12.7 The radius of the innermost electron orbit of a hydrogen atom is 5.3×10–11 m. What are the radii of the n = 2 and n =3 orbits?

4.2 Ionic or Electrovalent Bond other factors. The crystal structure of sodium chloride, NaCl (rock salt), for example isFrom the Kössel and Lewis treatment of the shown below.formation of an ionic bond, it follows that the formation of ionic compounds would primarily depend upon: • The ease of formation of the positive and negative ions from the respective neutral atoms; • The arrangement of the positive and negative ions in the solid, that is, the lattice of the crystalline compound. The formation of a positive ion involves ionization, i.e., removal of electron(s) from the neutral atom and that of the negative ion involves the addition of electron(s) to the Rock salt structure neutral atom. In ionic solids, the sum of the electron gain M(g) → M+(g) + e– ; enthalpy and the ionization enthalpy may be Ionization enthalpy positive but still the crystal structure gets X(g) + e– → X – (g) ; stabilized due to the energy released in the Electron gain enthalpy formation of the crystal lattice. For example: the ionization enthalpy for Na+(g) formation M+(g) + X –(g) → MX(s) from Na(g) is 495.8 kJ mol–1 ; while the electron The electron gain enthalpy, ∆egH, is the gain enthalpy for the change Cl(g) + e–→ enthalpy change (Unit 3), when a gas phase Cl– (g) is, – 348.7 kJ mol–1 only. The sum of the atom in its ground state gains an electron. two, 147.1 kJ mol-1 is more than compensated The electron gain process may be exothermic for by the enthalpy of lattice formation of or endothermic. The ionization, on the other NaCl(s) (–788 kJ mol–1). Therefore, the energy hand, is always endothermic. Electron released in the processes is more than the Reprint 2025-26 Chemical Bonding And Molecular Structure 107 energy absorbed. Thus a qualitative measure of the stability of an ionic compound is provided by its enthalpy of lattice formation and not simply by achieving octet of electrons around the ionic species in gaseous state. Since lattice enthalpy plays a key role in the formation of ionic compounds, it is important that we learn more about it. 4.2.1 Lattice Enthalpy The Lattice Enthalpy of an ionic solid is defined as the energy required to completely separate one mole of a solid ionic compound into gaseous constituent ions. For example, the lattice enthalpy of NaCl is 788 kJ mol–1. This means that 788 Fig. 4.1 The bond length in a covalent kJ of energy is required to separate one mole molecule AB. of solid NaCl into one mole of Na+ (g) and one R = rA + rB (R is the bond length and rA and rB are mole of Cl– (g) to an infinite distance. the covalent radii of atoms A and B respectively) This process involves both the attractive forces between ions of opposite charges in the same molecule. The van der Waals and the repulsive forces between ions of radius represents the overall size of the like charge. The solid crystal being three- atom which includes its valence shell in a dimensional; it is not possible to calculate nonbonded situation. Further, the van der lattice enthalpy directly from the interaction Waals radius is half of the distance between of forces of attraction and repulsion only. two similar atoms in separate molecules in Factors associated with the crystal geometry a solid. Covalent and van der Waals radii of have to be included. chlorine are depicted in Fig. 4.2.

4.1 KÖssel-Lewis Approach to the number of valence electrons. This number Chemical Bonding of valence electrons helps to calculate the common or group valence of the element.In order to explain the formation of chemical The group valence of the elements is generallybond in terms of electrons, a number of either equal to the number of dots in Lewisattempts were made, but it was only in symbols or 8 minus the number of dots or1916 when Kössel and Lewis succeeded valence electrons.independently in giving a satisfactory explanation. They were the first to provide Kössel, in relation to chemical bonding, some logical explanation of valence which was drew attention to the following facts: based on the inertness of noble gases. • In the periodic table, the highly Lewis pictured the atom in terms of a electronegative halogens and the highly positively charged ‘Kernel’ (the nucleus plus electropositive alkali metals are separated by the noble gases;the inner electrons) and the outer shell that could accommodate a maximum of eight • The formation of a negative ion from a electrons. He, further assumed that these halogen atom and a positive ion from eight electrons occupy the corners of a cube an alkali metal atom is associated with which surround the ‘Kernel’. Thus the single the gain and loss of an electron by the outer shell electron of sodium would occupy respective atoms; one corner of the cube, while in the case of • The negative and positive ions thus a noble gas all the eight corners would be formed attain stable noble gas electronic occupied. This octet of electrons, represents configurations. The noble gases (with the a particularly stable electronic arrangement. exception of helium which has a duplet Lewis postulated that atoms achieve of electrons) have a particularly stable the stable octet when they are linked by outer shell configuration of eight (octet) chemical bonds. In the case of sodium and electrons, ns2np6. chlorine, this can happen by the transfer of • The negative and positive ions are stabilized an electron from sodium to chlorine thereby by electrostatic attraction. giving the Na+ and Cl– ions. In the case of For example, the formation of NaCl fromother molecules like Cl2, H2, F2, etc., the bond sodium and chlorine, according to the aboveis formed by the sharing of a pair of electrons scheme, can be explained as:between the atoms. In the process each atom attains a stable outer octet of electrons. Na → Na+ + e– Lewis Symbols: In the formation of a [Ne] 3s1 [Ne] molecule, only the outer shell electrons take Cl + e– → Cl– part in chemical combination and they are [Ne] 3s2 3p5 [Ne] 3s2 3p6 or [Ar] known as valence electrons. The inner shell Na+ + Cl– → NaCl or Na+Cl– electrons are well protected and are generally Similarly the formation of CaF2 may benot involved in the combination process. shown as:G.N. Lewis, an American chemist introduced simple notations to represent valence electrons Ca → Ca2+ + 2e– in an atom. These notations are called Lewis [Ar]4s2 [Ar] symbols. For example, the Lewis symbols for F + e– → F– the elements of second period are as under: [He] 2s2 2p5 [He] 2s2 2p6 or [Ne] Ca2+ + 2F– → CaF2 or Ca2+(F– )2 The bond formed, as a result of the Significance of Lewis Symbols : The electrostatic attraction between the number of dots around the symbol represents positive and negative ions was termed as Reprint 2025-26 102 chemistry the electrovalent bond. The electrovalence chlorine atoms attain the outer shell octet of is thus equal to the number of unit charge(s) the nearest noble gas (i.e., argon). on the ion. Thus, calcium is assigned a The dots represent electrons. Suchpositive electrovalence of two, while chlorine structures are referred to as Lewis dota negative electrovalence of one. structures. Kössel’s postulations provide the basis for The Lewis dot structures can be written forthe modern concepts regarding ion-formation other molecules also, in which the combiningby electron transfer and the formation of ionic atoms may be identical or different. Thecrystalline compounds. His views have proved important conditions being that:to be of great value in the understanding and • Each bond is formed as a result of sharingsystematisation of the ionic compounds. At of an electron pair between the atoms.the same time he did recognise the fact that • Each combining atom contributes at leasta large number of compounds did not fit into one electron to the shared pair.these concepts. • The combining atoms attain the outer-4.1.1 Octet Rule shell noble gas configurations as a result Kössel and Lewis in 1916 developed an of the sharing of electrons. important theory of chemical combination • Thus in water and carbon tetrachloridebetween atoms known as electronic theory molecules, formation of covalent bondsof chemical bonding. According to this, can be represented as:atoms can combine either by transfer of valence electrons from one atom to another (gaining or