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Home  / GENERAL CHEMISTRY Textbook / Chapter 7.** Chemical Bonds in Solid Bodies

Chapter 7.** Chemical Bonds in Solid Bodies

In the preceding chapters we cited chemical bonds in molecules in the gas phase. Now let's see what kind of bonds there are in substances relative to their physical state. That is, let's cite the bonds between atoms in gas, liquid, and solid states

So far, the bonds we have studied were bonds between atoms, i.e., bonds within the molecule to which are added bonds that connect the molecules in liquid and solid states.

Which of the cited bonds can we expect between molecules? Let's study a few examples.

 Example I

In the gas phase we have a dual-homoatomic molecule where the outermost shells of both atoms being bonded are filled. These molecules can form only VWBs between themselves, i.e., in liquid and solid states these substances have covalent bonds and VWBs. When heated, these substances transit from the solid to the liquid state and then to the gas state where the atoms of these substances are connected in pairs via covalent homoatomic bonds. That is, the transition of these substances into liquid and gas phases is connected with the breaking of the VWB whose energy is dozens of times smaller than that of the covalent bond.

Correspondingly, the bond-breaking temperature of these bonds during their transition, from the liquid to the gas phase, is much lower than the temperature needed for breaking a dual-atomic molecule into atoms. Examples of such substances are nitrogen, oxygen, halogens (Cl2 I2 Br2) noble gases (He, Ne, etc.).

 Example II

In the gas phase we have a dual-atomic molecule where the outermost shell of one of the atoms to be bonded is completely filled while the other is not yet filled. Examples of such substances are molecules where the atoms are connected with heteroatomic covalent bonds. Since the shell of one atom in the molecules of these substances is completely filled, and the outermost shell of the other atom is not completely filled, such molecules can bond between themselves via donor-acceptor bonds (DAB).

Molecules of sodium chloride, as mentioned before, offer the dimmer Na2Cl2. In this dimmer the sodium (Na) and the chloride (Cl) are bonded via two covalent heteroatomic bonds and two DABs. The structure of Na2Cl2 can be illustrated as follows: 

Na : Cl
Cl : Na

where the arrows (↑­ & ↓) show the bonding DAB electrons and the dots ( : ) show the bonding electrons of the covalent hetero-polar bonds. According to this scheme, the outermost shell of the sodium atom (Na) in Na2Cl2 contains 4 electrons, while the outermost shell of chloride (Cl) - 8 electrons. That is, the outermost sodium shell is only half filled. Therefore, we can form two more DABs with sodium chloride along the scheme: 

Cl : Na
Na : Cl Na : Cl
Na Cl : Na Cl : Na
Na : Cl

 According to this scheme, the sodium is connected with 4 atoms of chloride, 3 DABs, and 1 covalent hetero-polar bond. The structure of such associates in the solid phase are easily imagined. (See Figure 7.1 )

7_1

Figure 7.1

Here each sodium atom is connected with 6 bonds of chloride atoms, and each chloride atom is connected with 6 bonds of sodium atoms. One of these bonds is a covalent hetero-polar one, 3 of them are DABs, and 2 of them are VWBs.

According to the theory of chemical bonding, if the molecular structure of a crystal can be represented in the form of isomers with close electron energy values, then the energies and the bond lengths in this molecule equalize. The electronic isomerization in the case of Na2Cl2 can be shown schematically thus: 

Na   Cl       Na Cl
 . . . .
Cl Na Cl Na

In accordance with the theory of chemical bonding, all the bonds between the sodium and chloride in a sodium-chloride crystal should be of the same length.

That is, the bonding electrons in the crystal constantly transit between covalent bonds, DABs, and VWBs while the nuclei occupy an intermediate position.

Electronic isomerization leads to the fact that the energy of all the 6 bonds where one sodium atom is bonded to 6 chloride atoms surrounding it (and vice-versa - 1 chloride atom with 6 sodium atoms) is the same, which is proven by the identical lengths of these bonds.

