Electron and the Chemical Bonding

Transcription

1 1 Electron and the Chemical Bonding Progress in any discipline comes slowly and often requires the efforts of many workers. One is sometimes inspired by the findings of the others, which result in a viable solution to the problem. This is true in particular, of the modern concept of atomic structure. Matter was considered to be composed of atoms which in turn were thought to be the smallest particles possible. Such an idea traces back to the classical times and was based mainly on the philosophical speculations of the Greek philosophers. But as scientific thought advanced and experimentation became possible, this view concerning the atom proved to be quite inadequate to explain the observed facts. istorically speaking, the development of the modern atomic theory commenced with the work of Dalton (1803) in the form of several postulates. One of these postulates stated that atoms could not be sub-divided or converted into one another. But this was subsequently proven to be incorrect. Important contributions in this direction were made by various chemists, and finally Thomson (1897) actually discovered electrons by his brilliant discharge tube experiments. This opened a new era in unfolding the structure of the atom. Rutherford (1911) presented a picture of the structure of the atom according to which the negatively charged particles called electrons revolve around a positively charged nucleus in analogy with the solar system. A nucleus is a very small dense, positively charged core of an atom. Bohr (1913) announced the quantum theory of the atom and gave a mathematical treatment for the simple hydrogen atom. de Broglie (1923) postulated the wave nature of the electrons analogous to light waves and finally Schrödinger s (1926) mathematical equation called the wave equation summed up the present concept of the electron. Now we know that an atom indeed, can be broadly sub-divided into protons, neutrons and electrons. In a neutral atom, the nucleus containing the positive protons and neutral neutrons that have no charge is surrounded by negatively charged electrons equal to the number of protons. The atomic number equals the number of protons in the nucleus of an atom, and is also numerically equal to the number of electrons in the neutral atom. The sum of the number of protons and neutrons in the nucleus of an atom is equal to the atomic mass. Each element is distinguished by the number of protons and neutrons in the nucleus. Atoms that have the same number of protons and electrons but different number of neutrons are called isotopes. The isotopes of an element always have the same atomic number but different atomic mass. These elements are unstable, i.e. their nuclei decompose radioactively (they emit some kind of radiation because of their nuclei being unstable). For example, carbon has a mass number of 12 and it is commonly symbolized as 12 C. Carbon also has mass number of 13 and 14, i.e. same number of protons but different number of neutrons C C C (6 6) (6 7) (6 8) Therefore, 13 C and 14 C are isotopes of carbon and designated by using superscript and subscript to show mass number and atomic number ( 13 6 C and 14 6 C).

2 2 A Textbook of Organic Chemistry In case the number of protons and electrons is not equal as a result of loss or gain of electrons then the atom or the molecule containing that atom must be charged and is called an ion. A negatively charged ion is called an anion and positively charged is a cation. 1.1 ATOMIC ORBITALS An electronic interpretation of chemical bond formation was proposed by Lewis according to which the elements tend to gain or lose electrons in such a way as to acquire a noble gas configuration. The model is undoubtedly useful for many purposes, but electrons, as we know now, do not stay still in one position. The modern discussion on chemical bonding is, therefore, related to wave functions or orbitals. From a consideration of wave mechanics, a basic concept arises called the eisenberg uncertainty principle which states that it is impossible to specify the position and velocity of an electron simultaneously. In other words, if we know the position of an electron accurately its velocity at that moment will be uncertain. We, therefore, consider an electron as having a certain probability of being located at any given instant in space. An orbital is thus a region of space about the nucleus of a single atom where there is a maximum probability of finding an electron. It may be visualized as a charged cloud being dense at places where such a probability is high and less dense where the probability is low. The boundaries of such an orbital is not very distinct because there is finite, even if small, probability of finding the electron relative to the distance from the nucleus. According to quantum theory a wave equation can be written for any atom or molecule and the solutions of the equation are termed as wave functions denoted by ψ. These wave functions give information about the orbitals occupied by the electrons in a system, and the square of the wave function (ψ 2 ) for a particular location (x, y, z) refers to the probability of finding an electron at that particular location in space. If ψ 2 is large in a unit volume of space, the probability of finding an electron in that volume is great; in other words, the electron probability density is large and vice versa. The solution of the wave equation gives the probable density of the electron in a given volume. Let us consider a hydrogen atom in the ground state. It is closest to the nucleus and most stable. This atom consists of a positively charged nucleus and one extranuclear electron in the 1s orbital. Since a 1s orbital is spherical in shape, the electron is likely to be found within the sphere surrounding the nucleus. Unfortunately we cannot locate the exact position by the uncertainty principle. It is only a matter of probability. The quantum theory predicts that the probability is about 90% than an electron in a 1s orbital will be found within a sphere of radius 1.4 Å around the nucleus. According to the wave mechanical theory of the atom, an electron is defined by a set of four numbers called the quantum numbers. These are often represented by n, l, m and s. These numbers can have the following values n = 1, 2, 3, 4,... any integer l = 0, 1, 2, 3, 4,... n 1 m = l, (l 1), (l 2),... 0, ( l 2), ( l 1) (0, ± 1, ± 2, ± 3,..., ± l) s = 1 1, 2 2 The number n is called the principal quantum number and it represents the energy of an electron in an orbit and hence the distance of the electron from the nucleus. The number l is known as the angular momentum quantum number and represents the angular momentum of the electron. It is generally related to the shape of the orbital. It is

