Movement of ions in electrolytes. Absolute speed of ion movement
Liquids, like solids, can be conductors, dielectrics (alcohol, water) and semiconductors (molten selenium, tellurium). Solutions of substances that conduct electricity are called electrolytes. Electrolytes are, for example, aqueous solutions of salts, acids and alkalis. Their (molecules consist of two parts with opposite and equal charges, i.e., of two ions. When they fall into water, the dielectric constant of which ε = 81, the strength of the electrical interaction between them decreases by 81 times. With such a decrease in the force of attraction between the ions that make up the molecules of the solute, the latter, from a collision with water molecules in the process of thermal motion, decompose into ions, i.e., electrolytic dissociation occurs. Hydrogen and metal ions are positive.
A certain number of oppositely charged ions in their movement can be so close to each other that the forces of electrical attraction unite them again into a neutral molecule. The value of the charge of an ion (valence) is determined by the number of electrons lost or acquired by an atom (or a group of atoms that make up an ion). Electrolytic dissociation is written in the form of equations, like any other chemical reaction:
So, there are free charge carriers in the electrolyte, are they? are positive and negative ions. They are in thermal motion.
We lower two electrodes into the electrolyte and connect them to the poles of a direct current source. Under the action of an electric field formed by a current source in the electrolyte, free ions, in addition to thermal movement, begin to move in opposite directions: positive - to the negative electrode, and negative - to the positive electrode. P The flow of positive and negative ions in the electrolyte under the action of the electric field of the current source is the current in the electrolyte. The more ions are in 1 cm 3 electrolyte and the greater the speed of their movement, the greater the current strength. The speed of the continuous movement of ions that form the current in the electrolyte is low. Even the fastest hydrogen ion at an electric field strength E = 100 w/m has a speed of about 12cm/h, and the sodium ion 1.6cm/h. For electrolytes, Ohm's law is valid.
When the current passes through the electrolyte, the ions, reaching the electrodes, are neutralized and released on them in the form of neutral molecules of the substance. Means, the passage of current through electrolytes is always accompanied by the transfer of matter. It follows from this that in electrolytes, in contrast to metallic conductors, current carriers are not free electrons, but ions. Unlike metals electrolytes are ionic. An electric current passes through the electrolyte until the solute in the solvent is completely released on the electrodes, after which the current stops.
The movement of ions in an electric field is used to introduce them into the body for therapeutic purposes through intact skin. For example, when calcium ions are introduced into the arm, its brush is placed in a bath with an aqueous solution of calcium chloride, the forearm is connected to the negative pole of the current source, and the electrode immersed in the electrolyte is connected to the positive pole (Fig. 107). Under the influence of an electric field, positive calcium ions enter the body and spread throughout the arm.
Let us find out how the resistance of the electrolyte depends on temperature. Let's assemble an electrical circuit from a current source, an ammeter and a test tube with an electrolyte in which the electrodes are immersed (Fig. 108). By heating the electrolyte, we notice an increase in the current strength in the circuit. This means that when electrolytes are heated, their resistance decreases. In this case, the speed of the molecules becomes greater, their kinetic energy increases, which causes more frequent and stronger collisions between the electrolyte molecules, as a result, there is a greater breakdown of the solute molecules into ions. An increase in the number of ions forming a current increases its strength. With increasing temperature, the resistance of the electrolyte to the directed movement of free ions increases, but an increase in their number causes a greater increase in current strength than a decrease in it due to an increase in the number of collisions of ions with electrolyte molecules. Ultimately heating decreases the resistance of the electrolyte.
The movement of ions in electrolytes can in some cases be shown very clearly.
Rice. 2.
Soak a sheet of filter paper with an electrolyte solution (sodium sulfate, Na 2 SO 4) and phenolphthalein and place it on a glass plate (Fig. 2).