According to experimental data, the distance between all the chloride and sodium atoms in crystal NaCl is identical and equal to 2.814Å while a NaCl molecule has a bond length between the sodium and chloride equal to 2.36Å. As a result of electronic isomerization, the bond lengths and energies become equal. And the lengths of the equalized bonds are greater than the length of the strongest bond (in this case - the covalent hetero-polar bond) in accordance with the theory.

Example III

When the atom has 4 electrons in the outermost shells of carbon or silicon, it can form 4 covalent homopolar bonds. For example, in diamond and graphite, each carbon atom is bonded by a covalent homo-polar bond and by 4 other carbon atoms. The melting and boiling points of these crystals depend on the breaking of the covalent homopolar bond or the carbon-carbon (C - C) bond.

All this proves the need for high temperatures and great melting and evaporation heat for these substances.      

Example IV

Unlike the molecules described in examples I, II and III, the molecules formed of atoms from group I of elements in the table of elements with one electron in the outermost shell (Li2, Na2, K2, etc.), according to the theory of chemical bonding, cannot form covalent bonds, DABs, or VWBs. As a matter of fact, when cooling the substances formed of these molecules to a temperature of about 100 degrees C, they transform into a solid substance.

According to the chemical bonding theory, the number of covalent bonds that an atom of group I can form is limited by the number of electrons in the outermost electronic shell. Two electrons are utilized to form one covalent bond: one electron from each of the atoms being bonded by this bond. That is, all the possibilities of forming covalent bonds in molecules of the Li2, Na2, type are utilized when forming dual atomic molecules.

Also according to the bonding theory, DABs and VWBs form between molecules when the atoms in the molecules have electrons in the outermost shell that do not take part in bond formation. That is, bonds between molecules formed of atoms of group I cannot be formed.

Though, as a matter of fact, a comparison of the temperatures at which substances are transformed into solids, has shown that there is a bond in solids between the molecules of these substances, for the breaking of which the substance will need a temperature of more than 100° C; that is, the bonds here are much stronger than VWBs for the breaking of which, in the case of nitrogen (N2) and oxygen (O) in the solid state, a temperature of minus 200°C will suffice.

The importance of the question concerning the nature of bonds between atoms in solid substances, formed of atoms of group I, has grown immensely since these substances belong to a group that has been historically known as metals.

These are known to include about 70% of the substances formed of identical atoms. Such substances are considered as a group of metals because they have a number of common properties (metallic shine, high electric and heat conductivity, plasticity, etc.).

The physical properties of metals, as noted above, speak in favor of the fact that the bonding between the atoms in metals is much stronger than in DABs. Besides the described kinds of bonds in molecules in the gaseous state (covalent, DABs, and VWBs) we should examine the covalent bonds that differ from the previously cited covalent bonds. The previously cited covalent bonds in dual atomic molecules in the gas phase, according to the above mentioned, were dual electronic.

The participation of two electrons in bond formation was based on the comparison of the experimental data in reference to the number of electrons in the outermost shells of the atoms and the number of atoms that these atoms can bond (for example, in hydrogen and chlorine).

On the other hand, the conclusion about the dual electronic covalent bond, between the atoms in dual atomic molecules, was confirmed by the coincidence of the dependencies of the energies and bond lengths on the FIEs of the atoms being bonded.

Now let's repeat this method in regard to metals. As seen in examples I - III, the same complex of bonds, their existence and nature explains the solid substance properties of non-metals, the structure of which we had elucidated after analyzing the experimental data received when studying the substances in the gaseous state.

A comparison of the data on the number of electrons in the outermost shell of atoms of  Li and Na, with the number of strong bonds they form between themselves in the solid phase, has shown that these atoms with one electron in the outermost shell, actually form eight strong bonds with identical atoms.

Strong bonds, as already mentioned, are formed when the bonding electrons enter the outermost shells of both atoms to be bonded. In the case of metals of group I, the bonding of one atom to more than one atom in the presence of one electron in the outermost shell (a single-valence electron) is possible if only 1 electron is utilized to form one bond (not 2). That is, it is logic to suppose that metal atoms in the solid state are bonded between themselves via a single-electron bond.

Bonding electrons enter the outermost shells of both atoms to be bonded which causes its rotation in the molecule on a plane perpendicular to the axis connecting the bonded nuclei.

To evaluate the bonding energy in the lithium cation Li2+ we can use the data on the potential energy of the lithium atom and the lithium molecule Li2 received experimentally

According to the experimental data, the first ionization energy  (FIE) of molecule Li2 is equal to 495 kJ/mol while that of the Li atom is equal to 523 kJ/mol, which means that it is easier to tear the electron away from the lithium molecule than from a lithium atom.

 When tearing two electrons from the Li2 molecule, this molecule breaks into two nuclei and two electrons; that is, the sum second ionization energy (SIE) of Li2 and the first ionization energy (FIE) of Li2+ is equal to the energy gain during Li2+ formation out of atoms Li and Li+1.

If we indicate the Li2 molecule's bonding energy as ELi2

Then:  FIELi2 + SIELi2 = 2 FIELi + ELi2

Experimental data also offer us the following results:

FIELi2 = 495 kJ/mol; and FIELi = 523 kJ/mol.

Thus: SIELi2 = 2 · 523 - 495 + ELi2 = 551 + ELi2.

As indicated above, SIELi2 is equal to the electronic energy Li2+. The bonding energy in molecule Li2+ is equal to SIELi2 - 523 where 523 kJ/mol is the ionization energy of atom Li.

Therefore: ELi2+ = 551 - 523 + ELi2 = 28 + ELi2. That is, the bonding energy in Li2+, according to the experimental data, is higher than in Li2, or, in other words, the mono-electronic bond in molecule Li2+ is much stronger than that in molecule Li2.

The same is true of the relation-ships between mono- and dual-electronic bonds in all the elements of group I. The MEB in Na2+, K2+, Rb2+, and Cs2+ is much stronger than the dual-electronic bond in molecules Na2, K2, Rb2, and Cs2.

Figure 7.2 shows the dependence of the bonding energy in dual-atomic molecules M2+ (where M is a hydrogen-like atom) from the FIE of atom M. This dependence is calculated via the equation given in section 6.4

According to figure 7.2 the dependence of the bonding energy curve on the FIEs in molecules M2+ (where M is the hydrogen-like atom) is a parabola whose maximal bonding energy value is reached when the FIE of the atoms to be bonded are in the interval of 4 eV - 5 eV). When the FIE is equal to 13 eV, the energy of a MEB is equal to zero.

That is, the formation of a MEB in molecules M2+ when the FIEM > 13 eV, according to the calculation, is hardly possible. According to the experimental data, molecule H2+ is an unstable molecule, which immediately breaks up into a hydrogen atom (H&) and a proton (H+). Recall that the FIE of a hydrogen atom is equal to 13.6 eV.


Figure 7.2

In figure 7.3 are given the energy dependencies for mono- and dual-electronic bonds in molecules x - x on the FIE of x.

According to the calculated data, the MEB, relative to energy, is commensurable with the dual-electronic bond up to the FIE value of about 10 eV. Elements with the physical properties of metals have a FIE equal to less than 10 eV. On the other hand, almost all the elements with the physical properties of non-metals, have a FIE greater than 10 eV.

During the formation of MEBs between two metal atoms, the number of electrons in the outermost shell of one of the atoms being bonded (donor atom) does not change. The number of electrons in the outermost shell of the acceptor atom is increased by 1. That is, the MEB is actually a donor-acceptor bond. 

7_3
Figure 7.3

The MEBs in metals explains the main difference between metals and non-metals. During MEB formation between atoms, one electron of the donor atom is utilized in order to form the bond. The electrons of the acceptor atom do not take part in bond formation. The number of electrons in the outermost shell of the acceptor atom increases by one unit during the formation of one MEB that causes the increase of the inter-electronic repulsion forces.

