EntranceHow to calculate the binding energy in a molecule. Basic types of chemical bond
Communication energy is the energy that is released when a molecule is formed from single atoms. Binding energy is the energy that is absorbed when two atoms move an infinite distance away from each other. And the enthalpy of formation is the heat that is released when a substance is obtained from simple substances, that is, if we speak in the language of binding energies, first the atoms of simple substances are spread over an infinitely large distance (with the absorption of energy), then they combine to form the desired substance (energy is released ). The difference is the enthalpy of formation.
The binding energy differs from ΔH arr. The heat of formation is the energy that is released or absorbed during the formation of molecules from simple substances. So:
N 2 + O 2 → 2NO + 677.8 kJ/mol – ∆H arr.
N + O → NO - 89.96 kJ/mol – E St.
For diatomic molecules, the bond energy is equal to the dissociation energy taken with the opposite sign: for example, in the F 2 molecule, the bond energy between atoms F-F equal to - 150.6 kJ/mol.
For polyatomic molecules with one type of bond, for example, for molecules AB n, the average bond energy is equal to 1/n part of the total energy of formation of a compound from atoms. Thus, the energy of formation of CH 4 = -1661.1 kJ/mol. Since there are four bonds in the CH 4 molecule, the energy of one C – H bond is 415.3 kJ/mol. Study large number The currently known data on binding energies shows that the binding energy between a particular pair of atoms often turns out to be a constant value, provided that the rest of the molecule changes insignificantly. Thus, in saturated hydrocarbons Eb (C – H) = 415.3 kJ/mol, Eb (C – C) = 331.8 kJ/mol.
Bond energies in molecules consisting of identical atoms decrease in groups from top to bottom. Bond energies increase over the period. Electron affinity also increases in the same direction.
In the last paragraph we gave an example of calculating the thermal effect of a reaction:
C(tv) + 2 H 2 (g) = CH 4 (g) + 76 kJ/mol.
In this case, 76 kJ is not just the thermal effect of this chemical reaction, but also heat of formation of methane from elements .
ENTHALPY is the heat effect of a reaction, measured (or calculated) for the case when the reaction occurs in an open vessel (i.e. at constant pressure). Denoted as ΔH.
When the volume occupied by the reaction products is different from the volume occupied by the reactants, the chemical system may extra work PΔV (where P is pressure and ΔV is change in volume). Therefore, ΔH and ΔE are related to each other by the relationship:
ΔH = ΔE + PΔV
So, if the reaction is not carried out in a “bomb,” then ENTHALPY and THERMAL EFFECT coincide with each other. Enthalpy is also called "heat content". If we carry out the reaction to produce water in an open vessel, then 286 kJ/mol is the “heat” ΔH contained in hydrogen and oxygen for the case when we obtain water from them. Since the starting substances (hydrogen and oxygen) were in our experiment under standard conditions (25 o C and a pressure of 1 atm), and we also brought the reaction product (water) to standard conditions, we have the right to say that 286 kJ/mol is STANDARD HEAT OF FORMATION OF WATER or, what is the same - STANDARD ENTHALPY OF FORMATION OF WATER. If we obtain from the same elements not water, but hydrogen peroxide H 2 O 2, then the “heat content” of such a chemical system will be different (187.6 kJ/mol). During reactions that produce 1 mole of water or 1 mole of H 2 O 2, different amounts of energy are released, as would be expected. In what follows, we will more often refer to the standard heat of formation of substances as standard enthalpy of formation ΔН. To emphasize the validity of this value only for standard conditions, in the tables it is designated as follows: ΔН about 298
The small “zero” next to ΔH traditionally symbolizes a certain standard state, and the number 298 reminds us that the values are given for substances at 25 o C (or 298 K). Standard enthalpy not necessary must be the enthalpy of formation of the substance from elements. You can get the standard enthalpy value ΔH about 298 for any chemical reaction. But in our case, with the production of water from hydrogen and oxygen, we received exactly the standard enthalpy of formation of water. It is written like this: H 2 + 0.5 O 2 = H 2 O (ΔH o 298 = -286 kJ/mol)
Where does the minus sign in front of the thermal effect value come from? Here the author, with a sigh, must inform the reader about another feature of the representation of heat (and enthalpy) in thermodynamics. It's accepted here lost represent energy by any system with a minus sign. Consider, for example, the already familiar system of methane and oxygen molecules. As a result exothermic reactions occur between them allocation heat: CH 4 (g) + 2 O 2 (g) = CO 2 (g) + 2 H 2 O (l) + 890 kJ
This reaction can also be written by another equation, where the released ("lost") heat has a minus sign: CH 4 (g) + 2 O 2 (g) – 890 kJ = CO 2 (g) + 2 H 2 O (l )
According to tradition, the enthalpy of this and others exothermic reactions in thermodynamics are usually written with the sign "minus": ΔH o 298 = –890 kJ/mol (energy released).
