Chemical_Bonding_and_Molecular_Structure.pdf

Chapter 2: Chemical Bonding and Molecular Structure

Institute of Lifelong Learning, University of Delhi

B.Sc (Prog.) 1st Year Paper No:CHPT -101

Unit No :1 Chapter No and Name: 2, Chemical Bonding and Molecular Structure

Fellow: Dr. V. C. Rao, Associate Professor Collge/Department: Sri Venkateswara College,University of Delhi

Author : Dr. Geetika Gandhi, Assistant Professor College/Department : Hindu College, University of Delhi

Reviewer: Prof. Pawan Mathur College/Department : Department of Chemistry, University of Delhi



2.1 Introduction

Structure and bonding lie at the heart of modern inorganic chemistry. We can deduce from chemical evidence that atoms combine to form larger units and the stability of these units is due to chemical bonds.

There are about 118 elements, but when the elements combine they can make a huge number of compounds. Some of them existed when the world began. Some have been made by men and women, either by accident or design. Bonding is a consequesnce of interaction of electrons in the outermost shells of atomic or ionic species involved. In this chapter, we shall encounter methods of explaining and predicting the bonding in a variety of compounds.

Why do chemical bonds form?

Chemical bonds form if the resulting arrangement of the atoms has lower energy than the separated atoms i.e., atoms combine to attain a state of lower energy (potential) than that in the isolated ones, e.g. H2, P4, S8, H2O, C6H12O6 etc. Various changes in energy that occur when bonds form results from the movement of the valence electrons (the electrons in the outermost shell) of atoms.

What holds atoms together in chemical compounds?

The forces that hold atoms together are called chemical bonds. A chemical bond is a manifestation of a force of attraction.

What is the nature of chemical bonds?

Atoms combine in a variety of ways. Mainly, three different types of bonds may be formed, depending on the electropositive or electronegative character of the atoms involved.

Ionic bond

It involves the complete transfer of one or more electrons from one atom to another and is characterized by a large difference in electronegativity. An ionic bond is formed between an electropositive and an electronegative element.

Covalent bond

It involves the sharing of a pair of electrons between two atoms and is characterized by a small difference in electronegativity. A covalent bond is formed between two electronegative elements or could be generated between a less electropositive and an electronegative element.

Metallic bond

It involves the free movement of valence electrons throughout the crystal and is also characterized by small difference in electronegativity. A metallic bond is formed between two electropositive elements.

Classification of chemical bonds based on the types of forces that hold the atoms together as shown in Fig. 2.1.



Figure 2.1: Classification of chemical bonds based on the type of forces that hold the atoms

Examples :

(i) Ionic bond NaCl, CaO (ii) Metallic bond Na, Cu, Alloys (iii) Hydrogen bond (NH3)n (H2O)n, (HF)n (iv) Dipolar (NF3)n (v) Polar covalent bond HF, H2O (vi) Nonpolar covalent bond a. simple molecules H2, Cl2 b. giant molecules C (diamond), SiC

2.2 Preliminary Survey

Classical theory

• In 1916, W. Kossel from Germany and G. N. Lewis from U.S. independently proposed theories of chemical bonding on the basis of the developments in the area of atomic structure. It was termed as electronic theory of valency. They attempted to explain the nature of bonds in ionic and nonpolar molecules. • A Lewis structure is a representation of covalent bonding using Lewis dot symbols in

which shared electron pairs are shown either as lines or as pairs of dots between two atoms and lone pairs are shown as pairs of dots on individual atoms. Only valence electrons are shown in a Lewis structure. In covalent bond formation, atoms go as far as possible towards completing their octets by sharing electron pairs. • Lewis octet rule:

Each atom shares electrons with neighbouring atoms to achieve a total of eight valence electrons. • Lewis electron-dot diagrams provide a good starting point for analysing the bonding in

molecules. These diagrams show the number of bonds between specific atoms and the resonance possibilities. A few examples of Lewis structures are given in Fig. 2.2.

Figure 2.2: Lewis structures

Limitations of octet rule

● The octet rule, though useful, is not universal. ● It fails to account for the stability of

(i) the molecules with incomplete octet on the central atom (BeCl2, BCl3) (ii) the molecules with expanded octet (PF5, SF6) (iii) odd-electron molecules (NO, NO2)

● It cannot account for the shape of a molecule (CO2 linear, SO2 bent). ● It does not mention anything regarding the relative stability of a molecule. ● Summarily, it may be concluded that the electronic theory of valence and the octet

rule are empirical in nature.

Modern theories

• Any description of bonding must be consistent with experimental data on bond lengths, bond angles and bond strengths. • Application of the quantum-mechanical approaches provide quantitative

understanding of the mechanisms of energy lowering in terms of electron behaviour.



• The number of atoms in a molecule, their ordering, their relative spacing, and the overall molecular shape are all fixed because the energy of the molecule is minimum (relative to isolated atoms) only for a particular number and arrangement of the constituent atoms. •

The magnitude of the bond energy is a measure of the strength of the bond.

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2.3 Ionic Bonding (Electrovalent Bonding)

The first explanation of chemical bonding was suggested by the properties of salts, substances now known to be ionic. The ionic bond is a consequence of electrostatic interaction between the oppositely charged ions that result from the transfer of one or more electrons from a less electronegative atom to a more electronegative atom. The atom that loses electrons becomes cation (positive ion), the atom that gains electrons becomes an anion (negative ion). Any given ion tends to attract as many neighbouring ions of opposite charge as possible. The formation of solid sodium chloride from sodium atom and chlorine atom is shown in Fig. 2.3.

Figure 2.3: Formation of Na+Cl- solid from sodium atom and chlorine atom

M (g) →M+ (g) + e- Ionization enthalpy X (g) + e- →X- (g) Electron gain enthalpy M+ (g) + X- (g) → MX (s) Lattice enthalpy

Ionic bonds will be formed more easily between elements with comparatively low ionization enthalpies and elements with comparatively high electron gain enthalpies.

We can represent electron transfer by the following equation

Na ([Ne] 3s1) + Cl ([Ne] 3s2 3p5) → Na+ ([Ne]) + Cl- ([Ne] 3s2 3p6)

As a result of the electron transfer, ions are formed, each of which has a noble gas configuration.

Characteristics of ionic solids

• Ionic compounds usually exist as crystalline solids. X-ray diffraction patterns of the electrovalent compounds have revealed that the constituent parts of the crystals are ions.

• Ionic bond is non-directional. • Ionic bonds are quite strong and hence ionic compounds have high melting

point/boiling point and are hard and brittle.



• Ionic compounds tend to have very low electrical conductivity as solids but conduct electricity quite well when molten or dissolved in water. This conductivity is attributed to the presence of oppositely charged ions, which are free to move under the influence of an electric field.

• Ionic compounds are soluble in polar solvents like water and insoluble in nonpolar solvents like benzene and carbon tetrachloride.

Structure of ionic solids

Ionic solids consist of positive and negative ions arranged in a manner so as to acquire minimum potential energy.

• The most stable arrangement is the one in which the ions are in contact with each other and arranged in a symmetrical manner (close packed geometry).

• Lattice coordination number is the number of immediate neighbouring oppositely charged ions.

• The size factors largely determine the geometry of the structures and coordination number.

• The radius ratio accounts for the geometry of many ionic solids (Table 2.1).

• A large number of ionic solids exhibit one of the following structures. i. rock salt type, NaCl ii. wurzite, ZnS iii. zinc blende, ZnS iv. fluorite, CaF2 v. anti fluorite, CsCl vi. rutile, TiO2

Table 2.1 Radius Ratio and Geometry of Ionic Solids Anion

Arrangement Coordination

Number Limiting radius ratio,

Examples

Linear 2 0 - 0.155 Uncommon among ionic solids

Triangular 3 0.155 - 0.225 Uncommon among ionic solids

Tetrahedral 4 0.225 - 0.414 ZnS

Octahedral 6 0.414 - 0.732 NaCl, TiO2

Cubic 8 0.732 – 1.0 CsCl, CaF2

2.3.1 Lattice Enthalpy (Lattice Energy) Lattice

We have seen in a qualitative manner why a sodium atom and chlorine atom might be expected to form an ionic bond. Energy changes involved in ionic bond formation helps to understand that why certain atoms form ionic bond and others do not. If atoms come together and bond, there should be a decrease in energy, because a bonded state should be more stable and therefore at a lower energy level as shown in Fig 2.4.



Figure 2.4: Potential Energy Diagram for ionic bond At a certain critical distance between the atoms (as shown in Fig.2.4) the energy drop is maximum that results in stability. If

the distance between the atoms is decreased further it results in repulsion.

The attraction of oppositely charged ion does not stop with the bonding of pairs of ions. The maximum attraction of ions of opposite charge with the minimum repulsion of ions of the same charge is obtained with the formation of crystalline solid. Then even more energy is released. Clustering of ion pairs to form an ionic solid and progressive release of energy is shown in Fig 2.5.

Figure 2.5: Clustring of ion pairs to form ionic solid

Lattice enthalpy of an ionic compound is defined as the energy released when one mole of the compound is formed in the regular lattice structure from requisite number of ions (1 mole of positive ions and 1 mole of negative ions) in the gaseous state. The lattice enthalpy of an ionic solid is also defined as the energy required for seperating completely. one mole of a solid ionic compound into its gaseous constituent ions. Lattice enthalpy cannot be measured experimentally. Lattice enthalpies are calculated from experimental data using the Born-Haber cycle.

• The force of attraction, , between two ions carrying unlike charges ‘’ separated by a distance, , is given by Coulomb’s law.Fer

• The corresponding potential energy would be obtained by computing the work done in bringing the charges to this distance from infinity. Thus,

• The negative sign indicates that this amount of energy is released by the system resulting in lowering of potential energy, which we expect when stable bonding has occurred.

Clustering of Ion- Pairs to form Ionic Solids



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2.3.2 Born-Lande Equation

Born-Lande Equation

• Consider NaCl crystal having face centered cubic (FCC) structure. • Eight Na+ ions form the corners of a cube and six more are centered on the faces

of the cube. • The Cl- ions are similarly arranged so that NaCl lattice consists of two

interpenetrating FCC lattices as shown in Fig 2.6.

Figure 2.6: The crytal structural of NaCl (Rock Salt) The quantitative evaluation of lattice energy of an ionic crystal is determined by coulombic interactions between all of its ions (both coulombic attractions and repulsions), Ec and repulsive forces because of the interpenetration of charge clouds, ER . ETotal = Ec + ER

The first theoretical interpretation of lattice enthalpy was given by Born and Lande. They derived an equation for the calculation of lattice enthalpy of an ionic compound.

Lattice enthalpy is defined as positive; ∆H for this process is negative.

Where U0 = Lattice enthalpy r0 = Equilibrium internuclear distance A = Madelung constant (this takes care of interaction with all other ions besides the nearest neighbours) NA = Avagadro constant n = Born’s exponent (it depends on the electronic configuration of the ions. Its value may be derived either theorehically from the measurement of the compressibility of the solid) π = Constant (3.14159) ε0 = Permittivity of free space Z+ = Charge on the positive ion Z- = Charge on negative ion e = Charge on an electron

For sodium chloride, the various factors are A = 1.74756 NA = 6.022 x 1023 ions pairs per mol Z+ = +1 Z- = -1 e = 1.60218 x 10-19 C ε0 = 8.854188 x 10-12 C2 J-1 m-1 n = 8 r0 = 2.814 x 10-10 m π = 3.14159



= -755.2 kJ mol-1 The Born-Lande equation gives a calculated value of lattice enthalpy, U0 = -755.2 kJ mol-1 for sodium chloride, which is close to the experimental value of -770 kJ mol-1 at 25° C. For more precise work, several other functions have been suggested for repulsion energy. Other variables like van der Waals forces, zero point energy and correction for heat capacity are included. The refined value for lattice enthalpy is -757.5 kJ mol-1.

The values of lattice enthalpy calculated by means of the above equation have been found to be in good agreement with those obtained experimentally as shown for some of the compounds in the Table 2.2.

Table 2.2 Lattice Enthalpy of Some Compounds

Compound Lattice Enthalpy (kJ mol-1)

Experimental Theoretical

AgCl -895 -849

CaF2 -2

The Madelung constant depends on the coordination number of each ion and geometric arrangement of ions in the crystal lattice. Hence, lattice enthalpy and stability of an ionic crystal is directly proportional to the Madelung constant. Values of Madelung constants for different ionic crystals are given in Table 2.3.

.

Table 2.3 Madelung Constant Values for Some Common Ionic Solid

Structure Formula Coordination number A

Sodium chloride NaCl Na+(6); Cl- (6) 1.7475

Cesium chloride CsCl Cs+ (8); Cl-(8) 1.7627

Zinc blend ZnS Zn2+(4); S2- (4) 1.6380

Wurzite ZnS Zn2+(4); S2-(4) 1.6413

Fluorite CaF2 Ca2+ (8); F-(4) 5.0388

Example

Calculate the value of Madelung constant for MgO from the following data. r0 = 2.10 x 10-10 m n = 7 U0 = -3940 kJ mol-1

Solution:

In case of MgO, the charges on cation and anion are +2 and -2 respectively.