In the first approach, the ionization energy of the first electron in the acceptor atom that was equal to the FIE of this atom before bond formation, can be evaluated close to the energy of the affinity to the acceptor atom's electron before bond formation. For example, during MEB formation between two Na atoms, we can expect the decrease of the ionization energy of the electron that does not take part in MEB formation from 5.14 eV to 0.55 eV, where 5.14 and 0.55 are the FIEs and the affinity of the Na atom to the electron respectively.

When forming one more MEB of an acceptor atom with another donor atom, we can expect a further decrease of the ionization energy of the acceptor atom's electron, which does not partake in the formation of the MEB. That is, in the solid state of metals where, according to the analysis, each metal atom is surrounded by 8 or 12 atoms of the same metal, we can presuppose with great assurance, that a situation will arise that if we extract the electrons that do not partake in bond formation, there will not only be no expenditure of energy (when the ionization energy is < 0), but there is a discharge of energy during the dissociation of the electron that does not take part in bond formation.

Atoms from which the electron separated have the same kind of negative affinity to the electron as, say, inert gases and the elements of group II. That is, a part of the electrons in the metal is not attached in the atom with the nuclei, and is present  in the form of a sort of electronic gas. From experiments with gas discharging tubes and from experience with electronic lamps, it is well known that free electrons in the electric field transit towards the positively charged pole (cathode) thereby producing electric current. That is, the presence of MEB in metals qualitatively explains their great electric conductivity (as compared to non-metals).

The great electric conductivity of metals correlates with their great heat conductivity. These correlations allow us to presuppose that the mechanism of electric and heat conductivity of metals are identical, and that heat, just as electricity, transits via electronic gas.

As indicated above, 8 or 12 identical atoms surround each atom in pure metal. During MEB formation, the bonding electron enters the two of the outermost electronic shells of the atoms to be bonded. In the case of alkali metals of group I, according to the experimental data, each metal atom is surrounded by 8 other atoms.

Respectively, the outermost shell of each atom contains 8 electrons, and 1/8 of the electrons are not bonded to the free atoms and are present in the metal in the form of electronic gas. The regularities of chemical bond formation, introduced by us when studying chemical bonding in dual-atomic molecules in the gas phase, are not violated. The number of electrons in the outermost shell of atoms does not exceed the maximum, i.e., eight.

However, 8 atoms surround one atom in metals only in 15 cases out of 41. These are metals of the 2nd — 5th periods in the table of elements. In the rest of the 26 cases, 12 other metal atoms surround each metal atom in the solid state.

Analogous to the explanations concerning the formation of stable molecules of the SF6 and PF5 types, in the gas phase, previously cited, we can suppose that all 12 bonds are equalized relative to energy and bond length (8 MEBs and 4 VWBs). All this occurs in the course of one electronic isomerization in solid metals very intensely.          

The much greater durability of the MEB as compared to the dual electronic bond, and all the more - to the dual-electronic DAB and VWB, very well explains the much higher boiling and evaporation temperatures for metals as compared to those of non-metals. More detailed information about bonds between the FIEs of elements and their physical properties will be given in the section devoted to the physical and chemical properties of substances.

The main advantage of the cited mono-electronic bond in the solid state is that its energy, if we suppose that this bond is formed analogously to that of the H2+ and can be evaluated via the computer program, is meant for solving the system of equations compiled for molecule H2+.

However, in the solid state, the mono-electronic bond can also be formed at the expense of the transition of one atom's electron into a non-ionized shell of another atom along this scheme: Na˙ + Na˙→ Na · Na˙  or  along the scheme:

Na˙  +  Na˙  + e- →   ·  Na  ·  Na˙

where the additional electron comes from the metal volume or from other atoms. These systems cannot be calculated with the same precision as the chemical bonding in systems like H2+ since it is difficult to evaluate the energy change of the electrons that do not partake in bond formation.

During chemical bond formation, as already mentioned, the effective charge increases as a result of the mutual approach of the nuclei to be bonded, which should lead to the increase of the potential of the electrons that do not partake in bond formation.