losing) or by sharing of valence electrons in order to have an octet in their valence shells. This is known as octet rule. 4.1.2 Covalent Bond Langmuir (1919) refined the Lewis postulations by abandoning the idea of the stationary cubical arrangement of the octet, and by introducing the term covalent Thus, when two atoms share onebond. The Lewis-Langmuir theory can be electron pair they are said to be joined byunderstood by considering the formation of a single covalent bond. In many compoundsthe chlorine molecule, Cl2. The Cl atom with we have multiple bonds between atoms. Theelectronic configuration, [Ne]3s2 3p5, is one formation of multiple bonds envisages sharingelectron short of the argon configuration. of more than one electron pair between twoThe formation of the Cl­2 molecule can be atoms. If two atoms share two pairs ofunderstood in terms of the sharing of a pair electrons, the covalent bond between themof electrons between the two chlorine atoms, is called a double bond. For example, in theeach chlorine atom contributing one electron carbon dioxide molecule, we have two doubleto the shared pair. In the process both bonds between the carbon and oxygen atoms. Similarly in ethene molecule the two carbon atoms are joined by a double bond. or Cl – Cl Double bonds in CO2 molecule Covalent bond between two Cl atoms Reprint 2025-26 Chemical Bonding And Molecular Structure 103 number of valence electrons. For example, for the CO32– ion, the two negative charges indicate that there are two additional electrons than those provided by the neutral atoms. For NH4+ ion, one positive charge indicates the loss of one electron from the group of neutral atoms. C2H4 molecule • Knowing the chemical symbols of the When combining atoms share three combining atoms and having knowledge electron pairs as in the case of two nitrogen of the skeletal structure of the compound atoms in the N2 molecule and the two (known or guessed intelligently), it is easy carbon atoms in the ethyne molecule, a to distribute the total number of electrons triple bond is formed. as bonding shared pairs between the atoms in proportion to the total bonds. • In general the least electronegative atom occupies the central position in the molecule/ion. For example in the NF3 and N2 molecule CO32–, nitrogen and carbon are the central atoms whereas fluorine and oxygen occupy the terminal positions. • After accounting for the shared pairs of electrons for single bonds, the remaining C2H2 molecule electron pairs are either utilized for multiple bonding or remain as the lone pairs. The basic requirement being4.1.3 Lewis Representation of Simple that each bonded atom gets an octet of Molecules (the Lewis Structures) electrons. The Lewis dot structures provide a picture Lewis representations of a few molecules/of bonding in molecules and ions in terms of ions are given in Table 4.1.the shared pairs of electrons and the octet rule. While such a picture may not explain the bonding and behaviour of a molecule Table 4.1 The Lewis Representation of completely, it does help in understanding the Some Molecules formation and properties of a molecule to a large extent. Writing of Lewis dot structures of molecules is, therefore, very useful. The Lewis dot structures can be written by adopting the following steps: • The total number of electrons required for writing the structures are obtained by adding the valence electrons of the combining atoms. For example, in the CH4 molecule there are eight valence electrons available for bonding (4 from carbon and 4 from the four hydrogen atoms). • For anions, each negative charge would mean addition of one electron. For cations, each positive charge would result in * Each H atom attains the configuration of helium subtraction of one electron from the total (a duplet of electrons) Reprint 2025-26 104 chemistry Problem 4.1 each of the oxygen atoms completing the octets on oxygen atoms. This, however, Write the Lewis dot structure of CO does not complete the octet on nitrogen molecule. if the remaining two electrons constitute Solution lone pair on it. Step 1. Count the total number of valence electrons of carbon and oxygen atoms. The outer (valence) shell configurations of carbon and oxygen atoms are: 2s2 2p2 Hence we have to resort to multiple and 2s2 2p4, respectively. The valence bonding between nitrogen and one of electrons available are 4 + 6 =10. the oxygen atoms (in this case a double bond). This leads to the following Lewis Step 2. The skeletal structure of CO is dot structures. written as: C O Step 3. Draw a single bond (one shared electron pair) between C and O and complete the octet on O, the remaining two electrons are the lone pair on C. This does not complete the octet on carbon and hence we have to resort to multiple bonding (in this case a triple 4.1.4 Formal Charge bond) between C and O atoms. This Lewis dot structures, in general, do not satisfies the octet rule condition for both represent