Across the paper we put an ordinary white thread moistened with a solution of caustic soda (NaOH). The paper under the thread will turn crimson due to the interaction of hydroxyl (OH) ions from NaOH with phenolphthalein. Then we press the wire electrodes attached to the galvanic cell to the edges of the sheet and turn on the current.
The hydroxide ions from the sodium hydroxide will 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 of an electric field inside the electrolyte. Experience shows that this speed is proportional to the field strength inside the electrolyte. For a given field, this velocity is somewhat different for different ions. But, in general, it is small and for commonly used fields it is measured in hundredths and even thousandths of a centimeter per second.
Theory of electrolytic dissociation
Svante Arrhenius drew attention to the close relationship between the ability of solutions of salts, acids and bases to conduct electric current and the deviations of solutions of these substances from the laws of van't Hoff and Raoult. He showed that the electrical conductivity of the solution can be used to calculate the value of its osmotic pressure, and, consequently, the correction factor i. The i values calculated by him from the electrical conductivity agreed well with the values found for the same solutions by other methods.
The reason for the excessively high osmotic pressure of electrolyte solutions is, according to Arrhenius, the dissociation of electrolytes into ions. As a result, on the one hand, the total number of particles in the solution increases, and, consequently, the osmotic pressure increases, the vapor pressure decreases, and the boiling and freezing temperatures change, on the other hand, ions determine the ability of the solution to conduct electric current.
These assumptions were further developed into a coherent theory, called the theory of electrolytic dissociation. According to this theory, when dissolved in water, electrolytes decompose (dissociate) into positively and negatively charged ions. Positively charged ions are called cations; these include, for example, hydrogen and metal ions. Negatively charged ions are called anions; these include ions of acid residues and hydroxide ions. Like solvent molecules, ions in solution are in a state of disordered thermal motion.
The process of electrolytic dissociation is depicted using chemical equations. For example, the dissociation of HCl is expressed by the equation:
HCl \u003d H + + Cl -
The breakdown of electrolytes into ions explains the deviations from the van't Hoff and Raoult laws. An example is the decrease in the freezing point of a NaCl solution. Now it is not difficult to understand why the drop in the freezing point of this solution is so great. Sodium chloride goes into solution in the form of Na + and Cl - ions. In this case, from one mole of NaCl, not 6.02 * 10 23 particles are obtained, but twice their number. Therefore, the decrease in the freezing point in the NaCl solution should be twice as large as in the non-electrolyte solution of the same concentration.
Similarly, in a very dilute solution of barium chloride, which dissociates according to the equation, the osmotic pressure is 3 times greater than that calculated according to the van't Hoff law, since the number of particles in the solution is 3 times greater than if barium chloride were in it in the form of BaCl 2 molecules.
BaCl 2 \u003d Ba 2+ + 2Cl -
Thus, the features of aqueous solutions of electrolytes, which at first glance contradict the laws of van't Hoff and Raoult, were explained on the basis of the same laws.
However, the Arrhenius theory did not take into account the complexity of phenomena in solutions. In particular, she considered ions as free particles independent of solvent molecules. Arrhenius's theory was opposed by Mendeleev's chemical or hydrate theory of solutions, which was based on the idea of the interaction of a solute with a solvent. In overcoming the seeming contradiction of both theories, great merit belongs to the Russian scientist I. A. Kablukov, who was the first to suggest the hydration of ions. The development of this idea led later to the unification of the theories of Arrhenius and Mendeleev.
In infinitely dilute solutions, the equivalent electrical conductivity reaches a limit and no longer depends on the concentration, since complete dissociation occurs in solutions of weak electrolytes (α = 1), and in solutions of strong electrolytes, the interionic interaction disappears.
The equivalent electrical conductivity of infinitely dilute solutions is called the electrical conductivity at infinite dilution and is denoted by l ∞ (or l 0).
The equivalent electrical conductivity at infinite dilution, according to the Kohlrausch law of independent motion of ions, is equal to the sum of the limiting ion mobilities
Mobility is related to the absolute speed of ion movement n:
l + =n + F, l - =n - F, =F, =F
where F- Faraday number, 96487 k. ≈ 96500 k.