3 Electron and the Chemical Bonding 3 given positive and integral values. Its value depends on the value of n. The l quantum number can have an integral value from zero to n 1, i.e., l = 0, 1, 2,... (n 1). The wave equation leads to a third quantum number m, the magnetic quantum number. Since the magnetism is due to the angular momentum, it is expected that the value of m will depend on l. It tells about the orientation of the orbital. The m quantum number can be zero as well as both positive and negative integers upto ± l, i.e., 0, ± 1, ± 2... ± l. Finally, the fourth number is called the spin quantum number. It has only two values and represents the spin of an electron on its own axis which can be either clockwise or anticlockwise relative to the orbital of the electron. This quantum number can assume either of two values 1 2 or 1 2. Two electrons can occupy the same orbital but their spin must be opposite. An atom with two electrons can have a total spin equal to zero (antiparallel) or spin equal to one (parallel). But in the later case they must occupy different orbitals according to potential energy (P.E.) considerations. Electrons can be grouped into shells or main energy levels (K,L,M,N). A shell contains electrons that have approximately the same energy and spend their time approximately the same distance from the nucleus. Electron shells are identified by a number n. It has values 1, 2, 3, 4,... etc. The lowest energy shell is assigned a value of l(n = 1). It accommodates 2 electrons. For n = 2, 3, 4, the number of electrons allowed are 8, 18 and 32 respectively. Each electron shell is divided into energy sub-shells. A sub-shell contains electrons that all have the same energy. Electrons are found in four types of sub-shells which are denoted by the lowercase letters s, p, d, f. These are listed in order of increasing energy within a shell. The lowest energy sub-shell within a shell is always the s sub-shell (n = 1). The next higher sub-shells are p, d, f. Not all types of sub-shells are found in all the shells. The lowest energy shell (n = 1) has only one sub-shell the 1s. The second shell (n = 2) has two sub-shells 2s, 2p. The 2p sub-shell has higher energy than 2s. The third sub-shell (n = 3) has three sub-shells 3s, 3p, 3d. It is not until the fourth shell (n = 4) that we encounter all four types of sub-shells Shapes of Atomic Orbitals The atomic orbitals (1s, 2s and three 2p) occupy definite regions in space. Both 1s and the next higher energy level 2s orbitals are spherically symmetrical (Fig. 1.1) about the nucleus. They are non-directional. The probability of finding an electron decreases with the increase in the distance from the nucleus. Evidently the greater probability of finding an electron is near the nucleus. The sign of the wave function ψ 1s is positive over the entire 1s orbital. The 1s and 2s orbitals differ primarily in size, the latter being slightly larger than the 1s orbital. The 2s orbital, in addition contains a nodal surface, i.e., an area where ψ 2 = 0, i.e., a region of zero electron density. The nodel surface in the 2s orbital is an infinitely thin sphere, therefore, the 2s orbital has the characteristic of two concentric balls of electron density. Note that the sign of the wave function ψ 1s is positive over the entire 1s orbital. y 1s y y 2s 1s Nodal surface Fig. 1.1 Shape of s atomic orbitals.

