Ticket№1

Chemistry- one of the most important and extensive areas of natural science, the science of substances, their properties, structure and transformations that occur as a result of chemical reactions, as well as the fundamental laws to which these transformations are subject. Since all substances are composed of atoms, which, thanks to chemical bonds, are able to form molecules, chemistry is mainly concerned with the study of interactions between atoms and molecules obtained as a result of such interactions. The subject of chemistry is chemical elements and their compounds, as well as the laws that govern various chemical reactions. Chemistry has much in common with physics and biology; in fact, the boundary between them is arbitrary. Modern chemistry is one of the most extensive disciplines among all natural sciences. Chemistry as an independent discipline was defined in the 16th-17th centuries, after a series of scientific discoveries that substantiated the mechanistic picture of the world, the development of industry, the creation of factories, and the emergence of bourgeois society. However, because chemistry, unlike physics, could not be expressed quantitatively, there was debate as to whether chemistry was a quantitative, reproducible science or some other type of knowledge. In 1661, Robert Boyle created the work “The Skeptical Chemist,” in which he explained the difference in the properties of various substances by the fact that they are built from different particles (corpuscles), which are responsible for the properties of the substance. Van Helmont, while studying combustion, introduced the concept gas for the substance that is formed with it, he discovered carbon dioxide. In 1672, Boyle discovered that when metals are fired, their mass increases, and explained this by the capture of “weighty particles of the flame.” Chemistry subject. One of the main objects of chemistry is the substances that make up all the bodies around us. A body is anything that has mass and volume. Raindrops, frost on branches, fog - bodies consisting of one substance - water. Phenomena in which new substances are formed from certain substances are called chemical. Chemistry studies such phenomena. Chemistry is the science of transformations of substances. This definition has become classic. Chemistry studies the composition and structure of substances, the conditions and ways of converting some substances into others, the dependence of the properties of substances on their composition and structure.

The main task of chemistry- identification and description of such properties of substances, due to which it is possible to transform some substances into others as a result of chemical phenomena or chemical reactions. Theoretical foundations of inorganic chemistry - the periodic law and Mendeleev's periodic system of elements. Modern inorganic chemistry studies the structure and properties of inorganic substances using not only chemical, but also physical methods (for example, spectroscopy).

Ticket#2

According to Heisenberg's uncertainty principle, the position and momentum of an electron cannot be simultaneously determined with absolute accuracy. However, despite the impossibility of accurately determining the position of an electron, it is possible to indicate the probability of an electron being in a certain position at any given time. The region of space in which there is a high probability of finding an electron is called an orbital. The concept of "orbital" should not be identified with the concept of orbit, which is used in Bohr's theory. In Bohr's theory, an orbit refers to the trajectory (path) of an electron around the nucleus. Electrons can occupy four different types of orbitals, which are called S-, p-, d- and f-orbitals. These orbitals can be represented by three-dimensional surfaces bounding them. The regions of space bounded by these surfaces are usually chosen so that the probability of finding a single electron within them is 95%. In Fig. Figure 1.18 schematically shows the shape of the s- and p-orbitals. The s-orbital is spherical and the p-orbital is dumbbell shaped. Since an electron has a negative charge, its orbital can be considered as some kind of charge distribution. This distribution is usually called an electron cloud.

Schrödinger equation- an equation that describes the change in space and time of the pure state specified by the wave function in Hamiltonian quantum systems. Plays the same important role in quantum mechanics as the equation of Newton's second law in classical mechanics. It can be called the equation of motion of a quantum particle. Installed by Erwin Schrödinger in 1926. The Schrödinger equation is intended for spinless particles moving at speeds much lower than the speed of light. In the case of fast particles and particles with spin, its generalizations are used.

Wave function, or psi function- a complex-valued function used in quantum mechanics to describe the pure state of a system. Is the coefficient of expansion of the state vector over a basis (usually a coordinate one):

where is the coordinate basis vector, and is the wave function in coordinate representation. |ψ| 2 – probability of finding a particle in a given region of space

Let the wave function be given in N-dimensional space, then at each point with coordinates , at a certain moment in time t it will look like . In this case, the Schrödinger equation will be written as:

where , is Planck’s constant; - the mass of the particle, - the potential energy external to the particle at the point, - the Laplace operator (or Laplacian), equivalent to the square of the nabla operator

Ticket No. 3

Atomic orbital- single-electron wave function in spherical symmetrical electric field atomic nucleus, wondering main n,orbital l And magnetic m quantum numbers.

The name "orbital" (not orbit) reflects the geometric idea of stationary states electron V atom; this special name reflects the fact that the state of an electron in an atom is described by the laws quantum mechanics and different from classical movement on trajectories. A set of atomic orbitals with the same value of the principal quantum number n constitute one electron shell.

Quantum numbers and nomenclature of orbitals

Radial probability density distribution for atomic orbitals at different n And l.

Principal quantum number n can take any positive integer value, starting from one ( n= 1,2,3, … ∞) and determines the total energy of the electron in a given orbital (energy level):

Energy for n= ∞ corresponds single-electron ionization energy for a given energy level.

The orbital quantum number (also called the azimuthal or complementary quantum number) determines angular momentum electron and can take integer values ​​from 0 to n - 1 (l = 0,1, …, n - 1). Momentum in this case is given by the relation

Atomic orbitals are usually named by the letter designation of their orbital number:

Magnetic quantum number m l determines the projection of the orbital angular momentum on the direction of the magnetic field and can take integer values ​​in the range from - l before l, including 0 ( m l = -l … 0 … l):

Ticket No. 4

Each orbital can contain no more than two electrons, differing in the value of the spin quantum number s(back). This prohibition is determined by the Pauli principle. The order of filling orbitals of the same level with electrons (orbitals with the same value of the principal quantum number n) is determined by the Klechkovsky rule, the order in which electrons fill orbitals within one sublevel (orbitals with the same values ​​of the principal quantum number n and orbital quantum number l) is determined by Hund's Rule.

A brief record of the distribution of electrons in an atom over various electron shells of the atom, taking into account their principal and orbital quantum numbers n And l called the electronic configuration of an atom.