Under the absolute speed of the ion movement v, we understand the speed of its movement in an electric field with a potential gradient of 1 V/cm. Dimension n cm 2 sec -1 - in -1. The value of the absolute speed of the ion, other things being equal (temperature, viscosity of the medium, field gradient) depends on the concentration of the solution and reaches the limit value in infinitely dilute solutions, i.e. at φ→∞, n + → , n - →.Since the speed of movement of ions is very small, the values in F times large - mobility l + and l - .
Mobility is also called the equivalent electrical conductivity of ions. It is measured in the same units as the equivalent electrical conductivity of the electrolyte (Ohm -1 cm 2 -g-eq -1). Ion mobilities depend on concentration, especially in solutions of strong electrolytes, in which the interionic interaction is high (f l < 1). Предельные подвижности ионов и достигаются при бесконечном разведении (φ→∞,f l →1), their meanings are given in the reference literature.
The dependence of the equivalent electrical conductivity on the degree of dissociation and interionic interaction is described by the equation:
In solutions of weak electrolytes, the number of ions involved in the transfer of electricity is determined by the degree of dissociation a. In concentrated solutions of weak electrolytes, α is very small; therefore, the number of ions in the solution is also small and there is practically no interionic interaction. With a strong dilution of solutions, α increases and the number
ions in solution, however, the interionic distances are so large that the interaction of ions is also absent (f l = 1). Thus, in solutions of weak electrolytes, at any dilution, the ions have the limiting mobility and the equivalent electrical conductivity depends only on the degree of dissociation
Therefore, the ratio of electrical conductivities will correspond to the degree of dissociation of weak electrolytes
This equation is called the Arrhenius formula, in practice it is used to determine the degree of dissociation of electrolyte solutions.
For a 1-1-valent weak electrolyte dissociating according to the scheme AB ↔ A + B - using the Ostwald dilution law and taking into account that it is possible to determine the dissociation constant through the equivalent electrical conductivity by the formula:
(10.8)
where C is the electrolyte concentration, mol/l.
According to the Debye-Hückel theory, strong electrolytes in solutions are completely dissociated into ions (α = 1) and interionic interactions are large (f l < 1), значит уравнение (10.6) должно быть записано в виде
whence the electrical conductivity coefficient is equal to
;
The electrical conductivity coefficient is a function of concentration, it is experimentally determined based on the equivalent electrical conductivity of the solution. The value depends on the valency of the ions: 1-1-valent electrolyte (such as NaCI, HCI) in 0.1 N. solution 0.8; for 1-2-valent (Na 2 SO 4, CaCI 2) f x~ 0.75; 2-2-valent (CuSO 4) ~ 0.4. When solutions are diluted, the interionic interaction decreases, and these differences are smoothed out: the equivalent electrical conductivity reaches a limit and
10.4 Mechanism of influence of atmospheric ions on electrical conductivity
solutions, Kohlrausch's square root law.
Qualitatively, the mechanism of the influence of the ionic atmosphere on electrical conductivity is as follows: the central ion, for example, a cation, moves towards the cathode when a constant electric field is applied, and the oppositely charged ionic atmosphere moves towards the anode. This causes the so-called electrophoretic inhibition.
The atmosphere surrounding the central ion should disappear behind the ion moving in the electric field and re-form in front of it. Both processes of destruction and formation of an ionic atmosphere do not occur instantly, for example, in a 0.1 N solution of potassium chloride in 0.6 10 -9 sec, and in a 0.001 N solution in 0.6 10 -7 sec. It causes relaxation inhibition. Therefore, the electrical conductivity coefficient takes on values less than unity, not as a result of incomplete dissociation, but due to the manifestation of these inhibitions.
