chemical bonding.pdf

# Introduction to chemical bonding Chemical bonding is the attractive force that holds atoms together in molecules and chemical species, driven by the tendency of systems to achieve lower energy and greater stability [1](#page=1). ## 1. Introduction to chemical bonding Matter is composed of elements, and under normal conditions, most elements do not exist independently but rather as groups of atoms called molecules, which possess distinct properties. The force responsible for holding these constituent atoms together within molecules is known as a chemical bond. The formation of chemical compounds involves the combination of atoms, prompting questions about why atoms combine, why only certain combinations are possible, and why molecules have specific shapes. Various theories, including the Kössel-Lewis approach, Valence Shell Electron Pair Repulsion (VSEPR) Theory, Valence Bond (VB) Theory, and Molecular Orbital (MO) Theory, have been developed to explain these phenomena. These theories are closely linked to advancements in understanding atomic structure, electronic configurations, and the periodic table [1](#page=1). ### 1.1 Kössel-Lewis approach to chemical bonding In 1916, Kössel and Lewis independently provided a satisfactory explanation for chemical bond formation based on electrons and the inertness of noble gases [2](#page=2). #### 1.1.1 Lewis's concept of the atom and stability Lewis viewed an atom as having a positively charged 'kernel' (nucleus plus inner electrons) and an outer shell capable of holding a maximum of eight electrons. He proposed that these eight electrons occupy the corners of a cube surrounding the kernel. The stable octet of electrons represents a particularly stable electronic arrangement. Lewis postulated that atoms achieve this stable octet when linked by chemical bonds [2](#page=2). > **Tip:** The drive towards stability by lowering energy is a fundamental principle underlying chemical bonding [1](#page=1). #### 1.1.2 Mechanisms of bond formation according to Kössel and Lewis Lewis suggested two primary ways atoms achieve a stable octet: 1. **Electron Transfer:** In the case of compounds like sodium chloride (NaCl), an electron can be transferred from one atom to another, forming ions (e.g., $Na^+$ and $Cl^-$) that then attract each other [2](#page=2). 2. **Electron Sharing:** For molecules like $Cl_2$ or $H_2$, bonds are formed by sharing a pair of electrons between atoms, allowing each atom to attain a stable outer octet [2](#page=2). #### 1.1.3 Lewis symbols Lewis introduced simple notations, known as Lewis symbols, to represent valence electrons in an atom. Only outer shell electrons (valence electrons) participate in chemical bonding, as inner shell electrons are shielded and typically not involved [2](#page=2). > **Example:** The Lewis symbol for Carbon (C), which has four valence electrons, is represented as $\cdot\underset{\cdot\cdot}{\stackrel{\cdot\cdot}{C}}\cdot$ [2](#page=2). #### 1.1.4 Significance of Lewis symbols The number of dots in a Lewis symbol indicates the number of valence electrons an atom possesses. This number is crucial for determining the common or group valence of an element, which is typically equal to the number of valence electrons or 8 minus the number of valence electrons [2](#page=2). #### 1.1.5 Kössel's contributions Kössel highlighted several key observations relevant to chemical bonding: * Noble gases are located between highly electronegative halogens and highly electropositive alkali metals in the periodic table [2](#page=2). * Halogen atoms tend to gain electrons to form negative ions, while alkali metal atoms lose electrons to form positive ions [2](#page=2). * These resulting ions achieve stable noble gas electronic configurations [2](#page=2). * Noble gases (except helium with a duplet) possess a stable octet ($ns^2np^6$) in their outer shell [2](#page=2). * Positive and negative ions are stabilized by electrostatic attraction [2](#page=2). > **Example:** The formation of sodium chloride (NaCl) involves the transfer of an electron from sodium to chlorine: > $$Na \rightarrow Na^+ + e^–$$ > $$[Ne 3s^1 \rightarrow [Ne]$$ > $$Cl + e^– \rightarrow Cl^–$$ > $$[Ne 3s^2 3p^5 \rightarrow [Ne 3s^2 3p^6 \text{ or } [Ar]$$ > $$Na^+ + Cl^– \rightarrow NaCl \text{ or } Na^+Cl^–$$ > Similarly, for calcium fluoride ($CaF_2$): > $$Ca \rightarrow Ca^{2+} + 2e^–$$ > $$[Ar]4s^2 \rightarrow [Ar]$$ > $$F + e^– \rightarrow F^–$$ > $$[He 2s^2 2p^5 \rightarrow [He 2s^2 2p^6 \text{ or } [Ne]$$ > $$Ca^{2+} + 2F^– \rightarrow CaF_2 \text{ or } Ca^{2+}(F^–)_2$$ > [2](#page=2). The bond formed due to the electrostatic attraction between positive and negative ions was termed an ionic bond [2](#page=2). --- # Theories of chemical bonding This topic explores the fundamental theories that explain how atoms connect to form molecules and compounds, focusing on the arrangement and behavior of electrons. ### 2.1 The Kössel-Lewis approach to chemical bonding In 1916, Kössel and Lewis independently developed a theory to explain chemical bonding based on electrons. Lewis envisioned an atom with a central "kernel" (nucleus + inner electrons) and an outer shell capable of holding up to eight electrons, arranged at the corners of a cube. This stable arrangement of eight electrons is known as an octet. Lewis proposed that atoms achieve this stable octet configuration when they form chemical bonds [2](#page=2). #### 2.1.1 Lewis symbols Lewis introduced a notation using dots to represent valence electrons, which are the electrons in the outermost shell and are involved in chemical bonding. The number of dots around an element's symbol indicates its valence electrons, which can help determine the element's common or group valence [2](#page=2). #### 2.1.2 Kössel's contributions Kössel highlighted several key observations related to chemical bonding [2](#page=2): * Noble gases are positioned between highly electronegative halogens and highly electropositive alkali metals in the periodic table [2](#page=2). * Halogen atoms tend to gain electrons to form negative ions, while alkali metal atoms lose electrons to form positive ions [2](#page=2). * These ions achieve stable noble gas electronic configurations. Noble gases, except helium (which has a duplet), possess a stable outer shell configuration of eight electrons ($ns^2np^6$) [2](#page=2). * The attraction between oppositely charged ions stabilizes them [2](#page=2). #### 2.1.3 Ionic or electrovalent bond The bond formed by the electrostatic attraction between positive and negative ions is termed the electrovalent bond. The electrovalence of an atom is equal to the number of unit charges on its ion. For example, calcium has a positive electrovalence of two, and chlorine has a negative electrovalence of one. Kössel's ideas form the basis for understanding ion formation through electron transfer and the creation of ionic crystalline compounds [3](#page=3). #### 2.1.4 Formation of NaCl and CaF2 * **NaCl formation:** Na $\rightarrow$ Na$^+$ + e$^-$ [2](#page=2). [Ne 3s$^1$ $\rightarrow$ [Ne [2](#page=2). Cl + e$^-$ $\rightarrow$ Cl$^-$ [2](#page=2). [Ne 3s$^2$ 3p$^5$ $\rightarrow$ [Ne 3s$^2$ 3p$^6$ or [Ar [2](#page=2). Na$^+$ + Cl$^-$ $\rightarrow$ NaCl or Na$^+$Cl$^-$ [2](#page=2). * **CaF2 formation:** Ca $\rightarrow$ Ca$^{2+}$ + 2e$^-$ [2](#page=2). [Ar 4s$^2$ $\rightarrow$ [Ar [2](#page=2). F + e$^-$ $\rightarrow$ F$^-$ [2](#page=2). [He 2s$^2$ 2p$^5$ $\rightarrow$ [He 2s$^2$ 2p$^6$ or [Ne [2](#page=2). Ca$^{2+}$ + 2F$^-$ $\rightarrow$ CaF$_2$ or Ca$^{2+}$(F$^-$)$_2$ [2](#page=2). ### 2.2 Octet rule In 1916, Kössel and Lewis proposed the electronic theory of chemical bonding, which states that atoms combine by transferring or sharing valence electrons to achieve an octet in their valence shells [3](#page=3). ### 2.3 Covalent bond Langmuir refined Lewis's ideas by introducing the term "covalent bond" and moving away from the stationary cubical arrangement of electrons. A covalent bond is formed by sharing a pair of electrons between atoms, with each atom contributing at least one electron to the shared pair. This sharing allows each atom to attain a stable noble gas configuration [3](#page=3). #### 2.3.1 Lewis dot structures Lewis dot structures use dots to represent valence electrons and illustrate bonding in molecules and ions through shared electron pairs. The key conditions for forming covalent bonds are [3](#page=3): * Each bond arises from the sharing of an electron pair [3](#page=3). * Each atom contributes at least one electron to the shared pair [3](#page=3). * Atoms achieve noble gas configurations through electron sharing [3](#page=3). #### 2.3.2 Multiple bonds * **Single covalent bond:** Formed by sharing one electron pair [3](#page=3). * **Double bond:** Formed by sharing two electron pairs between two atoms. Examples include CO$_2$ and ethene [3](#page=3). * **Triple bond:** Formed by sharing three electron pairs between two atoms. Examples include N$_2$ and ethyne [3](#page=3). #### 2.3.3 Writing Lewis dot structures Steps for writing Lewis dot structures include: 1. Sum the valence electrons of all combining atoms [4](#page=4). 2. For anions, add one electron for each negative charge; for cations, subtract one electron for each positive charge [4](#page=4). 3. Arrange the atoms to form a skeletal structure, generally placing the least electronegative atom in the center [4](#page=4). 4. Distribute the total electrons as bonding pairs (single bonds) to connect atoms, ensuring each bonded atom has an octet (except for hydrogen, which achieves a duplet) [4](#page=4). 5. Place remaining electrons as lone pairs on terminal atoms to satisfy their octets. If the central atom lacks an octet, use lone pairs to form multiple bonds. > **Tip:** The least electronegative atom is usually the central atom. #### 2.3.4 Formal charge Formal charge (F.C.) is the hypothetical charge assigned to an atom in a Lewis structure, calculated as: $$ \text{Formal charge (F.C.)