Pauli's principle(exclusion principle) is one of the fundamental principles of quantum mechanics, according to which two or more identical fermions cannot simultaneously be in the same quantum state.

The Pauli principle can be formulated as follows: within one quantum system, only one particle can be in a given quantum state, the state of the other must differ by at least one quantum number.

Formulation of Klechkovsky's rule

the orbital energy consistently increases as the sum increases, and at the same value of this sum, the atomic orbital with a lower value of the principal quantum number has relatively lower energy. For example, at orbital energies obey the sequence, since here the principal quantum number is the smallest for the for-orbital; the largest orbital occupies an intermediate position.

When filling the orbital shells of an atom, those states for which the sum of the main quantum number and the secondary (orbital) quantum number, i.e., have a smaller value, are more preferable (more energetically favorable), and, therefore, are filled earlier.

RuleHunda(Gunda) determines the order of filling the orbitals of a certain sublayer and is formulated as follows: the total value of the spin quantum number of electrons of a given sublayer must be maximum.

This means that in each of the orbitals of the sublayer, one electron is filled first, and only after the unfilled orbitals are exhausted, a second electron is added to this orbital. In this case, in one orbital there are two electrons with half-integer spins of the opposite sign, which pair (form a two-electron cloud) and, as a result, the total spin of the orbital becomes equal to zero.

Ticket#5

Ionization energy- a type of binding energy, or, as it is sometimes called, the first ionization potential (I 1), is the smallest energy required to remove an electron from a free atom in its lowest energy (ground) state to infinity.

Ionization energy is one of the main characteristics of an atom, on which the nature and strength of the chemical bonds formed by the atom largely depend. The reducing properties of the corresponding simple substance also significantly depend on the ionization energy of the atom.

For a multi-electron atom, there are also the concepts of second, third, etc. ionization potentials, which represent the energy of removal of an electron from its free unexcited cations with charges +1, +2, etc. These ionization potentials are usually less important for characterizing chemical element.

Ionization energy always has an endoenergetic value (this is understandable, since in order to remove an electron from an atom, energy must be applied; this cannot happen spontaneously).

The following factors have the most significant influence on the ionization energy of an atom:

effective nuclear charge, which is a function of the number of electrons in the atom that shield the nucleus and are located in deeper internal orbitals;

radial distance from the nucleus to the maximum charge density of the outer electron, most weakly bound to the atom and leaving it during ionization;

a measure of the penetrating power of that electron;

interelectron repulsion among outer (valence) electrons.

The ionization energy is also influenced by less significant factors, such as quantum mechanical exchange interaction, spin and charge correlation, etc.

The ionization energy of elements is measured in Electronvolts per atom or Joules per mole.

The energy of the atom's electron affinity, or just him electron affinity, is the energy released during the addition of an electron to a free atom in its ground state, transforming it into a negative ion (the affinity of the atom for the electron is numerically equal, but opposite in sign to the ionization energy of the corresponding isolated singly charged anion).

Electron affinities are expressed in kilojoules per mole (kJ/mol) or electronvolts per atom (eV/atom).

In contrast to the ionization potential of an atom, which always has an endoenergetic value, the electron affinity of an atom is described by both exoenergy and endoenergy values

Atomic radii. The values ​​found on the basis of certain assumptions are taken as atomic radii. Theoretically, the so-called orbital radii are calculated, or the distance from the center of the nucleus to the electron density maximum farthest from it.

The periodicity of changes in atomic radii is especially clearly expressed in s- and p-elements: in periods from left to right, the radii decrease, and in groups from top to bottom they increase. The patterns of changes in atomic radii for d- and f-elements are more complex

Ticket#6

Chemical element- a collection of atoms with the same nuclear charge and number of protons, coinciding with the serial (atomic) number in the periodic table. Each chemical element has its own name and symbol, which are given in the Periodic Table of the Elements by Dmitry Ivanovich Mendeleev.

The form of existence of chemical elements in free form is simple substances(singleton)

Currently, D. I. Mendeleev’s Periodic Law has the following formulation: “the properties of chemical elements, as well as the forms and properties of the simple substances and compounds they form, periodically depend on the magnitude of the charges of the nuclei of their atoms”.

The most common are 3 forms of the periodic table: “short” (short-period), “long” (long-period) and “extra-long”. In the “super-long” version, each period occupies exactly one line. In the “long” version, lanthanides and actinides are removed from the general table, making it more compact. In the “short” form of recording, in addition to this, the fourth and subsequent periods occupy 2 lines each; The symbols of the elements of the main and secondary subgroups are aligned relative to different edges of the cells.

The short form of the table, containing eight groups of elements, was officially retired by IUPAC in 1989. Despite the recommendation to use the long form, the short form continues to be given in a large number of Russian reference books and manuals even after this time. From modern foreign literature, the short form is completely excluded, and the long form is used instead.

Ticket#10

Molecular orbital method is the most important method quantum chemistry. The method is based on the idea that each electron of a molecule is described by its own wave function - a molecular orbital (MO). In the general case, the MO method considers the formation of chemical bonds as a result of the movement of all electrons in the total field created by all electrons and all nuclei of the original atoms. However, since the main contribution to the formation of bonds comes from the electrons of the outer (valence) shells, we usually limit ourselves to considering only these electrons. In chemistry, the MO method (especially in the form of LCAO MO) is important because it allows one to obtain data on the structure and properties of molecules based on the corresponding characteristics of atoms. Therefore, almost all modern concepts of chemical bonding and chemical reactivity are based on the concepts of the MO method. Molecular orbital theory(MO) gives an idea of ​​the electron density distribution and explains the properties of molecules. In this theory, quantum mechanical dependencies for an atom are extended to a more complex system - a molecule. The molecule is considered as a whole, and not as a collection of atoms that have retained their individuality. In a molecule (as in an atom) there are discrete energy states of individual electrons (molecular orbitals) with their self-consistent movement in the field of each other and all nuclei of the molecule. Each orbital is characterized by its own set of quantum numbers, reflecting the properties of electrons in a given energy state. Unlike the single-center orbitals of atoms, the orbitals of molecules are multicenter, that is, the molecules share orbitals with two or more atomic nuclei. Each molecular orbital has a certain energy, approximately characterized by the corresponding ionization potential.