In addition to electrophoretic and relaxation inhibition, there is a third force that inhibits the movement of ions in solution. This is a friction force that depends on the viscosity of the solvent in which the ion moves. Therefore, an increase in temperature causes an increase in the speed of movement of ions, and as a consequence, an increase in electrical conductivity.
For dilute solutions of strong electrolytes, the theory gives a linear dependence of the equivalent electrical conductivity on square root of concentration (Kohlrausch square root law)
(10.9)
Constant BUT, depending on the nature of the solvent, temperature, and valence type of the electrolyte, is experimentally determined by the tangent of the slope of the straight line to the x-axis (Fig. 10.2).
The limiting equivalent electrical conductivity of strong electrolytes can be found by extrapolating experimental data to a value of C = 0. It must be emphasized that, although limiting electrical conductivity is understood as conductivity at an electrolyte concentration close to zero, it is by no means identical to the equivalent electrical conductivity of a solvent.
Rice. 10.2 Dependence of the equivalent electrical conductivity on the square root of the concentration for strong electrolytes (НCI, KOH, LiCI) ,
and weak electrolyte (CH 3 COOH) in aqueous solutions.
For solutions of weak electrolytes, the dependence of the equivalent
electrical conductivity versus concentration follows from Ostwald's dilution law. For α1 we get
(10.10)
where
or in logarithmic form
This dependence is not linear, therefore, the value cannot be determined by extrapolation, it is determined only indirectly based on the law of independent movement of Kohlrausch ions.
Data on the mobility of ions show that the radii of ions in the crystal lattice are not conserved in solutions. For example, radii
alkali metal ions in a row Li +
With an increase in the charge of the ions, the speed of its movement in the electric field, and, consequently, the electrical conductivity of the solution increase. However, H+ ions (more precisely, hydronium ions) and OH - have the highest speeds. Only their mobilities are expressed in three-digit numbers (= 349.8; = 198.3 ohm -1 -cm 2 -eq -1). This, apparently, is explained by the fact that a proton can be transferred from a molecule to a water molecule according to the so-called "relay" mechanism.
anode (+) | H 3 O + H 2 O | cathode (-).
As a result of such a jump, the proton passes 0.86 A, which corresponds to the displacement of the hydronium cation by 3.1 Ǻ, or the transfer of hydroxyl in an electric field to the anode
anode (+) | H 2 O OH - | cathode (-),
at which the jump of the proton to the right results in the displacement of the hydroxyl to the left. In this case, the hydroxyl that accepts the proton turns into a water molecule, and instead of it, a new anion arises, which is closer to the anode than the one that disappears due to the addition of the proton. Naturally, with such a mechanism of conduction, the mobility of hydrogen and hydroxyl ions is much greater than that of ions that simply move in an electric field.
Electrical conductivity of solutions
Subject of electrochemistry
Modern electrochemistry is developing in several directions. First of all, this is the study of processes associated with the conversion of energy released during spontaneous chemical processes into electrical energy. Such transformations occur in electrochemical systems called galvanic cells. Based on these studies, a variety of chemical current sources have been created from miniature batteries that regulate the heartbeat of people suffering from heart disease to hydrogen fuel cells that provide electricity to spacecraft and powerful batteries for electric cars.
Another direction of electrochemistry is associated with processes that are essentially opposite to the processes occurring in galvanic cells. We are talking about electrolysis- chemical transformations of substances under the influence of electric current. Electrolysis underlies the isolation and purification of metals, the production of various chemicals, the deposition of metals on the surface of metal and non-metal products, the electrochemical polishing and milling of metals, and other important processes.
The third direction is connected with the study of corrosion processes and the development of effective methods for protecting metals from corrosion.
Important tasks of electrochemistry are the creation and improvement of methods for the quantitative analysis of chemicals, the study and control of chemical processes, the development of instruments for the detection and quantitative determination of harmful impurities in the environment, etc.