On the contrary, if as a result endothermic reaction system absorbed energy, then the enthalpy of such an endothermic reaction is written with the sign "plus". For example, for the already familiar reaction of producing CO and hydrogen from coal and water (when heated): C(solid) + H 2 O(g) + 131.3 kJ = CO(g) + H 2 (g)
(ΔH o 298 = +131.3 kJ/mol)
You just need to get used to this feature of the thermodynamic language, although at first, confusion with signs can be quite annoying when solving problems.
Let's try to solve the same problem first in thermodynamic scale (where the heat released by the reaction has a minus sign), and then in thermochemical scale (which we used in the previous paragraph and where the energy released by the reaction has a plus sign).
So, here is an example of calculating the thermal effect of a reaction: Fe 2 O 3 (s) + 3 C (graphite) = 2 Fe (s) + 3 CO (g)
This reaction occurs in a blast furnace at a very high temperature (about 1500 o C). In reference books where it is used thermodynamic scale, you can find the standard heats of formation of Fe 2 O 3 (ΔH o 298 = –822.1 kJ/mol) and CO (ΔH o 298 = – 110.5 kJ/mol). The other two substances in this equation, carbon and iron, are elements, meaning their heat of formation is by definition zero. Therefore, the standard heat of the reaction under consideration is:
ΔH o 298 = 3× (-110.5) - (-822.1) = -331.5 + 822.1 = +490.6 kJ
So, the reduction reaction of iron(III) oxide carbon is endothermic(ΔH o 298 is positive!), and it would be necessary to spend 490.6 kJ to reduce one mole of Fe 2 O 3 with three moles of carbon if the starting substances before the start of the reaction and the products after the end of the reaction are under standard conditions (that is, at room temperature And atmospheric pressure). It doesn't matter that the starting materials had to be very heated for the reaction to occur. The value ΔH o 298 = +490.6 kJ reflects the “pure” thermal effect of an endothermic reaction, in which the reactants were first heated by an external heat source from 25 to 1500 o C, and at the end of the reaction the products cooled again to room temperature, giving up all the heat to environment. In this case, the heat released will be less than what had to be spent on heating, because part of the heat was absorbed in the reaction.
Let's do the same calculation using thermochemical scale. Suppose the heats of combustion of carbon and iron in oxygen are known (at constant pressure):
1) C + 1/2 O 2 = CO + 110.5 kJ
2) 2 Fe + 3/2 O 2 = Fe 2 O 3 + 822.1 kJ
To get the thermal effect of the reaction we are interested in, we multiply the first equation by 3, and rewrite the second in reverse order:
1) 3 C + 3/2 O 2 = 3 CO + 331.5 kJ
2) Fe 2 O 3 + 822.1 kJ = 2 Fe + 3/2 O 2
Now let’s add both equations term by term: 3 C + 3/2 O 2 + Fe 2 O 3 + 822.1 kJ = 3 CO + 331.5 kJ + 2 Fe + 3/2 O 2
After reducing both sides of the oxygen equation (3/2 O 2) and transferring 822.1 kJ to the right side, we obtain: 3 C + Fe 2 O 3 = 3 CO + 2 Fe – 490.6 kJ
kinetics chemical reactions - chapter physical chemistry, studying the patterns of chemical reactions over time, the dependence of these patterns on external conditions, as well as the mechanisms of chemical transformations Chemical kinetics– the science of rates and patterns of flow chemical processes in time.
Chemical kinetics studies the mechanism of the process, i.e. those intermediate stages consisting of elementary acts through which the system passes from the initial state to the final state.
Chemical kinetics studies the rates of these steps and the factors that influence their rates.
The equation of a chemical reaction shows the initial state of the system (starting substances) and its final state (reaction products), but does not reflect the mechanism of the process.
Chemical bonding and molecular structure
As the properties of substances were studied, the need arose to explain and describe them. First of all, the very fact of the formation of molecules and structural units (SU) from atoms, i.e., required explanation. nature and magnitude of the energy of attraction of atoms in substances - energy chemical bond .
A special property of the chemical bond was also established, which
swarm can be defined as saturability: an atom in a molecule or CE has a certain valence and it may have a small number of valencies. For the properties of molecules and CE, it is important not only the number of certain atoms in them, but also the order of arrangement (the theory of the structure
A.M. Butlerov), the distance between atoms and the geometry of molecules and CE ( stereochemistry- Van't Hoff and Le Bel).
Finally, substances have certain optical (color, spectra), electrical (dipole moment, charges on atoms) and magnetic properties, which must be explained in terms of their structure.