Two-center molecular orbitals

The molecular orbital method uses the concept of a molecular orbital (similar to the atomic orbital for an atom) to describe the electron density distribution in a molecule. Molecular orbitals are the wave functions of an electron in a molecule or other polyatomic chemical particle. Each molecular orbital (MO), like an atomic orbital (AO), can be occupied by one or two electrons. The state of the electron in the bonding region is described by the bonding molecular orbital, and in the antibonding region - by the antibonding molecular orbital. The distribution of electrons among molecular orbitals follows the same rules as the distribution of electrons among atomic orbitals in an isolated atom. Molecular orbitals are formed by certain combinations of atomic orbitals. Their number, energy and shape can be deduced from the number, energy and shape of the orbitals of the atoms that make up the molecule.????????????????????????????? ???????????????????????????????????????????????? ???

Ticket No. 11: Ionic bond. Metal connection. Hydrogen bond. Van der Waals forces.

Ionic bond- a strong chemical bond formed between atoms with a large difference (> 1.7 on the Pauling scale) of electronegativity, in which the total electron parapolity goes to the atom with greater electronegativity. This is the attraction of ions as oppositely charged bodies. An example is the compound CsF, in which the “degree of ionicity” is 97%. Let us consider the method of formation using sodium chloride NaCl as an example. The electronic configuration of sodium and chlorine atoms can be represented as: 11 Na 1s2 2s2 2p 6 3s1; 17 Cl 1s2 2s2 2p6 3s2 3р5 Like these are atoms with incomplete energy levels. Obviously, to complete them, it is easier for a sodium atom to give up one electron than to gain seven, and for a chlorine atom it is easier to gain one electron than to give up seven. During a chemical interaction, the sodium atom completely gives up one electron, and the chlorine atom accepts it. Schematically, this can be written as follows: Na. - l e -> Na+ sodium ion, stable eight-electron 1s2 2s2 2p6 shell due to the second energy level. :Cl + 1е --> .Cl - chlorine ion, stable eight-electron shell. Electrostatic attraction forces arise between the Na+ and Cl- ions, resulting in the formation of a compound. Ionic bonding is an extreme case of polarization of a polar covalent bond. Formed between a typical metal and non-metal. In this case, the electrons from the metal are completely transferred to the non-metal. Ions are formed.

If a chemical bond is formed between atoms that have a very large difference in electronegativity (EO > 1.7 according to Pauling), then the common electron pair is completely transferred to the atom with a higher EO. The result of this is the formation of a compound of oppositely charged ions:

An electrostatic attraction occurs between the resulting ions, which is called ionic bonding. Or rather, this look is convenient. In fact, the ionic bond between atoms in its pure form is not realized anywhere or almost nowhere; usually, in fact, the bond is partly ionic and partly covalent in nature. At the same time, the bond of complex molecular ions can often be considered purely ionic. The most important differences between ionic bonds and other types of chemical bonds are non-directionality and non-saturation. That is why crystals formed due to ionic bonds gravitate towards various dense packings of the corresponding ions.

Characteristics Such compounds have good solubility in polar solvents (water, acids, etc.). This occurs due to the charged parts of the molecule. In this case, the dipoles of the solvent are attracted to the charged ends of the molecule, and, as a result of Brownian motion, they “tear” the molecule of the substance into pieces and surround them, preventing them from connecting again. The result is ions surrounded by solvent dipoles.

When such compounds are dissolved, energy is usually released, since the total energy of the formed solvent-ion bonds is greater than the energy of the anion-cation bond. Exceptions are many salts of nitric acid (nitrates), which absorb heat when dissolved (solutions cool). The latter fact is explained on the basis of the laws that are considered in physical chemistry.

A metallic bond is a chemical bond caused by the presence of relatively free electrons. Characteristic of both pure metals and their alloys and intermetallic compounds.

Metal link mechanism

Positive metal ions are located at all nodes of the crystal lattice. Between them, valence electrons move randomly, like gas molecules, detached from the atoms during the formation of ions. These electrons act as cement, holding the positive ions together; otherwise, the lattice would disintegrate under the influence of repulsive forces between the ions. At the same time, electrons are held by ions within the crystal lattice and cannot leave it. The coupling forces are not localized or directed. Therefore, in most cases high coordination numbers (for example, 12 or 8) appear.

[edit]Characteristic crystal lattices

Most metals form one of the following highly symmetrical lattices with close packing of atoms: body-centered cubic, face-centered cubic, and hexagonal.

In a body-centered cubic (bcc) lattice, the atoms are located at the vertices of the cube and one atom is at the center of the cube volume. Metals have a cubic body-centered lattice: Pb, K, Na, Li, β-Ti, β-Zr, Ta, W, V, α-Fe, Cr, Nb, Ba, etc.

In a face-centered cubic (fcc) lattice, the atoms are located at the vertices of the cube and at the center of each face. Metals of this type have a lattice: α-Ca, Ce, α-Sr, Pb, Ni, Ag, Au, Pd, Pt, Rh, γ-Fe, Cu, α-Co, etc.

In a hexagonal lattice, the atoms are located at the vertices and center of the hexagonal bases of the prism, and three atoms are located in the middle plane of the prism. Metals have this packing of atoms: Mg, α-Ti, Cd, Re, Os, Ru, Zn, β-Co, Be, β-Ca, etc.

[edit]Other properties

Freely moving electrons cause high electrical and thermal conductivity. Substances that have a metallic bond often combine strength with plasticity, since when atoms are displaced relative to each other, the bonds do not break.

Van der Waals forces- intermolecular interaction forces with energy 0.8 - 8.16 kJ/mol. This term originally denoted all such forces; in modern science it is usually applied to the forces arising from the polarization of molecules and the formation of dipoles. Discovered by J. D. van der Waals in 1869.

Van der Waals forces include interactions between dipoles (permanent and induced). The name comes from the fact that these forces cause the correction for internal pressure in the van der Waals equation of state for a real gas. These interactions mainly determine the forces responsible for the formation of the spatial structure of biological macromolecules.

