Chemical Bonding and Molecular Structure
Lewis Electron-Dot Symbols
Overview: These symbols, also known as Lewis dot structures, represent only the valence electrons (outermost shell electrons) of an atom. These are the electrons involved in chemical bonding and determine an atom's chemical properties.
Application: Electrons are depicted as dots placed around the element symbol, which represents the nucleus and inner-shell electrons. The dots are typically placed singly on the four sides of the symbol before pairing them up, representing the s and p orbitals in the valence shell.
Ions and Electron-Dots
Addition for Anions: For anions, one dot is added for each negative charge. This reflects the gain of electrons to achieve a stable electron configuration, often a full octet (eight valence electrons) for main group elements (e.g., O²⁻ gains 2 electrons, resulting in 8 dots around the oxygen symbol).
Removal for Cations: For cations, one dot is removed for each positive charge. This represents the loss of electrons, typically to also achieve a stable electron configuration, often resembling that of a preceding noble gas (e.g., Na⁺ loses its single valence electron, resulting in 0 dots).
Example Symbols:
Na⁺: No dots (Sodium loses its 1 valence electron)
Mg²⁺: No dots (Magnesium loses its 2 valence electrons)
Al³⁺: No dots (Aluminum loses its 3 valence electrons)
O²⁻: 2 dots added to its original 6, totaling 8 dots
Cl⁻: 1 dot added to its original 7, totaling 8 dots
Observation: The number of electron dots in ions varies depending on their charge, which directly indicates the electron configuration differences and confirms whether the atom has gained or lost electrons to achieve a more stable state, often an octet.
Potential Energy and Bond Length
Simplest Molecule: The hydrogen molecule (H₂) is often used to illustrate the relationship between potential energy and interatomic distance. As two hydrogen atoms approach each other, the potential energy initially decreases due to attractive forces between the nucleus of one atom and the electron of the other.
Key Measurement: The bond length of H₂ is 74 picometers (pm). At this optimal internuclear distance, the attractive and repulsive forces are balanced, and the potential energy of the system is at its minimum.
Bond Dissociation Energy: This is the energy required to break a specific covalent bond in a gas-phase molecule, essentially the energy needed to overcome the attractive forces at the bond length and separate the atoms. It represents the depth of the potential energy well.
Bond Distance: This is the equilibrium distance between the nuclei of two bonded atoms at which the potential energy of the molecule is minimized. It directly corresponds to the bond length.
Depicting Covalent Bonds (Lewis Structures)
Molecule Representations: Lewis structures show how valence electrons are arranged in molecules, including bonding pairs and lone pairs. For example:
HCl: One shared pair of electrons between H and Cl, and three lone pairs on Cl.
H₂O: Two shared pairs between O and each H, and two lone pairs on O.
NH₃: Three shared pairs between N and each H, and one lone pair on N.
NH₄⁺: Four shared pairs between central N and each H, with no lone pairs on N (the positive charge delocalizes electron density).
HO⁻: One shared pair between O and H, and three lone pairs on O (due to the negative charge).
CH₄: Four shared pairs between central C and each H, with no lone pairs on C.
Octet Rule: Atoms in a molecule (especially main group elements in periods 2 and 3) tend to achieve a stable configuration of eight electrons in their valence shell after bonding. Hydrogen, being an exception, tends to achieve a duet (two valence electrons).
Kekule Structures
Lewis Structure: Uses dots to represent individual valence electrons. This can become cumbersome for larger molecules.
Bonding Pairs: Shared pairs of dots between atoms represent covalent bonds where electrons are mutually attracted to both nuclei.
Lone Pairs: Unshared pairs of dots belonging to a single atom represent non-bonding electrons.
Kekule's Contribution: Kekule structures (often called line-angle or structural formulas) simplify Lewis structures by transforming bonding pairs of electrons into lines. This makes it visually clearer to identify connections and bond types:
Lines (-): Represent bonding pairs, with a single line indicating one bonding pair (single bond), a double line for two bonding pairs (double bond), and a triple line for three (triple bond).