Ideas about the nature of the forces of attraction between atoms followed the great discoveries in physics: the discovery of the law universal gravity- theory of gravitational interaction of atoms (Bergman and Berthollet); opening electrical phenomena- electrochemical theory (Berzelius); the discovery of electrons led to the development of the so-called electronic theories of chemical bonds (Morozov, Kossel, Lewis, Pisarzhevsky, Mikhailenko, Heitler and London, Mulliken and Hund, etc.).
Modern theory the structure of chemical bonds is based on quantum mechanical concepts of the movement of electrons in atoms, molecules and other CE substances; it proved that attraction between atoms can be represented as the electrostatic interaction of electron clouds and positively charged nuclei.
Basic characteristics of a chemical bond
A chemical bond is a decrease in the energy of atoms during the formation of a molecule or CE. Energy A chemical bond can be defined as the energy required to break that bond. For a diatomic molecule it is equal to the energy (enthalpy) of dissociation, for example:
H 2 = 2H, ΔH 0 = En-n = 432 kJ.
In the case of polyatomic molecules, the binding energy depends on the state of the reactants and products. That's why the energies of sequential breaking of identical bonds are not equal to each other, for example in a methane molecule:
CH 4 ® CH 3 + H, E 1 = 427 kJ/mol;
CH 3 ® CH 2 + H, E 2 = 368 kJ/mol;
CH 2 ® CH + H, E 3 = 519 kJ/mol;
CH ® C + H, E 14 = 335 kJ/mol;
CH 4 ® C + 4H, 4Ec-n = 1649 kJ/mol.
However, their sum is equal to the energy of simultaneous breaking of all bonds. The average energy of these four bonds, Ec-n = 1649/4 » 412 kJ, differs markedly from each of the four. On the other hand, there is an approximate pattern: chemical bonds between the same atoms in different molecules are approximately the same, if the atoms are in the same valence states. The valence state of an atom is understood as the number and type (see below) of the chemical bonds it forms in the compound in question. This is why the energies of sequential bond cleavage in methane differ.
Table 4.1 shows the average values of chemical bond energies, which are approximately the same for various compounds.
Other patterns can also be noticed. For example, the energies of chemical bonds between the same two atoms can differ by approximately 2 and 3 times. This led to the introduction of ideas about single (single), double and triple bonds (E c-c » 350, E c=c » 600, E cºc » 820 kJ/mol). This characteristic is called communication multiplicity.
It was also shown that in series of compounds of the same type, the binding energy changes naturally: E n-F > E H-Cl > E n-Br > E n-I.
However, in the other series the binding energy changes irregularly:
E F-F< E Cl-Cl >E Br-Br > E I-I, which requires explanation from the point of view of the structure of the molecules.
Link length. Unlike the size of an atom, it can be determined precisely: it is equal to the distance between the centers of neighboring atoms in a molecule. The bond lengths are of the same order of magnitude (» 100 pm) as the diameters of the atoms - this is a trivial conclusion, since the conditional (effective) radii of the atoms are found by dividing the internuclear distances into two parts. That is, the bond length can be approximately determined by adding the corresponding radii of atoms or ions:
d A-B » r A + r B » (d A-A + d B-B) /2
Bond lengths depend on the valence state of the atoms, that is, for example, on the bond multiplicity: d c-c » 154 pm, d c=c » 134 pm and
d сºс » 120 pm.
Comparison of bond lengths with their energies shows that there is an inverse relationship between them: the longer the length, the lower the binding energy(Table 4.1). There is also a natural change in the lengths of bonds of the same type depending on the position of the elements in Periodic table, which is due to similar changes in the sizes of atoms and ions.
Table 4.1
Average energies (Ebv) and lengths (dbv) of some chemical bonds
Bond angles- angles between bonds formed by one atom in a molecule or CE. They depend on the nature of the atoms (their electronic structure) and the nature of the chemical bond (covalent, ionic, hydrogen, metallic, single, multiple). Bond angles are now determined very accurately using the same methods as bond lengths. For example, it has been shown that molecules of the composition AB 2 can be linear (CO 2) or angular (H 2 O), AB 3 - triangular (BF 3) and pyramidal (NH 3), AB 4 - tetrahedral (CH 4), or square (PtCl 4) -, or pyramidal (SbCl 4) -, AB 5 - trigonal bipyramidal (PCl 5), or tetragonal pyramidal (BrF 5), AB 6 - octahedral (AlF 6) 3 - etc.
Bond angles naturally change with increasing atomic number in the Periodic Table. For example, angle H-E-H for H 2 O, H 2 S, H 2 Se decreases (104.5; 92 and 90 0, respectively).
Bond energies, lengths, and angles provide important information about the nature of a chemical bond. Dependency between electronic structure molecules and these characteristics are discussed below.