Van der Waals forces also occur between a particle (macroscopic particle or nanoparticle) and a molecule and between two particles.

Classification of van der Waals forces

The van der Waals interaction consists of three types of weak interactions:

Orientation forces, dipole-dipole attraction. It is carried out between molecules that are permanent dipoles. An example is HCl in liquid and solid states. The energy of such interaction is inversely proportional to the cube of the distance between the dipoles.

Dispersion attraction (London forces). Interaction between instantaneous and induced dipoles. The energy of such interaction is inversely proportional to the sixth power of the distance between the dipoles.

Inductive attraction. Interaction between a permanent dipole and an induced one. The energy of such interaction is inversely proportional to the sixth power of the distance between the dipoles.

Until now, many authors proceed from the assumption that van der Waals forces determine the interlayer interaction in layered crystals, which contradicts experimental data: the Debye temperature anisotropy scale and, accordingly, the lattice reflection anisotropy scale. Based on this erroneous assumption, many two-dimensional models have been built that “describe” the properties, in particular, of graphite and boron nitride.

Ticket No. 12

Coordination number in chemistry

In chemistry, the concept of coordination number appeared with the development of the chemistry of complex compounds. It refers to the number of ligands (atoms, molecules, ions) that form the first coordination (internal) sphere of the complexing agent.

For example, in the complex salt of potassium hexacyanoferrate(III) K 3 the coordination number of the Fe 3+ ion is 6, and in cis-dichlorodiammineplatinum (II) (Peyrone's salt) Pt(NH 3) 2 Cl 2 the central platinum atom is bonded to four ligands.

The concept of coordination number is also used to characterize the central atom in molecules, mainly for those cases when the number of chemically bonded nearby atoms is not equal to the numerical value of valence. For example, in a nitric acid molecule, the formal valency of the central nitrogen atom is 4, the oxidation state is +5, and the coordination number is 3.

The concept of coordination number is also used to describe the structure of liquids and amorphous bodies. In this case, the coordination number is a measure of short-range order, the average number of the nearest neighbors of an atom. It can be fractional.

Central atom(CA) or complexing agent is usually a metal ion or atom, although in some cases it can be a non-metal, for example, silicon and phosphorus in the 2– and – anions, respectively. CA forms chemical bonds with ligands and coordinates them around itself. As a result, a coordination compound is formed.

Ligand(from lat. ligare - to bind) - an atom, ion or molecule associated with a certain center (acceptor). The concept is used in biochemistry to denote agents that combine with biological acceptors (receptors, immunoglobulins), as well as in the chemistry of complex compounds, denoting particles attached to one or more central (complex-forming) metal atoms.

Orbitals of the hydrogen atom.

When wave functions for electrons in individual atoms are considered, these functions are called atomic orbitals(abbreviated as AO). Experimental evidence for the existence of atomic orbitals can be obtained from atomic spectra. For example, during an electrical discharge in hydrogen gas, H2 molecules dissociate into atoms, and the atoms emit light of strictly defined frequencies, which are grouped in series: in the visible region (the so-called Balmer series), ultraviolet (Lyman series), and infrared (Paschen series). Even in the pre-quantum period, it was noticed that all series satisfy one simple equation:

atomic molecular orbital quantization

The hydrogen atom is three-dimensional, so the Schrödinger equation must include kinetic energy in all three dimensions and will have a slightly more complex form than the equation for one-dimensional motion presented in Section 1.1 of this chapter. When solving it with the imposition of boundary conditions that follow from the probabilistic interpretation of the wave function, the following conclusions were obtained.

1. It is necessary to accept that there are three dimensionless quantum numbers, which are denoted by the symbols n, /, and m. The appearance of the quantum number n is caused by the fact that the electron can change its distance from the nucleus. Quantum

numbers / and T are related to the angular momentum of the electron, which can orbit the nucleus in three dimensions. The number / characterizes the magnitude of the angular momentum, and the number T- the orientation of angular momentum in space, since angular momentum is a vector quantity. Acceptable values ​​of quantum numbers that follow from the boundary conditions are n - 1, 2, 3.;

2. The energy of an electron, generally speaking, should depend on all three quantum numbers, or at least on two, but a unique feature of the hydrogen atom (but not other atoms) is that the electron energy depends only on n. For this reason n is called the principal quantum number. (So, for n = 3l can take on the values ​​0, 1 and 2, but the energy of the electron remains constant.) The allowed energies will be energies of the form En = R/n2.

The atomic orbitals of a hydrogen atom are very important because they show how the electron (or electron density) is distributed in space. The amplitude of AO w (r) is different in different places in space, and the probability of finding an electron in some infinitesimal region df around point r is. The spatial distribution of an electron can be depicted by indicating the magnitude using different shading densities on the diagram. The density distribution in some hydrogen AOs is shown in Fig. 1.1

The ground state orbital of the hydrogen atom is very simple: it is spherically symmetrical and its density decreases exponentially as it moves away from the nucleus. Therefore, it is most likely to find an electron near the nucleus, where q/ and, thus, y? ^ are maximum. This is consistent with the idea that in order to achieve the lowest potential energy, an electron must tend to the nucleus. However, the orbnthal is not completely “pressed” to the nucleus, but extends to areas quite distant from it. This situation arises due to the fact that not only the potential, but also the kinetic energy of the electron is of great importance. The latter cannot be represented as the kinetic energy of motion in an orbit around the nucleus, which leads to the appearance of a centrifugal force that keeps the electron away from the nucleus, since the angular momentum of the electron in the ground state of the hydrogen atom is zero. (For n = 1, there can be only one quantum number of angular momentum: / = 0, and therefore equal to zero.) Thus, in the classical sense, the electron in the ground state of the hydrogen atom does not seem to rotate around the nucleus, but simply swings along radius. This is what its kinetic energy is associated with. From the point of view of quantum theory, the kinetic energy of an electron is related to the wavelength of the electron propagating in the radial direction. If the orbital is “pressed” towards the nucleus, the wavelength in the radial direction inevitably decreases, and therefore the kinetic energy increases (Section 1.1). Real orbnthal is the result of a compromise between moderately low potential energy and moderately high kinetic energy. Closer to the nucleus, the electron density is higher, but it is also present at a distance from the nucleus.