4 4 A Textbook of Organic Chemistry The p-orbitals are three in number, i.e., p x, p y and p z, oriented along the three axes. They are identical but differ from one another in direction. Each 2p orbital is dumbbell in shape and are composed of two lobes that do not touch each other (Fig. 1.2). This point is a place of zero electron density and is known as the nodal plane. 2p x x 2p y x z y z y x z y Fig. 1.2 Shapes and orientation of p atomic orbitals. 2p z The sign of the wave function is positive in one lobe and negative in the other. These signs do not imply a greater or lesser probability of finding an electron. The orbitals drawings are great simplifications of extremely complex mathematical functions (called the wave functions) that describe the electron distribution in an atom. These are degenerate, i.e., equal in energy. The axis of each 2p orbital is oriented at an angle of 90 to each other. The p-orbitals are higher in energy than the s-orbitals. The 3s and 3p orbitals are similar to the 2s and 2p orbitals but higher in energy. The d-orbitals have still higher energies and very different geometries. They are five in numbers. The Pauli exclusion principle. This principle states that not more than two electrons can occupy an orbital unless their spins are paired ( ). Such a pair of electrons can occupy a single orbital. Electrons with unpaired electrons denoted by ( ) or ( ) are not accommodated into a single orbital. Electrons can be added or removed from atoms. The amount of energy required to remove an electron from an atom is known as the ionization potential (IP). The first ionization potential is the amount of energy required to remove the least tightly bound electron from an atom. Ionization potential energy is measured in electron volts. Na Na e IP = 5.11 ev = 118 kcal 11 electrons 10 electrons The ion so produced has the electronic configuration of the next lower noble gas. Na has the same electronic configuration as neon (10). The elements on the left side of the periodic table have relatively low ionization potential and are termed as electropositive. The amount of energy liberated when an electron is gained by an atom is known as the electron affinity (EA). Cl e Cl EA = 3.61 ev = 87.3 kcal 17 electrons 18 electrons The ion so produced also has the stable electronic configuration of the next higher noble gas. In this case it is the same as that of argon (18). Such elements are termed as electronegative.

5 Electron and the Chemical Bonding CEMICAL BOND FORMATION A chemical bond is an attraction between atoms that allows the formation of chemical substances that contain two or more atoms. Therefore, consideration of chemical combination of atoms and the forces that hold them together can be taken up. The outermost shell of electrons in an atom is called its valence shell. The electrons in this shell of the atom are called the valence electrons and the term valence or valency may be described as a certain combining power. The number of bonds an element could form is called its valence number. The valence electrons can be easily lost, gained or shared. It was recognized earlier that chemical properties of elements depend on the arrangement of their electrons and that the inert gases possess stable configurations. Lewis proposed the octet rule or the rule of eight. According to this rule, atoms bond together in such a manner that each participating atom is surrounded by eight valence electrons (2 electrons for hydrogen). Thus the outershell of each bonded atom will contain eight electrons (or two electrons for and Li). In the formation of an ionic bond, one electron is completely transferred from one atom to another of a different element forming charged particles called ions. During this transfer of electron, each atom acquires a stable octet or eight electrons analogous to inert gas elements since it is known that such configurations are of exceptional stability. Such bonds are formed between highly electronegative, i.e., electron-attracting, and highly electropositive, i.e., electron-donating elements. The alkali metals of the periodic table have relatively low ionization potential, i.e., they can lose electrons easily and are thus described as being electropositive. The halogens, on the other hand, can readily gain electrons; such elements are termed as electronegative. Thus in ionic bond formation between sodium and chlorine atoms, the latter can either relinquish seven electrons or gain one electron and become a negatively charged chloride ion (an anion). The former process is energetically difficult, therefore chlorine atom tends to gain one electron. The sodium atom loses an electron readily and becomes a positively charged sodium ion (a cation). In these structures atoms are represented by symbols. 2e 8e 1e 2e 8e 7e 2e Na Cl Na Cl The electronic configuration of these two ions obey the octet rule. Between the positively charged sodium ion and the negatively charged chloride ion, there exists a force of electrostatic attraction which holds the ions together. This attraction constitutes a chemical bond. This type of bond is called an ionic or an electrovalent bond. This bond is common in inorganic compounds such as potassium chloride, magnesium oxide, sodium hydroxide, etc., they all contain ionic bonds. The ionic bond is non-directional because ions radiate a spherically symmetrical positive or negative field. The compounds formed by these cations and anions are neutral, hard, soluble in water and crystalline. Ionic compounds are made of ions. They contain ionic bonds. The chemical bond on the other hand, in a non-ionic compound is a covalent bond. Lewis explained the formation of a covalent bond by sharing of an electron pair rather than by complete transfer of electrons. Accordingly a covalent bond results from the sharing of one or more pairs of electrons between atoms. Two chlorine atoms, for instance, combine in such a way that a pair of electrons (one electron provided by each atom) is shared by both the chlorine atoms. Each pair of electrons is drawn as a pair of dots. 8e 2e 8e 8e Na Cl

6 A Textbook of Organic Chemistry Cl.. Cl Cl Cl Cl Cl Shared electron pair A covalent bond denotes a shared electron pair Such structures in which atoms are represented by symbols and electrons by dots are called Lewis structures. In other words, molecules formed by covalent bonds are written as Lewis structure. Molecules like methane, hydrogen chloride, carbon tetrachloride, methyl alcohol, acetamide etc., are some of the additional examples. Cl O C, Cl, ClC Cl, C O, C CN Cl A Lewis structure shows all bonding electrons as well as those valence electrons which are nonbonding. To write a Lewis structure first count the number of electrons in the outermost shell, i.e. the valence electrons. Some of these electrons in certain atoms are nonbonding, for instance, N and S(2), O(4), halogens (6), etc. Then write its Lewis structure. Covalent compounds are either solids, liquids or exist in gaseous states. They are soluble in organic solvents, have low melting point and boiling point and react slowly in chemical reactions. A covalent bond can either be polar or non-polar depending on the electronegativities of the two linked atoms. Larger the difference in electronegativity of the bonded atoms, more polar is the bond. If more than one pair of electrons is shared by the atoms, then multiple covalent bonds are formed, for example, in carbon dioxide, ethylene and acetylene. OCO O C O, C C C C, C N C These are linear molecules as all the atoms are in a straight line. Covalent compounds do not ionize but dissolve as molecules. There is yet another way of octet formation. In this case the bonding electrons are provided by one of the partner and then shared jointly by the bonding atoms. For example, consider the ammonia boron hydride molecule, formed by combining N.. with B 3 3. Boron has three electrons in the outermost shell (the L shell) available for bonding. Boron utilizes these electrons to form covalent sp 2 hybridized bonds with three hydrogen atoms. Boron still has six electrons and is considered an electron deficient. It tends to gain two electrons to attain an electron octet. The nitrogen atom in N.. provides its unshared pair of electrons 3 and is referred to as the donor atom. The boron atom which accepts the electron pair is called the acceptor. The electron pair is now jointly shared by the two atoms to form a bond, as pictured below 120 N 3 N B B 3N B3 or 3 N B Such a bond is called a coordinate covalent or a dative bond and has a dipolar form. This bond can also be described by an arrow ( ) pointing towards the acceptor. A coordinate covalent bond has the same characteristics as a covalent bond. As we can see there is a change in configuration in such molecules as the trivalent boron (sp 2 hybridized) becomes tetrahedral (sp 3 ). N