On the other hand, the increase of the number of electrons in the outermost shell of the atoms to be bonded decreases the potential energy of the electrons that do not partake in bond formation. This leads to the decrease of the system's potential energy, that is, to a decrease in the energy gain during bond formation - a decrease in bonding energy.

The coincidence of the maximal number of electrons that can be situated in the outermost shell of an atom from groups IV —VIII of the 2nd  and 3rd periods with the maximal number of electrons that can be in the shell of the central atom after the formation of the maximal number of bonds - all this qualitatively proves that the above mentioned contradictions that act upon each other, are mutually counterpoised.

The high transition rate of the electrons, close to that of the organic polymers with conjugated bonds and good conductors, allows us to presuppose an alternative explanation for the electric and heat conductivity of metals.

In the case of organic polymers, the high electric conductivity of these polymers correlates with the high speed of electronic isomerization, which contains conjugated (single and double) chemical bonds.

From the viewpoint of physics, the analogy between the high speed of the electronic transitions and the high electric conductivity is not considered as being great. That is why the supposition that the rapid electronic isomerization, which occurs in solid metals and is conditioned by low ionization energies of the electrons in metals (both bonding and non-bonding) and by a great number of possible electronic states with close energy values, can be at least a second explanation concerning the high electric and heat conductivity of metals.

It is thus supposed that the electric current in metals occurs not as a result of the transition of free electrons (when the mechanism is observed in gas-discharging tubes) but along the mechanism where electro-conductivity occurs in organic conductors and super-conductors (conjugated polymers), that is, from atom to atom.

The two given explanations about electric conductivity of metals are not alternative, and have only a slight quantitative difference. For example, an electron bonded to an atom and having an ionization energy smaller than 0.5 eV, do not differ in performance (behavior) than the so-called 'free electron' because this electron takes part in the energy exchange with the electrons that have energy greater than 5 eV, and of which there are by one order of magnitude more in the system.

Thus, the difference in the properties of metals in the solid state and nonmetals is the comparatively high temperature, the boiling and melting heat; on the other hand, the general properties of metals are conditioned by low FIE values (<10) for atom metals.

Such a low FIE value is conditioned the possibility of forming a strong single-electron bond, which, in turn, conditions the high metal melting and boiling temperatures which are much higher than those of nonmetals.

On the other hand, the presence of a large number of possible positions for electrons with equal energies, the electron that takes part in a single-electron bond presupposes a high speed for the transiting for the bonding electrons between identical minimums of energy or a high transition speed of the bonding electrons, which, in turn, explains the high electric-conductivity of the metals.

The high speed transition of bonding electrons is also obvious among conjugated (single, double bonds) organic conductors which additionally proves that this property of a conducting system is most important for better electric conductivity and that the mechanism of electric conductivity in metals and in organic conductors are identical.

The likeness between the mechanism of conductivity in metals and organic conductors (in both cases the electro-conductivity correlates with the transition of the electrons) allows us to say that this mechanism, where the electrons move in jumps from atom to atom is more possible than a mechanism that presupposes the presence of electronic gas, and therefore a conductivity mechanism very much like the electro-conductivity mechanism in the gas-charged tubes.

Additionally, in favor of the above-mentioned mechanism, the electro-conductivity in metals speaks of the fact that at least, from the viewpoint of chemists, the supposition about the presence of free electrons (not bonded to atoms) is not at all convincing. This is because the whole volume of the conductor is filled with atoms: 1) whose outermost shells are not filled with electrons; 2) which have a positive affinity to electrons; 3) which have a positive charge.  See Appendix C for details.

Chapter 6. Molecule structure >> 
Chapter 7.** Chemical Bonds in Solid Bodies 
Chapter 8. Three-dimensional structures of chemical compounds  >>
Chapter 9.** Chemical Reactions   >>
Chapter 10.** Catalysis  >>
Chapter 11. Physical and chemical properties of substances  >>