Now consider a molecule that has a permanent dipole moment, such as water. In the absence of an electric field, the individual dipoles point in different directions, so that the total moment per unit volume is zero. But if an electric field is applied, two things immediately happen: first, an additional dipole moment is induced due to the forces acting on the electrons; this part leads to the same electronic polarizability that we found for a non-polar molecule. In a very precise study, this effect must, of course, be taken into account, but we will neglect it for the time being. (It can always be added at the end.) Second, the electric field tends to line up individual dipoles, producing a net moment per unit volume. If all the dipoles were lined up in the gas, the polarization would be very large, but this does not happen. At ordinary temperatures and field strengths, the collisions of molecules during their thermal motion do not allow them to line up properly. But some alignment still occurs, and hence a slight polarization (Fig. 11.2). The resulting polarization can be calculated by the methods of statistical mechanics described in Chap. 40 (issue 4).
Figure. 11.2. In a gas of polar molecules, individual moments are randomly oriented, the average moment in a small volume is zero (a); under the action of an electric field, on average, some alignment of molecules occurs (b).
To use this method, you need to know the energy of the dipole in the electric field. Consider a dipole with a moment in an electric field (Fig. 11.3). The energy of a positive charge is (1), and the energy of a negative charge is (2). From here we get the energy of the dipole
where is the angle between and . As expected, the energy gets smaller as the dipoles align along the field. Now, using the methods of statistical mechanics, we will find out how strongly the dipoles align. In ch. 40 (issue 4) we found that in a state of thermal equilibrium the relative number of molecules with potential energy is proportional to
where is the potential energy as a function of position. Using the same arguments, we can say that if the potential energy as a function of the angle has the form (11.14), then the number of molecules at the angle per unit solid angle is proportional to .
Figure 11.3. The energy of the dipole in the field is .
Assuming the number of molecules per unit solid angle directed at an angle equal to , we have
. (11.16)
For ordinary temperatures and fields, the exponent is small, and by expanding the exponent, we can use the approximate expression
(11.17)
Find by integrating (11.17) over all angles; the result should be equal to , i.e. the number of molecules per unit volume. The mean value when integrated over all angles is zero, so the integral is simply , times the full solid angle . We get
From (11.17) it can be seen that more molecules will be oriented along the field () than against the field (). Therefore, in any small volume containing many molecules, there will be a total dipole moment per unit volume, i.e. polarization . To calculate , you need to know the vector sum of all molecular moments per unit volume. We know that the result will be directed along , so we only need to sum the components in that direction (components perpendicular to will sum to zero):
We can estimate the sum by integrating over the angular distribution. The solid angle corresponding to , is ; from here
(11.19)
Substituting instead of its expression from (11.17), we have
,
which is easily integrated and leads to the following result:
The polarization is proportional to the field, so the dielectric properties will be normal. Also, as we would expect, polarization is inversely proportional to temperature because, at higher temperatures, collisions break alignment more. This type dependence is called the Curie law. The square of the constant moment appears for the following reason: in a given electric field, the alignment force depends on , and the average moment that occurs during alignment is again proportional to . The average induced moment is proportional to .
Now let's see how well equation (11.20) agrees with experiment. Let's take water vapor. Since we do not know what is equal to, we cannot directly calculate and, but equation (11.20) predicts that it should change inversely with temperature, and this we should check ..) In Fig. 11.4 we have plotted the measured values as a function of . The dependence predicted by formula (11.21) is satisfied well.
Figure 11.4. Measured values of the dielectric constant of water vapor, at several temperatures.
There is one more feature of the permittivity of polar molecules - its change depending on the frequency of the external field. Due to the fact that the molecules have a moment of inertia, it takes a certain time for heavy molecules to turn in the direction of the field. Therefore, if frequencies from the upper microwave band or from an even higher one are used, the polar contribution to the permittivity begins to decrease, since the molecules do not have time to follow the field. In contrast, the electronic polarizability still remains unchanged up to optical frequencies, because the electron inertia is smaller.