Spectra of molecules. Their spectra are of great importance for determining the size, geometry and electronic structure of molecules and condensed substances. They usually represent the dependence of the intensity (I) of absorption or emission of energy by a substance (in the form of photons, electrons or ions) on the energy of external action on the substance. Wherein I is usually measured by the number of quanta per unit time per unit surface or volume, and the energy scale is measured in units of energy, frequency or wavelength.
In science, there are currently a huge number of spectral methods for studying substances that differ greatly in the types of exposure (radio waves, infrared, visible or ultraviolet light, X-rays and g-rays, beams elementary particles- electrons, positrons, protons, neutrons.....), types of recorded phenomena associated with the structural elements of matter.
Methods electron spectroscopy ultraviolet and visible regions of the spectrum record and study transitions of valence electrons from one electronic state to another (this corresponds to transitions between valence atomic orbitals). The transitions correspond to lines E 1, E 2 and E 3, shown in Figure 3.1.
Vibrational vibrations of atoms in molecules and condensed substances are studied using infrared vibrational spectroscopy methods. Research has shown that these vibrations, like electronic transitions, are quantized. The transition energies for one bond change naturally (DEcol. in Fig. 3.1).
Measuring and studying these transitions, as well as the rotation spectra of molecules, makes it possible to determine the bond energy, size and shape of molecules.
Magnetic properties. As we know from physics courses, all substances interact with a magnetic field. There are two main types of interaction of matter with a magnetic field.
1. Paramagnetic interaction - atoms and molecules of a substance have unpaired electrons, the substance is magnetized in a magnetic field and is drawn between the poles of the magnet.
2. Diamagnetic interaction - in atoms and molecules of a substance, all electrons are paired, magnetic moments compensated, the substance is not magnetized, but experiences weak repulsion from the interpolar space.
In the first case, the field lines magnetic field condensed, and in the second - rarefied under the influence of the substance. Paramagnetic substances include all atoms (Li, B, N, F, etc.), as well as molecules (NO, NO 2, CO +, N 2 +, 3+) with an odd number of electrons. Some molecules and substances with an even number of electrons are also paramagnetic (O 2 , F 2 2+ , 2+ , etc.) Obviously, these facts are related to the electronic structure of the corresponding substances.
Other types of interaction - ferromagnetic and antiferromagnetic - are the result of the interaction of elementary magnets (unpaired electrons) of neighboring atoms and molecules in a substance and will not be considered in this course.
Bond energy is important concept in chemistry. It determines the amount of energy required to break a covalent bond between two gas atoms. This concept is not applicable to ionic bonds. When two atoms combine to form a molecule, you can determine how strong the bond between them is - just find the energy that needs to be expended to break this bond. Remember that a single atom does not have binding energy; this energy characterizes the strength of the bond between two atoms in a molecule. To calculate the binding energy for any chemical reaction, simply determine the total number of bonds broken and subtract the number of bonds formed from it.
Steps
Part 1
Identify broken and formed connections- Breaks of single, double and triple chemical bonds are considered as one broken bond. Although these bonds have different energies, in each case one bond is considered to be broken.
- The same applies to the formation of a single, double or triple bond. Each such case is considered as the formation of one new connection.
- In our example, all bonds are single.
-
Determine which bonds are broken on the left side of the equation. Left side chemical equation contains the reactants and represents all the bonds that are broken as a result of the reaction. This is an endothermic process, which means that certain energy must be expended to break chemical bonds.
- In our example, the left side of the reaction equation contains one H-H connection and one Br-Br bond.
-
Count the number of bonds formed on the right side of the equation. The reaction products are indicated on the right. This part of the equation represents all the bonds that form as a result of a chemical reaction. This is an exothermic process and releases energy (usually in the form of heat).
- In our example, the right side of the equation contains two H-Br bonds.
Part 2
Calculate binding energy-
Find required values binding energy. There are many tables that give binding energy values for a wide variety of compounds. Such tables can be found on the Internet or in a chemistry reference book. It should be remembered that binding energies are always given for molecules in the gaseous state.
-
Multiply the bond energy values by the number of broken bonds. In a number of reactions, one bond can be broken several times. For example, if a molecule consists of 4 hydrogen atoms, then the binding energy of hydrogen should be taken into account 4 times, that is, multiplied by 4.
- In our example, each molecule has one bond, so the bond energy values are simply multiplied by 1.
- H-H = 436 x 1 = 436 kJ/mol
- Br-Br = 193 x 1 = 193 kJ/mol
-
Add up all the energies of broken bonds. Once you multiply the bond energies by the corresponding number of bonds on the left side of the equation, you need to find the total.