7 Electron and the Chemical Bonding 7 C 3 C N O, 3 C 3 O O N O O O N O ( ) , R N BF R N BF and O S O O.. In water ( Ọ. ), the oxygen atom has two unshared electron pairs. It coordinates with a proton ( ) which has an empty orbital by accepting a pair of electrons from oxygen, and the proton achieves a full s shell. O O The resulting species is called a hydronium ion. The proton has one unit of positive charge spread over its small area. The high charge density makes it immensely reactive. It therefore, cannot exist by itself. It is stabilized by coordination with a water molecule. Many inorganic salts, in particular, contain more than one type of bonds between their atoms. For instance, KCN contains both ionic and covalent bonds; and CuSO O has ionic, covalent and dative covalent bonds. Problem 1.1 Write the number of valence electrons and electron lone pair(s) of the following atoms C, N, O,, Cl and F. Problem 1.2 Draw a Lewis structure including lone pairs of the following molecules O O O C 3 CNO, N 2,, 2 SO 4, C3OCO, C 3 N 2, SOCl 2, C 3 MgBr. N Formal Charge on an Atom Formal charge may be described as the excess or lack of electrons in an atom in the molecule as compared to the free atom. This is a method for electron book-keeping. Its value can be computed for each atom in a molecule. In order to calculate the formal charge on an atom, it is assumed that the atom has possession of half the shared electrons. The following equation can then be employed to calculate formal charge on an atom Formal charge = A B C where A = number of valence electrons in the isolated atom B = number of covalent bonds to the atom (a double bond is considered as two covalent bonds). C = number of electrons present to the atom The valence electrons are the number of electrons in terms of its position in the periodic table for boron it is 3, carbon 4, nitrogen 5, oxygen 6, halogens 7 and sulfur 8. In nitric acid O N O O, for nitrogen the number of the valence electrons is 5 (A = 5), there exists four covalent bonds to nitrogen (B = 4), each covalent bond is composed of two electrons for nitrogen, the total is 8 (C = 8).

8 8 A Textbook of Organic Chemistry ence A B C = = 1 Nitrogen has 1 formal charge. For oxygen A B C = = 1 The atoms in C Ṅ. molecule have no formal charge. In nitronium ion O N O nitrogen has 1 formal charge and oxygen has zero formal charge. Problem 1.3 Compute the formal charge on each atom in the following structures (a) Ammonium ion ( N ) (b) ydronium ion ( 4 3 O ) (c) 3 N B 3 (d) CO 2, Bond Formation using Atomic Orbitals Lewis structures for molecules assumes that a covalent bond is formed by sharing of electrons. owever, atomic orbitals can be used for bond formation, i.e., the bond formation involves the filling of incomplete or empty orbitals of an atom by the electrons of the other atom. The simplest chemical bond is formed between 2 atoms. Each hydrogen atom contains one electron in the 1s orbital. As the -atoms approach each other, the nucleus of one atom attracts the electron of the other. Interaction of 1s atomic orbitals on each of two hydrogen atoms form bonding (and antibonding) molecular orbital, i.e. the hydrogen molecule. Overlap As regards the shape of the bonding molecular orbital of 2, the electrons in this molecular orbital occup an ellipsoidal region, of space. No matter how we turn the 2 molecule about a line joining the two nuclei, its electron density looks the same. This means the hydrogen atom has cylindrical symmetry. Therefore, any bond with cylindrical symmetry is called a sigma (σ) bond. In the hydrogen molecule, the two electrons remain most of the time between the nuclei holding the molecule together. In wave mechanical terminology, the interaction is called overlap. The term overlap refers to the extent to which atomic orbitals on different atoms share the same region of space to form a molecular orbital. A hydrogen molecule results from the formation of a hydrogen hydrogen covalent bond. Such a process occurring with the pairing of spins is denoted as ( ). The orbital so obtained by overlap of atomic orbitals is called a molecular orbital. A molecular orbital corresponds to region of space encompassing two atoms where electrons can move. In the formation of a bond, certain amount of energy is always released. The hydrogen molecule releases kcal/mol and is more stable than each of the individual hydrogen atoms. The larger the degree of overlap of the atomic orbitals, the greater is the energy of the resultant bond formed between the atoms. The strength of a σ bond is of the following order s s > s p > p p The s s bond is the strongest bond. An energy diagram for the molecular orbital of hydrogen is shown in (Fig. 1.3). When two atomic orbitals (in this case of hydrogen) come together, two molecular orbitals ψ and