Electrical conductors are of two types:
1. Conductors of the first kind or conductors with electronic conductivity. All metals are included.
2. Conductors of the second kind with ionic conductivity are solutions and melts of electrolytes.
Since the processes considered in electrochemistry proceed mainly in electrolyte solutions, let us dwell in detail on ionic conductivity.
When acids, bases or salts are dissolved in water, ions are formed that are in continuous random motion. If two solid electrodes connected to a direct current source are immersed in an electrolyte solution, the movement of ions becomes directed - each ion moves towards the electrode with the opposite charge sign.
The following factors influence the speed of movement of ions in an electric field:
a) Ion size: the smaller the ion, the more mobile it is. When considering this factor, it must be remembered that ions in an aqueous solution are hydrated, which means that we are talking about sizes hydrated ion. For example, the free Li + ion is smaller than the K + ion, but the first ion has a lower speed of movement in solution. This is due to the fact that it is more hydrated.
b) The charge of the ion: the speed of the movement of the ion is greater, the higher its charge. However, it should be borne in mind that with increasing charge, the degree of hydration increases, which means that mobility decreases.
c) The nature of the solvent: the greater the viscosity of the solvent, the greater the resistance experienced by the ion, the lower its speed.
d) Electric field strength U, i.e. potential difference between the electrodes E, divided by the distance between them l:
U = E/ l (3.1.)
In order to eliminate the influence of the latter factor, it is customary to compare the speeds of ion movement at U = 1 V×cm -1, called absolute speeds. Absolute velocity unit: cm 2 ×V -1 ×s -1 . The influence of the first two factors can be traced in Table 3.1.
The table shows that H + and OH - ions have a significantly higher speed compared to other ions. It is customary to explain this by a special mechanism for the movement of these ions, called the relay race. The essence of the relay mechanism can be represented schematically as follows:
H 3 O + + H 2 O \u003d H 2 O + H 3 O + and
H 2 O + OH - \u003d OH - + H 2 O
Table 3.1.
Absolute velocities of ions in aqueous solutions (t=25 0 С)
| Cation | V+ | Cation | V+ | Anion | V- | Anion | V- |
| H + K + NH 4 + Ag + Na + Li + | 0.003620 0.000762 0.000760 0.000642 0.000520 0.000388 | Ba 2+ Ca 2+ S 2+ Mg 2+ | 0,000659 0,000616 0,000616 0,000550 | OH - Br - I - Cl - NO 3 - | 0,002050 0,000812 0,000796 0,000791 0,000740 | CH 3 COO - SO 4 2- ClO 4 - Fe (CN) 6 4- | 0,000424 0,000827 0,000705 0,001140 |
Thus, between hydroxonium ions H 3 O + and water molecules, as well as between water molecules and hydroxide ions, there is an exchange of H + ions. These processes occur at a tremendous speed - the average duration of the existence of the H 3 O + ion is approximately 10 -11 s. In the absence of an external field, such an exchange proceeds in any direction. Under the action of an electric field, the transfer of H + ions occurs in a direction.
10. Electrical conductivity of electrolyte solutions
The electrical conductivity ("Kappa") of a solution is the reciprocal of its resistance R, has the dimension of Ohm -1 . For conductor of constant cross section
,
where is the resistivity; S- cross-sectional area of the conductor; l- conductor length; - specific electrical conductivity.
The electrical conductivity ("kappa") of a solution is the electrical conductivity of a layer of solution 1 cm long, enclosed between electrodes with an area of 1 cm 2. It is expressed in Ohm -1. cm -1 . In the SI system, electrical conductivity is measured in Ohm -1. m -1 .
Equivalent electrical conductivity ("lambda") is the electrical conductivity of such a volume of solution, which contains 1 g-eq of the solute; provided that the electrodes are at a distance of 1 cm from each other, it is expressed in Ohm -1. cm 2. g-equiv -1.
where V = 1/C- dilution (or dilution) of the solution, i.e. the volume that contains 1 g-eq of a solute, and C- equivalent concentration (normality) of the solution. In the SI system, the equivalent electrical conductivity is expressed in Ohm -1. m 2. kg-sq -1.
The equivalent electrical conductivity of electrolyte solutions increases with increasing dilution of the solution and, at infinite dilution (i.e., at an infinitesimal concentration), reaches the limit value 0. which is called equivalent electrical conductivity of the solution at infinite dilution.
In dilute solutions of strong electrolytes, the empirical Kohlrausch's law(square root law):
where and 0 is the equivalent electrical conductivity of the solution at a concentration With and with infinite breeding, A is a constant (at a given temperature) for a given electrolyte and solvent.
In solutions of weak electrolytes, and 0 are related to the degree of electrolyte dissociation Arrhenius equation:
In addition, it performs Ostwald's law of breeding, which for a binary electrolyte is written as follows:
,
where K is the dissociation constant of a weak electrolyte.
The electrical conductivity of electrolytes is related to the speed of movement of ions in solution. Travel speed v i[m. s -1] of an ion in solution is proportional to the strength of the applied electric field E[AT. m -1]:
Proportionality factor u[m 2. s -1. In -1 ] is called absolute mobility and she.
Work u i F (F- Faraday's constant) is called mobility and she i[Ohm -1. m 2. kg-eq -1]:
i = u i F.
The mobility of an ion at infinite dilution is called marginal mobility ion and is denoted i 0 . Limit mobility i 0 some ions in an aqueous solution [Ohm -1. cm 2. g-eq -1] are given in Table 10.1.
According to law Kohlrausch on the independent migration of ions, the equivalent electrical conductivity of the solution at infinite dilution is equal to the sum of the limiting mobilities of cations and anions:
0 = 0 + + 0 - .
The fraction of current carried by a given ion is called carry number t i and she:
,
and by definition.
According to Stokes law, limiting mobility 0 of an ion with a charge z and radius r in a solvent with viscosity h is described by the formula:
where e- elementary charge, F is the Faraday constant.
Table 10.1
Limit mobility i 0 some ions in aqueous solution at 25 o C [Ohm -1. cm 2. g-equiv -1]
| H+ | 349.8 | oh- | 198.3 |
| Li + | 36.68 | F- | 55.4 |
| Na+ | 50.10 | Cl- | 76.35 |
| K+ | 73.50 | br- | 78.14 |
| Rb+ | 77.81 | I- | 78.84 |
| Ag+ | 61.90 | ClO 3 - | 64.6 |
| NH4+ | 73.55 | ClO 4 - | 67.36 |
| N(CH3)4 + | 44.92 | BrO 3 - | 55.74 |
| 1/2 Mg2+ | 53.05 | CN- | 78 |
| 1/2 Ca2+ | 59.50 | NO 3 - | 71.46 |
| 1/2 Ba2+ | 63.63 | CH 3 COO - | 40.90 |
| 1/2 Mg2+ | 56.6 | C 6 H 5 COO - | 35.8 |
| 1/2 CD 2+ | 54 | H2PO4- | 36 |
| 1/3Al3+ | 63 | 1/2 SO 4 2- | 80.02 |
| 1/3 La 3+ | 69.7 | 1/2 S 2 O 6 2- | 93 |
From this equation follows Walden-Pisarzewski rule, according to which for any ion or electrolyte:
.
Example 10-1. Specific electrical conductivity 0.135 mol. l -1 solution of propionic acid C 2 H 5 COOH is equal to 4.79. 10 -2 See m -1 . Calculate the equivalent electrical conductivity of the solution, the dissociation constant of the acid and the pH of the solution, if the limiting mobility of H + and C 2 H 5 COO - are 349.8 S. cm 2. mol -1 and 37.2 S. cm 2 mol -1. respectively.
0 \u003d 349.8 + 37.2 \u003d 387.0 See cm 2. mol -1.