- Let's find the total energy of broken bonds for our example: H-H + Br-Br = 436 + 193 = 629 kJ/mol.
Write an equation to calculate binding energy. By definition, binding energy is the sum of broken bonds minus the sum of formed bonds: ΔH = ∑H (broken bonds) - ∑H (formed bonds). ΔH denotes the change in binding energy, also called binding enthalpy, and ∑H corresponds to the sum of the binding energies for both sides of the chemical reaction equation.
Write down the chemical equation and indicate all the connections between the individual elements. If the reaction equation is given in the form chemical symbols and numbers, it is useful to rewrite it and indicate all the connections between the atoms. This visual notation will allow you to easily count the bonds that are broken and formed during a given reaction.
Learn the rules for counting broken and formed bonds. In most cases, average binding energies are used in calculations. The same bond can have slightly different energies depending on the particular molecule, so average bond energies are usually used. .
Lecture for teachers
A chemical bond (hereinafter referred to as a bond) can be defined as the interaction of two or more atoms, as a result of which a chemically stable polyatomic microsystem (molecule, crystal, complex, etc.) is formed.
The doctrine of communication occupies a central place in modern chemistry, since chemistry as such begins where the isolated atom ends and the molecule begins. In essence, all properties of substances are determined by the characteristics of the bonds in them. The main difference between a chemical bond and other types of interactions between atoms is that its formation is determined by a change in the state of the electrons in the molecule compared to the original atoms.
Communication theory should provide answers to a number of questions. Why are molecules formed? Why do some atoms interact while others do not? Why do atoms combine in certain ratios? Why are atoms arranged in a certain way in space? And finally, it is necessary to calculate the bond energy, its length and other quantitative characteristics. The correspondence of theoretical concepts to experimental data should be considered as a criterion for the truth of the theory.
There are two main methods for describing communication that allow you to answer the questions posed. These are the methods of valence bonds (BC) and molecular orbitals (MO). The first one is more visual and simple. The second is more strict and universal. Due to greater clarity, the focus here will be on the BC method.
Quantum mechanics allows us to describe the connection based on the most general laws. Although there are five types of bonds (covalent, ionic, metallic, hydrogen and intermolecular interaction bonds), the bond is uniform in nature, and the differences between its types are relative. The essence of communication is in Coulomb interaction, in the unity of opposites - attraction and repulsion. The division of communication into types and the difference in methods of describing it indicate not the diversity of communication, but rather the lack of knowledge about it at the present stage of development of science.
This lecture will cover topics such as chemical bond energy, the quantum mechanical model of covalent bonds, exchange and donor-acceptor mechanisms of covalent bond formation, atomic excitation, bond multiplicity, hybridization of atomic orbitals, electronegativity of elements and covalent bond polarity , concept of the molecular orbital method, chemical bonding in crystals.
Chemical bond energy
According to the principle of least energy, internal energy of a molecule compared to the sum of the internal energies of the atoms that form it should decrease. The internal energy of a molecule includes the sum of the interaction energies of each electron with each nucleus, each electron with each other electron, and each nucleus with each other nucleus. Attraction must prevail over repulsion.
The most important characteristic of a bond is energy, which determines its strength. A measure of the strength of a bond can be both the amount of energy spent on breaking it (bond dissociation energy) and the value that, when summed over all bonds, gives the energy of formation of a molecule from elementary atoms. The energy of breaking a bond is always positive. The energy of bond formation is the same in magnitude, but has a negative sign.
For a diatomic molecule, the binding energy is numerically equal to the energy of dissociation of the molecule into atoms and the energy of formation of the molecule from atoms. For example, the binding energy in a HBr molecule is equal to the amount of energy released in the process H + Br = HBr. It is obvious that the binding energy of HBr is greater than the amount of energy released during the formation of HBr from gaseous molecular hydrogen and liquid bromine:
1/2Н 2 (g.) + 1/2Вr 2 (l.) = НBr (g.),
on the energy value of evaporation of 1/2 mol Br 2 and on the energy value of decomposition of 1/2 mol H 2 and 1/2 mol Br 2 into free atoms.
Quantum mechanical model of covalent bonding using the valence bond method using the example of a hydrogen molecule
In 1927, the Schrödinger equation was solved for the hydrogen molecule by German physicists W. Heitler and F. London. This was the first successful attempt to apply quantum mechanics to solve communication problems. Their work laid the foundations for the method of valence bonds, or valence schemes (VS).
