MoleculeGroup III Bonding Energy MoleculeGroup IV Bonding Energy
FIE 498 736 577 787 1063 1000 1255 1519 Aff 117.2 <0 50 138 75 199.6 356 <
The affinity data given in the table is actually the result of studies of FIE values of atoms to which electrons were bonded. That is, for example, the energy discharged when connecting the electron to the Na atom [(the affinity value for sodium (Na)] via the reaction
Na + e-→ Na-1 is measure by defining the FIE in the reaction
Na-1→ Na + e-
The affinity values smaller than zero, indicated in the table, show that the electron does not bond to atoms with an affinity less than or equal to 0.
Another question might arise:
What is common between the FIE value, the affinity of the atom to the electron and the bonding energy? Or: Why do we think that the FIE values and those of the affinity can help us discover the cause of the great differences in bonding energy in a number of dual-atomic molecule?.
As we indicated in section 4, in the case of bond formation among multi-electronic atoms, just as in the case of hydrogen molecules, chemical bonding takes place via the electronic pair (one from each of the atoms being bonded), while both bonding electrons enter the outermost shell of both atoms to be bonded.
The observance of this rule for multi-electronic atoms was proven on the basis of chemical experimental data relative to the existence of stable compounds (for example, compounds of atoms of the 2nd and 3rd periods were taken) where the number of electrons surrounding each atom and entering the molecule does not exceed eight.
To explain the significant deviation of the bonding energies in multi-electronic atoms, as compared to that in a hydrogen molecule, it is necessary to deepen our understanding of the reason the number of electrons in the outermost shell is limited.
It has already been shown that the main forces in the atomic and molecular systems are the electric forces that attract electrons to the nucleus and the interelectronic repulsion forces.
The increase of the attractive forces increases the absolute value of the potential energy of the system: neutral atom + free electron. On the other hand, the increase of the interelectronic repulsion forces decreases the absolute value of the system's potential energy: neutral atom +
free electron.
The bonding of electron to atom occurs when there is energy gain, or, in other words, when the absolute value of the potential energy of the system atom + electron increases as a result of the bonding of the electron to the atom. The data on the affinity of the atom for the electron stored in table 6.4-3 gives us a digital value of the energy gain during the bonding of the electron to the atom.
During the bonding of the electron to the atom, the total attraction energy of the electrons to the nucleus increases at the expense of the increase of the number of electrons attracted to the nucleus. On the other hand, the inter-electronic repulsion energy increases because of the increase of the number of electrons. The bonding of the electron to the atom takes place if, as a result of this bonding, the attraction energy gain is greater than the energy loss at the expense of the increase of the repulsion energy.
To illustrate this, let's have a look at the inter-electronic repulsion forces, the electron-nuclear attraction and the effective nuclear charge when the electron is attached to a hydrogen-like atom (composed of one nucleus and one electron) and when it is attached to a helium-like atom (composed of one nucleus and two electrons).
When the electron is bonded to a hydrogen atom, an inter-electronic repulsion force appears, and the attraction energy of the electrons to the nucleus undergoes a change.
Let's calculate the potential energy change that occurs during the bonding of an electron to a hydrogen atom. The hydrogen atom turns into a helium-like atom with a nuclear charge of 1 proton unit and with 2 electrons at equal distances on either side of the nucleus. The potential energy of this system is equal to the difference between the electrons' attraction and replusion energies.
In the cited case (in which the nuclear charge and the electron's charge have identical absolute values), the electrons' attraction energy to the nucleus equals 2e2/R, where R is the radius of the orbit along which the electrons rotate. The inter-electronic repulsion energy equals e2/2R. The total potential energy is equal to the difference between the attraction energy and inter-electronic repulsion energy. That is:
2e2/ R - e2/ 2R = 3e2/2R (6.4-1)
In accordance with equation 6.1-1, the energy of a helium-like atom is equal to E = [13.6 (z - 0.25)2] · 2. At z = 1 (cited example):
E = [13.6 (1 - 0.25)2] · 2 = 15.3 eV. Here, 13.6 eV is the hydrogen atoms' energy (EH).
According to equation 5.6:
EH= e2/ 0.529
where 0.529 is the radius of a hydrogen atom. The potential energy equals 2EH. Thus, 2e2/0.529 = 27.2 eV and e2= 14.38. By substituting e2into equation 6.4-1, we get 3 · 14.38/2R = 30.6 eV, where 30.6 eV is the double energy (15.3 · 2) of the helium-like atom's charge of 1.