Dots (\cdot\cdot): Still represent lone pairs of electrons, maintaining information about non-bonding electrons.
Bond Order and Multiple Bonds
Definition: Bond order is defined as the number of covalent bonds (or bonding pairs) between two atoms in a molecule. It is a measure of the strength and stability of the bond.
Types of Bonds:
Single bonds (e.g., C-C in ethane) have a bond order of 1, involving one shared electron pair.
Multiple bonds (double/triple) have a higher bond order:
Double bonds (e.g., C=C in ethene) have a bond order of 2, involving two shared electron pairs.
Triple bonds (e.g., C\equivC in ethyne) have a bond order of 3, involving three shared electron pairs.
Example Structures for Bond Order:
C₂H₄ (ethene): The C=C bond has a bond order of 2. Each C-H bond has a bond order of 1.
C₂H₂ (ethyne): The C\equivC bond has a bond order of 3. Each C-H bond has a bond order of 1.
CH₂O (formaldehyde): The C=O bond has a bond order of 2. Each C-H bond has a bond order of 1.
Calculation: Determine the bond order for each bond by counting the number of lines connecting the atoms in the Kekule structure. A higher bond order generally indicates a stronger and shorter bond.
Bond Length and Covalent Radius
Definition of Bond Length: The bond length is the equilibrium distance between the nuclei of two atoms joined by a covalent bond. It is a characteristic property of a chemical bond, influenced by atom size and bond order.
Measurement Methods: Bond lengths are experimentally determined using techniques such as X-ray diffraction for solid compounds or microwave spectroscopy for gas-phase molecules. These methods provide precise internuclear distances.
Relation to Covalent Radii: The bond length (d) between two bonded atoms (A and B) can be approximated as the sum of their individual covalent radii (rA + rB). This additive property allows for estimation of bond lengths in various compounds.
Covalent Radii: These are empirical values assigned to atoms based on experimentally determined bond lengths in homonuclear (A-A) and heteronuclear (A-B) diatomic molecules. They provide a measure of an atom's size when it is engaged in a covalent bond.
The covalent radius is generally less than the atomic or ionic radius (for the neutral atom or its common ion) because atoms effectively 'overlap' when forming a bond.
Covalent radii tend to decrease across a period due to increasing effective nuclear charge pulling valence electrons closer to the nucleus.
Covalent radii tend to increase down a group as new electron shells are added, increasing the overall size of the atom.
Individual Covalent Radii Values
C has a covalent radius: 76 pm
O has a covalent radius: 66 pm
H has a covalent radius: 31 pm
Single Bond Length Predictions (calculated as rA + rB):
C-C Single Bonds (76 + 76 = 152 pm, experimentally 154 pm in ethane). The values 134 pm (double) and 120 pm (triple) represent shorter bond lengths for higher bond orders.
C-H Bonds (76 + 31 = 107 pm, experimentally ranging 106-111 pm depending on the molecule). The variety of values provided (110 pm, 110 pm, 108 pm, 106 pm, 111 pm) reflects the influence of the molecular environment on specific bond lengths.
C-O Bonds (76 + 66 = 142 pm single bond; 121 pm for C=O double bond).
O-H Bonds (66 + 31 = 97 pm, experimentally 96 pm).
Observation: As bond order increases (from single to double to triple bond), the bond length decreases. This is because a greater number of shared electron pairs leads to stronger attractive forces between the multiple electrons and the nuclei, pulling the atoms closer together.
Drawing Chemical Structures (Lewis/Kekule)
Steps to Draw Structures: A systematic approach ensures accurate representation of electron distribution.
Identify or predict the skeleton structure for the molecule. This means determining which atoms are bonded to which. The least electronegative atom (excluding hydrogen, which is almost always terminal) is typically the central atom. Elements that can form several bonds (like C, N, P, S) are often central; peripheral atoms, like halogens or hydrogen, usually form only one or two bonds.