} = (\text{Valence electrons in free atom}) - (\text{Non-bonding electrons}) - \frac{1}{2}(\text{Bonding electrons}) $$ [5](#page=5). Formal charges help in selecting the lowest energy Lewis structure, which generally has the smallest formal charges on atoms [6](#page=6). > **Example:** In ozone (O$_3$), the formal charges on the central O is +1, and on the terminal Os are 0 and -1, respectively [6](#page=6). #### 2.3.5 Limitations of the octet rule The octet rule is not universally applicable and has exceptions: * **Incomplete octet:** The central atom has fewer than eight valence electrons (e.g., LiCl, BeH$_2$, BCl$_3$, AlCl$_3$, BF$_3$) [6](#page=6). * **Odd-electron molecules:** Molecules with an odd number of electrons where not all atoms can satisfy the octet rule (e.g., NO, NO$_2$) [6](#page=6). * **Expanded octet:** Elements in the third period and beyond can accommodate more than eight valence electrons due to the availability of d orbitals (e.g., PF$_5$, SF$_6$, H$_2$SO$_4$) [6](#page=6). Other drawbacks include: * Failure to account for the shapes of molecules [7](#page=7). * Inability to explain the relative stability of molecules based on energy [7](#page=7). * It does not explain the reactivity of noble gases like Xenon and Krypton with fluorine and oxygen [7](#page=7). ### 2.4 Bond parameters These are measurable properties of chemical bonds. #### 2.4.1 Bond length Bond length is the equilibrium distance between the nuclei of two bonded atoms in a molecule. It is measured using spectroscopic techniques [8](#page=8). * **Covalent radius:** Half the distance between two similar atoms joined by a covalent bond in the same molecule [8](#page=8). * **Van der Waals radius:** Represents the overall size of an atom in a non-bonded situation, half the distance between two similar atoms in separate molecules in a solid [8](#page=8). For a covalent bond in molecule AB, the bond length R is approximately: $$ R = r_A + r_B $$ [8](#page=8). where $r_A$ and $r_B$ are the covalent radii of atoms A and B, respectively [8](#page=8). #### 2.4.2 Bond angle The bond angle is the angle between the orbitals containing bonding electron pairs around the central atom in a molecule or complex ion, expressed in degrees. It provides insight into the orbital distribution and molecular shape [9](#page=9). #### 2.4.3 Bond enthalpy Bond enthalpy is the energy required to break one mole of bonds of a particular type between two atoms in a gaseous state, measured in kJ mol$^{-1}$ [9](#page=9). * For diatomic molecules, it's the bond dissociation enthalpy. * For polyatomic molecules, the term "average bond enthalpy" is used because the energy to break equivalent bonds can vary due to different chemical environments [10](#page=10). $$ \text{Average bond enthalpy} = \frac{\text{Total bond dissociation enthalpy}}{\text{Number of bonds broken}} $$ [10](#page=10). #### 2.4.4 Bond order In the Lewis description, bond order is the number of bonds between two atoms in a molecule [10](#page=10). * Single bond: Bond order 1 * Double bond: Bond order 2 * Triple bond: Bond order 3 There is a general correlation: as bond order increases, bond enthalpy increases, and bond length decreases. Isoelectronic molecules and ions often have identical bond orders [10](#page=10). #### 2.4.5 Resonance structures When a single Lewis structure cannot accurately represent a molecule's experimentally determined parameters, the concept of resonance is introduced. Resonance involves writing multiple canonical or resonance structures that are considered contributing forms of a resonance hybrid, which accurately describes the molecule. Resonance stabilizes the molecule, lowering its energy, and averages bond characteristics [10](#page=10) [11](#page=11). > **Misconceptions about resonance:** Canonical forms do not have independent existence, molecules do not rapidly switch between forms, and there is no equilibrium between them [11](#page=11). #### 2.4.6 Polarity of bonds * **Nonpolar covalent bond:** Formed between two similar atoms where the shared electron pair is equally attracted by both nuclei [11](#page=11). * **Polar covalent bond:** Formed between two different atoms where the shared electron pair is displaced towards the more electronegative atom [11](#page=11). **Dipole moment (µ):** A measure of the polarity of a bond or molecule, defined as the product of the magnitude of the charge and the distance between the centers of positive and negative charge [12](#page=12). $$ \text{Dipole moment} (\mu) = \text{charge (Q)} \times \text{distance of separation (r)} $$ [12](#page=12). It is expressed in Debye units (D). Dipole moment is a vector quantity. In polyatomic molecules, the net dipole moment is the vector sum of individual bond dipoles and depends on molecular geometry [12](#page=12). > **Note:** In molecules like BeF$_2$ and BF$_3$, the bond dipoles cancel out due to symmetry, resulting in a zero net dipole moment [12](#page=12). **Fajans' rules:** These rules describe the partial covalent character of ionic bonds: * Smaller cation size and larger anion size increase covalent character [13](#page=13). * Greater charge on the cation increases covalent character [13](#page=13). * Cations with (n-1)d$^n$s$^0$ configuration (transition metals) are more polarizing than those with noble gas configurations (ns$^2$np$^6$) [13](#page=13). ### 2.5 Valence Bond (VB) Theory Valence Bond