the actual shapes of the molecules. atoms. In case of polyatomic ions, the net charge is possessed by the ion as a whole and not by a particular atom. It is, however, feasible to assign a formal charge on each atom. The formal charge of an atom in a polyatomic molecule or ion may be defined as the Problem 4.2 difference between the number of valence Write the Lewis structure of the nitrite electrons of that atom in an isolated or free ion, NO2– . state and the number of electrons assigned to that atom in the Lewis structure. It is Solution expressed as : Step 1. Count the total number of valence electrons of the nitrogen atom, Formal charge (F.C.) the oxygen atoms and the additional one on an atom in a Lewis = negative charge (equal to one electron). structure N(2s2 2p3), O (2s2 2p4) 5 + (2 × 6) +1 = 18 electrons total number of valence total number of non electrons in the free — bonding (lone pair) Step 2. The skeletal structure of NO2– is atom electrons written as : O N O total number of Step 3. Draw a single bond (one shared — (1/2) bonding (shared) electrons electron pair) between the nitrogen and Reprint 2025-26 Chemical Bonding And Molecular Structure 105 The counting is based on the assumption 4.1.5 Limitations of the Octet Rule that the atom in the molecule owns one The octet rule, though useful, is not universal. electron of each shared pair and both the It is quite useful for understanding the electrons of a lone pair. structures of most of the organic compounds Let us consider the ozone molecule (O3). and it applies mainly to the second period elements of the periodic table. There are threeThe Lewis structure of O3 may be drawn as: types of exceptions to the octet rule. The incomplete octet of the central atom In some compounds, the number of electrons surrounding the central atom is less than eight. This is especially the case with elements having less than four valence electrons. Examples are LiCl, BeH2 and BCl3. The atoms have been numbered as 1, 2 and 3. The formal charge on: • The central O atom marked 1 1 Li, Be and B have 1, 2 and 3 valence electrons = 6 – 2 – (6) = +1 only. Some other such compounds are AlCl3 2 and BF3.• The end O atom marked 2 Odd-electron molecules 1 = 6 – 4 – (4) = 0 In molecules with an odd number of electrons 2 like nitric oxide, NO and nitrogen dioxide, • The end O atom marked 3 NO2, the octet rule is not satisfied for all the 1 atoms = 6 – 6 – (2) = –1 2 Hence, we represent O3 along with the formal charges as follows: The expanded octet Elements in and beyond the third period of the periodic table have, apart from 3s and 3p orbitals, 3d orbitals also available for bonding. In a number of compounds of these elements there are more than eight valence electrons We must understand that formal charges around the central atom. This is termed as do not indicate real charge separation within the expanded octet. Obviously the octet rule the molecule. Indicating the charges on the does not apply in such cases. atoms in the Lewis structure only helps in Some of the examples of such compoundskeeping track of the valence electrons in are: PF5, SF6, H2SO4 and a number ofthe molecule. Formal charges help in the coordination compounds. selection of the lowest energy structure from a number of possible Lewis structures for a given species. Generally the lowest energy structure is the one with the smallest formal charges on the atoms. The formal charge is a factor based on a pure covalent view of bonding in which electron pairs are shared equally by neighbouring atoms. Reprint 2025-26 106 chemistry Interestingly, sulphur also forms many affinity, is the negative of the energy change compounds in which the octet rule is obeyed. accompanying electron gain. In sulphur dichloride, the S atom has an octet Obviously ionic bonds will be formed of electrons around it. more easily between elements with comparatively low ionization enthalpies and elements with comparatively high negative value of electron gain enthalpy.Other drawbacks of the octet theory Most ionic compounds have cations• It is clear that octet rule is based upon derived from metallic elements and anions the chemical inertness of noble gases. from non-metallic elements. The ammonium However, some noble gases (for example + ion, NH4 (made up of two non-metallic xenon and krypton) also combine with elements) is an exception. It forms the cation oxygen and fluorine to form a number of of a number of ionic compounds. compounds like XeF2, KrF2, XeOF2 etc. Ionic compounds in the crystalline • This theory does not account for the shape state consist of orderly three-dimensional of molecules. arrangements of cations and anions held • It does not explain the relative stability of together by coulombic interaction energies. the molecules being totally silent about These compounds crystallise in different crystal structures determined by the size of the energy of a molecule. the ions, their packing arrangements and