= /C? 1000 = 4.79 . 10 -2 See m -1 / 0.135 mol. l -1. 1000 \u003d 3.55 See cm 2. mol -1.
= / 0 = 3.55/387.0 = 0.009.
= 1.15 . 10 -5 (mol. l -1).
C=1.24 10 -3 (mol. l -1).
pH = -lg = 2.91.
Answer. \u003d 3.55 See cm 2. mol -1; = 0.009; K= 1.15 . 10 -5 mol. l -1; pH = 2.91.
Example 10-2. The electrical conductivity of a saturated solution of BaCO 3 in water at 18 o C is 25.475. 10 -4 See m -1 . Specific electrical conductivity of water 4.5 . 10 -5 See m -1 . The mobilities of Ba 2+ and CO 3 2- ions at 18 o C are 55 and 66 Sm. cm 2, respectively. g-eq -1 . Calculate the solubility of BaCO 3 in water at 18 o C in mol. l -1. assuming that the salt is completely dissociated, and the ion mobilities are equal to the mobilities at infinite dilution.
(BaCO 3) \u003d (solution) - (H 2 O) \u003d 25.475. 10 -4 - 4.5. 10 -5 = 25.025 . 10 -4 See m -1 .
0 (BaCO 3) = 0 (Ba 2+) + 0 (CO 3 2-) =
55 + 66 \u003d 121 See cm 2. g-equiv -1 \u003d 1.21. 10 -2 See m 2. g-equiv -1 .
С = / 0 = 0.206 g-eq. m -3 = 2.06. 10 -4 g-equiv. l -1 = 1.03. 10 -4 mol. l -1 .
Answer. With= 1.03 . 10 -4 mol. l -1 .
Example 10-3. The specific electrical conductivity of a 5% solution of Mg(NO 3) 2 at 18 o C is 4.38 See m -1. and its density is 1.038 cm -3. Calculate the equivalent electrical conductivity of the solution and the apparent degree of dissociation of the salt in the solution. The mobilities of Mg 2+ and NO 3 - ions at 18 o C are 44.6 and 62.6 cm, respectively. g-eq -1 .
0.35 mol. l -1 = 0.70 g-eq. l -1 .
= 
6.25. 10 -3 See m 2. g-eq -1 = 62.5 (See cm 2. g-eq -1).
0 \u003d 44.6 + 62.6 \u003d 107.2 (See cm 2. g-equiv -1).
= / 0 = 62.5/107.2 = 0.583.
Answer: \u003d 62.5 See cm 2. g-equiv -1. = 0.583.
10-2 . The specific electrical conductivity of infinitely dilute solutions of KCl, KNO 3 and AgNO 3 at 25 o C is 149.9, 145.0 and 133.4 Sm. m 2 mol -1, respectively. What is the electrical conductivity of an infinitely dilute solution of AgCl at 25 o C? (answer)
10-3. The electrical conductivity of infinitely dilute solutions of hydrochloric acid, sodium chloride and sodium acetate at 25 o C is 425.0, respectively. 128.1 and 91.0 See m 2 . mol -1 . What is the electrical conductivity of an infinitely dilute solution of acetic acid at 25 o C? (answer)
10-4 . The electrical conductivity of a 4% aqueous solution of H 2 SO 4 at 18 o C is 0.168 See cm -1. solution density - 1.026 cm -3. Calculate the equivalent electrical conductivity of the solution. (answer)
10-5. The specific electrical conductivity of a saturated solution of AgCl in water at 25 o C is 2.28. 10 -4 See m -1. and the specific electrical conductivity of water is 1.16. 10 -4 See m -1 . Calculate the solubility of AgCl in water at 25 o C in mol. l -1 . (answer)
10-6 . What fraction of the total current is carried by the Li + ion in an aqueous solution of LiBr at 25 o C? (answer)
10-7 . Calculate the transfer number of H + in a solution of HCl with a concentration of 1 . 10 -3 mol. l -1 . What will be the H + transfer number if NaCl is added to this solution so that its concentration is 1.0 mol. l -1 ? (answer)
10-9. Calculate the speed of the Na + ion in an aqueous solution at 25 o C if a potential difference of 10 V is applied to the electrodes located at a distance of 1 cm from each other. How long does it take for an ion to travel the distance from one electrode to another? (answer)
10-10. The specific electrical conductivity of an aqueous solution of KI is 89.00 Sm. m -1. and a KCl solution of the same concentration - 186.53 Sm. m -1. The specific electrical conductivity of a solution containing both salts is 98.45 Sm. m -1 . Calculate the proportion of KCl in the solution.