Fig.1.1

All orbitals with zero angular momentum are called s orbitals. The lowest energy orbital is called the 1s orbital. If n= 2 and 7=0, then this is a 2s orbital. Its energy is higher than the energy of the 1s orbital for two reasons. Firstly, it has a radial node (Fig. 1.2), which is a spherical surface, inside and outside of which the wave function has different signs, and on this surface itself the electron density is zero. The appearance of nodes in any orbital increases the energy of the electron occupying this orbital, and the more nodes, the higher the energy of the orbital.

This is due to the fact that as the number of nodes increases, the electron wavelength becomes shorter, i.e. a larger number of half-wills falls on the same area of ​​space and therefore its kinetic energy increases. Secondly, the increase in the energy of the 2s orbital compared to the 1s orbital is due to the fact that the 2s orbital extends to a distance further from the nucleus, and therefore the potential energy of the electron in it is higher than in the 1s orbital. Similar remarks can be made regarding higher lying s-orbitals: etc.

Fig.1.2

Orbital s n= 1 has no nodes. Orbitals with n=2 have one node, with n=3 - two nodes, etc. With respect to the inversion symmetry operation (the center of inversion coincides with the center of the nucleus), all s-orbitals are symmetrical, all s-orbitals are antisymmetric, all s-orbitals are symmetrical, etc.

If n=0, the only value allowed for l, is zero, but if n = 2, the quantum number of orbital angular momentum can take the values ​​0 (2n-orbit al) or 1. If n = 1, atomic orbitals are called R- orbngalei. At n= 2 And l= 1 we have 2p-orbnthal. It differs from the 2s orbital in that the electron occupying it has an orbital angular momentum of magnitude (2) Angular momentum is a consequence of the presence of an angular node (Fig. 1.2), which, as they say, “introduces curvature into the angular change of the wave function” (the ball turns into a dumbbell). The presence of orbital angular momentum has a strong influence on the radial shape of the orbital. While all the 5-orbitals at the nucleus have a non-zero value, there are no 1s orbitals there. This can be thought of as the electron being thrown away from the nucleus by orbital angular momentum. The force of Coulomb attraction of an electron to the nucleus is proportional to 1/r where r is the distance from the nucleus, and the centrifugal force repelling electrons from the nucleus is proportional to r 3 (3 is angular momentum). Therefore, if the angular momentum is <0, at very small r the centrifugal force exceeds the Coulomb force. This centrifugal effect also manifests itself in AO with l=2, which are called 1s orbitals, l=3 (s-orbitals) and higher orbitals (Ј-, /? -, y-orbitals). All these orbits, due to the fact that /^0, have zero amplitude at the nucleus and, therefore, the probability of finding electrons there is zero.

U 2/? - orbntali there is no radial node, but 3/? - the orbital has it. Sketches of the lower atomic orbits of alleys, illustrating the properties and symmetry of the AO (but not the probabilistic distribution of the electron within the orbital, as in Fig. 1.1), are shown in Fig. 1.2. Light and dark areas are places where the wave function has different signs. Since the choice of sign is arbitrary, it makes no difference whether we associate the dark areas with the positive and light areas with the negative sign of the wave function, or vice versa. The boundary between the light and dark areas of the orbntals is a node, i.e. the place where the wave function is zero, or, in other words, the place where the wave function reverses sign. The more nodes, the higher the energy of the electron occupying a given AO.

Since for orbitals l=0, the quantum number T can take the values ​​+1, 0 and - 1. Various values T correspond to orbitals with different orientations of orbital angular momentum, p-Orbital with m = 0 has a zero projection of angular momentum onto axis 2 (Fig. 1.2), and for this reason it is called R 2 -orbital. View R 2 - orbntali (see Fig. 1.1 and 1.2) indicates that the electron density is “collected in a backwater” along axis 2. In this case, there is a horizontal nodal plane passing through the nucleus, and the probability of finding an electron in this plane is zero. Two others R - orbitals can be represented by similar pictures with the orientation of the “blades” along the axes henna(see Fig. 1.1), that’s why they are called R x and R at - orbnthals.

If /? =3, then / can take on the values ​​0, 1 and 2. This applies to one 3^-orbngali, three 3/? - orbngals and five 3^-orbngals. 3b/-Orbngals are five, since when / = 2 T can take values ​​2, 1, 0, - 1 and - 2. All Oh- orbntals have zero amplitude near the nucleus. They do not have radial nodes (4с1 - orbnthals have radial nodes), but each has two nodal planes (see Fig. 1.2).

It was said above that the energy of an electron in a hydrogen atom depends on the principal quantum number of the orbital it occupies and does not depend on its orbital angular momentum. Thus, in a hydrogen atom, an electron in a 2p orbital has the same energy as in any of the 2p orbitals. If different orbitals have the same energy, they are called degenerate. The degeneracy of the hydrogen atom is something exceptional and is explained in physics by the special form of its Coulomb potential.

The physical and chemical properties of atoms, and consequently of matter as a whole, are largely determined by the characteristics of the electron cloud around the atomic nucleus. A positively charged nucleus attracts negatively charged electrons. Electrons rotate around the nucleus so quickly that it is impossible to accurately determine their location. Electrons moving around the nucleus can be compared to a cloud or fog, in some places more or less dense, in others completely sparse. The shape of the electron cloud, as well as the probability of finding an electron at any point in it, can be determined by solving the corresponding equationsquantum mechanics. The regions where electrons are most likely to be found are called orbitals. Each orbital is characterized by a certain energy and can contain no more than two electrons. Typically, the lowest energy orbitals closest to the nucleus are filled first, then the higher energy orbitals, etc.

A collection of electron orbitals with similar energies forms a layer (i.e., a shell, or energy level). Energy levels are numbered starting from the nucleus of the atom: 1, 2, 3,... . The further away from the nucleus, the more spacious the layers and the more orbitals and electrons they can accommodate. Yes, onn-th level n 2 orbitals, and they can accommodate up to 2n 2 electrons. In known elements, electrons are found only in the first seven levels, and only the first four of them are filled.