The calculation results can be presented graphically in the form of dependences of the interaction forces between atoms (Fig. 1, a) and the energy of the system (Fig. 1, b) on the distance between the nuclei of hydrogen atoms. We will place the nucleus of one of the hydrogen atoms at the origin of coordinates, and the nucleus of the second will be brought closer to the nucleus of the first hydrogen atom along the abscissa axis. If the electron spins are antiparallel, the attractive forces (see Fig. 1, a, curve I) and repulsive forces (curve II) will increase. The resultant of these forces is represented by curve III. At first, the forces of attraction predominate, then the forces of repulsion. When the distance between the nuclei becomes equal to r 0 = 0.074 nm, the attractive force is balanced by the repulsive force. The balance of forces corresponds to the minimum energy of the system (see Fig. 1, b, curve IV) and, therefore, the most stable state. The depth of the “potential well” represents the bond energy E 0 H–H in the H 2 molecule at absolute zero. It is 458 kJ/mol. However, at real temperatures, bond breaking requires slightly less energy E H–H, which at 298 K (25 ° C) is equal to 435 kJ/mol. The difference between these energies in the H2 molecule is the energy of vibrations of hydrogen atoms (E coll = E 0 H–H – E H–H = 458 – 435 = 23 kJ/mol).
Rice. 1. Dependence of the forces of interaction between atoms (a) and the energy of the system (b)
on the distance between the nuclei of atoms in the H 2 molecule
When two hydrogen atoms containing electrons with parallel spins approach each other, the energy of the system constantly increases (see Fig. 1, b, curve V) and a bond is not formed.
Thus, the quantum mechanical calculation provided a quantitative explanation of the connection. If a pair of electrons has opposite spins, the electrons move in the field of both nuclei. Between the nuclei there appears an area with a high density of electron cloud - an excess negative charge that attracts positively charged nuclei. From the quantum mechanical calculation follow the provisions that are the basis of the VS method:
1. The reason for the connection is the electrostatic interaction of nuclei and electrons.
2. The bond is formed by an electron pair with antiparallel spins.
3. Bond saturation is due to the formation of electron pairs.
4. The strength of the connection is proportional to the degree of overlap of the electron clouds.
5. The directionality of the connection is due to the overlap of electron clouds in the region of maximum electron density.
Exchange mechanism of covalent bond formation using the BC method. Directionality and saturation of covalent bonds
One of the most important concepts of the BC method is valence. The numerical value of valence in the BC method is determined by the number of covalent bonds that an atom forms with other atoms.
The mechanism considered for the H2 molecule for the formation of a bond by a pair of electrons with antiparallel spins, which belonged to different atoms before the formation of the bond, is called exchange. If only the exchange mechanism is taken into account, the valence of an atom is determined by the number of its unpaired electrons.
For molecules more complex than H2, the principles of calculation remain unchanged. The formation of a bond is caused by the interaction of a pair of electrons with opposite spins, but with wave functions of the same sign, which are summed. The result of this is an increase in electron density in the region of overlapping electron clouds and contraction of nuclei. Let's look at examples.
In the fluorine molecule, the F2 bond is formed by 2p orbitals of fluorine atoms:
The highest density of the electron cloud is near the 2p orbital in the direction of the symmetry axis. If the unpaired electrons of fluorine atoms are in 2p x orbitals, the bond occurs in the direction of the x axis (Fig. 2). The 2p y and 2p z orbitals contain lone pairs of electrons that are not involved in the formation of bonds (shaded in Fig. 2). In what follows we will not depict such orbitals.
Rice. 2. Formation of the F 2 molecule
In the hydrogen fluoride molecule HF, the bond is formed by the 1s orbital of the hydrogen atom and the 2p x orbital of the fluorine atom:
The direction of the bond in this molecule is determined by the orientation of the 2px orbital of the fluorine atom (Fig. 3). The overlap occurs in the direction of the x axis of symmetry. Any other overlap option is energetically less favorable.
Rice. 3. Formation of the HF molecule
More complex d- and f-orbitals are also characterized by the directions of maximum electron density along their symmetry axes.
Thus, directionality is one of the main properties of a covalent bond.
The direction of the bond is well illustrated by the example of the hydrogen sulfide molecule H 2 S:
Since the symmetry axes of the valence 3p orbitals of the sulfur atom are mutually perpendicular, it should be expected that the H 2 S molecule should have a corner structure with an angle between the S–H bonds of 90° (Fig. 4). Indeed, the angle is close to the calculated one and is equal to 92°.
Rice. 4. Formation of the H 2 S molecule
Obviously, the number of covalent bonds cannot exceed the number of electron pairs forming the bonds. However, saturation as a property of a covalent bond also means that if an atom has a certain number of unpaired electrons, then all of them must participate in the formation of covalent bonds.
This property is explained by the principle of least energy. With each additional bond formed, additional energy is released. Therefore, all valence possibilities are fully realized.
Indeed, the stable molecule is H 2 S, not HS, where there is an unrealized bond (the unpaired electron is designated by a dot). Particles containing unpaired electrons are called free radicals. They are extremely reactive and react to form compounds containing saturated bonds.