theory, developed by Heitler, London, and Pauling, explains bond formation through the overlap of atomic orbitals [18](#page=18). #### 2.5.1 Orbital overlap concept A covalent bond forms when atomic orbitals containing unpaired electrons with opposite spins overlap. The extent of overlap determines the strength of the bond; greater overlap leads to a stronger bond [19](#page=19). #### 2.5.2 Directional properties of bonds The directional nature of bonds, which dictates molecular geometry, is explained by the overlap and hybridization of atomic orbitals. Simple atomic orbital overlap does not fully account for the observed bond angles in molecules like CH$_4$, NH$_3$, and H$_2$O [20](#page=20). #### 2.5.3 Types of overlapping and nature of covalent bonds Covalent bonds are classified based on orbital overlap: * **Sigma ($\sigma$) bond:** Formed by end-to-end (head-on) overlap of atomic orbitals along the internuclear axis. This can occur between s-s, s-p, or p-p orbitals. $\sigma$ bonds are stronger than $\pi$ bonds due to greater overlap [21](#page=21). * **Pi ($\pi$) bond:** Formed by the sideways overlap of atomic orbitals, with their axes parallel and perpendicular to the internuclear axis. $\pi$ bonds consist of two saucer-type charged clouds above and below the plane of the participating atoms [21](#page=21). ### 2.6 Hybridization Hybridization is the process where atomic orbitals of slightly different energies mix to form new, equivalent hybrid orbitals with specific shapes and energies, which are then used for bond formation [21](#page=21). #### 2.6.1 Types of hybridization * **sp hybridisation:** Involves mixing one s and one p orbital to form two sp hybrid orbitals, resulting in linear geometry (180° bond angle). Example: BeCl$_2$ [22](#page=22). * **sp$^2$ hybridisation:** Involves mixing one s and two p orbitals to form three equivalent sp$^2$ hybrid orbitals, resulting in trigonal planar geometry (120° bond angle). Example: BCl$_3$ [22](#page=22) [23](#page=23). * **sp$^3$ hybridisation:** Involves mixing one s and three p orbitals to form four equivalent sp$^3$ hybrid orbitals, resulting in tetrahedral geometry (109.5° bond angle). Examples: CH$_4$ NH$_3$ (pyramidal, ~107°), H$_2$O (bent/angular, ~104.5°). The presence of lone pairs influences bond angles due to greater repulsion [17](#page=17) [23](#page=23). #### 2.6.2 Hybridisation involving d orbitals Elements in the third period and beyond can utilize d orbitals in hybridization: * **sp$^3$d hybridisation:** Involves one s, three p, and one d orbital to form five sp$^3$d hybrid orbitals, leading to trigonal bipyramidal geometry. Example: PCl$_5$ [26](#page=26). * **sp$^3$d$^2$ hybridisation:** Involves one s, three p, and two d orbitals to form six sp$^3$d$^2$ hybrid orbitals, resulting in octahedral geometry. Example: SF$_6$ [26](#page=26). * **dsp$^2$ hybridisation:** Involves one d, one s, and two p orbitals to form four equivalent dsp$^2$ hybrid orbitals, leading to square planar geometry. Example: [Ni(CN)$_4$]$^{2-}$ [25](#page=25). ### 2.7 Molecular Orbital (MO) Theory Developed by Hund and Mulliken, MO theory describes electrons in a molecule as occupying molecular orbitals (MOs) that are influenced by multiple nuclei [26](#page=26). #### 2.7.1 Formation of Molecular Orbitals: Linear Combination of Atomic Orbitals (LCAO) Atomic orbitals (represented by wave functions $\psi$) combine linearly to form molecular orbitals. For two atomic orbitals $\psi_A$ and $\psi_B$ [27](#page=27): $$ \sigma = \psi_A + \psi_B \quad (\text{bonding MO, lower energy}) $$ [27](#page=27). $$ \sigma^\ast = \psi_A - \psi_B \quad (\text{antibonding MO, higher energy}) $$ [27](#page=27). Bonding MOs have electron density between nuclei, stabilizing the molecule, while antibonding MOs have a nodal plane between nuclei, destabilizing the molecule [28](#page=28). #### 2.7.2 Conditions for the combination of atomic orbitals For effective LCAO: 1. Combining atomic orbitals must have similar energies [28](#page=28). 2. They must have the same symmetry about the molecular axis [28](#page=28). 3. They must overlap to the maximum extent [28](#page=28). #### 2.7.3 Types of Molecular Orbitals Molecular orbitals are designated by Greek letters: * **$\sigma$ (sigma) MOs:** Symmetrical around the bond axis, formed from s-s, p$_z$-p$_z$ overlap [28](#page=28). * **$\pi$ (pi) MOs:** Not symmetrical around the bond axis, formed from p$_x$-p$_x$ or p$_y$-p$_y$ overlap [29](#page=29). #### 2.7.4 Energy level diagram for molecular orbitals The relative energy levels of MOs depend on the specific atoms involved. For O$_2$ and F$_2$, the order is: $$ \sigma_{1s} < \sigma^\ast_{1s} < \sigma_{2s} < \sigma^\ast_{2s} < \sigma_{2p_z} < (\pi_{2p_x} = \pi_{2p_y}) < (\pi^\ast_{2p_x} = \pi^\ast_{2p_y}) < \sigma^\ast_{2p_z} $$ [29](#page=29). For molecules like Li$_2$, Be$_2$, B$_2$, C$_2$, and N$_2$, the $\pi$ MOs are lower in energy than $\sigma_{2p_z}$: $$ \sigma_{1s} < \sigma^\ast_{1s} < \sigma_{2s} < \sigma^\ast_{2s} < (\pi_{2p_x} = \pi_{2p_y}) < \sigma_{2p_z} < (\pi^\ast_{2p_x} = \pi^\ast_{2p_y}) < \sigma^\ast_{2p_z} $$ [30](#page=30). #### 2.7.5 Electronic configuration and molecular behavior * **Stability of molecules:** A molecule is stable if the number of electrons in bonding MOs (N$_b$) is greater than in antibonding MOs (N$_a$) [30](#page=30). * **Bond order (b.o.):** $$ \text{Bond order (b.o.)