Substituting the values in Born – Lande equation, we have

-3940 kJ mol-1

Therefore, A = 1.74.

Factors Influencing the Magnitude of Lattice Enthalpy

The lattice enthalpy is useful in correlating properties of ionic substances because the formation or destruction of the crystal is frequently more important step in reactions involving ionic substances. Some properties of ionic compounds can be explained on the basis of their lattice enthalpy values.

The higher the charge on cation and anion, the greater would be the magnitude of the lattice enthalpy.

Na+F - < Mg2+(F -)2 < Mg2+O2- U0 ( kJ mol-1) 914.2 2882.0 3895.0

Smaller the size of ions, the smaller would be inter-ionic distance, the higher would be the value of lattice enthalpy.

LiF > NaF > KF > RbF > CsF U0 ( kJ mol-1) 1034 914.2 812.1 780.3 743.9

LiF > LiCl > LiBr > LiI U0 ( kJ mol-1) 1034 840.1 781 718

Down the group, lattice enthalpy decreases as the size of the cation increases.

BeO > MgO > CaO > SrO > BaO U0 ( kJ mol-1) 4541 3895 3520 3325 3108

The greater the lattice enthalpy, the more stable is the ionic compound.

CaCl2 (2200 kJ mol-1) > CaCl (720 kJ mol-1)

Ionic compounds with high lattice enthalpy require a greater input of thermal energy to breakdown the crystal lattice. Consequently, the greater the strength of the ionic solid, higher will be its melting point.

LiF > LiCl > LiBr > LiI U0 (kJ mol-1) 1034 840.1 781 718

m.p. (°C) 870 613 597 446 The lattice enthalpy affects the solubility of the ionic compounds.

1. For a solid to dissolve in a solvent, the strong forces of attraction between its ions (U0) must be overcome.

2. The solvation of ions is referred to in terms of solvation energy,which is always exothermic.

3. M+(g) + aq → M+(aq) + hydration energy 4. X-(g) + aq → X-(aq) + hydration energy

1. These exothermic solvation energies have their origin in the electrostatic interaction between the polar solvent molecules and the solute ions.

2. Since cations are smaller than anions, the positive field of a cation will be greater than the negative field of an anion, so that the solvation energies of cations generally exceed those of anions.

3. An ion with high value of the ionic potential will tend to form the solvated ion more easily than the ion with a smaller value of ionic potential. Ionic potential is given by



Ions with small size and high charge get extensively hydrated.

(a)

Na+ Mg2+ Al3+ charge (+) (2+) (3+)

ΔHhydration (kJ mol-1) 422 1953 4694

(b)

Li+ Na+ K+ Rb+ Cs+ size (pm) 60 95 133 148 169 ΔHhydration(kJ mol-1) 531 422 338 318 280

Ionic crystals are generally soluble in polar solvents like water and insoluble in non-polar solvent such as carbon tetrachloride. As a general rule, for a solid to dissolve in a particular solvent, its solvation energy (ΔHhydration refers to hydration energy) should be greater than the lattice energy of that solid. solvation energy > lattice energy ….. salt dissolves in the solvent solvation energy < lattice energy ….. salt does not dissolve in the solvent Lithium chloride and lithium bromide are soluble in water since the hydration energy is greater than lattice energy in both the cases.

LiCl LiBr

∆Hhydration 883 854

U0 (kJ mol-1) 840 781

• Silver chloride and Silver bromide are insoluble in water since the hydration energy is smaller than lattice energy in both the cases.

AgCl AgBr ∆Hhydration 848 815

U0 (kJ mol-1) 895 877

Some ionic compounds like sulphates and phosphates of barium and strontium are insoluble in water inspite of being ionic. This can be attributed to the high lattice enthalpies associated with these compounds due to polyvalent nature of both cation and anion. In these cases, hydration of ions fails to liberate sufficient energy to offset the lattice enthalpy.

2.3.3 The Born-Haber Cycle

Direct calculation of lattice enthalpy is quite difficult because the required data is often not available. Therefore, lattice enthalpy is determined indirectly by the use of the Born Haber cycle. It is based on Hess’s law. Hess’s law states that the enthalpy of a reaction is the same, whether it takes place in a single step or in more than one step.

The formation of an ionic compound, MX, shown in Fig 2.7, may occur either by direct combination of the elements or by a stepwise process involving vaporisation of elements, conversion of the gaseous atoms into ions and the combination of the gaseous ions to form the ionic solid.



Figure 2.7: A Schematic Representation of Born-Haber Cycle for the Formation of Solid MX

∆H1 = enthalpy of atomization of the metal ∆H2 = enthalpy of atomization of the non-metal ∆H3 = ionization enthalpy ∆H4= electron gain enthalpy ∆H5 = lattice enthalpy

According to Hess’s law ∆fH = ∆H1+ ∆H2+ ∆H3+ ∆H4+ ∆H5 ∆H1, ∆H2and ∆H3 are endothermic while ∆H4 (first electron gain enthalpies are exothermic and second electron gain enthalpies are endothermic) and ∆H5 are exothermic.

The lattice enthalpy of a solid can be calculated with the help of other thermochemical quantities which can be measured experimentally. A schematic representation of Born-Haber cycle for the formation of solid NaCl is given in Fig 2.8.

Figure 2.8: A Schematic Representation of Born-Haber Cycle for the Formation of Solid NaCl

Let us use Born-Haber cycle for determining the enthalpy of formation of NaCl. The standard enthalpy change, ΔfH for the following reaction is -410.9 kJ mol-1.

Na(s) + ½ Cl2 (g) → NaCl(s)

Here, the formation of NaCl can be envisaged in five separate steps. The sum of enthalpy changes for these steps being equal to the enthalpy change for the overall reaction.

Na(s) + ½ Cl2 (g) → NaCl(s) ΔfH =?

Na(s) → Na(g) ∆H1= 108.4 kJ mol-1 ½Cl2 (g) → Cl (g) ∆H2 = 120.9 kJ mol-1 Na (s) → Na+ (g) + e- ∆H3 = 495 kJ mol-1 ½ Cl2 (g) + e- → Cl- (g) ∆H4 = -355 kJ mol-1 Na+ (g) + Cl- (g) → NaCl(s) ∆H5 =-757.3 kJ mol-1

Applying Born-Haber cycle, we have



[ΔfH]theoretical = +108.4 kJ mol-1 + 120.9 kJ mol-1 + 495.4 kJ mol-1 -355.5 kJ mol-1 – 757.3 kJ mol-1

= - 387.6 kJ mol-1 [ΔfH]experimental = - 410.9 kJ mol-1

• Close agreement between theoretical values (assuming ionic bonding) and experimental values indicates that the assumption that bonding is ionic is infact true.

• Born-Haber cycle is mainly used for the evaluation of • Lattice enthalpies • Electron affinities • Proton affinities and • Heats of formation.

Biographic Sketch

Biographic Sketch

Example

Calculate the lattice enthalpy of KCl from the following data by the use of Born-Haber cycle.

Enthalpy of sublimation for K(s) → K(g) ∆H1 = + 89 kJ mol-1

Enthalpy of dissociation for

Cl2 (g) → Cl (g) ∆H2= + 122 kJ mol-1 Ionization enthalpy for K (g) → K+ (g) + e- ∆H3= + 425 kJ mol-1

Electron gain enthalpy for

Cl2 (g) +e- → Cl- (g) ∆H4= - 355 kJ mol-1

Enthalpy of formation for

K(s) + Cl2 (g) → KCl (s) ∆Hf = -438 kJ mol-1

Solution:

According to Hess’s law, we have

∆fH= ∆H1 + ∆H2 + ∆H3 +∆H4 + ∆H5 -438 kJ mol-1 = (+89 + 122 + 425 – 355) kJ mol-1 + ∆H5

Hence, Lattice enthalpy of KCl, ∆H5 is – 719 kJ mol-1.

Example

Assuming, hypothetical NaCl2 would crystallize in the fluorite structure (A=2.52), calculate enthalpy of formation of NaCl2. Comment on the calculated value of ∆fH.

Enthalpy of sublimation of Na (s), ∆H1= + 109 kJ mol-1 Enthalpy of dissociation of Cl2 (g), ∆H2 = + 247 kJ mol-1 First ionization enthalpy of Na (g), ∆H3

I= + 494 kJ mol-1 Second ionization enthalpy of Na+ (g), ∆H3

II = + 4561 kJ mol-1 Electron gain enthalpy of Cl (g), ∆H4= - 355 kJ mol-1 Lattice enthalpy , ∆H5= -2155 kJ mol-1

Solution:



According to Hess’s law, we have

∆Hf = ∆H1 + ∆H2 + ∆H3 +2∆H4 + ∆H5 = (+109 + 247 + 494 + 4561 - 710 – 2155) kJ mol-1 = +2546 kJ mol-

Since ∆fH is positive, NaCl2 does not exist. The extra stabilization of the lattice is insufficient to compensate for the very large second ionization enthalpy of Na.

Summary of ionic bonding

2.3.4 Polarization and Polarizability

Anions are large in size than cations and therefore, their electron clouds are less tightly held. When two oppositely charged ions approach each other closely, the positively charged cation attracts the outermost electrons of the anions and repels its positively charged nucleus. This results in the distortion or polarization of the anion. This is illustrated in Figures 2.9 (a), (b) and (c) and 2.10. When a large and soft anion comes under the influence of small cation, the cation is able to polarize the anion. Due to the compact charge cloud of the cation, polarization of the cation is very small.

Figure 2.9: (a) Far apart: no influence on each other (b) Closer together: the negative ion is polarized by the positive ion (c) Even closer: the charge cloud of the negative ion merges with that of the positive ion; covalence

results



• The power of an ion to distort the other ion is known as its polarizing power.

• The polarizing power of a cation is proportional to its ionic potential, .

• The power of an ion to distort the other ion is known as its polarizing power. • The polarizing power of a cation is proportional to its ionic potential, change/ size • The large negative ion is highly polarizable.

Polarization and polarizablity


• As a consequence of polarization or deformation, there occurs a transition of ionic character to a covalent character. With increasing polarization, the charge clouds of neighbouring cations and anions would ultimately tend to merge with one another, as is observed in a covalent compound.

Figure 2.10: Diagram showing the polarization of a negative ion by a small positive ion

Fajans explained the trend of attaining covalent character by ionic compounds as a consequence of polarization in terms of Fajans rules (1923).

• In terms of the rules of Fajans

1. A small positive ion favours covalence. 2. In small ions the positive charge is concentrated over a small area. This makes

the ion highly polarizing, and very good at distorting the negative ion. 3. A large negative ion favours covalence. 4. Large ions are highly polarizable, that is easily distorted by the positive ion,

because the outermost electrons are shielded from the charge on the nucleus by filled shells of electrons.

5. Large charges on either ion, or on both ions, favour covalence. 6. This is because a high charge increases the amount of polarization. 7. Polarization, and hence covalence, is favoured if the positive ions does not have

noble gas configuration. A noble gas configuration is most effective at shielding the nuclear charge, so ions without the noble gas configuration will have high charges at their surfaces, and thus be highly polarizing.

The significance of these rules is that the induced covalent character in ionic compounds increases with decrease in size of the cation or increase in charge on the cation and an increase in size and charge of the anion. Cations with pseudo-noble gas configuration (18 electrons in the outer shell) exert greater polarizing power than cations with noble gas configuration (8 electrons in the outer shell).

Biographic

For example, cations Cu+ (3s23p63d10) and Na+(2s22p6) have similar ionic radii but the former is more polarizing and induces higher covalent character than the latter. This is due to the additional d-electrons in Cu+ provides inadequate shielding and therefore, the nuclear charge causes greater deformation of anion. The corresponding increase in induced covalent character in ionic compounds is reflected in the decreasing melting



points, solubility in polar solvents and decomposition temperatures of alkaline earth carbonates.

Effects of polarization

• Melting points decrease with increasing covalent character. • NaCl (800°C), CaCl2 (772°C) • NaBr (747°C), MgBr2 (700°C), AlBr3 (97.5°C) • LiF (870°C), LiCl (613°C), LiBr (547°C), LiI (446°C) • BeCl2 (405°C), CaCl2 (772°C) • Solubility in polar solvents decreases with increasing covalent character. • AgF, which is quite ionic, is soluble in water, but the less ionic AgI is insoluble.

Increasing covalence from fluoride to iodide is expected and decreased solubility in water is observed likewise, KI is soluble in ethyl alcohol, whereas, KCl is insoluble.

• CuCl, AgCl are insoluble in water, whereas, NaCl is highly soluble in water.

MCO3 → MO + CO2

• Stability of carbonates can often be rationalized in terms of the polarizing power of a particular cation. In the alkaline earth carbonates, for example, there is a tendency towards decomposition with evolution of carbon dioxide.

Small size cations show greater tendency to polarize the carbonate anion (CO32-) into an

oxide (O2-) and CO2. Hence, as the size of cation increases polarizing power of the cation decreases and the thermal stability of metal carbonates increases. BeCO3 (unstable) < MgCO3 (350°C) < CaCO3 (900°C) < SrCO3 (1290°C) < BaCO3 (1360°C).

2.3.5 Ionic Character in Covalent Compounds and Dipole Moment

Covalent bonds having partial ionic character are referred to as polar covalent bonds. The polarity of a bond, such as that in HF is characterized by a separation of electric charge (partial charge, δ). δ+ δ- H–F

The degree of polarity in a covalent bond can be expressed in terms of the bond moment, that is, the product of the charge, q and the internuclear distance, r, since each bond amounts to a dipole. µ = q x r = (4.8 x 10-10 esu) (10-8 cm) = 4.8 x 10-18 esu-cm = 4.8 D (1D =10-18 esu-cm)

In SI units, unit of charge is Coulombs (C) and that bond length in meters (m), therefore µ has units of C m. µ = (1.6022 x 10-19 C) (10-10m) = 1.6022 x 10-29 C m = 4.8 D (1 D = 3.336 x 10-30 Cm)

• The average polarity of a given species over a period of time is measured by its permanent dipole moment (), which is designated as a vector, pointing from the centre of positive charge to the centre of negative charge with a positive charge at one end. µ

• The permanent dipole moments of polar diatomic molecules are same as their bond moments. The permanent dipole moments of polyatomic molecules, however, are determined by both the bond moments and lone pair moments.

• A molecule will have a dipole moment if the summation of all of the individual bond moment vectors is nonzero.We can sometimes relate the presence or absence of a dipole moment in molecules to its molecular geometry. For



example, consider the carbon dioxide molecule, each carbon-oxygen bond has a polarity in which the more electronegative oxygen has a partial negative charge.

δ- δ+ δ- O = C = O

The two bond moments of equal magnitude but opposite direction cancel each other, giving rise to a net dipole moment of zero for the molecule. For comparison, consider water molecule. The bond moments point from the hydrogen atoms towards the more electronegative oxygen.

Here, however, the two bond moments do not points directly towards, or away from each other. As a result, they add together to give a nonzero dipole moments for the molecule.

The dipole moment of H2O has been observed to be 1.85 D. If the water molecules were linear, the dipole moment would be zero. Figs 2.11 and 2.12, and Table 2.4 give the geometries and dipole moments of some molecules.

Biographic

Table 2.4 Dipole Moments of Some Polar Molecules

Molecule Geometry Dipole Moment (D)

HF Linear 1.92

HCl Linear 1.08

HBr Linear 0.78

HI Linear 0.38

H2O Bent 1.85

NH3 Pyramidal 1.47

SO2 Bent 1.60

Table 2.5 summarizes the relationship between the molecular geometry and dipole moment for the molecules of type AXn in which all X atoms are identical. The geometries in which A–X bonds are directed symmetrically about the central atom (for example linear, trigonal planar, and tetrahedral) give molecules of zero dipole moment, that is the molecules are nonpolar. Those geometries in which the X atoms tend to be on one side of the molecule (for example bent and trigonal pyramidal) can have nonzero dipole moments, that is, they can give polar molecules.



Figure 2.11: Molecules with zero dipole moment

Figure 2.12: Molecules with net dipole moment

The NH3 and NF3 molecules present an interesting case in relation to the resultant dipole moment. Although fluorine is more electronegative than nitrogen the resultant dipole moment of NH3 (4.90 x 10-10C m) is greater than that of NF3 (0.80 x 10-30 C m) in both cases the central nitrogen atom has a lone pair whose bond moment points away from the nitrogen atom.

Table 2.5 Relationship Between Molecular Geometries and Dipole Moment

Formula Molecular Geometry Dipole Moment

AX Linear Can be nonzero

AX2 Linear; Bent

Zero; Can be nonzero

AX3 Trigonal planar; Trigonal pyramidal; T-shape

Zero; Can be nonzero; Can be nonzero

AX4 Tetrahedral; Square planar; See saw

Zero; Zero; Can be nonzero

AX5 Trigonal bi-pyramidal; Square pyramidal Zero; Can be nonzero

AX6 Octahedral Zero

In NH3 the resultant bond moments reinforce the moment of lone pairs,

resulting into a larger net dipole moment. In NF3, the resultant of the bond moments (fluorine is the negative end) act in opposition to the lone pair moment, cancel each other and hence, the net dipole moment of the NF3 molecule is lowered. Figure 2.13 shows the net dipole moments in NH3 and NF3.



Figure 2.13: Molecules with net dipole moment

Percentage of Ionic Character

• The ionic character in a covalent bond may be estimated from an empirical relationship between ionic character and electronegativity difference. Hanny and Smith (1946) proposed a simple and the most acceptable formula for the calculation of percentage ionic character. Hanny and Smith formula Percentage ionic character = 16 (χA ― χB) + 3.5 (χA ― χB)2 χA and χB are the electronegativities of the bonding atoms A and B.

Example Calculate the percentage of ionic character in HCl. The experimental dipole moment of HCl is 1.03 D and bond distance in HCl is 1.27 x 10-10 m.

Solution:

µobs = 1.03 D = (1.03)( 3.34 x 10-30) C m µcal = q x r = (1.6 x 10-19 C) (1.27 x 10-10 m)

Percentage ionic character

Therefore, HCl is 17 % ionic.

There are several different theories that explain the electronic structures and describes the shapes of different molecules

Example

The electronegativities of hydrogen and chlorine are 2.1 and 3.0. Calculate percentage ionic character in HCl.

Solution:

Percentage ionic character = 16 (χA ― χB) + 3.5 (χA ― χB)2 = 16 (3.0-2.1) + 3.5 (3.0-2.1)2=17.2

Therefore, HCl is 17.2 % ionic. In general, a bond corresponding to an electronegativity difference of 2.1 is nearly 50% ionic.

• The ionic character of a bond may be estimated in simple cases from its dipole moment values Percentage ionic character =



where µ = Dipole moment and µcalculated= Distance x Charge

The study of dipole moment is very useful for information on:

• polor and nonpolar character of molecules • extend of bond polarity or percentage ionic character • shapes of molecules • geometrical substitution on planar rings

2.4 Covalent Bonding

How do bonds form between atoms of the same or similar elements? How can we describe the bonds in substances such as H2, Cl2, CO2 and literally millions of other nonionic compounds? The answer is that the bonds in such compounds are formed by sharing electrons between atoms rather than by the transfer of electrons from one atom to another.

Characteristics of covalent compounds

• They generally exist in gaseous or liquid phase • They have low melting point/boiling points • They are poor conductors of electricity • They are soluble in nonpolar organic solvents • Covalent compounds have definite molecular geometry.

There are several different theories, which explain the electronic structures and describe the shapes of different molecules.

2.4.1 Lewis Theory: The Octet Rule

For many light atoms a stable arrangement is attained when the atom is surrounded by eight electrons. A formulation of this type indicates only the importance of a shared pair of an electron but gives no information as to how sharing is effected or as to the nature of the bond.

Theoretical approaches and interpretations

The characteristics of covalent compounds suggest that an increase in electronic charge density between bonded atoms occurs. This increase has been rationalized in terms of two somewhat different theoretical approaches, each of which is the result of approximate solutions of appropriate wave equations.

• The valence-bond, or directed bond approximation, which considers covalent interaction to occur between two atomic species as a consequence of the overlap of two atomic orbitals of the same or nearly the same energy and proper spatial orientation, each containing a single electron. As a result of this overlap the charge density in the internuclear region increases and serves to hold the two nuclei together and we say a bond is formed between atoms.

• The molecular-orbital or undirected-bond approximation, which involves delocalized molecular orbitals spread over the whole molecule. The original atomic orbitals lose their identities.

The valence-bond approximation is modular in concept and lends itself to representation by models or drawings depicting models, whereas the molecular-orbital approximation is energy oriented and describes bonding in terms of energy states. Both these methods make use of variation principle, a mathematical technique used to calculate the ground state energy of a system.

2.4.2 Heitler-London Theory (Valence Bond Approach)



The formation of a chemical bond of any type is possible only if the approach of the atoms towards one another is accompanied by decrease in energy.

According to valence bond theory, covalent bond may be seen as accumulation of high charge density in the internuclear region resulting from the overlapping of atomic orbitals. The strength of the bond depends on the extent of the overlapping-- greater the overlapping stronger the bond.

Consider the formation of the covalent bond between two hydrogen atoms to give the H2 molecule. As the atoms approach one another, their 1s orbitals begin to overlap. Each electron can then occupy the space around both atoms. In other words, the two electrons can be shared by the atoms. The electrons are attracted simultaneously by the positive charges of the two hydrogen nuclei. This attraction that bonds the electrons to both nuclei is the force holding the atoms together.

It is interesting to see how the potential energy of the atoms changes as they approach and then bond. Fig 2.14 shows the potential energy of the atoms for various distances between the nuclei. As the atoms approach (moving from right to left on the potential energy curve), the potential energy gets lower and lower. This continues till a certain distance called as the bond length and on further decreasing the distance between the two atoms, the repulsive forces become predominant and the energy increases.

Figure 2.14: The potential energy curve for the formation of H2 molecule as a function

of internuclear distance Now imagining the process to be reversed, energy must be added to seperate the atoms in the molecule from their normal bond length to infinite distance. This energy that must be added is called the bond dissociation energy. Higher the bond dissociation energy, the stronger would be the bond.]

In the case of hydrogen molecule, the distance between the two hydrogen atoms corresponding to minimum energy is 74 pm and the decrease in potential energy in the formation of H2 molecule has been found to be 431.4 kJ mol-1. Therefore, H2 molecule would be much more stable than hydrogen atoms due to decrease of energy.

Heitler-London proposed quantum-mechanical treatment of the hydrogen molecule. According to this theory, the calculated bond distance is 74.9 pm and the decrease in potential energy is 388 kJ mol-1. Introduction of sufficient parameters can improve the wave function to any desired accuracy, giving rise to the bond distance 74 pm and potential energy 431.4 kJ mol-1.

By making use of the concept of hybridization, VB theory, succeeds in accounting for the principles of molecular geometry. By introducing the idea of resonance, it rationalizes the chemical properties of many molecules.

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Types of Overlapping of Atomic Orbitals and Orbital Diagrams



Different types of overlapping which we come across are

i. overlappings-s ii. s-p overlapping iii. pz-pz overlapping iv. px-px overlapping v. py-py overlapping vi. p-d overlapping vii. d-d overlapping, etc.

A sigma bond (σ) is formed by the overlap of atomic orbitals along the internuclear axis while a pi bond is formed by the lateral (sideways) overlap of atomic orbitals. Sigma bond is a stronger bond because the extent of overlap is quite large. Pi bond is a weaker bond because the extent of overlapping is small.

Hydrogen fluoride molecule forms through s-p overlap. The half filled 2pz orbital of fluorine overlapps with half filled 1s orbital of hydrogen atom resulting in the formation of sigma bond. The formation of sigma bond in hydrogen fluoride molecule is shown in Fig 2.15.

Figure 2.15: Formation of a sigma bond

Formation of a pi bond occurs if a sigma bond is already present i.e., it cannot be present alone. Formation of pi bond is illustrated in the formation of a nitrogen molecule. Electronic configuration of nitrogen is 2s22px

12py12pz

1. Thus there are three p orbitals having unpaired electrons, the 2pz orbital of one nitrogen atom overlaps with 2pz orbital of the other nitrogen atom forming a sigma bond. The 2px

1 and 2py1 of one

nitrogen atom overlap with 2px1 and 2py

1 of the other nitrogen atom laterally to form two pi bonds. Thus nitrogen atom has one sigma bond and two pi bonds i.e., a triple bond. The formation of one sigma bond and two pi bonds in nitrogen molecule are shown in Fig 2.16.

Figure 2.16: Formation of N2 molecule

Although a simple orbital overlapping concept is able to describe the formation of bonds in simple molecules but fails in the case of molecules like BeF2, BF3, CH4, PF5, SF6, etc. Let us discuss the linear geometry of BeF2. The electronic configuration of beryllium (Z=4) is 1s22s2. According to the atomic orbital overlap concept, beryllium should behave like noble gas since it has no half filled orbital. But beryllium forms a number of compounds like BeF2 and BeH2 in which it is bivalent. In order to explain these anomalies and describe the geometries of covalent molecules, we make use of new concept called hybridization.



2.4.3 Concept of Hybridization

Linus Pauling in 1931 introduced the idea of hybrid orbitals. Hybridization is the mixing of atomic orbitals in an atom (usually a central atom) to generate a set of new atomic orbitals called hybrid orbitals. Hybrid orbitals are used to form covalent bonds. Hybridization is a concept and takes place in chemist calculations not in actual molecules. We accept hybridization not because of its objective reality but because it gives results that are consistent with our knowledge of molecular bonding and molecular geometry.

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Rules of hybridization

• Hybridization is a process of mixing of orbitals on a single atom (or ion). • Hybridization is not a ‘predictive’ tool but simply reproduces observed shapes;

they ‘describe’ not ‘explain’ experimental facts. • Only orbitals of similar energies can be mixed to form good hybrid orbitals. • The number of orbitals mixed together always equals the number of hybrids

obtained. • In hybridization, we mix a certain number of orbitals, not a number of

electrons. The electrons are arranged in the hybrid orbitals. • Most hybrids are similar, but they are not necessarily identical in shape; they

differ from one another largely in orientation in space. • Since s orbitals are directionless in xyz space, they add no direction when

contributing to hybrids. They add “plumpness” only. • Other orbitals with pronounced direction in space (p, d, etc) determine the

directional properties of hybrids. • The particular type of hybrid chosen for a structure discussion is determined by

the experimentally known geometry of the molecule i.e., observe bend angles of 120° should hint of sp2 hybrids, linear systems of sp hybrids, and tetrahedral shapes or 109° bond angles of sp3 hybrids.

The concept of hybridization is described in the following examples. The linear geometry of BeF2 can be described by assuming Be to be sp hybridized. The two sp hybrid orbitals overlap with the two 2pz orbitals of fluorine to form two covalent bonds.

The electronic configuration of Be atom in its ground state is 1s22s2. The promotion of 2s electron to 2p orbital results in an excited state configuration of Be, i.e; 1s22s12pz

1. It is then postulated that the s and p orbitals of Be mixed with each other i.e., hybridised to give identical orbitals i.e., (orbitals of equivalent energy)(Figure 2.17, 2.18 and 2.19).

Figure 2.17: sp hybridization for Be

Figure 2.18: Shape of a sp hybrid orbital



Figure 2.19: Formation of two sp hybrid orbitals by mixing s and p orbitals

Figure 2.20: Linear beryllium fluoride molecule resulting from overlapping of sp

hybrid orbitals of Be and 2pz orbital of fluorine atom.

Since in the formation of bivalent compounds of beryllium one s and one p orbital is involved in hybridization, it is called sp hybridization and the resulting orbitals are called hybrid orbitals. The electronic configuration of fluorine is 2s22px

2 py2 pz

1. The half filled pz orbital of each fluorine atom overlaps with each of the two half filled sp hybrid orbitals of beryllium to form two covalent bonds (Figure 2.20).

Thus, with the help of concept of hybridization, we are successful in describing the bonding as well as the geometry in BeF2 molecule.

• .The quantum mechanical wave functions for s and p atomic orbitals derived from Schrodinger wave equation can be mathematically combined to form a new set of equivalent wave functions called hybrid atomic orbitals

For sp hybridization, we have the following equations.

Ψsp1 = N (Ψs +Ψp)

Ψsp2 = N (Ψs - Ψp)

is the normalizing coefficient and Ψsp1 and Ψsp2 are the new diagonal or sp hybrid orbitals.

Energetics of Hybridization

As an illustration, we may consider the formation of methane molecule. The outer electronic configuration of carbon atom in the ground state is 2s2p2. Energy is required for the promotion of an electron 2s to 2p.



Figure 2.20: Linear beryllium fluoride molecule resulting from overlapping of sp

hybrid orbitals of Be and 2pz orbital of fluorine atom.

Energy is released in the formation of covalent bonds involving sp3 hybrid orbitals. Formation of hybrid orbitals of equivalent energy is shown in Fig. 2.21

Figure 2.21: Formation of hybrid orbitals of equivalent energy

Figure 2.22: Formation of four sp3 hybrid orbitals by overlapping of one s and

three p orbitals The energy of the resulting hybrids is the weighted average of the participating atomic orbitals.

Esp3 = [Es + 3EP]

= = -1241 kJ mol-1

sp3d Hybridization

Non metal atoms like phosphorus (3s23p33d) can exhibit variable covalency due to availability of vacant 3d orbitals. The possibility of sp3d hybridization in phosphorus describes the formation and trigonal bipyramidal (TBP) geometry of PF5 molecule (Fig 2.23) and for PCl5 molecule (Fig 2.24).



Figure 2.23: TBP geometry of PF5 molecule resulting from sp3d hybridization of valence Shell orbitals of central P atom

sp3d hybrid orbitals are directed towards the corners of a trigonal bipyramid. They form three coplanar bonds with bond angles of 120º and two bonds at right angles to this plane, one above and one below.

Figure 2.24: Trigonal bipyramidal geometry of PCl5

sp3d2 or d2sp3 Hybridization

Sulphur hexafluoride (SF6) provides an example of sp3d2 hybridization.

Combination of one s, three p, and two d orbitals leads to six hybrid orbitals which are directed towards the corners of regular octahedron (Fig 2.25).

Figure 2.25: Octahedral geometry

for SF6 involving sp3d2 hybridization

Hybridization in Molecules Montaining Multiple Bonds

Let us consider the geometry of carbon dioxide, CO2 . The electronic configuration of carbon in ground state is 2s2 2px

1 2py1 and in the excited state is 2s1 2px

1 2py1 2pz

1. The outer electronic configuration of oxygen atom in ground state is 2s2 2px

2 2py1 2pz

1.



In the formation of CO2 molecule, hybridization of orbitals of carbon occurs only to a limited extent i.e.; sp hybridization is assumed. The two sp-orbitals of carbon overlap with 2pz orbitals of each oxygen atom to form two σ-bonds. The carbon atom is still left with two unpaired 2p electrons whose axes are perpendicular to each other and to the internuclear axes. These unhybridized orbitals of carbon (p orbitals) engage in the formation of π bonds with p orbitals of oxygen atom by the lateral overlap of these orbitals (Figs 2.26 and 2.27).

Figure 2.26: Linear geometry of CO2 molecule resulting from sp hybridization of carbon atom

Figure 2.27: Formation of CO2 molecule by the overlapping of sp hybrid

orbitals of carbon and two pz orbitals of two oxygen atoms as well as pπ- pπ overlapping.

We have seen that hybridization is a useful theoretical concept, as it helps us in describing many structural features of molecules. Hybrid orbitals and their geometries are shown in Fig 2.28 and summarized in Table 2.6.

Table 2.6 Hybrid Orbitals and Their Geometry

Hybridization Number of Hybrid Orbitals

Shape of Molecule Example

sp 2 Linear BeCl2

sp2 3 Triangular planar BCl3

sp3 4 Tetrahedral CH4

dsp2 4 Square planar [PtCl4]2-

sp3d 5 Trigonal bipyramid PCl5

sp3d2 6 Octahedral SF6

2.4.4 Valence Shell Electron Pair Repulsion Theory (VSEPR)

VSEPR theory was originally proposed by Sidgwick and Powel in 1940 and further developed and refined by Gillespie and Nyholm in 1957. VSEPR theory is a simple treatment for understanding the shapes of molecules. It is not exactly a model for explaining the formation of the bond or chemical bonding. It is an approach that can be



visualized as an extension of the simple concept of shared electron pair to rationalise and predict the geometry of a molecule that compares favourably with those determined experimentally (X-ray diffraction, neutron diffraction etc.)

Figure 2.28: Hybrid orbitals and their geometry

• The stereochemistry of the central atom in a molecule is determined by the repulsive interactions among all the electron pairs (eps) in its valence shells. The electron pairs may be bonded (bps) or lone pairs (lps) pairs.

• The number of electron pairs is ‘half’ of the summation of electrons present in the valence shell of the central atom and the electrons contributed by the combining atoms.

• Thus, in the case of CH4, NH3 and OH2 molecules, the number of electron pairs present around the central atom would be

• , , . • However, the number of bps are 4, 3 and 2 and lone pairs are 0, 1, and 2

respectively. • Electron pairs tend to minimize repulsions. If the central atom is surrounded by

only bond pairs, then the repulsions among bps are equal and the molecule would have a regular geometry. On the other hand, when the central atom is surrounded by both bps as well as lps, then the repulsions among them are unequal, which is of the order: lone pair - lone pair > lone pair - bond pair > bond pair - bond pair and the molecule would have a distorted or irregular geometry.

• Accordingly, the presence of one or more orbitals with lone pairs of electrons has the effect of altering the bond angles i.e., the molecules with lps of electrons do not retain regular geometry.

For the prediction of geometrical shapes of molecules with the help of VSEPR model, it is convenient to divide molecules into two categories

1. molecules in which the central atom has no lone pairs, i.e., surrounded by only bond pairs and

2. molecules in which the central atom has one or more lone pairs, i.e., surrounded by both bond pairs as well as lone pairs.

Tables 2.7 shows the arrangement of electron pairs about a central atom (A) and X represents the surrounding atom.



Table 2.7 Geometric arrangements of electron pairs around central atom

Molecule Number of electron pairs

Number of bond pairs Regular geometry Example

AX2 2 2 Linear BeCl2

AX3 3 3 Planar Trigonal BF3

AX4 4 4 Tetrahedral CH4

AX5 5 5 Trigonal bipyramidal PCl5

AX6 6 6 Octahedral SF6

Let us take an example wherein we take different systems containing four electron pairs with different combinations of lone pairs and bond pairs and observe their shape and bond angles. In CH4 molecule, all of the valance-shell electron pairs about the carbon atom are bonding and because all of the bonds are alike, we expect the CH4 molecule to have an exact tetrahedral geometry with bond angle 109.50. However, if one or more of the electron pairs is non bonding or if there are dissimilar bonds, all four valence-shell electron pairs will not be alike. Then we expect the bond angles to deviate from 109.50 and geometry becomes distorted.

.

Table 2.8 Molecular geometries of molecules with four electron pairs with different combinations of lone pairs and bond pairs resulting into irregular geometry.

Molecule Number of bond pairs

Number of lone pairs Molecular geometry Bond angles

CH4 4 0 Tetrahedral 109.5°

NH3 3 1 Trigonal pyramidal 107°

OH2 2 2 Angular 104.5°

Figure 2.29:

Molecular geometries of molecules with 4 electron pairs with different combinations of lone pairs and bond pairs resulting into irregular geometry.

Consider the trigonal pyramidal molecule, NH3. The lone pair on the nitrogen atom requires more space than the bonding pairs. Therefore, the N-H bonds are effectively pushed away from the lone pair, and the H-N-H bond angles become smaller than the tetrahedral value of 109.5°. Consequently, NH3 molecule has distorted tetrahedral or trigonal pyramidal geometry with a bond angle 107°. Similarly H2O molecule with two lone pairs has bent geometry with a bond angle 104° (Table 2.8 and Fig 2.29).

Central atom with five or six valence-shell electron pairs

Five electron pairs tend to have a trigonal bi-pyramidal (TBP) arrangement and six electron pairs tend to have an octahedral arrangement. In trigonal bi-pyramidal



geometry, the vertexes are not all equivalent (that is, the angles between the electron pairs are not all the same). Thus, the directions to which the electron pairs are directed are not equivalent. Two of the directions, called axial directions, form an axis through the central atom. The other three directions are called equatorial directions. The equatorial orbitals point towards the corners of the equilateral triangle that lies on a plane through the central atom, perpendicular (at 90º) to the axial directions. The equatorial directions are 120º from each other.

When one or more of the five electron pairs are lone pairs, the TBP geometry gets distorted. Consider the SF4, ClF3 and XeF2 molecules with one, two and three lone pairs on the central atoms respectively. Lone pairs in TBP geometry always occupy equatorial positions to minimise repulsions. Accordingly, sulphur tetrafluoride has see-saw geometry, chlorine trifluoride has T-shaped geometry and xenon difluoride has linear molecular geometry.

In case of sulphur tetraflouride, the central atom is surrounded by five sp3d hybrid orbitals. One of these contains a lone pair of electrons while the other four contain one unpaired electrons each of which ovrlap with p orbitals of fluorine atoms to form four S-F bonds. According to VSEPR theory, such a molecule with five electron pairs and repulsions among them should have a trigonal bipyramidal geometry with bond angles of 90° and 120°. However, due to the presence of a lone pair of electrons, there is a distortion in the geometry of SF4 molecule resulting in see-saw geometry (Fig 2.30).

Figure 2.30: Structure (see-saw) of

SF4 Molecule in which one pair (lps) of electrons occupy equatorial position

It may be noted that lone pair present in SF4 molecule can either occupy an equatorial position or an axial position as shown below in Fig. 2.31. Considering the postulate of VSEPR theory, that repulsions between electron pairs at angles greater than 115° apart are neglected, we will be able to assign the most stable geometry of SF4 molecule.

Figure 2.31: Possible geometries of SF4 molecule



Figure 2.32:Structure (T-shaped) of ClF3 molecule in which two lone pairs (lps)

occupy equatorial positions

As a rule, if lone-pair occurs in a trigonal bi-pyramidal geometry, the lp always occupies equatorial position to minimize the repulsions. Consequently, the molecule will have distorted trigonal bi pyramidal geometry.

Similar arguments indicate that ClF3 will have T-shaped geometry (Fig 2.32).

In sulphur hexafluoride, there are six electron pairs (all bonding pairs) around sulphur atom. Thus, it has an octahedral molecular geometry, with sulphur at the centre of the vertexes. In iodine pentachloride, IF5 (five bond pairs and one lone pair) the lone pair of iodine occupies one of the six equivalent positions in the octrahedral arrangement, giving a square pyramidal geometry. In xenon tertafluoride, XeF4 (four bond pairs, two lone pairs), the two lone pairs on xenon occupy opposite positions in the tetrahedral arrangement to minimize their repulsion. The result is a square planar geometry. Molecular geometries of molecules with a total of five and six electron pairs with different combination of lone pairs and bond pairs are summarized in Table 2.9.

Table 2.9 Table 2.9 Molecular Geometries of Molecules with a total of five and six electron pairs with different combinations of lone pairs and bond Pairs.

No. of electron pairs Shape Examples Total Bond pairs Lone pairs

5 5 0 trigonal bi-pyramidal PCl5, SnCl5- 5 4 1 see - saw TeCl4, SF4 5 3 2 T - shaped ClF3, BrF3 5 2 3 linear XeF2, ICl2- 6 6 0 octahedral SF6, PF6

- 6 5 1 square pyramidal IF5 6 4 2 square planar BrF4

-, XeF4

Limitations of VSEPR Theory

• It fails for most of the 14 electron systems. • The geometry of alkaline earth halides (vapour) is V-shaped, although there are

no lone pairs on the central atom. • Lone pairs in some cases are stereochemically active and in some cases

stereochemically inactive.

2.4.5 Hybridization and VSEPR Theory Together

The best way to describe the geometry of covalent molecule/ion is by combining both hybridization and VSEPR theory. Table 2.10 shows the geometries of some molecules in which the central atom is surrounded by only bond pairs (bps) of electrons. As already mentioned, the presence of one or more orbitals, containing lone pairs in the valance shell and the participation of unshared electron pairs (lps) in the hybridization scheme, causes the distortion in the regular geometry (Table 2.11 and Figures 2.33, 2.34, 2.35, 2.36, 2.37 and 2.38).



Table 2.10 Geometry of Covalent molecules involving different types of Hybrid orbitals of the central atom Molecule Type of Hybridization

Involved Number of

Electron Pairs (All Bond Pairs)

Geometry of the Molecule

Bond Angles

BeF2 sp 2 Linear 180° BF3 sp2 3 Trigonal planar 120° CH4 sp3 4 Tetrahedral 109.5° PCl5 sp3d 5 Trigonal bi

pyramidal 120°and 90°

SF6 sp3d2 6 Octahedral 90° IF7 sp3d3 7 Pentagonal bi-

pyramidal 72° and 90°

Table 2.11 Geometry of covalent molecules involving different types of hybrid orbitals, lone pairs and bond pairs on the central atom

Type of Molecule

Number of Valence Shell Electron Pairs on a

Central Atom Hybridization and Distribution of

Orbitals

Shape of Molecule

Example

Bond Pair Lone Pair Total

AX2 2 0 2 sp Linear Linear Cl-Be-Cl AX2L 2 1 3 sp2 Trigonal

planar Bent (V - shaped)

AX2L2 2 2 4 sp3 Tetrahedral Bent (V - shaped)

AX2L3 2 3 5 sp3d Trigonal bi-pyramidal

Linear

AX3 3 0 3 sp2 trigonal planar

triangular

AX3L 3 1 4 sp3 Tetrahedral Trigonal pyramidal

AX3L2 3 2 5 sp3d Trigonal bi-pyramidal T - shaped

AX4 4 0 4 sp3 Tetrahedral Tetrahedral

AX4L 4 1 5 sp3d Trigonal bi-pyramidal See-Saw

AX4L2 4 2 6 sp3d2 Octahedral Square planar

AX5 5 0 5 sp3d Trigonal bi-pyramidal

Trigonal bi-pyramidal



AX5L 5 1 6 sp3d2 Octahedral Square pyramidal

AX6 6 0 6 sp3d2 Octahedral Octahedral

Geometry of molecules involving sp3 hybridization

Water molecule is formed with sp3 hybridization involving two bond pairs and two lone pairs (Figure 2.33).

Figure 2.33: Angular geometry of H2O molecule resulting from sp3 hybridization.

Geometry of molecules involving sp3d hybridization

The molecules involving sp3d hybridization are

1. SF molecule (Figure 2.34)4 2. ClF3 molecule (Figure 2.35) 3. XeF2 molecule (Figure 2.36)

Figure 2.34: Distorted 4-coordinate geometry of SF4 molecule resulting from sp3d hybridization.

Figure 2.35: Distorted T-shaped geometry of ClF3 molecule involving sp3d hybridization



Figure 2.36: Linear geometry of XeF2 molecule involving sp3d hybridization.

Geometry of molecules involving sp3d2hybridization

Molecules IF5 (five bond pairs and one lone pair) and XeF4 (four bond pairs and two lone pairs) involve sp3d2 hybridization (Figure 2.37 and Figure 2.38).

Figure 2.37: Square pyramidal geometry of IF5 involving sp3d2 hybridization

Figure 2.38: Square planar geometry of XeF4 involving sp3d2 hybridization

The geometries of molecules described by a generic formula AXmLn, are shown in Fig 2.39, where A is the central atom, X is any atom or group of atoms surrounding the central atom, and L represents a lone pair of electrons.

Hybridization and VSEPR Theory Together




Figure 2.39: Regular and distorted geometries of some covalent molecules

Geometry of some ions

The number of sigma bonds involved in bonding of atoms and the number of lone pairs of electrons present around the central atom determines the geometry of the ion. Electrons involved in multiple bond formation do not take part in the hybridization scheme. The pi bonds are excluded from hybridization. X-ray crystallography has indicated that NO3

- ion (Fig 2.40) and CO32- ion have trigonal planar geometry; SO4

2- ion (Fig 2.40) and ClO4

- ion have tetrahedral geometry and ClO3- ion has pyramidal

geometry.

Figure 2.40: Geometries of NO3

- and SO42- ions as indicated by X-ray

crystallography

Let us describe geometries of different ions with the help of hybridization concept.

Geometry of the nitrate ion

The outer electronic configuration of nitrogen atom 2s22p3 and oxygen atom is 2s22p4. Since the nitrate ion carries a unit negative charge, one of the oxygen atoms carries one extra electron, i.e., it becomes O- ion. The three orbitals (one 2s and two 2p) of the nitrogen atom hybridize to give three sp2 hybrid orbitals.



Figure 2.41: Trigonal planar geometry of nitrate ion involving sp2 hybridization of the central atom

Geometry of sulphate ion

The ground state electronic configuration of S atom is 3s23px2py

1pz1 and the excited state

electronic configuration is 3s13px1py

1pz1dxy

1dyz1. One 3s and three 3p orbitals hybridize to

produce four sp3 hybrid orbitals, involving four sigma bonds. The d orbitals are excluded from hybridization and they involve in the formation of pi bonds.

Figure 2.42: Tetrahedral geometry of sulphate ion involving sp3 hybridization of

the central atom

The sulphate ion carries two units of negative charge. Therefore, two of the oxygen atoms may be considered to have one additional electron each forming O- ion. This is a case of sp3 hybridization involving four sigma bonds. The SO4

2- ion has tetrahedral geometry (Figure 2.42).

Geometry of chlorate ion

The ground state configuration of chlorine atom is 3s23px2py

2pz1 and the second excited

state is 3s23px1py

1pz1dxy

1dyz1. One 3s and three 3p orbitals of the chlorine atom hybridize

to give four sp3 hybrid orbitals. Chlorine atom forms three sigma bonds with three oxygen atoms and also two pi bonds by lateral overlapping of 3d orbitals.

Figure 2.43: Geometry of ClO3

-

The geometry of ClO3- ion is actually pyramidal. This is due to the fact that a lone pair of

electrons occupies one of the sp3 hybrid orbitals. The repulsions between lone pair-bond



pair electrons results in the distortion of the tetrahedral geometry leading to pyramidal geometry (Figure 2.43).

The geometry of ClO4- ion, on the other hand, is tetrahedral. In the excited state of

chlorine atom, three electrons (two from p orbitals and one from s orbital) get excited to give the configuration 3s13px

1py1pz

1dxy1dyz

1dxz1. One 3s and three 3p orbitals of the

chlorine atom hybridize to give four sp3 hybrid orbitals. These orbitals contain one electron each and are used in the formation of four bonds with four oxygen atoms. The three electrons from 3d orbitals are used for the π bond formation with three oxygen atoms (Figure 2.44).

Figure 2.44: Geometry of of ClO4

-

2.4.6 Bond Angles

Bond angles in covalent molecules / ions are influenced by various factors such as

i. Electrons on the central atom. CO has no lone pair; bp-bp repulsion places the bond at 180. In SO, repulsion of the bond pairs by the lone pairs on S makes the molecule SO bent NO > NO > NO 180 132 115 Decreasing bond angle is due to the increasing number of electrons on the central nitrogen atom, from zero on NO to one in NO and two in NO. The repulsion caused by a lone pair of electrons is greater than that due to a lone electron.

2°22

2+

22-

°°° 2+

22-

ii. Electronegativity of the central atom The bond angle decreases with decrease in electronegativity of the central atom. NH3 > PH3 > AsH3 > SbH3 107° 94° 92° 91.3° H2O > H2S > H2Se > H2Te 104.5° 92.6° 91° 90.5°

More electronegative central atom draws the bond pairs towards itself and repulsions among bond pairs increase and hence bond angle increases.

iii. Electronegativity of substituents (surrounding atoms) The bond angle increases with the decrease in electronegativity of the surrounding atoms.

PF3 < PCl3 < PBr3 < PI3 97° 100° 101° 102° OH2 > OF2

104.5° 103.2°

NH3 > NF3 107° 102°

iv. As the electronegativity of the surrounding atoms increases, the bond pair is



drawn away from the central atom, repulsions among bond pairs decrease and hence bond angle decreases.

v. Molecules involving multiple bonding PH3 < PF3 94° 98° The increase in bond angle is attributed to the enhanced repulsion due to the presence of double bond in PF3. Due to multiple bond, the bp-bp repulsions increase to give a higher bond angle.

2.4.7 Concept of Resonance and Resonance Energy

Some covalent compounds cannot be assigned one single structure to explain all their properties. A number of closely resembling structures are drawn, which in a combined way explain all their properties. These closely resembling structures are known as resonating structures and the phenomenon is known as resonance. By giving the central oxygen an octet in ozone, the possible Lewis structures are:

I II

Which of the above possible structures for O3 is correct?

Infact, neither is correct by itself. Structural studies show that O―O bonds are indistinguishable. The actual electronic structure is an average of the different possibilities, called a resonance hybrid (fig 2.45).

Figure 2.45: Resonance in Ozone Molecule. I and II Represent the Canonical

Forms.

Various resonating structures for NO3- ion are given in Fig 2.46.

• The electron pair, which forms a double bond wherever written is not localized in any one of the two bonds, but rather ‘smeared out’ over all the bonds.

• The various structures of which the ions/molecules is said to be a resonance hybrid are known as contributing structures or canonical forms or mesomeric structures. They cannot be isolated, i.e., the canonical forms have no real existence.



Figure 2.46: Resonance in NO3

- ion I , II and III represents the canonical forms. A straight, double- headed arrow always indicates resonance; it is never used any other

purpose

There are certain rules to write various canonical forms which contribute towards resonance.

• The contributing structures should have the same relative arrangement of atoms. They should differ only in the positions of electrons.

• The contributing structure should have the same number of unpaired electrons. • The contributing structures should be of comparable energy. • The contributing structures should be such that the negative charge resides on an

electronegative element and positive charge resides on an electropositive element.

• In contributing structure, like charges should not reside on atoms close to each other and unlike charges should not be widely separated.

• The larger the total number of covalent bonds, the more important is the contributing structure.

Misconceptions

Benzene does not contain equal properties of molecules with structures shown in Fig 2.47, nor is there a tautomeric equilibrium nor can it be said that benzene exists for a

certain fraction of time in the form (I) and for another fraction of time as (II).

• The molecule itself has a single structure of its own which cannot be described directly by a conventional bond diagram.

Figure 2.47: Resonance in benzene molecule

Analogy

Compare the true structure with a ‘mule’ which is described in terms of two other animals a ‘donkey’ and a ‘horse’. Thus the mule is an animal in its own right but it has the characteristics of both a horse and a donkey, however, it is not either of these.

Characteristic of Resonance (Experimental Evidence)



• Measured internuclear distances do not always conform to summations of appropriate single, double, and triple bond radii. They have intermediate values. Different canonical forms for CO2 molecule are given in Fig 2.48.

Figure 2.48: Resonance in CO2 molecule

The calculated bond length between two oxygen atoms (O-O) is 244 pm and that observed is 230 pm. The observed bond length is smaller than the calculated bond length of any canonical forms.

• Stability of a molecule in question is more (by resonance energy) than that predicted by any contributing molecular structure (Fig 2.49) .

The resonance energy can be evaluated as the difference between observed enthalpy of formation and that calculated for the most stable canonical structure.

Figure 2.49: Resonance energy for the structures I, II and III of CO2

For example, the enthalpy of formation of benzene ∆fH° calculated from its enthalpy of combustion and the enthalpies of formation of its products is -5535 kJ mol-1, whereas the value calculated from the summation of bond energies, 6 C─H + 3 C─C + 3 C=C bonds, is ─5381 kJ mol-1. The benzene molecule is thus more stable by 154 kJ mol-1 due to resonance. Similarly, for CO2, the resonance energy is 138 kJ mol-1.

∆E = Resonance Energy = Eactual – Emost stable canonical structure = Eobserved – Ecalculated = -1602.5 kJ mol-1 - 2[Energy of C=O bond] = -1602.5 kJ mol-1 + 1464.5 kJ mol-1 = -138.0 kJ mol-1

• The dipole moment of a molecular species is less than that predicted in terms of contributing structures.

• The chemical properties of a given species are not those of a specific canonical form but rather those of a hybrid of all forms.

2.4.8 Limitations of Valence Bond Treatment

B theory accounts for the stability of the covalent bond in terms of an overlap of atomic orbitals, it explains structural features of molecules and polyatomic ions. Hybridization and resonance concepts are useful in describing the geometry and chemical properties of many molecules and ions. However, VB theory has certain limitations.

• It assumes that the electrons in a molecule occupy atomic orbitals of the individual atoms.



• It fails to explain the bonding in electron deficient compounds, metals and intermetallic compounds.

• VB model is unable to predict correctly the magnetic properties of many molecules e.g., O2, B2 are paramagnetic and C2 diamagnetic etc.

2.4.9 Molecular Orbital Method (Undirected Bond Approach)

The molecular orbital (MO) theory is the second approach to bonding in molecules. The basic principles of molecular orbital theory are as follows:

• MO theory describes covalent bonds in terms of molecular orbitals, which result from merging of the atomic orbitals of the bonding atoms.

• The molecular orbital is associated with all of the atomic species involved and is polycentric while an electron in an atomic orbital is influenced by one positive nucleus only (monocentric).

• Each molecular orbital is described by a wave function Ψ, known as molecular orbital wave function.

• The molecular orbital wave function is such that the value of Ψ2 at a point represents the probability of finding the electron at that point provided the wave function is a normalized wave function.

• The wave function describing a molecular orbital may be obtained by Linear Combination of Atomic Orbitals (LCAO).

Linear Combination of Atomic Orbitals (LCAO)

According to this approach the atomic orbitals (on different atoms) of comparable energies and of appropriate symmetry combine (merge) to give rise to an equal number of molecular orbitals. Atomic orbitals of constituent atoms combine in a linear (additive) fashion to form molecular orbitals.

Linear Combination of Atomic Orbitals (LCAO)

According to this approach the atomic orbitals (on different atoms) of comparable energies and of appropriate symmetry combine (merge) to give rise to an equal number of molecular orbitals. Atomic orbitals of constituent atoms combine in a linear (additive) fashion to form molecular orbitals.

Consider two atoms A and B each possessing a single valence electron. Let ψA and ψB represent the wave function (amplitude) of atoms A and B respectively. Wave functions which have the same sign may be regarded as waves that are in phase, which when combined add up to give a larger resultant wave. Similarly wave functions of different signs correspond to waves that are completely out of phase and which cancel each other by destructive interference. Atomic orbitals ψA and ψB combine to give molecular orbitals, bonding (ψb) and antibonding (ψa).

Case (i) When the two waves are in phase, they add up and the amplitude of the new wave is bonding molecular orbital. ψb = ψA + ψB

Case (ii) When the two waves are out of phase, the waves are subtracted from each other so that amplitude of the new wave is antibonding molecular orbital. ψa = ψA - ψB

Knowing that the probability is given by square of the amplitude ψb

2 = ψA2 + ψB

2 + 2ψAψB ψa

2 = ψA2 + ψB

2 - 2ψAψB

ψAψB dv is known as overlap integral, S, where dv is a small volume element. S is a measure of the bond strength in the resulting molecular species.



If S = 0, there is no overlap, no bonding (the orbitals are non-bonding) If S > 0, there is bonding interaction (the orbitals are bonding) If S < 0, there is opposition to bonding (the orbitals are antibonding)

Pictorial representation of combination of atomic orbitals to form molecular orbitals is shown in Figs 2.50, 2.51 and 2.52. The differences between bonding molecular orbitals and antibonding molecular orbitals are given in Table 2.12.

Figure 2.50: Formation of molecular orbitals from two 1s atomic orbitals

Figure 2.51: Combination of pz orbitals (sigma bond) and combination of px and

py orbitals (pi bond)

Nonbonding molecular orbitals

The combining orbitals must have similar symmetries along internuclear axis. No molecular orbital can result inspite of the overlap of the px or py orbital with s orbital of two different atoms. In fact, ++ overlap is cancelled by + - overlap (Figure 2.52).

Figure 2.52: Formation of non-bonding molecular orbitals from 2s and 2 px

orbitals



Table 2.12 Differences between bonding molecular orbitals and anti bonding molecular orbitals

Bonding molecular orbital (BMO) Antibonding molecular orbital (ABMO)

1. ABMO is formed by the addition overlap of atomic orbitals. = + ψaψAψB

An ABMO is formed by the subtraction overlap of atomic orbitals ψa = ψA - ψB

2. It has lower energy than the atomic orbitals from which it is formed.

It has higher energy than the atomic orbitals from which it is formed.

3. The electron charge density in between the nuclei is high and hence the repulsion between the nuclei is very low. This results in stabilization of the BMO.

The electron charge density in between the nuclei is low and hence the repulsion between the nuclei is high. This results in de-stabilization of ABMO.

Stability of molecules in terms of bonding and antibonding electrons

The energy of the bonding molecular orbital is lower than that of the atomic orbital by an amount ∆, stabilization energy. Similarly, the energy of the antibonding molecular orbital is increased by ∆', destabilization energy (Fig 2.53).

Figure 2.53: Molecular orbitals (BMO and ABMO)

Stability of molecules in terms of bond order

Let Nb represent the number of electrons present in the bonding orbitals and Na the number of electrons present in the antibonding orbitals. Then

i. If > , the molecule is stable.NbNa ii. If Nb < Na, the molecule is unstable. iii. If Nb = Na, the molecule is again unstable.

Bond order = [Nb - Na]

• The molecule is stable if Nb >Na i.e, if bond order is positive. • The molecule is unstable if Nb < Na or Nb = Na i.e, if the bond order is negative or

zero. • For diatomic molecules, the stability (as expressed in terms of bond dissociation

energy) is directly proportional to the bond order. Thus a molecule with a bond order 3 is more stable than a molecule with a bond order 2.

• Bond length is found to be inversely proportional to the bond order. Greater the bond order, shorter is the bond length.

• Addition of an electron to an antibonding molecular orbital result in an increase in bond length and decrease in bond energy. Removal of an electron from an antibonding molecular orbital increases the bond order and an increase in bond energy and decrease in bond length of the resulting ion is observed.



Diamagnetic and paramagnetic nature of the molecules

If all the electrons in the molecule are paired, it is diamagnetic in nature. On the other hand, if the molecule has some unpaired electrons, it is paramagnetic in nature.

The order of energy of molecular orbitals

The order of energy of molecular orbitals has been determined from spectroscopic data. In simple homonuclear diatomic molecules the order is

(σ1s), (σ*1s), (σ2s), (σ*2s), (σ2pz), (π2px) = (π2py), (π*2px) = (π2py)

For the lighter elements boron, carbon and nitrogen, the (π2px) and (π2py) are probably lower than (σ2pz).

For these molecules, the order is

(σ1s), (σ*1s), (σ2s), (σ*2s), (π2px) = (π2py), (σ2pz), (π*2px) = (π*2py) , (σ2pz)

Reversal in the order of σ and π orbitals

The sequence of energy levels in which they are filled shows that (σ2pz) orbital has lower energy than (π2px) = (π2py) molecular orbitals, i.e.,

(σ2pz) < (π2px) = (π2py)

The sequence of energy levels shown above applies to systems where mixing of ( σ2s) and (σ2p) atomic orbitals is negligible. This sequence applies only for O2 and F2 molecules (Fig 2.54).

Figure 2.54: Energy levels of different molecular orbitals for O2, F2 and Ne2

However, this sequence of energy levels does not apply to homonuclear diatomic molecules of lighter elements, i.e., boron through nitrogen (Figs 2.55 and 2.56).

The difference in the energy of 2s and 2pz atomic orbitals in kJ mol-1 for the lighter elements is given below

Li Be B C N O F 178 262 449 510 570 1430 1970

Figure 2.55: Mixing of atomic orbitals with same symmetry



Atomic orbitals with comparable energies can mix and form stabler atomic orbitals, hence, molecular orbitals result from mixed s and p orbitals. The mixing is important for elements with lower effective nuclear charge and leads to stabilization of (σ2s) and (σ*2s) orbitals and destabilization of (σ2pz) and (σ*2pz) orbitals resulting in the reversal of the order of the (σ2pz) and (π2px) = (π2py) oribtals. That is, (π2px) = (π2py) < (σ2pz).

Figure 2.56: The change in energies of MOs due to mixing of orbitals of same energy

We may now consider the formation of diatomic molecules from H2 to Ne2. Molecular orbital theory shall give us information about the nature of homonuclear diatomic species.

Hydrogen molecule, H2

The hydrogen molecule is formed by the combination of the hydrogen atoms. 1s orbital of each hydrogen atom form two molecular orbitals, BMO and ABMO. Each hydrogen atom has one electron in 1s orbital and, therefore, there are two electrons to be accommodated in MOs. Both these electrons would be accommodated in the (σ1s) BMO. The energy level diagram for H2 molecule is shown in Fig 2.57.

Figure 2.57: Energy level diagram for H2 molecule

Thus, H2 molecule will have the electronic configuration [ (σ1s)2] The bond order in H2 = 1/2[2-0] = 1 Bond dissociation energy in H2 molecule is 431.4 kJ mol-1 and bond length is 74 pm.

Hydrogen molecule ion, H2+

The molecular ion has only one electron and its electronic configuration is [(σ1s)1] and the bond order is ½ (Fig 2.58).



Figure 2.58 Energy level diagrams for H2

+ molecule ion and H2 molecule

The hypothetical He2 molecule

There are four electrons to be accommodated in He2 molecule. Since each molecular orbital can accommodate two electrons with opposite spins, only one pair can be accommodated in (σ1s) bonding molecular orbital and the other in (σ*1s) antibonding molecular orbital.

Thus, the electronic configuration for He2 is [(σ1s)2 (σ*1s)2] and the bond order is zero. In effect, the bonding and antibonding cancel each other and hence the molecule He2 does not exist.

Boron molecule, B2

The electronic configuration of Boron atom is 1s2 2s2 2px1.

There are ten electrons to be accommodated in B2 molecule (Fig .2.59)

Figure 2.59: Energy level diagram for B2 molecule

Energy Level Diagram for various molecules http://www.illldu.edu.in/mod/book/print.php?id=5635

Oxygen molecule, O2

The electronic configuration of oxygen atom is 1s2 2s2 2px2 2py

1 2pz1

There are sixteen electrons to be accommodated in O2 molecule (Fig 2.60).

Figure 2.60: Energy level diagram for O2 molecule



Molecular orbital energy level diagrams showing electronic configuration of homonuclear diatomic molecules of second period are summarized in Fig 2.61 and Table 2.13.

Figure 2.61: Molecular orbital energy level diagrams showing electronic configuration for Li2, Be2, B2, C2, N2, O2, F2 and Ne2 Table 2.13 The physical properties of homonuclear diatomic molecules of the second period

Molecule/ Molecule Ion

Bonding electrons

Anti bonding electrons

Bonds r(pm) Bond energy kJ mol-1

Magnetic property

H2+ 1 0 0.5 106 255 Paramagnetic

H2 2 0 1 74 431.4 Diamagnetic He2

+ 2 1 0.5 108 293 Paramagnetic He2 2 2 0 -- 0 -- Li2 2 0 1 267 113 Diamagnetic Be2 2 2 0 -- 0 -- B2 4 2 1 159 288 Paramagnetic C2 6 2 2 131 585 Diamagnetic N2 8 2 3 110 940 Diamagnetic N2

+ 7 2 2.5 112 ~800 Paramagnetic O2 8 4 2 121 493 Paramagnetic O2

+ 8 3 2.5 112 600 Paramagnetic O2

- 8 5 1.5 130 -- Paramagnetic O2

2- 8 6 1 148 -- Diamagnetic F2 8 6 1 144 ~150 Diamagnetic

Ne2 8 8 -- -- 0 --

Whatever has been studied so far in connection with molecular orbital theory can be summarized as follows.

• The positive value of bond order ½ with H2+ ion indicates that the bond does get

formed and the molecule is stable. The molecule ion H2+ has been detected

through spectroscope when electric discharge is passed through hydrogen gas under pressure.

• The zero bond order in He2, Be2 and Ne2 molecules indicate their non-existence. However, He2

+ ion has been isolated and its existence was proved in cosmic rays.

• Surprisingly, the σ bond in Li2 molecule is much longer and weaker than in H2. This may be attributed to

• the 2 orbital of Li is bigger in size than 1 orbital of hydrogen and the overlap involving orbitals of Li is less effective and diffuse.ss2s-2s

• the 1s2 electrons of Li cause repulsion between the atoms and thus do not allow two Li atoms to come nearer to each other than 2.67Å.

• The observed paramagnetic character of B2 is explained on the basis of the mixing of molecular orbitals of the same symmetry as discussed earlier. Due to this mixing, the π2px and π2py molecular orbitals lie at lower energy level than the σ2pz molecular orbital. Since each bonding molecular orbital contains a single, i.e., an unpaired electron, the molecule B2 is paramagnetic.

• The molecule C2 should be stable, since π2p bonding orbitals provide four lots of stabilization energy giving two bonds. The fact that carbon exists as macromolecules in graphite and diamond illustrates the point that an even more stable arrangement is formed in preference, where each atom forms four bonds.



• The bond order in N2 molecule is three and thus nitrogen molecule contains a triple bond. Hence, the nitrogen molecule is highly stable. This is confirmed by its high bond dissociation energy (940 kJ mol-1).

• Since there are two unpaired electrons (one in each) in π*2px and π*2py the oxygen molecule is paramagnetic. Bond order in this case is 2 and thus oxygen molecule contains a double bond.

Example

Of the species O2, O2+, O2

-, O22-, which would have the maximum bond strength?

Solution:

The bond orders, bond lengths of the above species are in the order:

i. Bond order: O (2.5) > O (2) > O (1.5) > O (1) 2+

22-22-

ii. Bond length O2

2-> O2-> O2 > O2

+

Higher bond orders are associated with shorter bond lengths and higher bond strengths. Since O2

+ has the highest bond order, it has the shortest bond length and hence the maximum bond strength.

• Bond order and bond length and bond energy of homonuclear diatomic molecules are given below. Bond order

B2 (1) < C2 (2) < N2 (3) > O2 (2) > F2 (1) Bond Length (pm) B2 (159) > C2 (130) > N2 (100) < O2 (121) < F2 (144) Bond Energy (kJ mol-1) B2 (288) < C2 (585) < N2 (940) > O2 (493) > F2 (151)

Hence bond order is directly proportional to bond strength and inversely proportional to bond length.

Biographic

Table 2. 13

Table 2.13 The physical properties of homonuclear diatomic molecules of the second period

Molecule/ Molecule Ion

Bonding electrons

Anti bonding electrons

Bonds r(pm) Bond energy kJ mol-1

Magnetic property

H2+ 1 0 0.5 106 255 Paramagnetic

H2 2 0 1 74 431.4 Diamagnetic He2

+ 2 1 0.5 108 293 Paramagnetic He2 2 2 0 -- 0 -- Li2 2 0 1 267 113 Diamagnetic Be2 2 2 0 -- 0 -- B2 4 2 1 159 288 Paramagnetic C2 6 2 2 131 585 Diamagnetic N2 8 2 3 110 940 Diamagnetic N2

+ 7 2 2.5 112 ~800 Paramagnetic O2 8 4 2 121 493 Paramagnetic O2

+ 8 3 2.5 112 600 Paramagnetic O2

- 8 5 1.5 130 -- Paramagnetic O2

2- 8 6 1 148 -- Diamagnetic F2 8 6 1 144 ~150 Diamagnetic

Ne2 8 8 -- -- 0 --

Heteronuclear Diatomic Molecules



In heteronuclear diatomic molecules, the two atoms constituting a molecule are different. The molecular orbital diagram may not be symmetrical in heteronuclear case due to bonding between different atoms which may have different electronegativities. The more electronegative atom will have its atomic orbitals lower in energy than the less electronegative atom (Figure 2.62).

Figure 2.62: Molecular orbitals resulting from mixing of atomic orbitals of different

energy

The MO configurations for heteronuclear diatomic molecules are developed based on isoelectronic principle, i.e. two molecular species with the same number of atoms and the same total number of valence electrons are said to be isoelectronic. Isoelectronic principle states that such molecular species will have similar molecular orbitals and molecular structures.

Carbon monoxide CO

CO is isoelectronic with N2 molecule.

C 1s2 2s2 2p2 O 1s2 2s2 2p4

A total of 14 electrons are to be accommodated in the molecular orbitals of CO molecule (Figure 2.63).

CO [KK (σ2s)2 (σ*2s)2 (σ2pz)2 (π2px)2 (π2py)2]

Bond order =

Thus CO contains a triple bond. Its bond dissociation energy has been found to be 1067 kJ mol-1 and bond length is equal to 114 pm.

Figure 2.63: Molecular orbital diagram for CO molecule

Nitric Oxide, NO

The electronic configuration of N and O atoms are

N 1s2 2s2 2p3 O 1s2 2s2 2p4



There are five electrons in the outer shell of N and six electrons in the outer shell of O. Thus, a total of 11 outer electrons are to be accommodated in the molecular orbitals of NO molecule.

Molecular Orbital Diagram of Co and No str. http://www.illldu.edu.in/mod/book/print.php?id=5635

NO molecule is isoelectronic with O2+ ion.

The MO configuration of NO molecule is thus NO [KK (σ2s)2 (σ*2s)2 (σ2pz)2 (π2px)2 (π2py)2 (π*2px)1]

The Bond order = Since NO contains an unpaired electron, it is paramagnetic.

Nitrosyl ion, NO+

Removal of an electron from NO gives a nitrosyl ion NO+. The electron is removed from the highest energy π* anti bonding molecular orbital. NO+ [KK (σ2s)2 (σ*2s)2 (σ2pz)2 (π2px)2 (π2py)2]

NO+ is isoelectronic with CO

Bond order in NO+

Bond order of three is supported by bond length of 106 pm in NO+, NO+ is diamagnetic because of paired configuration. Loss of unpaired electron in antibonding π* orbital gives NO+ ion of higher bond energy (shortened bond) NO+ > NO

Cyanide ion, CN-

CN- is isoelectronic with CO

CN- [KK (σ2s)2 (σ*2s)2 (σ2pz)2 (π2px)2 (π2py)2]

Bond order in CN-

Hydrogen Fluoride, HF

The electronic configuration of hydrogen and fluorine are H 1s1 F 1s2 2s2 2px

2 2py2 2pz

1

In the formation of molecular orbitals in HF molecule, 1s1(H) - 1s2(F), 1s1(H) - 2s2(F), 1s1(H) – 2px

2(F) and 1s1(H) – 2py2(F) overlaps giving rise to non-bonding molecular

orbitals. Thus singly filled 2pz1 on fluorine atom overlaps with the singly filled 1s1 orbital

of hydrogen atom and forms two sigma molecular orbitals which are designated as σsp and σsp*. The molecular orbital energy diagram can thus be shown as given in Fig 2.64.

HF [(1s)2 (2s)2 (σspx)2 (2px)2 (2py)2] Bond order = ½ [2-0] = 1



Figure 2.64: Energy level diagram for HF molecule

2.4.10 Comparison Between Valence Bond Theory (VBT) and Molecular Orbital Theory (MOT)

Common Features

• Both the theories are theoretical approximations, based on quantum mechanical model of the atom and are called modern theories of chemical bonding.

• Both interpret covalent bonds as orbitals embracing two atoms. • The energies of the overlapping orbitals, according to both the theories, must be

comparable and their symmetries should be the same. • In bond formation, the orbitals of the bonding atoms must overlap according to

both the theories. • Both predict the concentration of electron density between the nuclei.

Differences

• The VBT visualizes the bond formation as localized interaction between two atomic orbitals belonging to the constituent atoms while the molecular orbital theory involves delocalized molecular orbitals spread over the whole molecule.

• While VBT fails to account for paramagnetic character of oxygen, MOT offers satisfactory explanation.

• While resonance plays an important role in VBT, this concept has no place in MOT.

• VBT is simple to apply, while MOT is difficult to apply, i.e., the calculations involved in MOT are much more tedious than those involved in VBT.

• The MO description, however, provides better descriptions of simple species such as H2

+ and O2 than do the one and three electron bonds that must be involved in VB approach.

• The MO method has the additional advantages of better describing excited states, multiple bonding and bond weakening via occupancy of antibonding orbitals.

In summary, each approximation has its own specific uses and advantages and it is often desirable to use the approach that is better suited to the specific situation in question. In general, molecular orbital theory is more relevant as it considers two possibilities of bonding, i.e., the electrons can occupy both bonding and antibonding molecular orbitals whereas in valence bond theory the electrons represent only bonding state.

Summary of Covalent bonding



Summary

• Atoms combine in order to achieve maximum stability. • A chemical bond is a strong attractive force that exists between certain atoms in

a substance. • Lewis electron-dot formulas are simple representations of the valence shell

electrons of atoms in molecules and ions. In such formulas, the atoms usually satisfy the octet rule.

• An ionic bond is the product of the electrostatic forces of attraction between positive and negative ions. An ionic compound consists of a large network of ions in which positive and negative charges are balanced. The structure of a solid ionic compound maximizes the net attractive forces among the ions.

• Lattice enthalpy can be calculated using the Born-Landé equation. Lattice enthalpy is a measure of the stability of an ionic solid. Lattice enthalpy affects the solubility of ionic compound.

• Hess’s law enables enthalpy changes to be determined by using Born-Haber cycle.

• Covalent character in ionic compounds occurs due to polarization of charge clouds of ions. Cations exert great polarizing effect on the anions. Greater the polarization, larger is the induced covalent character in an ionic compound which is reflected in the decreasing melting points and solubility in polar solvents.

• Bonds between different atoms are normally polar, and the magnitude of the dipole moment depends on the difference in the electronegativity between the atoms involved. The dipole moment of a molecule is the resultant of whatever bond moments are present. The study of dipole moment is very useful for information on percentage ionic character in a covalent bond and for elucidation of molecular geometry of covalent molecules.

• A covalent bond is a strong attractive force that holds two atoms together by their sharing of electrons. In multiple covalent bonds, two or three pairs of electrons are shared by two atoms.

• There are two quantum mechanical approaches for covalent bond formation: valence bond theory and molecular orbital theory.

• In valence bond approach, a bond is formed by the overlap of orbitals from two atoms. Multiple bonds occur via the overlap of atomic orbital to give sigma and pi bonds.

• By making use of the concept of hybridization, VB theory, succeeds in accounting for the principles of molecular geometry.



• Hybridization is the mixing of atomic orbitals on an atom as it interacts with another atom. The hybridized orbitals are all of equivalent energy. Valence-shell expansion can be explained by assuming hybridization of s, p and d orbitals.

• The VSEPR model for predicting molecular geometry is based on the assumption that valence-shell electron pairs repel one another and tends to stay as far apart as possible. The electron pairs include bonding pairs and lone pairs. The shape of the molecule is described by the positions of the bonding pairs only. Lone pairs repel other pairs more forcefully than bonding pairs do and thus distort bond angles from ideal geometry. Lone pairs take up more space than bonding pairs, so the strength of repulsions decreases in the order:

• lp-lp > lp-bp > bp-bp • The best way to describe the geometry of covalent molecule/ion is by combining

both hybridization and VSEPR theory. • Bond angles in covalent molecule/ion are influenced by factors such as electrons

on the central atom, electronegativity of the substituents, electronegativity of the central atom etc.

• By introducing the idea of resonance, the VB theory rationalizes the chemical properties of many molecules. Resonance structures are used to explain bonding in molecules with bonds that appear to be different in the Lewis structure but are found to be the same experimentally.

• Molecular orbital theory describes bonding in terms of the combination and rearrangement of atomic orbitals to form orbitals that are associated with a molecule as a whole.

• The linear combination of two hydrogen 1s orbitals gives a bonding molecular orbital and an antibonding molecular orbital.

• Bonding molecular orbitals increase the electron density between the nuclei and are lower in energy than individual atomic orbitals. Antibonding molecular orbitals have a region of zero electron density between the new nuclei, and an energy level higher than that of the individual atomic orbitals.

• Molecular orbitals in an energy level diagram are filled using the Aufbau principle, the Pauli exclusion principle and Hund’s rule.

• Molecular orbital energy level diagrams can be used to predict whether molecules or ions exist.