A molecule (atom, ion) consists of neutral and positively and negatively charged particles. There are two types of particles - with a symmetrical charge distribution (H 2, CH 4, C 6 H 6, etc.) and asymmetric (HX, CH 3 X, C 6 H 5 X: X - halogen, etc.). These are non-polar and polar molecules. A polar molecule is also called a dipole or dipole molecule.
In a diatomic dipole molecule, one of the atoms has an excess of negative charges, and the other has the same excess of positive charges. The total charge is zero. Polyatomic molecules have some regions with excess positive and negative charges. However, even here one can imagine two centers of charges.
The dipole moment ( , C×m) is the product of the charge ( , C) and the distance between the charges ( , m):
The dipole moment should be considered as a vector directed from a negative charge to a positive one (in chemistry they usually take the opposite direction). If a molecule consists of many atoms, then its dipole moment is defined as a vector sum:
Under normal conditions, the dipole moments of molecules in a substance are arbitrarily oriented and compensate each other.
When a substance is placed in an electric field (created by a capacitor or a polar molecule, ion, etc.), polar molecules tend to orient themselves along the direction of the field. The total dipole moment of the molecules in this case > 0, it is called the orientational dipole moment.
When both polar and non-polar molecules are placed in an electric field, the charges are displaced relative to each other, which creates an induced (induced) dipole moment. It is called the deformation dipole moment.
The occurrence of a dipole moment of the molecules of a substance under the action of an electric field is called connection polarization. It is the sum of the deformation and orientation dipole moment of the molecules.
Deformation polarization of a molecule is proportional to the field strength ( , V/m). The resulting induced dipole moment is related to the quantity by the relation:
in which the coefficient of proportionality ( , m 3) is called the deformation polarizability of the molecule. The deformation polarizability of a molecule is the sum of the electronic and atomic contributions:
due to displacement from equilibrium positions under the action of an external electric field of atoms and electrons. The more remote the outer electrons of a molecule (atom) from the nuclei, the higher the electronic polarizability. The displacement of atomic nuclei, which are heavy compared to electrons, is small and amounts to approximately 5 to 10% of .
Orientation polarization of the compound - polar molecules in an electric field are oriented along the field lines of force, striving as a result to take the most stable position corresponding to the minimum potential energy. This phenomenon is called orientational polarization and is equivalent to an increase in polarizability by an amount called orientational polarizability:
where k is the Boltzmann constant, J/K;
T- absolute temperature, K.
The orientational polarizability is usually an order of magnitude higher than the bending polarizability. It follows from equation (43) that decreases with increasing temperature, since thermal motion prevents the orientation of molecules.
The total polarizability of a molecule is the sum of three quantities:
. (44)
Polarizability has the dimension of volume and is expressed in m 3 .
The total polarization of a substance (molar polarization, m 3 / mol) is related to the relative permittivity of a substance by the Debye equation:
, (45)
where is the molar mass of the substance, g/mol;
is its density, g/m3;
is the relative dielectric constant of the medium.
Full polarization is observed only in a static field and in a low frequency field. In a high-frequency field, dipoles do not have time to orient themselves. Therefore, for example, in the field of infrared radiation, electronic and atomic polarization occurs, and in the field of visible radiation, only electronic polarization occurs, since only the lightest particles, electrons, are displaced due to the high frequency of field oscillations. For non-polar substances, the orientational polarization is zero.
Refraction
Maxwell's electromagnetic theory for transparent non-polar substances leads to the relation:
where is the refractive index (for polar substances). Substituting equation (46) into equation (45) and assuming that , we obtain:
. (47)
The quantity is called the molecular refraction of the substance.
It follows from equation (47) that the quantity R, defined in terms of the refractive index of a substance, serves as a measure of the electronic polarizability of its molecules. Generally speaking, the refractive index n depends on the radiation wavelength, and the equality is strictly valid for l = ¥. Extrapolation n to n¥ is usually carried out according to the Cauchy formula:
n= n¥ + b/l.(48)
Constants b and n¥ determined by measuring n for two different l, for example l F and l C lines of the hydrogen spectrum. In most cases, it is not determined R¥, a R D by measuring n D for yellow D sodium lines.
