Chapter Notes

CHEMICAL BONDING AND MOLECULAR STRUCTURE

Introduction to Chemical Bonds

Matter consists of elements, which, apart from noble gases, rarely exist as single, independent atoms. Instead, atoms group together to form molecules. The attractive force that holds these atoms, ions, or other constituents together in a chemical species is called a chemical bond.

The study of chemical bonding helps us answer fundamental questions like:

• Why do atoms combine?
• Why do only certain combinations of atoms form molecules?
• Why do molecules have definite, predictable shapes?

Atoms form bonds to lower their overall energy and achieve a more stable state. Several theories have been developed to explain chemical bonding, including the Kössel-Lewis approach, Valence Shell Electron Pair Repulsion (VSEPR) Theory, Valence Bond (VB) Theory, and Molecular Orbital (MO) Theory.

KÖSSEL-LEWIS APPROACH TO CHEMICAL BONDING

In 1916, Kössel and Lewis independently proposed a theory of chemical bonding based on the chemical inertness of noble gases. They suggested that atoms combine to achieve a stable electron configuration similar to that of the nearest noble gas.

Lewis's Theory

• Lewis imagined an atom as a positively charged 'Kernel' (the nucleus plus inner electrons) surrounded by an outer shell of valence electrons.
• He proposed that a stable outer shell contains eight electrons, an octet.
• Atoms can achieve this stable octet by either transferring electrons (forming ions) or sharing electrons (forming covalent bonds).

Lewis Symbols To simplify the representation of valence electrons, G.N. Lewis introduced Lewis symbols. These consist of the element's symbol surrounded by dots, where each dot represents one valence electron.

• Significance: The number of dots indicates the number of valence electrons, which helps determine the element's group valence. The group valence is often equal to the number of dots or 8 minus the number of dots.

Kössel's Theory (Ionic Bonding) Kössel focused on the formation of ionic compounds and highlighted these key points:

• Highly electropositive alkali metals (which easily lose electrons) and highly electronegative halogens (which easily gain electrons) are separated by the stable noble gases in the periodic table.
• Alkali metals form positive ions (cations) by losing electrons, and halogens form negative ions (anions) by gaining electrons.
• By gaining or losing electrons, these atoms achieve the stable octet electron configuration ($ns^2np^6$) of a noble gas.
• The resulting positive and negative ions are held together by strong electrostatic attraction, forming an electrovalent bond (or ionic bond).

1. Sodium (Na) loses one electron to form a sodium ion ($Na^+$) and achieve the electron configuration of Neon (Ne). $\text{Na} \rightarrow \text{Na}^+ + e^-$ $[\text{Ne}]3s^1 \rightarrow [\text{Ne}]$
2. Chlorine (Cl) gains that electron to form a chloride ion ($Cl^-$) and achieve the electron configuration of Argon (Ar). $\text{Cl} + e^- \rightarrow \text{Cl}^-$ $[\text{Ne}]3s^23p^5 \rightarrow [\text{Ne}]3s^23p^6 \text{ or } [\text{Ar}]$
3. The oppositely charged ions attract each other to form NaCl. $\text{Na}^+ + \text{Cl}^- \rightarrow \text{NaCl}$

Octet Rule

The Octet Rule, developed by Kössel and Lewis, states that atoms tend to combine by transferring or sharing valence electrons in such a way that each atom has an octet (eight electrons) in its outermost shell. This gives them the stable electron configuration of a noble gas.

Covalent Bond

In 1919, Langmuir refined Lewis's ideas by introducing the term covalent bond to describe the bond formed by the mutual sharing of electrons between atoms.

Key Conditions for Covalent Bonding:

• Each bond is formed by sharing a pair of electrons.
• Each combining atom contributes at least one electron to the shared pair.
• Through sharing, the atoms achieve a stable outer-shell noble gas configuration.

Structures that use dots to represent shared and unshared valence electrons are called Lewis dot structures.

Single, Double, and Triple Bonds

• Single Bond: Formed when two atoms share one pair of electrons (e.g., H-H in $H_2$, C-Cl in $CCl_4$).
• Double Bond: Formed when two atoms share two pairs of electrons (e.g., C=O in $CO_2$, C=C in $C_2H_4$).
• Triple Bond: Formed when two atoms share three pairs of electrons (e.g., N≡N in $N_2$, C≡C in $C_2H_2$).