Thus: R = 0.705 Å
Knowing the radius of the helium-like atom, we can calculate the change of both the potential attraction energy and the potential repulsion energy, since we know that (e2/ 0.529) · 2 = 13.6 eV (energy of 1 gram of hydrogen atoms): e2= 14.4 eV. From this we get:
2e2/ R = 2 · 14.4 / 0.705 = 40.8 eV; e2/ 2R = 10.2 eV.
The potential energy of the system, where the electron is separated from the hydrogen atom by an infinite distance, is equal to the potential energy of a hydrogen atom alone: 2 · 13.6 = 27.2 eV.
That is, when the electron is bonded to a hydrogen atom, the potential energy of the electrons' attractions to the nucleus increases by 13.6 eV. On the other hand, when bonding an additional electron to a hydrogen atom, the interelectronic repulsion energy increases by 10.2 eV. There is no inter-electronic repulsion present in the initial hydrogen atom.
Thus, when adding an electron to a hydrogen atom, the absolute potential energy value increases by 3.4 eV (13.6 - 10.2 = 3.4). The potential energy of 1 gram of hydrogen atoms equals 27.2 eV (double the value of the hydrogen atoms' energies).
The energy of 1 gram of helium-like atoms, with a charge equal to that of a hydrogen atom, constitutes, according to the calculation, 30.6 eV (27.2 + 3.4 = 30.6). According to experimental data, the potential energy of such atoms comprises
28.7 eV [(13.6 + 0.74) · 2 = 28.7,
where 13.6 is the energy of a hydrogen atom and 0.74 eV is the affinity of the hydrogen atom for the electron.
Processes occurring via attraction forces (for example, a stone falling onto the ground or an electron striving towards a nucleus) occur spontaneously with a discharge of energy. In accordance with the calculation, the bonding of the electron to a hydrogen atom occurs spontaneously with a discharge of energy. In other words, the hydrogen atom should have a positive affinity to the electron. This has been confirmed via experiments.
Now let's discuss the change in potential energy caused by bonding an electron to a helium atom. The calculations described above have shown that the change of the system's energy during the
bonding of the electron is equal to the value of the potential energy change divided by 2. According to the virial theorem, half of the system's potential energy is equal to the system's energy. Therefore, when calculating the energy of a system consisting of electrons and nuclei, we need not necessarily calculate the kinetic energy of the electrons.
It is enough to define the potential energy of the system (the distance between the electrons and the nuclei) and divide the result by two. To compare the calculated and experimental results, we define the ionization energies of all the electrons. The sum of all these energies is equal to the energy of the system.
According to equation 6.1-1, the energy of 1 gr. mol of atoms with a nuclear charge of 2 proton units and with 2 electrons orbiting in a circle around the nucleus, on one plane, is calculated by the equation
EHe= 13.6 (2 - 0.25)2· 2,
where 13.6 is the energy of the hydrogen atom, 2 is the nuclear charge of the helium atom and 0.25 is the allowance for inter-electronic repulsion.
Analogously, the energy of 1 mol of atoms with a nuclear charge of 2 proton units and with 3 electrons rotating around the nucleus in one circle can be calculated by the equation
E3= 13.6 (2 - 0.577)2· 3,
where 0.577 is the inter-electronic repulsion allowance (relative to three electrons). See the book "How Chemical Bonds Form and Chemical Reactions Proceed" (p.42). The calculation concludes as follows:
E2= 83.3 eV ; E3= 82.6 eV
That is, the bonding of the electron leads not to the increase of the potential energy, but to its decrease. Recall that the absolute value of the system's energy is equal to half of its potential energy. The bonding of one electron to a helium atom is accompanied by a decrease of the absolute value of the potential energy and therefore cannot take place spontaneously, i.e., without the use of energy. Indeed, stones do not reveal themselves from under the ground spontaneously.
In other words, the calculation shows that an electron cannot bond to a helium atom, which has been proven experimentally. The affinity of a helium atom is less than zero.
Therefore the bonding or nonbonding capacity of the electron to the atom is defined by the difference in the change of the absolute values of the potential attraction energies of all the electrons to the nucleus and the mutual interelectronic repulsion. If this difference is greater than zero— the electron will bond; if it is smaller than zero — it won't.