Excitation of atoms
Let's consider the valence possibilities according to the exchange mechanism of some elements of the 2nd and 3rd periods of the periodic table.
The beryllium atom at the outer quantum level contains two paired 2s electrons. There are no unpaired electrons, so beryllium must have zero valence. However, in compounds it is divalent. This can be explained by the excitation of the atom, which consists in the transition of one of the two 2s electrons to the 2p sublevel:
In this case, excitation energy E* is expended, corresponding to the difference between the energies of the 2p and 2s sublevels.
When a boron atom is excited, its valence increases from 1 to 3:
and the carbon atom has from 2 to 4:
At first glance, it may seem that excitation contradicts the principle of least energy. However, as a result of excitation, new, additional connections arise, due to which energy is released. If this additional energy released is greater than that expended on excitation, the principle of least energy is ultimately satisfied. For example, in a CH4 methane molecule, the average C–H bond energy is 413 kJ/mol. The energy expended for excitation is E* = 402 kJ/mol. The energy gain due to the formation of two additional bonds will be:
D E = E additional light – E* = 2,413 – 402 = 424 kJ/mol.
If the principle of least energy is not respected, i.e. E add.st.< Е*, то возбуждение не происходит. Так, энергетически невыгодным оказывается возбуждение атомов элементов 2-го периода за счет перехода электронов со второго на третий квантовый уровень.
For example, oxygen is only divalent for this reason. However, the electronic analogue of oxygen - sulfur - has greater valence capabilities, since the third quantum level has a 3d sublevel, and the energy difference between the 3s, 3p and 3d sublevels is incomparably smaller than between the second and third quantum levels of the oxygen atom:
For the same reason, the elements of the 3rd period - phosphorus and chlorine - exhibit variable valence, in contrast to their electronic analogues in the 2nd period - nitrogen and fluorine. Excitation to the corresponding sublevel can explain the formation of chemical compounds of group VIIIa elements of the 3rd and subsequent periods. No chemical compounds were found in helium and neon (1st and 2nd periods), which have a completed external quantum level, and they are the only truly inert gases.
Donor-acceptor mechanism of covalent bond formation
A pair of electrons with antiparallel spins forming a bond can be obtained not only by the exchange mechanism, which involves the participation of electrons from both atoms, but also by another mechanism, called donor-acceptor: one atom (donor) provides a lone pair of electrons for the formation of the bond, and the other (acceptor) – vacant quantum cell:
The result for both mechanisms is the same. Often bond formation can be explained by both mechanisms. For example, an HF molecule can be obtained not only in the gas phase from atoms according to the exchange mechanism, as shown above (see Fig. 3), but also in an aqueous solution from H + and F – ions according to the donor-acceptor mechanism:
There is no doubt that molecules produced by different mechanisms are indistinguishable; connections are completely equivalent. Therefore, it is more correct not to distinguish the donor-acceptor interaction in special kind bond, but consider it only a special mechanism for the formation of a covalent bond.
When they want to emphasize the mechanism of bond formation precisely according to the donor-acceptor mechanism, it is denoted in structural formulas by an arrow from the donor to the acceptor (D® A). In other cases, such a connection is not isolated and is indicated by a dash, as in the exchange mechanism: D–A.
Bonds in the ammonium ion formed by the reaction: NH 3 + H + = NH 4 +,
are expressed by the following scheme:
The structural formula of NH 4 + can be represented as
.
The second form of notation is preferable, since it reflects the experimentally established equivalence of all four connections.
The formation of a chemical bond by the donor-acceptor mechanism expands the valence capabilities of atoms: valence is determined not only by the number of unpaired electrons, but also by the number of lone electron pairs and vacant quantum cells involved in the formation of bonds. So, in the example given, the valency of nitrogen is four.
The donor-acceptor mechanism is successfully used to describe the bonding in complex compounds using the BC method.
Multiplicity of communication. s- and p -Connections
The connection between two atoms can be carried out not only by one, but also by several electron pairs. It is the number of these electron pairs that determines the multiplicity in the BC method - one of the properties of a covalent bond. For example, in the ethane molecule C 2 H 6 the bond between the carbon atoms is single (single), in the ethylene molecule C 2 H 4 it is double, and in the acetylene molecule C 2 H 2 it is triple. Some characteristics of these molecules are given in table. 1.
Table 1
Changes in bond parameters between C atoms depending on its multiplicity
As the bond multiplicity increases, as one would expect, its length decreases. The bond multiplicity increases discretely, that is, by an integer number of times, therefore, if all bonds were the same, the energy would also increase by a corresponding number of times. However, as can be seen from table. 1, the binding energy increases less rapidly than the multiplicity. Consequently, the connections are unequal. This can be explained by differences in the geometric ways in which the orbitals overlap. Let's look at these differences.