In physical and chemical studies, specific refraction is also used:
. (49)
Refraction has the dimension of a volume related to a certain portion of a substance:
specific refraction - (cm 3 / g);
molecular - (cm 3 / mol).
Very approximately, a molecule can be considered as a sphere of effective radius rM with a conductive surface. In this case:
Then from equations (47, 50) we get:
Thus, molecular refraction is equal to its own volume N A substance molecules.
For non-polar substances R", for polar substances R less by the value of the orientational polarization.
As follows from equation (47), the molecular refraction is determined only by the polarizability and therefore does not depend on the temperature and state of aggregation of the substance. Thus, refraction is the characteristic constant of matter.
DIPOLE MOMENT OF MOLECULES
ELECTRIC AND MAGNETIC PROPERTIES OF MOLECULES
HYDROGEN BOND
The hydrogen bond is intermediate between molecular and chemical forces of interaction. This peculiar bond is established between the hydrogen atom, which has distinctive features from all other atoms. Giving its electron to form a bond, it remains in the form of a nucleus (proton) without an electron, i.e. in the form of a particle whose diameter is a thousand times smaller than the diameters of other atoms. In addition, due to the absence of electrons in it, the H + ion does not experience repulsion from the electron shell of another atom, but rather is attracted by it. This allows it to get closer to other atoms, interact with their electrons, and even intrude into their electron shells. Therefore, in liquids, the hydrogen ion is not preserved as an independent particle, but is associated with the molecules of other substances. In water, it binds with H 2 O molecules, forming hydronium ions H 3 O +, with ammonia molecules NH 4 +.
The hydrogen bond is, as it were, the second side valency of the hydrogen atom.
Bond strength ¸ 20-30 kJ/mol
The hydrogen bond plays a very important role in the structure of water and ice.
The H-O bond length is covalent = 0.99 A°, the length of the hydrogen bond is 1.76 A°.
When ice melts, hydrogen bonds are destroyed, and when heated, expansion occurs. The destruction of hydrogen bonds leads to a decrease in volume and, as a result, the density of water passes through a maximum at 4°C.
When the centers of gravity of electric charges do not coincide in a molecule, electric poles arise - positive and negative. Such molecules are called polar. A system of two identical opposite charges is called a dipole.
The measure of polarity is the value of the dipole moment m, which is the product of the charge q and the distance l
In order of magnitude, the dipole moment is equal to the electron charge multiplied by the distance (10 -10 el.st.ed.´ 10 -8 cm), which is 10-18 el.st.ed.cm and equals 1 debye.
If there are several polar bonds in a molecule, then the total moment is equal to the vector sum of the dipole moments of the individual bonds
Various changes that molecules undergo under the influence of an external electric field on them are called polarization. There are orientational, atomic and electronic polarizations.
Orientational polarization represents the orientation of polar molecules in space according to the direction of the external electric field. With increasing temperature, the orientational polarization decreases.
Atomic polarization refers to the relative displacement of the atoms that make up the molecule. It characterizes the displacement of positively charged nuclei relative to the negative pole.
With electronic polarization, the electrons are displaced relative to the nucleus of the atom.
Atomic and electronic polarizations do not depend on temperature. The sum of electronic, atomic and orientational polarizations is called the total or molar polarization.
R \u003d R a + R e + R op \u003d R op + R d
R d \u003d R a + R e
The sum of atomic and electronic polarization is called deformation polarization.
When molecules interact with electromagnetic fields, in particular with visible light (l = 4000-8000 A), atomic and orientational polarizations do not arise, since atoms do not have time to move at the same speed as light vibrations occur. Electrons respond to light vibrations. In this case, the molar polarization is equal only to the electronic polarization and is called molar refraction
Molar refraction has additive properties and is a characteristic constant of a given substance.