There are four types of orbitals, they are designateds , p , d And f . At each level (layer) there is ones -orbital that contains the electrons most tightly bound to the nucleus. Followed by threep-orbitals, five d -orbitals and, finally, sevenf-orbitals.

Shell n	Number of orbitals n 2	Orbital type	Number of electrons 2n 2
		s, p
		s, p, d
		s, p, d, f

s - Orbitals are spherical in shapep – the shape of a dumbbell or two touching spheres,d-orbitals have 4 “petals”, and f -orbitals 8. In cross-section, these orbitals look approximately as shown in the figure.

Three R-orbitals are oriented in space along the axes of the rectangular coordinate system and are designated accordinglyp x, p y And p z; d- And f -orbitals are also located at certain angles to each other; sphericals -orbitals have no spatial orientation.

Each subsequent element in a period has an atomic number one greater than the previous element and contains one more electron. This extra electron occupies the next orbital in ascending order. It must be borne in mind that the electronic layers are diffuse and the energy of some orbitals of the outer layers is lower than that of the inner ones. Therefore, for example, it is first filleds -fourth level orbital (4s -orbital), and only after it is the filling of 3 completedd -orbitals. The order of filling the orbitals is usually as follows: 1s , 2 s , 2 p , 3 s , 3 p , 4 s , 3 d , 4 p , 5 s , 4 d , 5 p , 6 s , 4 f , 5 d , 6 p , 7 s . In the notation used to represent the electronic configuration of an element, the superscript on the letter representing the orbital indicates the number of electrons in that orbital. For example, record 1 s 2 2 s 2 2 p 5 means that by 1s -the orbital of an atom contains two electrons, 2s -orbitals two, on 2R five electrons. Neutral atoms that have 8 electrons in their outer electron shell (i.e. are filleds- And R -orbitals) are so stable that they practically do not enter into any chemical reactions. These are the atoms of inert gases. Electronic configuration of helium 1 s 2, neon 2 s 2 2 p 6, argon 3 s 2 3 p 6, krypton 4 s 2 3 d 10 4 p 6, xenon 5 s 2 4 d 10 5 p 6 and finally radon 6 s 2 4 f 14 5 d 10 6 p 6 .

Orbitals exist regardless of whether an electron is present in them (occupied orbitals) or absent (vacant orbitals). The atom of each element, starting with hydrogen and ending with the last element obtained today, has a complete set of all orbitals at all electronic levels. They are filled with electrons as the atomic number, that is, the charge of the nucleus, increases.

s-Orbitals, as shown above, have a spherical shape and, therefore, the same electron density in the direction of each three-dimensional coordinate axis:

At the first electronic level of each atom there is only one s- orbital. Starting from the second electronic level in addition to s- three orbitals also appear R-orbitals. They are shaped like three-dimensional eights, this is what the area of ​​the most likely location looks like R-electron in the region of the atomic nucleus. Each R-the orbital is located along one of three mutually perpendicular axes, in accordance with this in the name R-orbitals indicate, using the corresponding index, the axis along which its maximum electron density is located:

In modern chemistry, an orbital is a defining concept that allows us to consider the processes of formation of chemical bonds and analyze their properties, while attention is focused on the orbitals of those electrons that participate in the formation of chemical bonds, that is, valence electrons, usually the electrons of the last level.

The carbon atom in the initial state has two electrons in the second (last) electronic level. s-orbitals (marked in blue) and one electron in two R-orbitals (marked in red and yellow), the third orbital is p z-vacant:

Hybridization.

In the case when a carbon atom participates in the formation of saturated compounds (not containing multiple bonds), one s- orbital and three R-orbitals combine to form new orbitals that are hybrids of the original orbitals (the process is called hybridization). The number of hybrid orbitals is always equal to the number of original ones, in this case, four. The resulting hybrid orbitals are identical in shape and outwardly resemble asymmetrical three-dimensional figure eights:

The whole structure appears to be inscribed in a regular tetrahedron - a prism assembled from regular triangles. In this case, the hybrid orbitals are located along the axes of such a tetrahedron, the angle between any two axes is 109°. Carbon's four valence electrons are located in these hybrid orbitals:

Participation of orbitals in the formation of simple chemical bonds.

The properties of electrons located in four identical orbitals are equivalent; accordingly, the chemical bonds formed with the participation of these electrons when interacting with atoms of the same type will be equivalent.

The interaction of a carbon atom with four hydrogen atoms is accompanied by the mutual overlap of elongated hybrid orbitals of carbon with spherical orbitals of hydrogen. Each orbital contains one electron; as a result of overlap, each pair of electrons begins to move along the united molecular orbital.

Hybridization only leads to a change in the shape of the orbitals within one atom, and the overlap of the orbitals of two atoms (hybrid or ordinary) leads to the formation of a chemical bond between them. In this case ( cm. Figure below) the maximum electron density is located along the line connecting two atoms. Such a connection is called an s-connection.

Traditional writing of the structure of the resulting methane uses the valence bar symbol instead of overlapping orbitals. For a three-dimensional image of a structure, the valence directed from the drawing plane to the viewer is shown in the form of a solid wedge-shaped line, and the valence extending beyond the drawing plane is shown in the form of a dashed wedge-shaped line:

Thus, the structure of the methane molecule is determined by the geometry of the hybrid orbitals of carbon:

The formation of an ethane molecule is similar to the process shown above, the difference is that when the hybrid orbitals of two carbon atoms overlap, a C-C bond is formed:

The geometry of the ethane molecule resembles methane, bond angles are 109°, which is determined by the spatial arrangement of carbon hybrid orbitals:

Participation of orbitals in the formation of multiple chemical bonds.

