The movement of ions in electrolytes in some cases can be shown very clearly.
We saturate a piece of filter paper with a solution of electrolyte (sodium sulfate) and phenolphthalein and place it on a glass plate (Fig. 107). Place an ordinary white thread across the paper, moistened with a solution of caustic soda (NaOH). The paper under the thread will turn crimson due to the interaction of hydroxyl ions (OH) from NaOH with phenolphthalein. Then we press the wire electrodes connected to the galvanic cell to the edges of the sheet and turn on the current. Hydroxyl ions from the caustic soda will begin to move towards the anode, turning the paper crimson. By the speed of movement of the crimson edge one can judge the average speed of movement of ions under the influence electric field inside the electrolyte. Experience shows that this speed is proportional to the field strength inside the electrolyte. For a given field, this speed for different ions somewhat different. But in general it is small and for commonly used fields it is measured in hundredths and even thousandths of a centimeter per second.
Rice. 107. Experiment showing the movement of ions. A piece of filter paper is soaked in a solution of electrolyte and phenolphthalein, - a thread moistened with an electrolyte solution
68.1. To determine the sign of the source poles, “pole finders” are used, which are a small glass ampoule with two wires inserted into it (Fig. 108). Ampoule
filled with solution table salt with phenolphthalein added to it, which turns red under the influence of alkali. At which pole will the red color appear?
Rice. 108. For exercise 68.1
Electrolyte solutions. Theory of electrical dissociation.
Electrolytes– substances that, in a solution or melt, consist entirely or partially of ions. These substances are capable of conducting electric current.
Arinus theory:1) When dissolved in water, electrolyte molecules break down into cations and anions, which leads to a change in the Gibbs energy. . 2) The dissociation process is reversible, i.e. There is equilibrium in the solution. And when diluted, complete dissociation is possible. . 3) The sum of cations is equal to the sum of anions. 4) Solutions behave like ideal gases(true only for solutions weak electrolytes).
For quantitative characteristics electrolytes, the degree of dissociation was introduced: - the number of dissociated molecules; - total number molecules in solution; Based on the degree of dissociation, a distinction is made between strong (=1, dissociation is complete) and weak (electrolytes.
A characteristic of weak electrolytes is the dissociation constant:
The connection between and describes Osfald's dilution law: . Electrolyte solutions differ significantly from ideal solutions the fact that particles increase as a result of dissociation.
Isotonic coefficient– the ratio of the actual number of particles in the solution to the one that would have been without dissociation. Relationship between and: K is the total number of ions formed during the dissociation of 1 electrolyte molecule.
Strong electrolytes.
ü In solutions they completely dissociate into ions;
ü There is an electrostatic interaction between the ions - each ion is surrounded by reversely charged ions, the so-called ionic atmosphere.
For solutions strong electrolytes use activities rather than concentrations.
Activity factor() is a measure of the difference between the properties of electrolyte solutions and the properties of ideal solutions.
For strong electrolytes, it is necessary to take into account the forces of electrostatic interaction between ions, because the speed of ion movement decreases due to two effects: 1) Catoffetic– inhibition of ions during movement due to the presence of an ionic atmosphere. 2) Relaxation– destruction of the old ionic atmosphere and formation of a new one.
Mechanism of ion movement. Absolute speed ions.
To turn on the electric field, the ions move randomly, and when the field is applied, one of the directions predominates, and the movement is from A to K. As the speed of movement increases, the resistance of the medium increases, it is greater, the greater the viscosity of the medium and the radius of the ion. The absolute speed of movement of the ions is equal ion movement speed at electric field strength = 1 volt/m2. As the concentration, the number of ions in the solution increases.
The movement of ions occurs due to: 1) unequal distribution of ions on both sides of the membrane; 2) selective permeability of the membrane for ions. At rest, the membrane is unequally permeable to different ions.