The additivity of refraction is used to elucidate the structure of organic molecules.
R m = å n Ri , where n is the number of atoms
Ri - increments of molar refraction
CH 3 -CH 2 -COOH - propionic acid
R m \u003d 3Rc + 6Rn + Ro-hydrox + Ro-carbox =
3×2.418 + 6×1.10 + 1.325 + 2.211 = 17.59 cm3/g-at
Experience gives 17.68 cm 3 /g-at.
The refractive index, as already noted, depends on the polarizability of atoms, molecules, and ions. Therefore, the study of the electrical characteristics of a substance provides important information about the distribution of charges in a molecule and makes it possible to establish some properties of a substance due to its electrical asymmetry.
Let us consider some questions concerning the nature of the occurrence of a dipole moment in a molecule.
Polarizability and dipole moment
Any molecule is a collection of positively charged nuclei and negatively charged electrons. With a total charge equal to +e, the charge of all electrons will be equal to -e.
If the distribution of nuclei and electrons in space is such that the centers of "gravity" of positive and negative charges do not coincide, then the molecule has a constant dipole moment:
where l is the distance between the centers of electric charges.
Such a molecule is polar. A measure of the polarity of a molecule is the magnitude of the dipole moment, which is expressed in debyes (D):
D = 3.33564 10?30 C m
The dipole moment is a vector quantity. The direction of the vector ">" is selected from the negative pole to the positive. In the chemical literature, however, the opposite direction is traditionally taken, i.e. from "+" to "?".
If in diatomic molecules of simple substances, i.e., consisting of identical atoms, and in polyatomic molecules of complex substances with high symmetry, the centers of "gravity" of opposite electric charges coincide (l \u003d 0), then such molecules do not have a constant moment (m = 0) and are nonpolar.
If any non-polar molecule is placed in a constant electric field created, for example, by a capacitor, then its polarization occurs, which is expressed in a multidirectional displacement of charges (deformation polarization). Heavy nuclei of atoms will shift somewhat towards the negative pole, and electrons of insignificant mass will easily shift towards the positive pole. As a result, the centers of "gravity" of positive and negative charges will not coincide, and an induced (induced) dipole will appear in the molecule, the moment of which is proportional to the electric field strength:
m ind = b D E, (11)
where E is the strength of the internal electric field in the molecule [el. Art. units/cm 2 ; C / cm 2]
b D - coefficient of proportionality, which shows what dipole moment is created when the electric field strength is equal to unity. The more b D , the easier the molecule is polarized. The coefficient b D, called the deformation polarizability, is equal to the sum of the electronic b D and atomic polarizabilities b at:
b D = b el + b at (12)
The farther the outer (more mobile) valence electrons are removed from the atomic nuclei, the higher the electronic polarizability of the molecule. Since the displacement of atomic nuclei is insignificant (b at is 5 - 10% of b el) and can be neglected, it will be approximately b D = b el.
Thus, in an electric field, a dipole is formed with an induced or, as it is called, an induced dipole moment.
If any polar molecule is placed in an electric field, two processes will occur. Firstly, the molecule will be oriented along the field, and secondly, the distance between the centers of "charge gravity will increase, increasing the dipole moment of the molecule."
Thus, polar molecules in an electric field, just like non-polar ones, experience deformation polarization. In addition, under the influence of an electric field, they orient themselves along its lines of force, trying to take a stable position corresponding to a minimum of potential energy. This phenomenon, called orientational polarization, has an effect equivalent to an increase in the polarizability of a molecule by an amount bor, called orientational polarizability:
where k is the Boltzmann constant (1.380662(44) 10 −23 J/K);
T is the absolute temperature, K.
Thus, the total polarizability of a molecule b is the sum of three quantities:
b = b el + b at + b op or b = b D + b op (14)
From equations (11) and (12) it follows that the total polarizability b will have the dimension of volume [cm3 or A3].