9 Electron and the Chemical Bonding 9 ψ*(or π and π*) are formed according to LCAO i.e. by addition and subtraction. The one with the lower electronic energy (ψ) is the bonding orbital which is more stable than the component atomic orbitals. This lower electronic energy is the ground state of the hydrogen molecule. The one with the higher electronic energy (ψ ) is the antibonding orbital and is less stable than the component atomic orbitals. An electron may occupy the antibonding orbital in what is called the excited state of the molecule. This state forms when the molecule in the ground state absorbs a photon of light of proper energy. The bonding between the atoms of hydrogen involves molecular orbitals of the lowest possible energy states. y* (1 s 1 s) antibonding Energy 1s 1s y (1 s 1 s) bonding Fig. 1.3 Energy diagram for the hydrogen molecule. In molecular orbital, bonding orbitals being of lower energy will fill first and each will accommodate a pair of electrons which must have opposite spins. Electrons in the bonding orbital will stabilize the molecule, whereas electrons in the antibonding orbital will destabilize. 1.3 BOND DISSOCIATION ENERGY When atoms combine to form molecules, energy is released. The molecule has a lower energy than its constituent atoms. For instance, when two hydrogen atoms combine to form a hydrogen molecule, the reaction is exothermic and kcal of heat is evolved per mol of hydrogen produced and the value of is negative... = kcal/mol Atoms are held together by forces which can be estimated. We may define this force as the energy contained between the two atoms and may be termed as bond energy (E) or the heat of formation of the bond. The total energy contained in a molecule is the sum of the bond energies of all the bonds constituting the molecule. The amount of energy required to break a covalent bond into its fragments is called the bond dissociation energy (D). It is a measure of the strength of a bond. This is an endothermic process. The energy absorbed to break a bond is exactly equal to that evolved in its formation, but is now positive... = kcal/mol Determination of bond dissociation energy is an experimental process and is usually calculated from thermochemical data. Bond dissociation energy values for some common bonds are given in Table 1.1. The dissociation energy of a bond increases with the increase in the difference in the electronegativities of the bonded atoms. Furthermore, the shorter the bond, the stronger it is and higher the bond energy.

10 10 A Textbook of Organic Chemistry Table 1.1 Single Bond Dissociation Energies ( ) (kcal/mol at 25 C) A B A. B. Bond Bond Dissociation Bond Bond Dissociation Energy (kcal/mol) Energy (kcal/mol) F 136 D D 106 Cl C Br 88.0 C C I 71.4 C C O C C 83.5 O O 35 C O 85.5 C I 56 C O 176 a C F 108 C O 179 b C Cl 83.5 I I 36.1 C Br 70 Cl Cl C 104 Br Br 46.1 Na Cl 98.1 F F 38 a For aldehydes b For ketones 1.4 ELECTRONEGATIVITY AND BOND POLARITY Electronegativity is a measure of the relative attraction that an atom has for the shared electrons in a bond. The elements with high electronegativity are up and to the right of the periodic table, i.e., going across the top row, the electronegativity increases in the order Li < C < N < O < F. The electronegativity of the halogen atoms decreases in the sequence F > Cl > Br > I, i.e., Iodine is the least and fluorine is the most. The relative order of electronegativity of atoms commonly encountered in organic molecules is as follows < C < I < Br < Cl < N < O < F In this series, hydrogen is the least electronegative. Fluorine is the most electronegative among the halogens and the most powerful oxidising agent. The more electronegative an element, the greater will be its hold on the electrons. In a covalent bond the sharing of electrons between the atoms need not be equal except in the case of two identical atoms. Disimilar atoms bonded together have different electronegativities and the value of electronegativity is often used to determine whether a bond is polar or nonpolar. The difference in electronegativity gives a partial negative (δ ) charge to the more electronegative atom and a partial positive (δ ) charge to the second atom, as in the Cl molecule. 1s d d Cl Cl Cl 3p x The center of the negative charge (due to electrons) does not coincide with the center of the positive charge due to the nuclei in polar molecules. A greater share of the shared pair of electrons is held by the chlorine atom then hydrogen and as a result the molecular orbital is unsymmetrical. A bond in which sharing of electrons is unequal is called a polar covalent