads to the fact that the degree of dissociation of a strong electrolyte found experimentally is less than 1. It is called apparent degree of dissociation and calculated by the formula
where n- the number of ions formed during the dissociation of one electrolyte molecule; i- isotonic van't Hoff coefficient.
Isotonic ratio i shows how many times the experimentally found property of an electrolyte solution differs from the same property calculated for a non-electrolyte solution at the same concentration:
where the property of the solution can be R osm, D R, D T kip or D T deputy Therefore, an electrolyte solution will be isotonic to a non-electrolyte solution of the same concentration if the calculated value of the property of the non-electrolyte solution is multiplied by the isotonic coefficient:
p \u003d i × C M × R× T; D R exp = i × p ×;
= I × K × b and D T = I × E × b.
Solution
K 2 SO 4 dissociates according to the equation K 2 SO 4 Û 2 K + + SO. Therefore, the equilibrium concentrations of ions are equal:
2 FROM M = 2 × 0.01 \u003d 0.02 mol / dm 3; = FROM M = 0.01 mol / dm 3.
Example 2 Calculate the activity of NaI in a 0.05 molar solution if it is known that the average ionic activity coefficient is 0.84.
Solution
a 2 \u003d a + × a - \u003d C M 2 × f ± 2 \u003d 0.05 2 × 0.84 2 \u003d 1.76 × 10 -3.
Example 3 What are the active concentrations of Sr 2+ and ions in a 0.06 molar solution of Sr(NO 3) 2 obtained during the isolation of strontium from a celestine concentrate?
Solution
Sr(NO 3) 2 dissociates according to the equation Sr(NO 3) 2 Û Sr 2+ + 2. Since FROM M = 0.06 mol / dm 3, then the equilibrium concentrations of ions are:
= FROM M = 0.06 mol / dm 3; = 2 FROM M = 2 × 0.06 mol / dm 3.
Find the ionic strength of the solution:
I= 1/2 ×( ×z + ×z) = 1/2×(0.06×2 2 + 2×0.06×1 2) = 0.18.
Based on the value of the ionic strength of the solution, we calculate the activity coefficients of the ions:
lg f+=- 0,5z=-0.5 × 2 2 × = -0.85,
Consequently, f + = 0,14.
lg f – = -0,5z=-0.5×1 2× = -0.21,
Consequently, f – = 0,61.
We calculate the active concentrations of ions:
a+= × f+= 0.06 × 0.14 \u003d 0.0084 mol / dm 3;
a – = × f – = 2 × 0.06 × 0.61 = 0.0734 mol / dm 3.
Example 4 An aqueous solution of hydrochloric acid ( b= 0.5 mol/kg) freezes at –1.83 °C. Calculate the apparent degree of dissociation of the acid.
Solution
Calculate D T deputy non-electrolyte of the same concentration:
D T=K× b.
Using table. 2 applications, we will determine the cryoscopic constant of water: K(H 2 O) = 1.86.
D T=K× b= 1.86 × 0.5 \u003d 0.93 ° C.
Consequently, i =
Problem 529.
Calculate the approximate value of the ion activity K+ and SO 4 2- in 0.01 M K solution 2 SO 4 .
Solution:
Dissociation equation K 2 SO 4 has the form:
K 2 SO 4 ⇔ 2K + + SO 4 2-.
The activity of an ion (mol/l) is related to its molecular concentration in solution by the relation: = fCM.
Here f is the ion activity coefficient (dimensionless value), C M is the ion concentration. The activity coefficient depends on the charge of the ion and the ionic strength of the solution, which is equal to half the sum of the products of the concentration of each ion and the square of the charge of the ion:
The ionic strength of the solution is:
I = 0.5 = 0.5(0.02 . 1 2) + (0,01 . 2 2) = 0,03.
The activity coefficient of K + and SO 4 2- ions is found by the formula, we get:
Now we calculate the activity of K + and SO 4 2- ions from the relation = fCM we get:
(K+)=0.02 . 0.82 = 0.0164 mol/l; (SO 4 2-) = 0.01 . 0.45 = 0.0045 mol/l.
Answer:(K +) = 0.0164 mol/l; (SO 4 2-) \u003d 0.0045 mol / l.
Problem 530.
Calculate the approximate value of the activity of Ba 2+ and Cl - ions in 0.002 N. BaCl 2 solution.
Solution:
M (BaCl 2) \u003d C E (BaCl 2)
C M \u003d C H \u003d 2 .
0.002 = 0.004 mol/l.
The dissociation equation for barium chloride has the form:
BaCl 2 ⇔ Ba 2+ + 2Cl -.
The activity of an ion (mol/l) is related to its molecular concentration in solution by the relation: = fC M .
Here f is the ion activity coefficient (dimensionless value), C M is the ion concentration. The activity coefficient depends on the charge of the ion and the ionic strength of the solution, which is equal to half the sum of the products of the concentration of each ion and the square of the charge of the ion:
The ionic strength of the solution is:
I = 0.5 = 0.5(0.004 . 2 2) + (0,008 . 1 2) = 0,024.
The activity coefficient of Ba2+ and Cl- ions is found by the formula, we get:
Now we calculate the activity of Ba 2+ and Cl - ions from the relation = fC M we get:
(Ba2+) = 0.004 . 0.49 = 0.0196 mol/l; (Cl-) = 0.008 . 0.84 = 0.00672 mol/l.
Answer:(Ba 2+) = 0.0196 mol/l; (Cl -) \u003d 0.00672 mol / l.
Problem 531.
Find the approximate value of the activity coefficient of a hydrogen ion in a 0.0005 M solution of H 2 SO 4 containing, in addition, 0.0005 mol/l HCI. Assume that sulfuric acid completely dissociates in both steps.
Solution:
The total concentration of hydrogen ions is the sum of the H 2 SO 4 concentration and the HCI concentration. Acids dissociate according to the scheme:
H 2 SO 4 ⇔ 2H + + SO 4 2-;
HCl ⇔ H + + Cl -
It follows from the equations that the concentration of hydrogen ions in sulfuric acid is 2 times higher than that of acids and will be: 2 . 0.0005 = 0.001 mol/l. The total concentration of hydrogen ions in the solution will be:
0.001 + 0.0005 = 0.0015 mol/L.
The ion activity coefficient is calculated by the formula:
where f is the ion activity coefficient (dimensionless value), I is the ionic strength of the solution, Z is the charge of the ion. The ionic strength of the solution is calculated by the equation:
Here the concentration of the ion in the solution, we get:
I = 0.5 = 0.002.
Let us calculate the activity coefficient of the hydrogen ion.
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 is a measure of the intensity of the 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 a solution is of 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 activity coefficient of the ion 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 dilute aqueous solutions of non-electrolytes, the activity coefficient is equal to one. Experience shows that as the concentration of the electrolyte increases, the values of f decrease, pass through a minimum, and then increase again and become significantly greater than unity 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 affected by the second phenomenon, which is due to the interaction between ions and water molecules (hydration). At the same time, 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 created by the center. 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 of 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.
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 interval 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 vapor, respectively, A are the activities of the pure metal and its oxide, respectively.
Calculate activity by calculation method electromotive force a galvanic cell formed by a solution or melt of an electrolyte. 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. In the analysis, it should be taken into account that less value 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 tells how much working capital 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 has increased demand for cash and she 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.
Useful 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”.