The data on atoms' affinities to the electron given in Table 6.4-3 show that for the atoms of periods 1, 2, and 3 in the table of elements, besides the atoms of helium (He), beryllium (Be), magnesium (Mg), neon (Ne) and argon (Ar), the atoms' affinities to the electron are greater than zero. During the bonding of electrons to atoms of periods 2 and 3 (besides Be, Mg, Ne and Ar), an energy gain occurs. Thus, the increase of the attraction energy during the bonding of electrons to the nucleus is greater than the increase of the repulsion energy.
In the case of the He, Be, Mg, Ne and Ar atoms, the increase of the attraction energy during the bonding of the electrons to the nucleus is smaller than the energy increase of the inter-electronic repulsion. An independent confirmation of this conclusion is found in the data on the FIEs for atoms of the 2nd and 3rd periods, given in Table 6.4-2. Each of the numbered elements differs from the next by its nuclear charge and by the amount of electrons surrounding the nucleus. The atom of each of the following elements has a positively charged nucleus by one proton more. The number of electrons in the electronic shell of each of the following atoms is by one electron more than in the previous shell.
The transition from one element to the next – for example, from sodium (Na) to magnesium (Mg) – can be represented schematically as two consecutive processes; first the nuclear charge of the Na atom increases by one proton unit and turns into a Mg nucleus, then one electron is bonded to the atom that has a nuclear charge of 12 proton units and an electronic shell that has 11 electrons (the shell of a sodium (Na) atom).
With such considerations, the atoms' FIE values correspond to the energy gain during the bonding of the electron to an atom whose nuclear charge had been increased by one proton unit. The FIE values of Table 6.4-3 increase the values of the atoms' affinities to the electrons. For example, the FIE for Na is equal to 498 kJ/mol, while the affinity is equal to 117.2 kJ/mol. Thus, the bonding of an electron to an atom with a nuclear charge of 11 proton units and surrounded by 10 electrons offers an energy gain of 498 kJ/mol. The bonding of an electron to an atom with a nuclear charge of 11 proton units and surrounded by 11 electrons offers energy gain of about 4 times smaller (117.2 kJ/mol). That is, during the bonding of an electron to an atom, the increase of the nuclear charge abruptly increases the energy gain.
During chemical bond formation, the number of electrons in the atoms' outermost electronic shells increases by one electron, and the effective charges of the atoms being bonded are changed. The effective charges of the nuclei to be bonded are changed because of the attraction of the charged nuclei and because of the increase of the number of electrons in the outermost shells of the atoms being bonded.
In order to compare the bond formation process with the processes of bonding an electron to an atom without changing the nuclear charge of the atom and the process of bonding the electron to the atom with a simultaneous increase of its nuclear charge by one proton unit, we should evaluate the influence of the atoms being bonded on the effective nuclear charge, and the attraction of the nuclei of these atoms that occurs during bond formation.
An additional attractive force of the electron to the atom's nucleus in a hydrogen molecule (a force occurring as a result of the attraction of the atom's nucleus) is equal to the projection of force F1that attracts the electron to a nucleus that bonds the same electron to another nucleus. (See Figure 6.1.1) The value of this projection force is equal to
F1· cos 60º = 0.5 F1.
That is, the mutual approach of the nuclei leads to a 50% increase in the attraction force of the bonding electrons to the nuclei, which equals the increase of the effective charge of the nuclei to be bonded by 0.5 proton units.
Bond formation is, from the viewpoint of energy gain, a sort of middle process between the bonding of the electron to a neutral atom (measured affinity to the electron) and the bonding of the electron to the atom the nuclear charge of which is increased by one unit.
Data on the affinity of atoms to the electron and on the FIEs allow us to elucidate exactly why the bonding energy in molecules given in table 6.4- 2 is much smaller than the bonding energy in a hydrogen molecule.
When an additional electron is introduced to the outermost shells of Be and Mg, the inter- electronic repulsion energy is increased to a greater extent than is the attraction energy of the electrons to the nucleus
According to the data in Table 6.4-3, when going from lithium (FIE - 519 kJ/mol) to beryllium (FIE - 900 kJ/mol), the FIE increases by 400 kJ/mol, but, when going from beryllium to boron (FIE - 799 kJ/mol), the energy gain decreases to 100 kJ/mol.