Molar polarizability
In an electric (electromagnetic) field, the molecules are polarized and a state of tension arises, characterized by the value of the dielectric constant (e) of the substance, which is included in the equation of the Coulomb law and can be determined experimentally.
By measuring the dielectric permittivity, which characterizes the substance as a whole, it is possible to determine, according to the theory of polarization of dielectrics, the electro-optical parameters of its molecules, associated with the Clausius-Mossotti formula:
where N A is Avogadro's number;
M is the molecular weight of the substance;
C is the density of the substance, g/ml.
P M - molar polarization - a value that characterizes the measure of the induced moment in the volume that occupies 1 mole of a substance.
Molar polarization, dipole moment and total polarizability of a molecule are related to each other by the Debye equation, which is derived from equations (12) - (14):
Using the Debye equation, one can calculate the values of b and m from the known values of e, M, and c.
The polarization of molecules of substances that have relatively large values of e and P (for example, H 2 O, HCN, HCl) depends on temperature, decreasing as it rises. Molecules of such substances, having no center of charge symmetry, are permanent dipoles. For them, the molar polarization in the Debye equation is expressed as a linear function of 1/T:
Substances with m \u003d 0 consist of symmetrical molecules (for example, O 2, CO 2, CS 2, molecules of many hydrocarbons). In an electric field, an induced dipole moment arises in such molecules. The polarization of molecules of this type does not depend on temperature (Fig. 3).
For the case of permanent dipole molecules (straight line a; Fig. 3), the ordinate segment OA = a determines the value of the polarizability b, and tgv = b - the value of the dipole moment m
Complete polarization of molecules can be observed either in a static electric field or in a low frequency electromagnetic field, but not in a high frequency field, where the dipoles do not have time to orient themselves. Therefore, for example, in the field of low-frequency infrared radiation, both electronic and atomic polarization occurs, and in a higher-frequency field of visible light, only electronic polarization occurs (P el = 4/3pN A b el), because with high-frequency vibrations, only very light particles - electrons - have time to move. For non-polar substances: P OP = 0 and P = P D? R EL.
Rice. 3. Molar polarization dependence
from return temperature
a - for a molecule, constant dipoles;
b - for non-polar molecules.
Ionov, on the other - polarizability.
Polarizing action of the cation. Depends on the electronic structure of the ion, the magnitude of the charge and radius. The polarizing effect will be the more significant, the smaller the radius, the main quantum number of the outer electron orbitals and the larger the charge.
For example: a strong polarizing effect is characteristic of the cations of the first rows of the Periodic Table.
polarizability of anions. Depends on the same factors as the polarizing effect of cations. The larger the anion's radius and charge, the more it polarizes.
The polarizing effect of the cation is to pull the electron cloud away from the anion. As a result, the degree of covalence increases, the ionicity of the bond decreases, that is, the bond becomes covalent polar.
The polarization of ions is opposite in its effect to the polarization of a covalent bond.
Polarizability and its properties
Definition 2
Polarizability- the ability of a substance to acquire an electric dipole moment under the action of an external electric field. This is the ability to deform the electron cloud of a particle under the action of the electrostatic field of another ion. The polarizing action of the ion will determine the intensity of this field.
Polarizability characterizes the ability of a molecule to become polar as a result of the action of an external electric field. The compound is also polarized by the action of molecules on each other, for example, during chemical reactions.
The result of polarization can be a complete break in communication. In this case, the transition of the binding electron pair to one of the atoms occurs and opposite ions are formed. Asymmetric bond breaking with the formation of such ions is called heterolytic:
Picture 1.
Polarizability can be caused by:
displacement of electrons or atomic nuclei under the action of an electric field;
change in the geometry of the molecule;
rotation of the molecule;
displacement of an ion to a neighboring free crystallographic position (Scanavi polarizability), etc.
The polarizability of ions depends on the electronic structure of the ion, its charge and size. In each subgroup of the periodic system, the polarizability of element ions increases with an increase in their atomic number.