} = \frac{1}{2} (N_b - N_a) $$ [30](#page=30). A positive bond order indicates a stable molecule, while zero or negative indicates instability [30](#page=30). * **Nature of the bond:** Integral bond orders of 1, 2, or 3 correspond to single, double, or triple bonds, respectively [30](#page=30). * **Bond length:** Decreases as bond order increases [30](#page=30). * **Magnetic nature:** Molecules with all doubly occupied MOs are diamagnetic; those with singly occupied MOs are paramagnetic (e.g., O$_2$) [30](#page=30). --- # Bond parameters and properties This section details various measurable properties of chemical bonds, such as bond length, bond angle, bond enthalpy, bond order, and bond polarity, along with the concept of resonance structures. ### 3.1 Bond length Bond length is defined as the equilibrium distance between the nuclei of two bonded atoms in a molecule. This parameter is measured using spectroscopic, X-ray diffraction, and electron-diffraction techniques. Each atom contributes to the bond length; in a covalent bond, this contribution is known as the covalent radius. The covalent radius is approximately half the distance between two similar atoms joined by a covalent bond within the same molecule. The van der Waals radius, on the other hand, represents the overall size of an atom in a nonbonded situation and is half the distance between two similar atoms in separate molecules within a solid [8](#page=8). | Bond type | Covalent Bond Length (pm) | | :--------------------------------- | :------------------------ | | O–H | 96 | [9](#page=9). | C–H | 107 | [9](#page=9). | N–O | 136 | [9](#page=9). | C–O | 143 | [9](#page=9). | C–N | 143 | [9](#page=9). | C–C | 154 | [9](#page=9). | C=O | 121 | [9](#page=9). | N=O | 122 | [9](#page=9). | C=C | 133 | [9](#page=9). | C=N | 138 | [9](#page=9). | C≡N | 116 | [9](#page=9). | C≡C | 120 | [9](#page=9). Some typical average bond lengths for single, double, and triple bonds are provided in the table above. Table 4.3 lists bond lengths for common molecules [9](#page=9). ### 3.2 Bond angle A bond angle is defined as the angle between the orbitals that contain the bonding electron pairs around the central atom in a molecule or complex ion. Bond angles are measured in degrees and can be determined experimentally using spectroscopic methods. They provide insight into the distribution of orbitals around the central atom and thus help in determining the molecule's shape. For instance, the H–O–H bond angle in water is a key descriptor of its molecular geometry [9](#page=9). ### 3.3 Bond enthalpy Bond enthalpy, also known as bond dissociation enthalpy, is the amount of energy required to break one mole of a specific type of bond between two atoms in the gaseous state. Its unit is kJ mol–1. A larger bond dissociation enthalpy indicates a stronger bond [9](#page=9). For example, the H–H bond enthalpy in hydrogen is 435.8 kJ mol–1 [9](#page=9): `H2(g) → H(g) + H(g); ∆aH° = 435.8 kJ mol–1` [9](#page=9). For multiple bonds: `O2 (O = O) (g) → O(g) + O(g); ∆aH° = 498 kJ mol–1` [9](#page=9). `N2 (N ≡ N) (g) → N(g) + N(g); ∆aH° = 946.0 kJ mol–1` [9](#page=9). For heteronuclear diatomic molecules like HCl: `HCl (g) → H(g) + Cl (g); ∆aH° = 431.0 kJ mol–1` [9](#page=9). In polyatomic molecules, bond strength measurement is more complex due to the varying chemical environments of the same bond type. For instance, in water, the enthalpy to break the two O–H bonds differs. The first O–H bond requires 502 kJ mol–1, while the second requires 427 kJ mol–1 [10](#page=10). `H2O(g) → H(g) + OH(g); ∆aH1° = 502 kJ mol–1` [10](#page=10). `OH(g) → H(g) + O(g); ∆aH2° = 427 kJ mol–1` [10](#page=10). Because of these variations, the term **average bond enthalpy** is used for polyatomic molecules. It is calculated by dividing the total bond dissociation enthalpy by the number of bonds broken. For water, the average bond enthalpy is [10](#page=10): `Average bond enthalpy = (502 + 427) / 2 = 464.5 kJ mol–1` [10](#page=10). ### 3.4 Bond order In the Lewis description of covalent bonding, bond order is defined as the number of bonds between two atoms in a molecule. For example, H2 has a bond order of 1 (single bond), O2 has a bond order of 2 (double bond), and N2 has a bond order of 3 (triple bond). Similarly, CO has a bond order of 3 [10](#page=10). There is a general correlation between bond order, bond enthalpy, and bond length: * With an increase in bond order, bond enthalpy increases. * With an increase in bond order, bond length decreases [10](#page=10). Isoelectronic molecules and ions often share identical bond orders. For example, F2 and O2^2- have a bond order of 1, while N2, CO, and NO+ have a bond order of 3 [10](#page=10). ### 3.5 Resonance structures When a single Lewis structure is insufficient to accurately represent a molecule's experimentally determined parameters, the concept of resonance