Lewis Representation of Simple Molecules (the Lewis Structures)

Lewis dot structures are useful for visualizing bonding. Here is a step-by-step guide to drawing them:

1. Count Total Valence Electrons: Sum the valence electrons of all combining atoms.
2. Adjust for Charge:
   • For an anion (negative ion), add one electron for each negative charge.
   • For a cation (positive ion), subtract one electron for each positive charge.
3. Draw the Skeletal Structure: Connect the atoms with single bonds. The least electronegative atom is usually the central atom.
4. Distribute Remaining Electrons: Place the remaining electrons as lone pairs on the terminal atoms to satisfy their octets. Any leftover electrons are placed on the central atom.
5. Form Multiple Bonds if Necessary: If the central atom does not have an octet, move lone pairs from terminal atoms to form double or triple bonds until the central atom's octet is complete.

Given

• Atoms: Carbon (C) and Oxygen (O)

To Find

The Lewis dot structure for CO.

Solution

Step 1. Count valence electrons. Carbon (Group 14) has 4 valence electrons. Oxygen (Group 16) has 6 valence electrons. Total valence electrons = $4 + 6 = 10$.

Step 2. Draw the skeletal structure. The skeletal structure is C-O. This uses 2 electrons for the single bond.

Step 3. Distribute remaining electrons. $10 - 2 = 8$ electrons remain. We place them to complete the octet on the more electronegative atom, Oxygen. Oxygen gets 3 lone pairs (6 electrons), and Carbon gets the remaining 1 lone pair (2 electrons). The structure is: $:C - \ddot{O}:$ In this structure, Oxygen has an octet, but Carbon only has 4 electrons.

Step 4. Form multiple bonds. To satisfy Carbon's octet, we move lone pairs from Oxygen to form multiple bonds. If we form a double bond, Carbon has 6 electrons. If we form a triple bond, both atoms have an octet.

Final Answer The correct Lewis structure for CO is with a triple bond, which satisfies the octet rule for both atoms. $:C \equiv O:$

Given

• Ion: Nitrite ($NO_2^-$)

To Find

The Lewis structure for $NO_2^-$.

Solution

Step 1. Count valence electrons. Nitrogen (N) has 5 valence electrons. Each Oxygen (O) has 6 valence electrons, so $2 \times 6 = 12$. The -1 charge adds 1 electron. Total valence electrons = $5 + 12 + 1 = 18$.

Step 2. Draw the skeletal structure. Nitrogen is the central atom: O-N-O. This uses 4 electrons for two single bonds.

Step 3. Distribute remaining electrons. $18 - 4 = 14$ electrons remain. Distribute them to the terminal oxygen atoms first to complete their octets (6 electrons each, totaling 12). The remaining 2 electrons are placed on the central nitrogen atom as a lone pair. The structure is: $[:\ddot{O} - \ddot{N} - \ddot{O}:]^-$ In this structure, the oxygens have octets, but nitrogen only has 6 electrons.

Step 4. Form a multiple bond. To complete nitrogen's octet, we move a lone pair from one of the oxygen atoms to form a double bond with nitrogen. Since either oxygen can do this, it leads to two possible (resonance) structures.

Final Answer The Lewis structure for $NO_2^-$ involves one single bond, one double bond, and a lone pair on the nitrogen. $[\ddot{O}=\ddot{N}-\ddot{O}:]^- \leftrightarrow [:\ddot{O}-\ddot{N}=\ddot{O}]^-$

Formal Charge

The formal charge is a hypothetical charge assigned to an atom in a molecule, assuming that electrons in a covalent bond are shared equally between atoms. It helps in selecting the most stable Lewis structure among different possibilities.

The formula for calculating formal charge is: $\text{Formal Charge} = \left[\begin{array}{c} \text{Total valence} \\ \text{electrons in} \\ \text{free atom} \end{array}\right] - \left[\begin{array}{c} \text{Total non-bonding} \\ \text{(lone pair)} \\ \text{electrons} \end{array}\right] - \frac{1}{2} \left[\begin{array}{c} \text{Total bonding} \\ \text{(shared)} \\ \text{electrons} \end{array}\right]$

Limitations of the Octet Rule

While useful, the octet rule is not universal. Here are its main exceptions:

• The incomplete octet of the central atom: The central atom has fewer than eight electrons. This is common for elements with less than four valence electrons, like in $LiCl$, $BeH_2$, and $BCl_3$.
• Odd-electron molecules: Molecules with an odd total number of valence electrons cannot satisfy the octet rule for all atoms. Examples include nitric oxide ($NO$) and nitrogen dioxide ($NO_2$).
• The expanded octet: Elements in the third period and beyond have vacant d-orbitals and can accommodate more than eight electrons in their valence shell. Examples include $PF_5$ (10 electrons around P), $SF_6$ (12 electrons around S), and $H_2SO_4$.