Count total number of valence electrons in the molecule or ion:
Add the number of valence electrons for each element in the molecule (corresponding to its group number for main group elements).
Adjust for charges: Add one electron for each negative charge (for anions), or subtract one electron for each positive charge (for cations).
Position the bonding electron pairs around the central atom. Connect the central atom to each peripheral atom with a single bond (a line or two dots). Subtract these electrons (2 per bond) from the total valence electron count.
Distribute remaining electrons to peripheral atoms to achieve octets (or duets for hydrogen). Start with the most electronegative peripheral atoms first. Subtract these electrons (as lone pairs) from the remaining electron count.
Place any leftover electrons on the central atom as lone pairs. If the central atom still does not have an octet after all peripheral atoms and lone pairs are placed, convert lone pairs from peripheral atoms (usually single-bonded halogens or oxygen) into multiple bonds (double or triple bonds) to satisfy the central atom's octet.
Exceptions: Central atoms may not always obey the octet rule (e.g., expanded octets for elements in period 3 and beyond, or incomplete octets for B and Be). Sometimes, lone pairs on peripheral atoms can convert into additional bonds to satisfy the central atom's octet, especially with oxygen or nitrogen, forming double or triple bonds.
Example structures for practice: Drawing these helps solidify the rules:
CF₄ (Carbon tetrafluoride): Central C, four C-F single bonds, 3 lone pairs on each F. C achieves octet.
CCl₃OH (Trichloromethanol): Central C, bonded to 3 Cl atoms, and one OH group. O bonded to C and H. Follow octet rule for all C, Cl, O, and H.
CCl₂O (Phosgene): Central C, double bond to O, single bonds to 2 Cl atoms. All atoms satisfy octet (except H if present).
CO₂ (Carbon dioxide): Central C, double bonds to each O. All atoms satisfy octet.
BF₃ (Boron trifluoride): Central B, single bonds to 3 F atoms. B has an incomplete octet (6 electrons).
SF₆ (Sulfur hexafluoride): Central S, single bonds to 6 F atoms. S has an expanded octet (12 electrons).
Bond Polarity: Use \delta+ and \delta- to indicate polar covalent bonds. This notation signifies a partial positive or negative charge on atoms within a bond due to differences in electronegativity, creating a dipole moment.
Analyzing Formal Charge in Ions
Examples of Ions: NH₄⁺ (ammonium) and HO⁻ (hydroxide) are great examples to illustrate formal charge calculations, which help determine the most plausible Lewis structure and identify charge localization.
Identifying Charge Localization: Formal charge helps pinpoint where the positive or negative charge in an ion or molecule is most likely to reside, contributing to an understanding of its reactivity and properties.
Formal Charge Calculation: Formal charge (FC) is a theoretical charge assigned to an atom in a molecule, assuming that electrons in all covalent bonds are shared equally between the bonded atoms. This is a formalism and doesn't represent the true charge.
Share all bonding electrons equally between bonded atoms for the purpose of calculation.
Assign all non-bonding (lone pair) electrons exclusively to the atom they belong to.
Calculate formal charge (FC) using two equivalent formulas:
FC = \text{# of valence electrons} - \frac{1}{2}(\text{# of bonding electrons}) - \text{# of lone pair electrons}
FC = \text{# of valence electrons} - (\text{# of bonds}) - (\text{# of lone pair electrons})
The sum of formal charges in a molecule must equal the overall charge of the molecule (zero for a neutral molecule) or the charge of the ion.
Concepts of Resonance
Kekule Structures: Resonance occurs when a single Lewis (or Kekule) structure cannot adequately describe the true bonding in a molecule or ion. Instead, two or more valid Lewis structures, called resonance structures, are required. For the NO₂⁻ ion, two equivalent resonance structures can be drawn, showing the double bond alternating between the central nitrogen atom and each oxygen atom. This implies multiple distributions of electrons, particularly those in pi bonds and lone pairs.