A bond formed by overlapping electron clouds along an axis passing through the nuclei of atoms is called s-bond.
If the s-orbital is involved in the bond, then only s - connection (Fig. 5, a, b, c). This is where it got its name, since the Greek letter s is synonymous with the Latin s.
When p-orbitals (Fig. 5, b, d, e) and d-orbitals (Fig. 5, c, e, f) participate in the formation of a bond, s-type overlap occurs in the direction of the highest density of electron clouds, which is the most energetically favorable. Therefore, when forming a connection, this method is always implemented first. Therefore, if the connection is single, then this is mandatory s - connection, if multiple, then one of the connections is certainly s-connection.
Rice. 5. Examples of s-bonds
However, from geometric considerations it is clear that between two atoms there can be only one s -connection. In multiple bonds, the second and third bonds must be formed by a different geometric method of overlapping electron clouds.
The bond formed by the overlap of electron clouds on either side of an axis passing through the nuclei of atoms is called p-bond. Examples p - connections are shown in Fig. 6. Such overlap is energetically less favorable than s -type. It is carried out by the peripheral parts of electron clouds with lower electron density. Increasing the multiplicity of the connection means the formation p -bonds that have lower energy compared to s - communication. This is the reason for the nonlinear increase in binding energy in comparison with the increase in multiplicity.
Rice. 6. Examples of p-bonds
Let's consider the formation of bonds in the N 2 molecule. As is known, molecular nitrogen is chemically very inert. The reason for this is the formation of a very strong NєN triple bond:
A diagram of the overlap of electron clouds is shown in Fig. 7. One of the bonds (2рх–2рх) is formed according to the s-type. The other two (2рz–2рz, 2рy–2рy) are p-type. In order not to clutter the figure, the image of the overlap of 2py clouds is shown separately (Fig. 7, b). To get the general picture, Fig. 7, a and 7, b should be combined.
At first glance it may seem that s -bond, limiting the approach of atoms, does not allow the orbitals to overlap p -type. However, the image of the orbital includes only a certain fraction (90%) of the electron cloud. The overlap occurs with a peripheral region located outside such an image. If we imagine orbitals that include a large fraction of the electron cloud (for example, 95%), then their overlap becomes obvious (see dashed lines in Fig. 7, a).
Rice. 7. Formation of the N 2 molecule
To be continued
V.I. Elfimov,
professor of Moscow
State Open University
Chemical bond energy equal to the work that must be expended to divide a molecule into two parts (atoms, groups of atoms) and remove them from each other at an infinite distance. For example, if E. x. With. H 3 C-H in a methane molecule, then such particles are the methyl group CH 3 and the hydrogen atom H, if E. chemistry is considered. With. H-H in a hydrogen molecule, such particles are hydrogen atoms. E. x. With. - a special case of binding energy (See Bonding energy) ,
it is usually expressed in kJ/mol(kcal/mol);
depending on the particles forming a chemical bond (See Chemical bond), the nature of the interaction between them (Covalent bond, Hydrogen bond
and other types of chemical bonds), bond multiplicity (for example, double, triple bonds) E. x. With. has a value from 8-10 to 1000 kJ/mol. For a molecule containing two (or more) identical bonds, E. ch. With. each bond (bond breaking energy) and the average bond energy equal to the average value of the breaking energy of these bonds. Thus, the energy of breaking the HO-H bond in a water molecule, i.e., the thermal effect of the reaction H 2 O = HO + H is 495 kJ/mol, rupture energy N-O connections in the hydroxyl group - 435 kJ/mol, average E. x. With. equal to 465 kJ/mol. The difference between the values of the rupture energies and the average E. ch. With. due to the fact that during partial dissociation (See Dissociation) of a molecule (breaking one bond), the electronic configuration and relative arrangement of the atoms remaining in the molecule change, as a result of which their interaction energy changes. The value of E. x. With. depends on the initial energy of the molecule; this fact is sometimes referred to as the dependence of E. x. With. on temperature. Usually E. x. With. are considered for cases when the molecules are in the standard state (See Standard states) or at 0 K. It is these values of E. x. With. are usually given in reference books. E. x. With. - an important characteristic that determines reactivity(See Reactivity)
substances and used in thermodynamic and kinetic calculations of chemical reactions (See Chemical reactions). E. x. With. can be indirectly determined from calorimetric measurements (see Thermochemistry) ,
by calculation (see Quantum chemistry) ,
as well as using mass spectroscopy (See Mass spectroscopy) and spectral analysis(See Spectral Analysis).
Big Soviet encyclopedia. - M.: Soviet Encyclopedia. 1969-1978 .
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