The ethylene molecule is also formed with the participation of hybrid orbitals, but only one is involved in hybridization s-orbital and only two R-orbitals ( p x And RU), third orbital – p z, directed along the axis z, does not participate in the formation of hybrids. From the initial three orbitals, three hybrid orbitals arise, which are located in the same plane, forming a three-rayed star, the angles between the axes are 120°:

Two carbon atoms attach four hydrogen atoms and also connect to each other, forming a C-C s-bond:

Two orbitals p z, which did not participate in hybridization, overlap each other, their geometry is such that the overlap occurs not along the C-C communication line, but above and below it. As a result, two regions with increased electron density are formed, where two electrons (marked in blue and red) are located, participating in the formation of this bond. Thus, one molecular orbital is formed, consisting of two regions separated in space. A bond in which the maximum electron density is located outside the line connecting two atoms is called a p-bond:

The second valence feature in the designation of a double bond, which has been widely used to depict unsaturated compounds for centuries, in the modern understanding implies the presence of two regions with increased electron density located on opposite sides of the C-C bond line.

The structure of the ethylene molecule is determined by the geometry of hybrid orbitals, the H-C-H bond angle is 120°:

During the formation of acetylene, one s-orbital and one p x-orbital (orbitals p y And p z, do not participate in the formation of hybrids). The two resulting hybrid orbitals are located on the same line, along the axis X:

The overlap of hybrid orbitals with each other and with the orbitals of hydrogen atoms leads to the formation of C-C and C-H s-bonds, represented by a simple valence line:

Two pairs of remaining orbitals p y And p z overlap. In the figure below, colored arrows show that, from purely spatial considerations, the most likely overlap of orbitals with the same indices x-x And ooh. As a result, two p-bonds are formed surrounding a simple s-bond C-C:

As a result, the acetylene molecule has a rod-shaped shape:

In benzene, the molecular backbone is assembled from carbon atoms having hybrid orbitals composed of one s- and two R-orbitals arranged in the shape of a three-rayed star (like ethylene), R-orbitals not involved in hybridization are shown semi-transparent:

Vacant orbitals, that is, those not containing electrons (), can also participate in the formation of chemical bonds.

High level orbitals.

Starting from the fourth electronic level, atoms have five d-orbitals, their filling with electrons occurs in transition elements, starting with scandium. Four d-orbitals have the shape of three-dimensional quatrefoils, sometimes called “clover leaves”, they differ only in orientation in space, the fifth d-orbital is a three-dimensional figure eight threaded into a ring:

d-Orbitals can form hybrids with s- And p- orbitals. Options d-orbitals are usually used in the analysis of the structure and spectral properties of transition metal complexes.

Starting from the sixth electronic level, atoms have seven f-orbitals, their filling with electrons occurs in the atoms of lanthanides and actinides. f-Orbitals have a rather complex configuration; the figure below shows the shape of three of seven such orbitals, which have the same shape and are oriented in space in different ways:

f-Orbitals are very rarely used when discussing the properties of various compounds, since the electrons located on them practically do not take part in chemical transformations.

Prospects.

At the eighth electronic level there are nine g-orbitals. Elements containing electrons in these orbitals should appear in the eighth period, while they are not available (element No. 118, the last element of the seventh period of the Periodic Table, is expected to be obtained in the near future; its synthesis is carried out at the Joint Institute for Nuclear Research in Dubna).

Form g-orbitals, calculated by quantum chemistry methods, are even more complex than those of f-orbitals, the region of the most probable location of the electron in this case looks very bizarre. Below is the appearance of one of nine such orbitals:

In modern chemistry, concepts of atomic and molecular orbitals are widely used in describing the structure and reaction properties of compounds, also in analyzing the spectra of various molecules, and in some cases to predict the possibility of reactions occurring.

Mikhail Levitsky

Composition of the atom.

An atom is made up of atomic nucleus And electron shell.

The nucleus of an atom consists of protons ( p+) and neutrons ( n 0). Most hydrogen atoms have a nucleus consisting of one proton.

Number of protons N(p+) is equal to the nuclear charge ( Z) and the ordinal number of the element in the natural series of elements (and in the periodic table of elements).

N(p +) = Z

Sum of neutrons N(n 0), denoted simply by the letter N, and number of protons Z called mass number and is designated by the letter A.

A = Z + N

The electron shell of an atom consists of electrons moving around the nucleus ( e -).

Number of electrons N(e-) in the electron shell of a neutral atom is equal to the number of protons Z at its core.

The mass of a proton is approximately equal to the mass of a neutron and 1840 times the mass of an electron, so the mass of an atom is almost equal to the mass of the nucleus.

The shape of the atom is spherical. The radius of the nucleus is approximately 100,000 times smaller than the radius of the atom.

Chemical element- type of atoms (collection of atoms) with the same nuclear charge (with the same number of protons in the nucleus).

Isotope- a collection of atoms of the same element with the same number of neutrons in the nucleus (or a type of atom with the same number of protons and the same number of neutrons in the nucleus).

Different isotopes differ from each other in the number of neutrons in the nuclei of their atoms.

Designation of an individual atom or isotope: (E - element symbol), for example: .

Structure of the electron shell of an atom

Atomic orbital- state of an electron in an atom. The symbol for the orbital is . Each orbital has a corresponding electron cloud.

Orbitals of real atoms in the ground (unexcited) state are of four types: s, p, d And f.

Electronic cloud- the part of space in which an electron can be found with a probability of 90 (or more) percent.

Note: sometimes the concepts of “atomic orbital” and “electron cloud” are not distinguished, calling both “atomic orbital”.

The electron shell of an atom is layered. Electronic layer formed by electron clouds of the same size. The orbitals of one layer form electronic ("energy") level, their energies are the same for the hydrogen atom, but different for other atoms.

Orbitals of the same type are grouped into electronic (energy) sublevels:
s-sublevel (consists of one s-orbitals), symbol - .
p-sublevel (consists of three p
d-sublevel (consists of five d-orbitals), symbol - .
f-sublevel (consists of seven f-orbitals), symbol - .

The energies of orbitals of the same sublevel are the same.

When designating sublevels, the number of the layer (electronic level) is added to the sublevel symbol, for example: 2 s, 3p, 5d means s-sublevel of the second level, p-sublevel of the third level, d-sublevel of the fifth level.

The total number of sublevels at one level is equal to the level number n. The total number of orbitals at one level is equal to n 2. Accordingly, the total number of clouds in one layer is also equal to n 2 .