According to Table 6.4-3, there are 3 electrons in the outermost electronic shell of boron, while there are 2 electrons in the outermost shell of beryllium. When the electron is bonded to beryllium, with an increase of the nuclear charge by one proton unit, the electron being bonded enters the existing outermost shell of beryllium, and the energy gain will thus be 100 kJ/mol less than during the entrance of the electron into the outermost shell of lithium (when going from lithium to beryllium).
Thus the decrease in the energy gain, when the electron enters the outermost shell of a beryllium atom, can be evaluated as greater than 100 kJ/mol and smaller than 400 kJ/mol.
During the formation of molecules Li2, Be2and B2, two electrons enter the outermost shells of the atoms being bonded (one electron into each atom). In the case of lithium and boron, according to the data on the affinity of atoms to the electron, the energy gain amounts to 77 kJ/mol and 32 kJ/mol respectively for each of the two atoms being bonded, and therefore these atoms have 154 kJ/mol and 64 kJ/mol respectively.
In the case of beryllium, when the electron enters the outermost shell of this element, according to the atoms' affinity to the electron, energy is not gained, but even lost. According to the above - the energy loss is generally equal to 100 kJ/mol or 200 kJ/mol.
Since the energy gain during, for example, hydrogen molecule formation out of hydrogen atoms with a positive (>0) affinity value to the electron comprises 250 kJ/mol, but the abrupt decrease of bonding energy carpet for atoms with a negative atom affinity to the electron, mentioned in Table 6.4-3, is quite comprehensible.
The explanation concerning the anomalously small bonding energies in elements of Groups II and VIII of the table of elements is an independent semi-quantitative proof of the fact that during covalent bond formation, both bonding electrons enter the outermost shells of the atoms to be bonded. This conclusion was drawn only on the basis of the comparison of the data on the number of electrons in the outermost shell with the elements' valences.
The fact that atoms of Group II form stronger bonds than the inert gases is also proof that, in the course of covalent bond formation, the effective charge of the atoms to be bonded increases. Now let's answer the question: Why is the bonding energy of di-atomic molecules shown in Table
6.4-1, namely, in molecules of carbon (C2), nitrogen (N2) and oxygen (O2), and so son,. 1.5 to 2
times greater than the bonding energy in a hydrogen molecule?
The outermost shells of carbon (C), nitrogen (N) and oxygen (O) atoms contain 4, 5 and 6 electrons respectively. The number of bonds these atoms form is limited by the number of additional electrons that enter their outermost shells. Thus, atoms of C, N and O can form 4, 3 and 2 chemical bonds respectively. And not one but several chemical bonds can be formed between any two atoms listed in Table 6.4-2, which presupposes a much greater energy gain, as compared with the formation of 1 bond in the case of a dual-atomic molecule where the atoms being bonded each have one electron in the outermost shell.
The data on bonding energy in multi-atomic molecules, where the possibilities for the formation of additional bonds between two atoms of C, N and O come to naught at the expense of bond formation with, say, hydrogen atoms, is additional confirmation of the correctness of this explanation.
It was found experimentally that the bonding energies between carbon atoms in the molecule H3C - CH3, nitrogen atoms in the molecule H2N - NH2, and oxygen atoms in the molecule HO - OH are 1.5 to 2 times less and closer in value to the bonding energy of a hydrogen molecule. When atoms are bonded with one chemical bond, this bond is known as a common chemical
bond or a single chemical bond. When atoms are bonded with several common or single bonds,
thereby forming double or triple bonds, such bonds are known as multiple bonds.
Single bonds, when describing chemical structures, are illustrated with a dash (—). For example, the structure of methane (CH4) is described by the diagram:
H Ι
Ι H
Each dash represents a bond between a pair of electrons. The electron structure of methane is described by the following formula:
H H : C : H
H
Here the dots represent bonding electrons. Multiple bonds, as in nitrogen (N2) and oxygen (O2) molecules are described by structural formulas:
N ≡ N and O = O and by electronic ones:
. . . . : N : : : N : and : О : : О :
. . . .
Here the electrons between the atoms are the bonding ones, while those, sort of on the outside, are nonbonding ones (which do not take part in bond formation).
According to electronic formulas after the formation of a triple chemical bond, in nitrogen (N) remain two nonbonding electrons or one free electronic pair with each of the atoms. After the formation of a dual chemical bond in oxygen, two free electronic pairs remain in each of the two