The ability of electrolyte solutions to conduct electric current depends on the nature of the electrolyte and solvent, concentration and temperature. In an electrolyte solution, solvated ions are in random thermal motion. When an electric field is applied, an ordered movement of ions occurs towards oppositely charged electrodes - migration (transfer). The movement of ions occurs under the influence of a force that imparts acceleration to them, but simultaneously with an increase in the speed of their movement, the resistance of the medium increases. As a result, the speed of ion movement becomes constant after a short period of time.
Comparison of driving speeds various types ions are produced at the same field potential gradient equal to 1 V/m. The speed of ion movement under these conditions is called absolute ion velocity (electrical mobility or absolute mobility) (u)(it is measured in)
The movement of a hydrated ion can be likened to the movement of a microscopic ball in a viscous medium. This fact allows you to estimate the absolute velocity of ions i-type Stokes formula:
where is the force acting on the ion; medium viscosity coefficient; the effective radius of the particle, which depends on the size of the ion and its hydration.
From equation (32.41) it follows that the larger the effective radius of the ion, the lower the speed of its movement. For example, the sizes of ions alkali metals increase in series
while the ability to hydrate decreases in the same sequence (the ion is more hydrated than other ions). As a result, the effective radii decrease, and the absolute velocities increase when moving from to:
Along with the absolute velocity of ions, the concept of ion mobility is often used. Product of absolute ion velocity and Faraday constant F called ion mobility (molar electrical conductivity). Constant Faraday equals C/mol.
This is the charge of one mole of electrons, i.e. the amount of electricity during electrolysis that must be spent to change the oxidation state of 1 mole of a substance per unit. Ion mobility unit 
, where Cm is (Siemens) the unit of measurement of electrical conductivity, the reciprocal of the unit of measurement of resistance (Ohm), i.e. .
The mobility of multiply charged ions is referred to a unit of charge, i.e., we speak, for example, about the mobility of but cations and but anions
Carry numbers
Each type of ion carries a certain amount of electricity, depending on the charge and concentration of the ions, as well as the speed of their movement in the electric field. The ratio of the amount of electricity transferred by ions of a type, to total number electricity transferred by all ions in solution is called the number ion transport:
In accordance with this definition, the sum of the transport numbers of all types of ions in a solution is equal to one.
For a symmetrical electrolyte K.A., dissociating into two types of ions And , the amount of electricity transferred by cations and anions will be, respectively:
Where elementary charge; charge of cation and anion; molar concentration cations and anions absolute velocities of ions. The ratio of the transfer numbers of cations and anions is equal to the ratio of their absolute velocities or mobilities:
and since then
From the equations it is clear that the transfer number of a given type of ion depends on the absolute speed and mobility of both types of ions, i.e. in solutions of different electrolytes the transfer numbers of the same ion are different.
The degree of ion hydration, their absolute velocity and transport number are affected by solution concentration and temperature. As the concentration increases to approximately 0.1 mol/L, for most electrolytes the ion transport numbers change slightly; in the region of higher concentrations this change is more noticeable. With increasing temperature, the sizes of the hydration shells of weakly hydrated ions decrease less sharply than those of strongly hydrated ions (and sometimes even increase). As a result, the absolute mobility values of cations and anions become closer, and their transfer numbers tend to 0.5.
Dielectric constant is a value that shows how many times the force of interaction between two charges in the medium under study is less than in vacuum.
The charge of the ion z is the ratio of the charge of the ion, expressed in coulombs, to the charge of the electron Cl; charge of the ion, in coulombs, respectively, equal to the product ez.
Further, in all cases where this is not specifically stated, for the sake of simplicity we will talk about the activity coefficient and activity of electrolytes, understanding that we're talking about about the average activity coefficient and average activity. In what follows, the difference between the three methods of expressing activity (activity coefficient) is also neglected, which is quite acceptable for dilute solutions.
The following definitions are also used: the radius (thickness) of the ionic atmosphere, the Debye radius.
The designation of the Siemens unit of electrical conductivity, as well as all other units derived from proper names, is written with capital letter(Cm). This designation should not be confused with the designation of the unit of measurement of length - centimeter (cm).
The speed of directional movement of an ion, i.e., the path traveled by an ion in a solution under the influence of an electric field in the direction of the electrode per unit time, depends on the force acting on the ion, i.e., on the electric field strength:
V = andE
Where V- ion speed, m/s; E- field strength, V/m; And - proportionality coefficient, called the electrical mobility of the ion or simply the mobility of the ion, m 2 / (V s).
ION MOBILITY characterizes its ability to overcome the resistance of the medium during directed movement in an electric field. Let us consider the main factors affecting the mobility of an ion in aqueous solutions in the presence of an electric field.
Ion charge and radius, i.e. its nature: than more charge and the smaller the radius of the ion, the more hydrated the ion, the lower the mobility of the ion in solution.
The nature of the solvent his permittivity and viscosity. The more polar the solvent, the larger sizes hydrated ion and its mobility is lower. The viscosity of the solvent determines the resistance of the medium to the moving ion: the higher the viscosity, the lower the mobility of the ion.
Solution temperature. As the temperature increases, the viscosity of the solvent and the thickness of the solvation shells of the ions decrease, and the interionic interaction also decreases. All this leads to an increase in ion mobility.
Ionic strength of the solution. The greater the ionic strength of the solution, the stronger the interionic electrostatic interaction and the inhibitory effects it creates.
Ion concentration. The higher the concentration of ions in the solution, the stronger the electrostatic interaction of the ions, which reduces their mobility. The concentration of ions depends on the strength of the electrolyte and its amount in the solution. When solutions of strong electrolytes are diluted, the mobility of the corresponding ions increases, since their concentration decreases, and, consequently, the interionic interaction in the solution decreases. In solutions of weak electrolytes (usually a< 0,03) подвижность ионов практически не зависит от разбавления, так как концентрация ионов в этих растворах всегда невелика.
Since the mobility of ions depends on many factors, and primarily on their concentration in the solution, the values of the maximum electrical mobility of ions in a given solvent at a given temperature are used to characterize the properties of ions.
Limiting ion mobility ( and°, m 2 /( IN c)) is called average speed of his directed movement, acquired by him V an infinitely dilute solution in a uniform electric field of 1 V/m.
7. Electrical conductivity
A quantitative characteristic of the ability of solutions to conduct current is electrical conductivity.
Electrical conductivity is a physical quantity that is the reciprocal of the electrical resistance of a conductor: ω = 1 / R.
The SI unit of electrical conductivity is the siemens (Sm), 1 Sm - 1 .
The electrical resistance of a homogeneous conductor is directly proportional to its length l and inversely proportional to its cross-sectional area in:
where p - resistivity, characterizing the nature of the conductor and expressed in Ohm m.
Specific electrical conductivity characterizes the properties of a conducting medium - an electrolyte solution.
Electrical conductivity of an electrolyte solution is equal to the amount of electricity transferred by the ions contained in it through a cross-section of the solution with an area of 1 m 2 in a uniform electric field of intensity 1 V/m for 1 second.
Specific electrical conductivity depends on many factors, and primarily on the nature of the electrolyte, its concentration and temperature. The analysis allows us to draw the following conclusions:
Specific electrical conductivity is maximum for solutions strong acids and slightly less for solutions strong reasons, which is explained by the complete dissociation of these electrolytes and the high mobility of H 3 0+ and OH - ions.
The lowest values in the entire concentration range are the specific electrical conductivity of solutions of weak electrolytes (CH3COOH) due to the low concentration of ions in their solutions (a « 1).
Specific electrical conductivity increases with concentration up to certain maximum values, which corresponds to an increase in the number of ions per unit volume of solution. Having reached a maximum, the electrical conductivity begins to decrease despite the increase in electrolyte concentration. A similar nature of the dependence in strong electrolytes is associated with a decrease in the mobility of ions due to the interionic interaction increasing as the concentration of the solution increases, and in weak electrolytes it is associated with a decrease in the degree of electrolytic dissociation, and therefore with a decrease in the number of ions.