Designations: - free orbital (without electrons), - orbital with an unpaired electron, - orbital with an electron pair (with two electrons).

The order in which electrons fill the orbitals of an atom is determined by three laws of nature (the formulations are given in simplified terms):

1. The principle of least energy - electrons fill the orbitals in order of increasing energy of the orbitals.

2. The Pauli principle - there cannot be more than two electrons in one orbital.

3. Hund's rule - within a sublevel, electrons first fill empty orbitals (one at a time), and only after that they form electron pairs.

The total number of electrons in the electronic level (or electron layer) is 2 n 2 .

The distribution of sublevels by energy is expressed as follows (in order of increasing energy):

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p ...

This sequence is clearly expressed by an energy diagram:

The distribution of an atom's electrons across levels, sublevels, and orbitals (electronic configuration of an atom) can be depicted as an electron formula, an energy diagram, or, more simply, as a diagram of electron layers ("electron diagram").

Examples of the electronic structure of atoms:

Valence electrons- electrons of an atom that can take part in the formation of chemical bonds. For any atom, these are all the outer electrons plus those pre-outer electrons whose energy is greater than that of the outer ones. For example: the Ca atom has 4 outer electrons s 2, they are also valence; the Fe atom has 4 outer electrons s 2 but he has 3 d 6, therefore the iron atom has 8 valence electrons. Valence electronic formula of the calcium atom is 4 s 2, and iron atoms - 4 s 2 3d 6 .

Periodic table of chemical elements by D. I. Mendeleev
(natural system of chemical elements)

Periodic law of chemical elements(modern formulation): the properties of chemical elements, as well as simple and complex substances formed by them, are periodically dependent on the value of the charge of atomic nuclei.

Periodic table- graphic expression of the periodic law.

Natural series of chemical elements- a series of chemical elements arranged according to the increasing number of protons in the nuclei of their atoms, or, what is the same, according to the increasing charges of the nuclei of these atoms. The atomic number of an element in this series is equal to the number of protons in the nucleus of any atom of this element.

The table of chemical elements is constructed by “cutting” the natural series of chemical elements into periods(horizontal rows of the table) and groupings (vertical columns of the table) of elements with a similar electronic structure of atoms.

Depending on the way you combine elements into groups, the table may be long-period(elements with the same number and type of valence electrons are collected into groups) and short period(elements with the same number of valence electrons are collected into groups).

The short-period table groups are divided into subgroups ( main And side), coinciding with the groups of the long-period table.

All atoms of elements of the same period have the same number of electron layers, equal to the period number.

Number of elements in periods: 2, 8, 8, 18, 18, 32, 32. Most of the elements of the eighth period were obtained artificially; the last elements of this period have not yet been synthesized. All periods except the first begin with an alkali metal-forming element (Li, Na, K, etc.) and end with a noble gas-forming element (He, Ne, Ar, Kr, etc.).

In the short-period table there are eight groups, each of which is divided into two subgroups (main and secondary), in the long-period table there are sixteen groups, which are numbered in Roman numerals with the letters A or B, for example: IA, IIIB, VIA, VIIB. Group IA of the long-period table corresponds to the main subgroup of the first group of the short-period table; group VIIB - secondary subgroup of the seventh group: the rest - similarly.

The characteristics of chemical elements naturally change in groups and periods.

In periods (with increasing serial number)

• nuclear charge increases
• the number of outer electrons increases,
• the radius of atoms decreases,
• the strength of the bond between electrons and the nucleus increases (ionization energy),
• electronegativity increases,
• the oxidizing properties of simple substances are enhanced ("non-metallicity"),
• the reducing properties of simple substances weaken ("metallicity"),
• weakens the basic character of hydroxides and corresponding oxides,
• the acidic character of hydroxides and corresponding oxides increases.

In groups (with increasing serial number)

• nuclear charge increases
• the radius of atoms increases (only in A-groups),
• the strength of the bond between electrons and the nucleus decreases (ionization energy; only in A-groups),
• electronegativity decreases (only in A-groups),
• the oxidizing properties of simple substances weaken ("non-metallicity"; only in A-groups),
• the reducing properties of simple substances are enhanced ("metallicity"; only in A-groups),
• the basic character of hydroxides and corresponding oxides increases (only in A-groups),
• weakens the acidic character of hydroxides and corresponding oxides (only in A-groups),
• the stability of hydrogen compounds decreases (their reducing activity increases; only in A-groups).

Tasks and tests on the topic "Topic 9. "Structure of the atom. Periodic law and periodic system of chemical elements by D. I. Mendeleev (PSHE) "."

• Periodic law - Periodic law and structure of atoms grades 8–9
  You must know: the laws of filling orbitals with electrons (the principle of least energy, the Pauli principle, Hund's rule), the structure of the periodic table of elements.

  You must be able to: determine the composition of an atom by the position of the element in the periodic table, and, conversely, find an element in the periodic system, knowing its composition; depict the structure diagram, electronic configuration of an atom, ion, and, conversely, determine the position of a chemical element in the PSCE from the diagram and electronic configuration; characterize the element and the substances it forms according to its position in the PSCE; determine changes in the radius of atoms, properties of chemical elements and the substances they form within one period and one main subgroup of the periodic system.

  Example 1. Determine the number of orbitals in the third electron level. What are these orbitals?
  To determine the number of orbitals, we use the formula N orbitals = n 2 where n- level number. N orbitals = 3 2 = 9. One 3 s-, three 3 p- and five 3 d-orbitals.

  Example 2. Determine which element's atom has electronic formula 1 s 2 2s 2 2p 6 3s 2 3p 1 .
  In order to determine what element it is, you need to find out its atomic number, which is equal to the total number of electrons of the atom. In this case: 2 + 2 + 6 + 2 + 1 = 13. This is aluminum.

  After making sure that everything you need has been learned, proceed to completing the tasks. We wish you success.

  
  Recommended reading:
  • O. S. Gabrielyan and others. Chemistry 11th grade. M., Bustard, 2002;
  • G. E. Rudzitis, F. G. Feldman. Chemistry 11th grade. M., Education, 2001.