is employed. Resonance occurs when a molecule can be represented by multiple Lewis structures, called canonical or resonance structures, which have similar energies and the same arrangement of nuclei and electron pairs. The actual structure of the molecule is a hybrid of these canonical forms, known as the resonance hybrid. Resonance is depicted using a double-headed arrow between canonical structures [10](#page=10). For example, the ozone molecule (O3) can be represented by two canonical structures, each with one single and one double oxygen-oxygen bond. Experimentally, the oxygen-oxygen bond lengths in O3 are identical (128 pm), which is intermediate between a typical single bond (148 pm) and a double bond (121 pm). The resonance hybrid accurately reflects this intermediate bond character [10](#page=10). > **Tip:** The canonical forms of resonance have no real existence; the molecule exists as a single resonance hybrid, not as a rapid interconversion between different forms. Resonance contributes to molecular stability by lowering the energy of the resonance hybrid compared to any single canonical structure. It also averages the bond characteristics across all involved bonds [11](#page=11). Other examples of resonance include the carbonate ion (CO3^2-) and the carbon dioxide molecule (CO2). In CO3^2-, experimental findings show all carbon-oxygen bonds are equivalent, necessitating a resonance description of three canonical forms where the negative charge is delocalized. For CO2, the experimentally determined carbon-oxygen bond length (115 pm) lies between a double bond (121 pm) and a triple bond (110 pm), indicating resonance between structures with C=O and C≡O character [11](#page=11). ### 3.6 Polarity of bonds In reality, no bond is purely ionic or purely covalent; all bonds exhibit some degree of both characters [11](#page=11). **Nonpolar covalent bonds** are formed between two similar atoms (e.g., H2, O2, Cl2), where the shared electron pair is attracted equally by both nuclei and resides precisely between them [12](#page=12). **Polar covalent bonds** form between atoms with different electronegativities. The shared electron pair is displaced towards the more electronegative atom, creating partial positive and negative charges on the atoms. For example, in HF, the electron pair is pulled towards the more electronegative fluorine [12](#page=12). This charge separation results in a **dipole moment** ($\mu$), defined as the product of the magnitude of the charge and the distance between the centers of positive and negative charge [12](#page=12). $$ \text{Dipole moment } (\mu) = \text{charge } (Q) \times \text{ distance of separation } (r) $$ Dipole moments are typically expressed in Debye (D) units, where $1 \text{ D} = 3.33564 \times 10^{-30} \text{ C m}$ [12](#page=12). A dipole moment is a vector quantity. Conventionally, it is shown with an arrow pointing from the positive to the negative center. In chemistry, a crossed arrow is often used on Lewis structures, with the cross on the positive end and the arrowhead on the negative end, indicating the direction of electron density shift [12](#page=12). For polyatomic molecules, the net dipole moment is the vector sum of individual bond dipoles and depends on the molecule's spatial arrangement [12](#page=12). * In water (H2O), a bent molecule, the two O–H bond dipoles add up to a net dipole moment of approximately 1.85 D ($6.17 \times 10^{-30}$ C m) [12](#page=12). * In BeF2, a linear molecule, the two equal bond dipoles point in opposite directions and cancel out, resulting in a zero net dipole moment [12](#page=12). * Similarly, BF3, a trigonal planar molecule, has a zero dipole moment because the three bond moments cancel each other vectorially [12](#page=12). * In NH3 and NF3, both pyramidal molecules with a lone pair on nitrogen, the net dipole moments differ. NH3 has a larger dipole moment (1.47 D) than NF3 (0.23 D) because in NH3, the lone pair dipole reinforces the bond dipoles, while in NF3, it opposes them [13](#page=13). | Type of Molecule | Example | Dipole Moment, $\mu$(D) | Geometry | | :----------------- | :------ | :----------------------- | :------- | | Molecule (AB) | HF | 1.78 | linear | [13](#page=13). | | HCl | 1.07 | linear | [13](#page=13). | | HBr | 0.79 | linear | [13](#page=13). | | HI | 0.38 | linear | [13](#page=13). | | H2 | 0 | linear | [13](#page=13). | Molecule (AB2) | H2O | 1.85 | bent | [13](#page=13). | | H2S | 0.95 | bent | [13](#page=13). | | CO2 | 0 | linear | [13](#page=13). | Molecule (AB3) | NH3 | 1.47 | trigonal-pyramidal | [13](#page=13). | | NF3 | 0.23 | trigonal-pyramidal | [13](#page=13). | | BF3 | 0 | trigonal-planar | [13](#page=13). | Molecule (AB4) | CH4 | 0 | tetrahedral | [13](#page=13). | | CHCl3 | 1.04 | tetrahedral | [13](#page=13). | | CCl4 | 0 | tetrahedral | [13](#page=13). Ionic bonds also exhibit partial covalent character, as described by Fajans' rules [13](#page=13): * Smaller cation size and larger anion size increase covalent character. * Greater charge on the cation increases covalent character. * For cations of similar size and charge, those with $(n-1)d^n ns^0$ configurations (transition metals) are more polarizing than those with noble gas configurations $ns^2 np^6$ (alkali and alkaline earth metals) [13](#page=13). The cation's polarising power, the anion's polarisability, and the extent of anion distortion determine the percent covalent character of an ionic bond [13](#page=13). --- # Hydrogen bonding and its types Hydrogen bonding is an attractive force between molecules that arises from the partial positive charge on a hydrogen atom bonded to a highly electronegative atom [32](#page=32). ### 4.1 Cause of formation of hydrogen bond When a hydrogen atom is covalently bonded to a highly electronegative element (such as nitrogen, oxygen, or fluorine), the electron pair shared in the covalent bond is pulled significantly towards the electronegative atom. This causes the hydrogen atom to acquire a partial positive charge ($\delta+$), while the electronegative atom gains a partial negative charge ($\delta-$). This partially positively charged hydrogen atom can then form an attractive force with another highly electronegative atom of an adjacent molecule. This attraction is known as a hydrogen bond and is weaker than a covalent bond. The magnitude of hydrogen bonding influences the physical state and properties of compounds, being strongest in the solid state and weakest in the gaseous state [32](#page=32) [33](#page=33). ### 4.2 Types of hydrogen bonds There are two primary types of hydrogen bonds: intermolecular and intramolecular [33](#page=33). #### 4.2.1 Intermolecular hydrogen bond An intermolecular hydrogen bond occurs between two different molecules. These molecules can be of the same compound or different compounds [33](#page=33). > **Example:** The hydrogen bond in hydrogen fluoride (HF) molecules is an intermolecular hydrogen bond, where the hydrogen of one HF molecule is attracted to the fluorine of another HF molecule. Hydrogen bonding in alcohol and water molecules are also examples [32](#page=32) [33](#page=33). #### 4.2.2 Intramolecular hydrogen bond An intramolecular hydrogen bond is formed within the same molecule. This type of hydrogen bond occurs when a hydrogen atom is situated between two highly electronegative atoms (F, O, or N) that are part of the same molecule [33](#page=33). > **Example:** In the *ortho*-nitrophenol molecule, the hydrogen atom is positioned between two oxygen atoms, allowing for the formation of an intramolecular hydrogen bond [33](#page=33). --- ## Common mistakes to avoid - Review all topics thoroughly before exams - Pay attention to formulas and key definitions - Practice with examples provided in each section - Don't memorize without understanding the underlying concepts

| Term | Definition | |------|------------| | Chemical Bond | An attractive force that holds together the constituent atoms, ions, or other particles within different chemical species, enabling the formation of molecules and compounds. | | Molecule | A group of atoms that are found to exist together as a single, distinct species possessing characteristic properties, held together by chemical bonds. | | Kössel-Lewis Approach | A historical approach to understanding chemical bonding that was based on the inertness of noble gases and the role of valence electrons in achieving stable electron configurations. | | Octet Rule | The principle that atoms tend to combine in such a way that each atom has eight electrons in its valence shell, leading to a stable electron configuration similar to noble gases. | | Valence Electrons | The electrons located in the outermost shell of an atom, which are involved in chemical bonding and determine the chemical properties of the element. | | Lewis Symbols | Simple notations, introduced by G.N. Lewis, that use dots around an element's symbol to represent its valence electrons, aiding in the visualization of chemical bonding. | | Electrostatic Attraction | The attractive force that exists between oppositely charged ions, which plays a crucial role in stabilizing ionic compounds formed through chemical bonding. | | Inertness of Noble Gases | The characteristic property of noble gas elements to be unreactive under normal conditions, attributed to their stable, complete outer electron shells, often an octet. | | Covalent Bond | A chemical bond formed by the sharing of electron pairs between atoms, allowing each atom to achieve a stable outer octet of electrons. | | Electrovalent Bond | A bond formed by the electrostatic attraction between oppositely charged ions, which are created by the transfer of electrons from one atom to another. | | Formal Charge | The hypothetical charge assigned to an atom in a molecule or polyatomic ion, calculated as the difference between the valence electrons of a free atom and the electrons assigned to it in the Lewis structure. | | Resonance Structures | Multiple Lewis structures that are necessary to accurately represent a molecule when a single structure is insufficient, indicating that the actual molecule is a hybrid of these structures. | | Bond Length | The equilibrium distance between the nuclei of two bonded atoms in a molecule. | | Bond