Calculation of Formal Charge: For NO₂⁻, calculating formal charges on N and O atoms in each resonance structure helps assess their plausibility. The true N-O bond order is an average (1.5 in NO₂⁻, not a pure single or double bond), and the formal charge on the oxygen atoms is delocalized.
Resonance Hybrid: The actual structure of a molecule or ion for which resonance structures can be drawn is an average, or hybrid, of all contributing resonance structures. The resonance hybrid is more stable than any single resonance structure because the electron density is delocalized over a larger area.
Examples to Practice:
CO₃²⁻ ion (carbonate): Has three equivalent resonance structures, with the double bond delocalized over all three C-O bonds.
CO₂ molecule (carbon dioxide): Has three resonance structures, two of which are minor contributors with formal charges.
Emphasis on understanding how resonance structures share the same atomic framework (connectivity) while differing only in the placement of pi bonds and lone pair electrons. This electron delocalization leads to increased stability.
Factors Favoring the Stability of Resonance Structures
When multiple resonance structures are possible, some contribute more to the overall resonance hybrid than others. The following criteria help determine the relative stability (and thus contribution) of resonance structures:
Minimize charges across resonance structures: Structures with fewer or no formal charges are generally more stable and contribute more significantly to the resonance hybrid. Separating charges increases potential energy.
In CO₂: If all atoms have octets, the best matching electronegativity is chosen: If formal charges are unavoidable, structures where negative charges reside on more electronegative atoms and positive charges on less electronegative atoms are more stable. For example, in CO₂, the resonance structure with two C=O double bonds and no formal charges is the most stable.
For structures lacking octets: Prioritizing octets is paramount. Favor those structures where all atoms (especially second-period elements) satisfy the octet rule, regardless of charge considerations (even if it means a less electronegative atom carries a positive charge). An incomplete octet is a major destabilizing factor.
Example Resonance Structures: Analyzing stability criteria through structures of N₂O (nitrous oxide) and CO (carbon monoxide):
N₂O: The structure N\equivN-O (with a formal positive charge on the central N and negative on O) is more stable than N-N\equivO (negative on terminal N, positive on O) because the negative charge is on the more electronegative oxygen.
CO: The primary resonance structure has a triple bond (C\equivO) with a formal positive charge on O and negative on C, despite O being more electronegative, because it fulfills the octet rule for both C and O. Other structures would have incomplete octets.
Exceptions to the Octet Rule
While the octet rule is a powerful guiding principle, there are several important exceptions:
Examples of Expanded Octets: Occur for elements in Period 3 and beyond (e.g., P, S, Cl, Br, I, Xe). These atoms have readily accessible vacant d-orbitals that can participate in bonding, allowing them to accommodate more than eight valence electrons.
Molecules like PCl₅ (10 electrons around P), SF₆ (12 electrons around S), SO₃²⁻ (10 electrons around S), SO₄²⁻ (12 electrons around S) are common examples of expanded octets. The maximum number of electrons can be 10, 12, or even more, depending on the number of bonds and lone pairs.
Incomplete Octets: Found in compounds of Group 2 (Be) and Group 3 (B, Al). These elements are electron-deficient and are stable with fewer than eight valence electrons.
Examples: BeH₂ (4 electrons around Be), BF₃ (6 electrons around B), AlCl₃ (6 electrons around Al). These molecules act as Lewis acids, readily accepting electron pairs.
Unpaired Electrons (Odd-Electron Species or Radicals): These molecules or ions have an odd total number of valence electrons, making it impossible for all atoms to achieve an octet. They typically contain a single unpaired electron and are highly reactive.
Examples: NO (nitric oxide, 11 valence electrons), NO₂ (nitrogen dioxide, 17 valence electrons). These are often called free radicals.
Practice Tasks: Draw Lewis or Kekule structures for various nitrogen oxides (N₂O, NO, N₂O₃, NO₂, N₂O₄, N₂O₅) to observe both octet rule obedience and exceptions, particularly odd-electron species and differences in bonding arrangements.