When the electrolyte concentration decreases to very low values (at c -> 0) the specific electrical conductivity of electrolyte solutions tends to the specific electrical conductivity of pure water (10" 6 -1()- 5 S/m).
An increase in temperature increases the electrical conductivity, as the mobility of ions and the degree of electrolytic dissociation of a weak electrolyte increase.
Ionic conductivities(mobility) – is obtained by multiplying the absolute velocities of the ions v + and v _ by the Faraday number: for the cation + = v + *F and the anion: - = v - *F.
Examples of problem solving
Example 1.
Calculate the emf of the corresponding galvanic cell, the equilibrium constant of the redox reaction and determine the most likely direction of the spontaneous occurrence of the reaction:
Cd 0 (tv) + Ag + (p) Cd 2+ (p) + Ag 0 (tv),
if the ion concentrations are equal:
C A g + = 10 4 mol/l; C C d 2+ = 10 3 mol/l.
Solution:
Let us calculate the electrode potentials of the corresponding electrodes using the Nernst formula:
E 1 = E 0 1 + log C C d 2+ ;
The standard electrode potential of cadmium is – 0.40 V.
E 1 = 0.40 + log 10 3 = 0.49 V;
For silver standard potential equals +0.80 V, then:
E 2 = E 0 2 + log C A g +
E 2 = 0.80 + log 10 4 =+ 0.56 V.
Since E 1 E 2, the reaction will proceed from left to right, i.e.
Сd 0 (tv) + 2Аg + (p) Сd 2+ (p) + 2Аg 0 (tv)
Let's write down the circuit of the galvanic cell:
Сd 0 Сd 2+ Аg + Аg 0 +,
Сd 0 2е Сd 2+ – oxidation process occurs at the anode;
Ag + + e Ag 0 a reduction process occurs at the cathode.
The emf of such an element will be equal to:
EMF = E 2 E 1
EMF = 0.56 (0.49) = 1.05 V.
To calculate the equilibrium constant, recall the relationship between the standard EMF and the standard Gibbs energy: G = nFE.
On the other hand, G is related to the equilibrium constant K by the equation G = 2.3 RT log K. For 25°C (298 K), the last equation after substituting the values of R (8.31 J/mol K) and F into it (96485 C/eq) is converted to this form (E = E 2 E 1):
log K = ;
2 (0,8 – (– 0,4)) 2 1,2
log K = = = 35.6.
Hence K = 10 35.6.
It follows from this that the reaction between cadmium and silver ions practically proceeds towards the reaction products.
Example 2.
A current of 2.5 A, passing through an electrolyte solution for 30 minutes, releases 2.77 g of metal from the solution. Find the equivalent mass of the metal.
Solution:
According to Faraday's law:
m = (EI)/F.
Then E = (m F)/ I; E = (2.77 96485)/(2.5 30 60) = 59.4 g/mol.
Example 3.
Which of the metals: cadmium, copper, platinum, molybdenum, mercury, paired with nickel in a galvanic cell, will be the anode? Draw a diagram of a galvanic cell.
Solution:
Let us write down the values of standard electrode potentials for these metals:
E Cd Cd +2 = 0.40 V; E Mo Mo +2 = 0.20 V;
E Cu Cu +2 = + 0.34 V; E Pt Pt +2 = + 1.20 V;
E Ni Ni +2 = 0.25 V.
When a galvanic cell operates, the electrochemical system with a higher electrode potential is reduced, acting as an oxidizing agent, and with a lower one, it is oxidized, acting as a reducing agent.
The electrode at which the oxidation process occurs during the reaction is called the anode. Therefore E ANODE E CATHODE. Comparing the values of the electrode potentials of metals with the value E Ni Ni ++, we obtain E Cd Cd +2 E Ni Ni +2. Therefore, the anode paired with nickel in galvanic cell there will be cadmium.
The circuit of a galvanic cell is written as follows:
Cd Cd 2+ Ni 2+ Ni.
Example 4.
In contact with which of the metals: platinum, nickel, iron, chromium - will corrosion of zinc occur faster and why?