Angle | The angle between the orbitals containing bonding electron pairs around the central atom in a molecule or complex ion, expressed in degrees. | | Bond Enthalpy | The amount of energy required to break one mole of bonds of a particular type between two atoms in the gaseous state. | | Bond Order | In the Lewis description of covalent bonding, it is the number of bonds between two atoms in a molecule, representing the number of shared electron pairs. | | Valence Bond Theory | A theory that explains chemical bond formation based on the overlap of atomic orbitals, where atomic orbitals combine to form new equivalent orbitals. | | Sigma (σ) Bond | A type of covalent bond formed by the head-on overlap of atomic orbitals along the internuclear axis. | | Pi (π) Bond | A type of covalent bond formed by the sideways overlap of atomic orbitals, where their axes remain parallel to each other and perpendicular to the internuclear axis. | | Hybridization | The process of intermixing atomic orbitals of slightly different energies to form a new set of equivalent orbitals, known as hybrid orbitals, which are used in bond formation. | | Molecular Orbital Theory | A theory that describes chemical bonding in terms of molecular orbitals, which are formed by the combination of atomic orbitals and are influenced by two or more nuclei. | | Bonding Molecular Orbital | A molecular orbital formed by the constructive interference (addition) of atomic orbitals, possessing lower energy and greater stability than the original atomic orbitals. | | Antibonding Molecular Orbital| A molecular orbital formed by the destructive interference (subtraction) of atomic orbitals, possessing higher energy and lower stability than the original atomic orbitals. | | Linear Combination of Atomic Orbitals (LCAO) | An approximate method used in molecular orbital theory where molecular orbitals are formed by the addition or subtraction of the wave functions of atomic orbitals. | | VSEPR Theory (Valence Shell Electron Pair Repulsion Theory) | A theory that predicts the geometry of molecules based on the principle that electron pairs in the valence shell of the central atom repel each other and arrange themselves to minimize this repulsion. | | Covalent Radius | In a covalent bond, this is the contribution of each atom to the bond length, representing approximately half the distance between the nuclei of two similar atoms joined by a covalent bond in the same molecule. | | Van der Waals Radius | This radius represents the overall size of an atom, including its valence shell, in a nonbonded situation. It is determined as half the distance between two similar atoms in separate molecules within a solid. | | Resonance Hybrid | The actual structure of a molecule that is accurately described as a combination (hybrid) of several contributing resonance structures. Its energy is lower than any individual resonance structure, leading to stabilization. | | Nonpolar Covalent Bond| A covalent bond formed between two identical atoms where the shared pair of electrons is attracted equally by both nuclei, resulting in an even distribution of electron density. | | Polar Covalent Bond | A covalent bond formed between two different atoms where the shared electron pair is displaced more towards the atom with higher electronegativity, creating partial positive and negative charges on the atoms. | | Dipole Moment | A measure of the polarity of a molecule, defined as the product of the magnitude of the charge separation and the distance between the centers of positive and negative charge. It is a vector quantity usually expressed in Debye units. | | Hydrogen Bond | An attractive force that binds a hydrogen atom of one molecule to an electronegative atom (such as Fluorine, Oxygen, or Nitrogen) of another molecule. This bond is weaker than a covalent bond and acts as a bridge between atoms. | | Intermolecular Hydrogen Bond | A hydrogen bond that is formed between two different molecules, which can be of the same or different compounds. Examples include hydrogen bonding in HF, alcohol, or water molecules. | | Intramolecular Hydrogen Bond | A hydrogen bond that forms when a hydrogen atom is positioned between two highly electronegative atoms (Fluorine, Oxygen, or Nitrogen) that are present within the same molecule. An example is found in ortho-nitrophenol, where hydrogen is situated between two oxygen atoms. | | Electronegativity | A measure of the tendency of an atom to attract a bonding pair of electrons. Highly electronegative elements like Nitrogen, Oxygen, and Fluorine play a crucial role in the formation of hydrogen bonds. | | Fractional Positive Charge ($\delta+$) | A partial positive charge that develops on an atom, such as hydrogen, when the electron pair in a covalent bond is shifted towards a more electronegative atom, making the hydrogen atom more electropositive. | | Fractional Negative Charge ($\delta-$) | A partial negative charge that develops on an atom, such as Fluorine, Oxygen, or Nitrogen, when it attracts the electron pair from a covalent bond more strongly than the bonded hydrogen atom, becoming more electronegative. |