10-11 . The specific electrical conductivity of an aqueous solution of a strong electrolyte at 25 o C is 109.9 cm. cm 2 . mol -1 at a concentration of 6.2. 10 -3 mol. l -1 and 106.1 See cm 2. mol -1 at a concentration of 1.5. 10 -2 mol. l -1 . What is the electrical conductivity of the solution at infinite dilution? (answer)
10-12 . Calculate the radius of the N(CH 3) 4 + ion according to the Stokes law from its limiting mobility in an aqueous solution at 25 o C. The viscosity of water at 25 o C is 8.91? 10 -4 Pa. with. Estimate the limiting mobility of this ion in glycerol, the viscosity of which is 1.49 Pa. with. (answer)
10-13 . Estimate the limiting mobility of the K + ion in formamide and methyl acetate if the viscosity of formamide is 3.7 times higher and the viscosity of methyl acetate is 2.6 times lower than the viscosity of water. (answer)
10-14 . Calculate the electrical conductivity 1.0 . 10 -3 M NaCl aqueous solution at 25 o C, assuming that the ion mobilities at this concentration are equal to their limiting mobilities. A current of 1 mA is passed through a layer of solution 1 cm long, enclosed between electrodes with an area of 1 cm 2. How far will Na + and Cl - ions travel in 10 minutes? (answer)
10-15. Calculate the effective radius of the Li + ion at 25 o C from its limiting mobility using the Stokes law. Calculate the approximate number of water molecules in the hydration shell of the Li + ion. The crystallographic radius of the Li + ion is 60 pm. The viscosity of water at 25 o C is 8.91. 10 -4 Pa. with. The intrinsic volume of a water molecule can be estimated from the parameters of the van der Waals equation. (answer)
10-16. The dissociation constant of ammonium hydroxide is 1.79. 10 -5 mol. l -1 . Calculate the concentration of NH 4 OH at which the degree of dissociation is 0.01. and the equivalent electrical conductivity of the solution at that concentration. (answer)
10-17 . Equivalent electrical conductivity 1.59 . 10 -4 mol. l -1 solution of acetic acid at 25 o C is equal to 12.77 See cm 2 . mol -1 . Calculate the dissociation constant of the acid and the pH of the solution. (answer)
10-18 . The dissociation constant of butyric acid C 3 H 7 COOH is 1.74. 10 -5 mol. l -1 . Equivalent electrical conductivity of the solution when diluted 1024 l. mol -1 is equal to 41.3 See cm 2. mol -1 . Calculate the degree of dissociation of the acid and the concentration of hydrogen ions in this solution, as well as the equivalent electrical conductivity of the solution at infinite dilution. (\u003d 0.125; \u003d 1.22. 10 -4 mol. l -1; 0 \u003d 330.7 See cm 2. mol -1.) (answer)
10-19 . The equivalent electrical conductivity of a solution of ethylammonium hydroxide C 2 H 5 NH 3 OH at infinite dilution is 232.6 S. cm 2. mol -1 . Calculate the dissociation constant of ethylammonium hydroxide, the equivalent electrical conductivity of the solution, the degree of dissociation, and the concentration of hydroxyl ions in the solution at a dilution of 16 L. mol -1. if the specific electrical conductivity of the solution at a given dilution is 1.312. 10 -3 See cm -1 .
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