Other Drawbacks of Octet Theory:

• It cannot explain why some noble gases (like Xenon and Krypton) form compounds (e.g., $XeF_2$).
• It does not predict the shape of molecules.
• It gives no information about the energy or relative stability of molecules.

IONIC OR ELECTROVALENT BOND

The formation of a stable ionic compound depends on two main factors:

1. Ease of ion formation: This involves the ionization enthalpy (energy required to remove an electron from an atom) and the electron gain enthalpy (energy change when an atom gains an electron). Ionic bonds form most easily between elements with low ionization enthalpies (metals) and elements with highly negative electron gain enthalpies (non-metals).
2. Arrangement in the crystal lattice: Ions in a solid are arranged in an orderly three-dimensional pattern called a crystal lattice, held together by strong electrostatic (coulombic) forces.

Lattice Enthalpy The stability of an ionic compound is ultimately determined by its lattice enthalpy.

Lattice Enthalpy is the energy required to completely separate one mole of a solid ionic compound into its constituent ions in the gaseous state. For example, for NaCl: $\text{NaCl}(s) \rightarrow \text{Na}^+(g) + \text{Cl}^-(g) \quad \Delta_{\text{lattice}}H^\ominus = +788 \text{ kJ mol}^{-1}$ A large release of energy during lattice formation (highly negative enthalpy of formation) is what makes an ionic compound stable, even if the initial energy cost to form the ions is positive.

BOND PARAMETERS

Bond parameters are the measurable properties of a chemical bond that help define its characteristics.

Bond Length

Bond length is the equilibrium distance between the nuclei of two bonded atoms in a molecule.

• It is related to the covalent radius of each atom, which is roughly half the distance between two identical atoms joined by a covalent bond.
• Bond length decreases as the number of bonds between two atoms (bond order) increases. A triple bond is shorter than a double bond, which is shorter than a single bond. (e.g., C≡C < C=C < C-C).

Bond Angle

Bond angle is the angle between the orbitals containing bonding electron pairs around a central atom. It is expressed in degrees and is crucial for determining the overall shape of a molecule. For example, the H-O-H bond angle in water is $104.5^\circ$.

Bond Enthalpy

Bond enthalpy is the amount of energy required to break one mole of a specific type of bond between two atoms in the gaseous state. It is a measure of bond strength.

• The unit is kJ mol⁻¹.
• A higher bond enthalpy indicates a stronger bond. For example, the N≡N bond in $N_2$ has a very high bond enthalpy ($946.0 \text{ kJ mol}^{-1}$), making the molecule very stable.
• In polyatomic molecules like $H_2O$, the energy to break the first O-H bond is different from the second. In such cases, we use the average bond enthalpy.

Bond Order

In the Lewis description, bond order is the number of chemical bonds between a pair of atoms.

• Single bond: Bond order = 1
• Double bond: Bond order = 2
• Triple bond: Bond order = 3
• General Correlation: As bond order increases, bond enthalpy increases, and bond length decreases.

Resonance Structures

Sometimes, a single Lewis structure cannot accurately describe the bonding in a molecule or ion. For example, in ozone ($O_3$), experimental data shows that both oxygen-oxygen bonds are identical in length (128 pm), which is intermediate between a single bond (148 pm) and a double bond (121 pm).

To address this, we use the concept of resonance.

• We draw multiple valid Lewis structures, called canonical structures or resonance structures.
• The actual structure of the molecule, called the resonance hybrid, is an average of all the canonical forms. It is more stable (lower in energy) than any single canonical structure.
• Resonance is indicated by a double-headed arrow ($\leftrightarrow$).

• Canonical forms are imaginary; only the resonance hybrid is real.
• The molecule does not switch back and forth between canonical forms. It exists as a single, stable hybrid structure.

Given

• Ion: Carbonate ($CO_3^{2-}$)

To Find

An explanation of its structure using resonance.

Solution

A single Lewis structure for $CO_3^{2-}$ would show one C=O double bond and two C-O single bonds. This would imply that one bond is shorter and stronger than the other two. However, experimental evidence shows that all three carbon-oxygen bonds are identical in length and strength.

This is explained by resonance. The carbonate ion is a resonance hybrid of three equivalent canonical structures. In the hybrid structure, the double bond character and the negative charge are delocalized, or spread out, over all three oxygen atoms.

Final Answer The structure of the carbonate ion is best described as a resonance hybrid of the following three canonical forms: