General Chemistry: Structure and Bonding

• The material reviews general chemistry, specifically structure and bonding.
• Focus is given to electronic structure of the atom

Location of Electrons

• According to the Heisenberg uncertainty principle, it's impossible to determine exactly where an electron is.
• Electrons residing near nuclei are located in orbitals; examples include s, p, d, and f orbitals.
• Electron density indicates probability of finding an electron in a specific part of the orbital (Ψ²).
• Ψ² > 0 means there's a nonzero probability of finding an electron.
• Ψ² = 0 indicates zero probability.
• Electron density is highest at the nucleus, decreasing exponentially with distance.

Orbital Shapes

• 1s and 2s orbitals are spherical.
• The 2s orbital a nodal sphere with zero probability density.
• Three 2p orbitals include 2px, 2py, and 2pz.
• Each p orbital is dumbbell-shaped with a nodal plane perpendicular to its direction.
• A nodal plane is an area where Ψ = 0, indicating zero probability of finding electrons.
• Three p orbitals align along the x, y, & z axes.

Quantum Numbers

• Electrons are described by 4 quantum numbers.
• The principal quantum number (n) is 1, 2, 3, etc., relevant to the distance of the electron from the nucleus and the atomic shell.
• The second quantum number (l) is 0, 1, 2, 3, ...(n − 1), relevant to the shape of orbitals.
• l = 0 corresponds to an s orbital, l = 1 to a p orbital, and l = 2 to a d orbital.
• The third quantum number (ml) ranges from −l...0...+l, relevant to the orientation of the orbital in space.
• If l = 1, ml can be +1, 0, -1 (corresponding to px, py, pz).
• The fourth quantum number (s value) is ±1/2.

Relationships Between Quantum Numbers

• There are relationships between n, l, and ml.
• For n = 1, l = 0, ml = 0, the orbital designation is 1s.
• For n = 2, l = 0, ml = 0, the orbital designation is 2s.
• For n = 2, l = 1, ml = -1,0,+1 the orbital designation is 2p.
• For n = 3, l = 0, ml = 0, the orbital designation is 3s.
• For n = 3, l = 1, ml = -1,0,+1 the orbital designation is 3p.
• For n = 3, l = 2, ml = -2,-1,0,1,2, the orbital designation is 3d.

Energy of Orbitals

– E(1s) < E(2s) < E(2p).

• 2p orbitals have the same energy (they are degenerate).

Aufbau Principle & Hund's Rule

• The Aufbau principle states that orbitals are filled in order of increasing energy.
• Hund's Rule states the greatest number of unpaired (parallel) spins has the lowest energy.

Pauli Exclusion Principle

• Pauli Exclusion Principle states no two electrons can have the same values ​​for all four quantum numbers.
• 1s² has two unique electrons in the 1s orbital.

Electronic Configurations of Atoms

• Valence electrons are those in the atom's outermost shell.
• Examples given are atomic numbers 1 to 10, specifically H, He, Li, Be, B, C, N, O, F and Ne

Obtaining Noble Gas Configuration

• Chemistry aims to obtain a stable noble gas configuration.
• Octet rule mentions how the greatest stability is when the outer shell is full.
• This applies as in noble gases He, Ne, Ar, Kr, Xe, and Rn.
• Octet rule is 2 for n=1, and 8 for n=2.
• Ionic and covalent bonds derive from the tendency of atoms to attain their stable electronic configurations.

Lewis Structures

• Lewis Structures diagrams show valence electrons for elements 1-18.
• Lewis structures represent bonding electrons as single bonds (single lines).
• Single bonds mean atoms share one pair of electrons
• Double bonds atoms share two pairs of electrons
• Triple bonds share three pairs of electrons
• Nonbonding electrons refer to valence-shell electrons not shared between atoms.
• A pair of nonbonding electrons comprises a lone pair.

How to draw Lewis Structures

• Count the number of valence electrons available, adding for each (-) charge and subtracting for each (+) charge on the molecule.
• Example: CF4*
• Carbon has 4 valence electrons and Fluorine has 7; for a total of 32 electrons
• Connect bonded atoms by lines (covalent bonds).
• Count shared electrons and subtract from total valence electrons for electrons to be added.
• Add electrons in pairs to complete octets, or 2 electrons for hydrogen, when possible.
• If any atom has fewer than 8 electrons, form double or triple bonds to complete the octet.
• Formal charge represents a number of valence electrons - the electrons assigned to the atom
• Example: CF4*
• C: 4 - (4+0) = 0
• F: 7 - (1+6) = 0

Common Bonding

• Molecules may have nonbonding electrons, also called lone pairs.
• Double bonds share two pairs of electrons.
• Triple bonds share three pairs of electrons.

Lewis Structures

• Lewis Structures: shows Common Bonding Patterns (No Charges) for groups in the periodic table

Exceptions to the Octet Rule

• Molecules containing atoms of Group 3A elements, particularly boron and aluminum, may not satisfy the octet rule.
• Only 6 electrons are in the valence shells of boron and aluminum.
• Group 5A or 6A elements can form expanded-octet structures.
• Sulfur can form up to 6 bonds, since 3d orbitals are available to be filled.

Formal Charges

• The equation for formal charge = [group number ] - [nonbonding electrons ] - 1/2 [shared electrons]
• Formal charges track electrons and do not correspond to actual charges in the molecule.
• Rules for Evaluating Lewis Structures avoid placing like charges (+/+ or -/-) on adjacent atoms.
• Keep the total number of charges in the structure to a minimum.
• Minimize the magnitude of charges on any atom, avoiding multiple charges (+2, -3, etc.).
• Negative charges should be placed on the most electronegative elements.
• Positive charges should be placed on the least electronegative elements.

Ionic and Covalent Bonds

• Ionic bonds arise from the transfer of electrons.
• Lithium fluoride (LiF) forms by the transfer of one electron from Li to F. Li → Li⁺: Electrons loss leaves lithium with a full outer shell of two electrons. F → F⁻: The gain of one electron provides fluorine with a full outer shell of eight electrons.
• Covalent bonds are a result from sharing electrons (e.g., molecule F2).
• Each fluorine atom has seven valence electrons; by sharing a pair, they complete their octets (8 valence electrons).
• Other examples: HF, H₂O, NH3, and CH4.
• Non-Polar Bonds happen with bonding electrons that that are equally shared and symmetrically distributed
• Homonuclear diatomic molecules have non-polar bonds for example H2, Cl2, F2, etc
• Electronegativity measures an atom's attraction for shared electrons in a chemical bond.
• When two atoms of different electronegativity form covalent bonds, the resultant electrons are unequally distributed.
• The more electronegative atom draws these electrons drawing closer to it, with a partial negative charge (δ⁻).
• The less electronegative atom gains a partial positive charge of equal and opposite magnitude (δ⁺).
• • Fluorine has more electronegative than hydrogen. There, there is a greater electron density around fluorine.
• The measure of polarity is called dipole moment, μ which measures from the +ve attraction to the -ve
• <0.5: non-polar covalent bond
• 0.5 < 1.7: polar covalent bond

• 1.7: ionic bond

Covalent Bonds

• Electrons are no longer confined to a single atom orbital; instead, they are shared over the entire molecule.

Molecular Orbital Theory

• Covalent bonding results from the overlap of atomic orbitals (AOs) when two atoms converge.
• Atomic orbitals combine to form molecular orbitals (MOs).
• Molecular orbitals are regions of space where electrons are likely to be found.
• Molecular orbitals are generated as Linear Combinations of Atomic Orbitals (LCAOs)
• LCAOs generate from the addition and subtraction of atomic orbital wavefunctions (Ψ).
• The number of resulting MOs is equal to the number of starting AOs
• LCAO Method includes:*
• Derive a set of molecular orbitals.
• Arrange the molecular orbitals in order of increasing energy.
• Distribute the electrons among the available molecular orbitals to get bonding information

Sigma Bonding

• Sigma bonds have electron density between the nuclei.
• A sigma bond can be formed by s—s, p—p, and s—p overlaps, or hybridized orbital overlaps.
• The boning molecular orbital (MO) is less in energy compared to the original atomic orbitals
• The antibonding MO is higher in energy.
• Electrons in bonding region attract both nuclei and mask the charges of repelling each other
• When 1s orbitals of atoms overlap in phase with each other, they interact constructively to form a bonding MO
• sigma-antibonding MO: When two 1s orbitals overlap out of phase, they interact destructively to form an antibonding MO.

Overlap Examples

• Cl2 results when two p orbitals overlap along the nucleus line.
• This generates a bonding orbital and an antibonding orbital, with most of the electron density being on the bond line.
• Linear overlap gives a sigma bonding MO.
• An s orbital overlapping with a p orbital creates sigma-bonding MO and sigma*-antibonding MO.

Pi Bonding

• The sideways overlap of two parallel p orbitals leads to a π-bonding MO and a π*-antibonding MO.
• A pi (π) bond is not as strong as most sigma bonds.

Hybridized Atomic Orbitals

• Carbon may have two unpaired electrons.
• Carbon forms two bonds with two hydrogen atoms.
• In methane (CH4), carbon is bonded to four hydrogens.
• Carbon may require 4 unpaired electrons.
• Hybridization with four unpaired electrons is required.
• Two sigma bonds and Two Pi Bonds are also possible
• sp³ Hybridization mixes the 2s and three 2p orbitals to form four equivalent hybrid orbitals.
• One s + three p = four sp³ hybrid orbitals.
• Four hybrid AOs is = the number of starting AOs.
• hybrid orbitals have electron density concentrated in one direction.
• Hybrids are directional with enhanced overlap.
• Methane(CH4) each CH bonds overlap tetrahedron.
• With a C-H bond energy of 104 kcal/mol.

Sp2 Hybrid Orbitals

• Three orbitals (one s and two p) create three sp² orbitals
• These demonstrate trigonal planar geometry.
• 120° bond angle

Sp Hybrid Orbitals

• Hybrid orbitals merge when orbitals result in different energy from the same combined energy levels.
• Two orbitals (s and p) combine to create two sp orbitals.
• LineaElectron pair repulsion happens
• 180° Bond Angle

Multiple bonds

• A double bond with 1 sigma/ pi bond
• Tripple bond has 1 sigma plus 2 pi bond strength

Molecular Shapes and VSEPR - Valence Shell Electron Repulsion theory

• bond angles are not defined with simple s/p orbitals
• bond angles, Valence shell electron repulsion theory (VSEPR) explains how the shape of bonding explains the energy needed for formation.
• shapes include
  • Tetrahedral
  • Triangle planar
  • linear

Overview of VSEPR theory- Valence Shell Electron Repulsion theory

• Explains the 'shape' of a molecular structure
• The 'Premise' assumes is that electron pairs repel atoms that are further away.
• Coordination number (CN) or Steric number with electron pairs determines the kind of bond structure created..
• Note, one 'Bonding structure' has a triple/ double bond

Examples of VSEPR models and Shapes

• CN=2 Shape is linear, bond angle of 180" (AB2- BEI2 and CO2 for example
• • Linear molecules have a deviations of 180 degree angles in its structure.
• CN-3, is triangular w bond angle of 120 (AB3 and BF3 for example
• The electron rich double bonds cause deviations of 120" bond angels
• CN=4 is "tetrahedral" bond angle of 109.5 AB4 and CH4 (methane) for example.
• Propane is defined as distorted tetrahedron in the CN-4 configuration
• Ammonia results in trigonal pyramidal with lone pairs of electrons, with with bond angle of 107 degrees due to electron repulsion
• Water has a tetrahedral structure bond shape of 105 degrees cause of repulsion.

Dipole Moments and Molecular Polatirty

• To determine the polarity depends on: if
• if the molecule has polar bonds, the arrangement of polar bonds determines the 'shape.'

Bondal arrangements

• Polar Bond strength are different in electronegative environments
• depend on the amount of charge and the degree of seperation with debyes (D).
• Molecular Dipole strength depends on vector sums of bond dipole strength.
• Lone Pairs of electrons determine the 'shape' that determines the polarity.

Review of general chemistry focusing on structure, bonding, and electronic structure. Discussion of electron location based on the Heisenberg uncertainty principle. Examination of orbital shapes including s, p, d, and f orbitals, and electron density.