The polarizing effect of ions is the more significant than:
the electron shell of the ion is more stable;
more charge;
smaller ion radius.
Polarizability increases:
with an increase in the size of a molecule (atom);
with increasing atomic number;
increasing the ease of excitation of the atom.
For example: Octane is more polarizable than hexane because it has more electrons. But hexadiene will also be more polarizable than hexane, which is due to the presence of mobile $\pi $ electrons in hexadiene. And $\pi $-electrons are more sensitive to changes in the electric field than $\sigma $-electrons.
Polarizability affects:
acidity and basicity of molecules in the gas phase;
hardness of Lewis acids and bases;
the rate of nucleophilic substitution.
Calculation of the polarizability of molecules
Polarization manifests itself in the appearance of an induced dipole moment $\mu_(ind)$; particles (as a result of the displacement of electrons and nuclei).
The induced dipole moment is proportional to the strength of the external electric field:
$\mu_(ind) = \alpha \cdot \varepsilon_0 \cdot E$,
where $\mu_ind$ is the induced dipole moment, D;
$\alpha $ -- coefficient of proportionality -- particle polarizability, $\frac(Kl \cdot f (m^2))(B)$;
$E$ -- electric field strength, $B$.
For ions, the polarizability is proportional to the cube of their radius.
In an electric field, a polar molecule with a constant dipole moment has an additional induced dipole moment. Then the total relative permittivity is taken into account. This is expressed Debye equation:
$N(\frac(\alpha + \mu^2)(3\varepsilon_0kT))=3(\varepsilon-1)(\varepsilon+2)$,
where $N$ is the number of molecules per unit volume of the sample;
$\alpha $ - polarizability of the molecule;
$\varepsilon_0$ - permanent dipole moment of the molecule;
$k$ - Boltzmann's constant;
$T$ - absolute temperature.
If we plot the dependence of the right side of this equation on $\frac(1)(T)$, then
one can determine $\frac(\mu^2)(3\varepsilon_0k)$ and hence the constant dipole moment of the molecule. The polarizability is determined by the segment cut off on the y-axis at $\frac(1)(T) = 0$.
At very high temperatures, the dipole rotates so rapidly that its magnitude is nullified and only the induced dipole remains. It is located in the direction of the field that induces it and can be preserved at the highest temperatures.
Effect of polarization on the properties of substances.
Polarizability can explain some of the properties of substances:
Solubility.
For example: silver chloride $AgCl$ is much less soluble in water than sodium chloride $NaCl$ or potassium chloride $KCl$. The radius of the silver ion $Ag^+$ is commensurate with the radii of sodium $Na^+$ and potassium $K^+$ ions, but the polarizability of the silver ion is much greater (it has $18$ electrons at the outer level) than that of sodium and potassium ions. Therefore, the internuclear distance in silver chloride is smaller, and the bond breaking energy is greater than in molecules of sodium and potassium chlorides.
Melting temperature. Mutual polarization of ions contributes to the destruction of crystals. In this case, the melting temperature decreases, and the more, the more the crystal lattice is deformed.
For example: In the molecules of rubidium $RbF$ and titanium $TiF$ fluorides, the cation radii are the same, but the titanium ion $Ti^+$ is more strongly polarized and therefore has a stronger polarizing effect on the fluorine ion $F^-$ than the rubidium ion $Rb^+$. The melting point of rubidium fluoride is $798^\circ C$, and mp. titanium fluoride $327^\circ C$.
dissociation temperature. The polarization process will be facilitated by an increase in temperature. In this case, the amplitude of ion oscillations increases, which sometimes leads to a rearrangement of the structure of the substance. A polymorphic transformation is observed. When heated, a complete transition of electrons from an anion to a cation is also possible - thermal dissociation of the substance occurs. The stronger the polarizing effect, the lower the dissociation temperature.
For example: in the series of compounds of a given cation $MCl - MI$ and a given nion $NaГ - LiГ$, the decomposition temperature will decrease.