Solution:
Corrosion is a spontaneous process, and for it G = nFE, therefore, than more value EMF, the greater the likelihood of corrosion.
E = E Pt Pt +2 E Zn Zn +2 = 1.2 (0.76) = 1.98 V;
E = E Ni Ni +2 E Zn Zn +2 = 0.25 (0.76) = 0.51 B;
E = E Fe Fe +2 E Zn Zn +2 = 0.44 (0.76) = 0.32 B;
E = E Cr Cr +3 E Zn Zn +2 = 0.74 (0.76) = 0.02 B.
Therefore, in contact with platinum, zinc corrosion occurs faster.
Example 5.
What substance is released at the cathode and anode during the electrolysis of an aqueous solution of a mixture of salts: CuSO 4 ; NaNO3; K2SO4. The concentrations of all salts in the solution are the same.
Solution:
If the system in which electrolysis is carried out contains various oxidizing agents, then the most active of them will be reduced at the cathode, i.e. the oxidized form of the electrochemical system to which the highest electrode potential corresponds.
Cu 2+ + 2e - = Cu: E Cu Cu +2 = + 0.34 V
2H + + e - = H 2: E N H+ = 0.0 V
K + + e - = K: E K K+ = 2.92 V
Na + + e - = Na: E Na Na + = 2.71 V
Since E Cu Cu +2 has highest value electrode potential, then it is copper that will be released at the cathode. Similarly, if there are several reducing agents in the system, the most active of them will be oxidized at the anode, i.e. the reduced form of that electrochemical system, which is characterized by the lowest value of the electrode potential.
With electrolysis aqueous solutions nitrates and sulfates in inert electrolysis, oxidation of hydroxide ions occurs with the formation of oxygen:
4 OH – = O 2 + 2H 2 O + 4e - E 0 = 0.40 V.
Example 6.
What happens if you put a piece of iron into a solution of copper sulfate CuSO 4?
Solution:
Let's write down the electrode half-reactions:
Cu 0 Cu 2+ + 2e - E Cu Cu +2 = + 0.34 V;
Fe 0 Fe 2+ + 2e - E Fe Fe+2 = - 0.44 V;
because E Cu Cu +2 E Fe Fe +2, then the first half-reaction is most preferable.
Indeed, the negative value of the standard electrode potential FeFe 2+ means that iron should be oxidized by hydrogen cations more strongly than copper:
Fe + 2H + Fe 2+ + H 2.
E Cu Cu +2 = + 0.34 V shows that hydrogen is more easily oxidized:
Cu 2+ + H 2 Cu 0 + 2H + .
Summing up the reactions, we get: Fe + Cu 2+ Fe 2+ + Cu 0. Hence, full reaction Iron oxidation proceeds spontaneously in the indicated direction, i.e. A layer of copper metal is deposited on the surface of the iron.
Example 7
Calculate the electrochemical equivalent of cadmium.
Solution:
The electrochemical equivalent of the metal is calculated using the following formula:
E = ,
where M – molar mass element; n – valence; F – Faraday number.
112.41 g/mol
E = = 5.83 * 10 – 4 g/C = 0.583 mg/C.
2 * 96485 C/mol
Example 8
Calculate the transfer number of the anion C1 - in an infinitely dilute solution of NaCl at 25 °C, if the mobilities of the cation and anion in this solution are known: Na + = 50.1 cm 2 / Ohm * mol; Cl - = 76.35 cm 2 / Ohm * mol.
Solution:
In electrolysis, equal amounts of electricity pass through each electrode, but each type of ion carries unequal amounts of electricity due to differences in the velocities of the ions.
Transport numbers (t) can be expressed through the ratio of the absolute velocity of the ion to the sum of the absolute velocities of both ions or, respectively, through the ratio of ionic electrical conductivities, for example:
t - = --- = ---
v + + v _ + + _
We substitute the known data into the formula:
76.35 cm 2 /Ohm*mol
t - = = 0.60
76.35 cm 2 /Ohm*mol + 50.1 cm 2 /Ohm* mol