• Molecular orbitals of the same symmetry interact through s-p mixing. This mixing is important for B2, C2 and N2. The molecular orbital energy level order is different from that expected if you assume independent overlap of the s orbitals and p orbitals.

• The configuration of a diatomic molecule such as O2 can be predicted from the order of filling of the molecular orbitals. From this configuration, we can predict the bond order and whether the molecular substance is diamagnetic or paramagnetic.

• The MO configuration for heteronuclear diatomic molecules are developed based on isoelectronic principle. Heteronuclear diatomics can have non-bonding orbitals, in addition to bonding and antibonding orbitals.

Exercises

1. Why do atoms combine in a definite and not in an arbitrary number to form a given molecule?

2. (Water is H2O but neither H3O nor HO2). 3. Explain why H2 is a stable molecule formed from two hydrogen atoms while He2 is

unstable? 4. Write Lewis structures for N2, C2, O3, PO4

3-, SO42- and HClO4.

5. Oxalic acid, , is a poisonous substance found in uncooked spinach

leaves. If oxalic acid has a 6. Dichlorodifluoromethane, CCl2F2, is a gas used as a refrigerant and aerosol

propellant. It is also known commercially as one of the freons. Write the Lewis formula for CCl2F2.

7. Why is hydrogen an exception to octet rule? 8. Distinguish clearly between ‘bond energy’ and 'bond dissociation energy', giving

numerical values and units for the energy terms in each instance. 9. Define lattice enthalpy of an ionic solid. Write the Born-lande equation and give

the significance of the terms involved in it. 10. Calculate the lattice enthalpy of NaCl using the following data: 11. Enthalpy of sublimation of Na (s) = +108.3 kJ mol-1 12. Enthalpy of dissociation of Cl2 (g) = +119.7 kJ mol-1 13. Ionization enthalpy of Na (g) = + 493.3 kJ mol-1 14. Electron gain enthalpy of Cl (g) = - 361.9 kJ mol-1



15. Enthalpy of formation of NaCl (s) = - 410.9 kJ mol-1 16. What is Madelung constant? Does it depend upon the geometry of an ionic solid? 17. Give reasons why? 18. a) BaSO4 is insoluble in water. 19. b) melting point of BaO is high. 20. c) Noble gases do not form ionic halides. 21. d) KCl2 is not formed. 22. What is Born-Haber cycle? Using Born-Haber cycle, calculate the electron affinity

of chlorine from the following data: 23. Bond enthalpy of Cl2 = + 240.0 kJ mol-1 24. Enthalpy of formation of NaCl(s) = ─ 440.0 kJ mol-1 25. Enthalpy of sublimation of Na(s) = + 110.0 kJ mol-1 26. Enthalpy of ionization of Na(g) = + 480.0 kJ mol-1 27. Enthalpy of lattice formation of NaCl(s) = ─ 810.0 kJ mol-1 28. Comment on 29. NaCl exists but NaCl2 does not, CaF2 exists but CaF does not. 30. The stabilization of noble gas configuration is meaningless since the formation of

O2-, S2-, Li+, Na+ etc., are endothermic. 31. Although the lattice energy is high for AgCl (-910 kJ mol-1), yet the heat of

formation is much less (ΔfH = -127 kJ mol-1). 32. Explain the effect of polarizing power and polarizability on the properties of ionic

compounds. 33. What is meant by ‘partial ionic character of a covalent bond’? What are its

consequences? 34. Describe Fajans rules. How does it explain the relative covalent/ionic nature of

the following pairs of compounds 35. FeCl2, FeCl3 36. LiI, CsI 37. CuCl, NaCl 38. Explain why 39. Melting point of NaCl is higher than that of AlCl3? 40. Stability of alkaline earth carbonates increases with increase in size of alkaline

earth metal. 41. ZnCl2 is soluble in organic solvents and MgCl2 is insoluble. 42. Which compound of each of the following pairs is more covalent? 43. AgCl or AgI 44. LiCl or KCl 45. MgCl2 or BeCl2 46. CaCl2 or CdCl2 47. ZnO or ZnS 48. NaF or CaO 49. Which of the following molecules would you predict to be polar? 50. H2S, BCl3, CCl4, C2H6, CO2 51. The dipole moment of HCl molecule is known to be 1.03 D and the bond distance

H―Cl is 1.27Ǻ. Calculate the percentage ionic character in H―Cl. 52. (Ans: 17%) 53. Explain why CO2 has zero dipole moment while SO2 has 1.6 D. 54. Which of the following molecules have zero dipole moment and why? 55. (i) benzene (ii) p-dichlorobenzene 56. (iii) p-dihydroxybenzene (iv) chlorobenzene 57. The dipole moment of NF3 is much less than that of NH3 though both have same

structure. Explain. 58. The dipole moments of NH3 and NF3 are in opposite directions. Explain. 59. 60. Using hybridization concept, describe the bonding in C2H6, C2H4, C2H2 and

O=C=O 61. Predict the type of hybridization and shape of the following species using valence

bond theory: 62. ICl4- 63. CO3

2- 64. Xe2F2 65. ClF3 66. Predict the shapes of the following molecules using valence bond theory 67. NO3

- 68. SF4 69. XeF6 70. What is VSEPR theory and what are its limitations? 71. Predict the shapes of the following molecules or ions on the basis of VESPR

theory 72. I3

- 73. BF4

-



74. NH4+

75. XeF2 76. SiCl4 77. On the basis of VSEPR theory, write the possible structures of ClF3 and predict

the most favoured structure showing your arguments. 78. State the d-orbitals involved in sp3d, sp3d2 and sp3d3 hybridizations. 79. Describe the shapes of 80. ClO3

- 81. CO3

2- and 82. I3

- ions on the basis of hybridization. 83. Explain the concept of resonance and resonance energy. 84. The nitrate ion has three equivalent oxygen atoms, and its electronic structure is

a resonance hybrid of three electron dot structures. Draw them. 85. What are the conditions of resonance (selection rules)? Draw as many electron-

dot resonance structures as possible for each of the following molecules or ions, giving all atoms octets:

86. SO2 87. CO3

2- 88. BF3 89. Nitrous oxide (N2O), called ‘laughing gas’, is sometimes used by dentists as an

anaesthetic. Given the connections N―N―O draw two electron-dot resonance structures for N2O.

90. Describe the potential energy diagram for H2 molecule and deduce various postulates of valence bond theory.

91. Briefly discuss the concept of LCAO to produce molecular orbitals. 92. What are bonding and antibonding molecular orbitals? Explain with examples. 93. Using LCAO method, draw the shapes of p-p combination of atomic orbitals, both

axial as well as sideways. 94. Draw the molecular orbital energy level diagrams for the following molecules/

ions and predict their bond order and magnetic character 95. B2 96. C2 97. NO 98. NO+ 99. CN- 100. Write the molecular configuration of O2, O2

+, O2- and O2

2- and arrange them in increasing order of their bond length and bond strength.

101. Indicate the effects of the following ionization process and bond orders and bond lengths

102. i) O2 + e- → O2-

103. ii) N2 – e- → N2+

104. Why does CO form numerous metal complexes while the isoelectronic nitrogen molecule does not? Explain on the basis of MO theory.

105. NO can readily lose electron to form NO+ ion. Explain Why? 106. Draw molecular orbital diagram for CO molecule. 107. Explain 108. Geometries of HO, HS, HSe are the same but the bond angles are HO >

HS > HSe222222 109. All P-F bonds in PF5 are not equivalent 110. The bond angles in phosphorus compounds are PF3< PCl3 < PBr3< PI3 and

PF3 > PH3 111. NCl5 does not exist while PCl5 exists. 112. PCl5 exists but PH5 does not. 113. Sulphur forms SF6 but oxygen does not form OF6 or SCl6 or SH6. 114. Explain 115. NF is pyramidal but BF is planar.33 116. BeCl2 is linear, CO2 is linear but SO2 is bent. 117. The bond angle in F2O is smaller than that in H2O 118. Compare and contrast valence bond theory and molecular orbital theory. 119. 120. single bond and no C-H bond, draw its electron dot structure.

References

• Book References • Inorganic Chemistry, • Principles of Structure and Reactivity • James E. Huheey et al. • Addison-Wesley Publishing Company • Advanced Inorganic Chemistry



• F. Albert Cotton et al. • J.Wiley & Sons • Models in Structural Inorganic Chemistry • A.F. Wells • Oxford University Press, London (1970). • Inorganic Chemistry • Therald Moeller • John Wiley & Sons • Concise Inorganic Chemistry • J.D. Lee • Blackwell Science Ltd., London • Concepts and Models of Inorganic Chemistry • Bodie Douglas, Dare Mc. Danial, John Alexander • Wiley-India • Inorganic Chemistry • Gary L. Miesslar Donald A. Tarr • Pearson Education (Singapore) Pvt. Ltd. • Chemistry: Molecules, Matter and Change • Peter Atkins, Loretta Jones • W.H. Freeman and Company, New York • Chemistry • John Mc Murry, Robert C. Fay • Pearson Education Chemistry • Chemistry • Raymond Chang • Mc Graw-Hill Publishing Company • Inorganic Chemistry • Peter Atkins, Tina Overton • Oxford University Press • Advanced Chemistry • Philip Mathews • Cambridge University Press • Principles of Inorganic Chemistry • B. R. Puri, L. R. Sharma, K. C. Kalia • Vallabh Publications, Delhi 110088 • Inorganic Chemistry • Ramesh Kapoor, S. K. Vashisht, R. S. Chopra • R. Chand & Co., New Delhi – 110002 • Valence and Molecular Structure • Cartmell, E. and Fowels, G.W.A • ELBS and Butterworth, London • J.D.Lee : A New Concise inorganic Chemistry, E.L.B.S • F.A.Cotton & G.Wilkinson: Basic Inorganic Chemistry, John Wiley. • Web Side References

14. http://www.visionlearning.com/library/module_viewer.php?mid=55 (chemical bonding)

15. http://pages.towson.edu/ladon/carbon.html (hybridization in carbon) 16. http://www.intute.ac.uk/sciences/reference/plambeck/chem1/p02201.htm 17. http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch8/mo.html

(molecular orbital theory) 18. http://www.chem.qmul.ac.uk/software/download/mo/ (molecular orbital theory)

Glossary

• Born-Haber cycle- It is an indirect way to calculate the lattice enthalpy which is difficult to calculate directly. It is based on Hess’s law.

• Covalent Bond- It involves the sharing of a pair of electrons between two atoms.

• Fajans’ rules- An ionic compound will have a high degree of covalency if the positive ion is small and highly charged and the negative ion is large.

• Hess’s law- Hess’s law states that the enthalpy of a reaction is the same, whether it takes place in a single step or in more than one step.

• Hybridization- Is the mixing of atomic orbitals in an atom (usually a central atom) to generate a set of new atomic orbitals called hybrid orbitals. Hybrid orbitals are used to form covalent bonds.

• Ionic Bond –It involves the complete transfer of one or more electrons from one atom to another.

• Lewis octet rule -Each atom shares electrons with neighbouring atoms to achieve a total of eight valence electrons.



• Limitations to octet rule- It fails to account for the stability of incomplete octet, expanded octet, odd-electron and shape of a molecule.

• Lattice- The ion exists in three dimensional arrays, which we call the lattice. The lattice energy is a measure of the energetic stability of the crystal.

• Lattice Enthalpy- Is defined as the energy released when one mole of the compound is formed in the regular lattice structure from requisite number of ions.

• Linear Combination of Atomic Orbitals (LCAO)-According to this approach the atomic orbitals (on different atoms) of comparable energies and of appropriate symmetry combine (merge) to give rise to an equal number of molecular orbitals. Atomic orbitals of constituent atoms combine in a linear (additive) fashion to form molecular orbitals.

• Metallic Bond – It involves the free movement of valency electron throughout the whole crystal and it is also characterised by small difference in electronegativity.

• Molecular orbital method-All the orbitals in the ion or molecule are assumed to take part in bonding. The individual orbitals are combined to give the molecular orbitals, which may stretch over the entire molecule.

• Polarisibilty- When a large negative ion is put near to the small negative ion, since the outer electrons of the large ion are far from nucleus, they are not held very tightly. They will be attracted towards the positive ion. The charged cloud of negative ion will be distorted. This is called the polarization of negative ion by positive ion.

• Polarisibile-Anions are large in size than cations and, therefore, their electron clouds are less tightly held. When two oppositely charged ions approach each other closely, the positively charged cation attracts the outer most electrons of the anions and repels its positively charged nucleus. This results in the distortion or polarisation of the anion.

• Polarizing power-The power of an ion to distort the other ion is known as its polarizing power.

• Resonance- When a compound cannot be assigned by one single structure then closely resembling structures are drawn to explain all their properties. These closely resembling structures are known as resonating structures and the phenomenon is known as resonance.

• Valance bond approach- Covalent bond may be seen as accumulation of high charge density in the internuclear region resulting from the overlapping of atomic orbitals. The strength of the bond depends on the extent of the overlapping, greater the overlapping stronger the bond.

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