3.2 Chemical Bonds

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3.2.1 Atomic radius

I. ionic model: a description of chemical bonding in terms of ions

II. ionic solid: an assembly of cations and anions stacked together in a regular array

III Ionic solids are hard, rigid (does not bend), and often brittle (forms cracks)

1. multiple cations and anions are bonded together by electrostatic force (forces resulting from opposite charges) and therefore is rigid and is hard to remove individual ions

2. When sudden force is applied, the cations that used to touch the anions can now touch with the cations, which leads to an electrostatic repulsion. (accounts for brittleness)

IV Ionic solids often are electric conductors in solution (electrolyte) or as a liquid (melt) state

V lattice energy: the difference in energy between the state of separated gaseous cations and anions and the state as an ionic solid

1. a Born-Haber cycle is used to calculate the lattice energy of an ionic solid (Ref. Figure 19)

2. You can imagine formation of the solid from its neutral gaseous components in 3 steps:

   1. gaseous metal atoms release electrons, forming cations.

   2. The released electrons attach to gaseous nonmetal atoms, forming anions.

   3. The gaseous cations and anions clump together as a crystalline solid.

3. Ionic bonding is favorable if the final state (ionic compound) is more favorable in energy than its initial state (separate ions)

VI Ionic bonding is a global interaction that is a characteristic of the entire crystal.

1. all anions attract all cations, and like ions repel all like ions.

2. The interaction of two individual ions can be expressed quantitatively using Coulomb's potential energy: $E_{p,12} = \frac{(z_{1}e)(z_{2}e)}{4 \pi \epsilon_{0} r_{12}}$ (Eq. 20)

   1. $z_{1}e$ and $z_{2}e$ represent the magnitude of charges for a cation and an anion

   2. $r_{12}$ represents the distance between the two ions

   3. $\epsilon$ (epsilon) is the permittivity; its value depends on the nature of the medium between the charges, such as air, water, or oil.

   4. The vacuum permittivity ($\epsilon_{0}$) is the permittivity when the medium is a vacuum.

   5. illustrates that if the distance between the two ions decrease or if the magnitude of charge of either of the ions increase, the interaction becomes stronger.

3. If the global interaction property of ionic bonding is taken into account (like in crystalline solids), the molar potential energy of a one-dimensional is: $E_{p} = -A \times \frac{N_{A} z^{2} e^{2}}{4 \pi \epsilon_{0} d}$ (Eq. 21)

   1. Madelung constant (A): a numerical value that depends on arrangement of ions.

VII As illustrated in Figure 1, as the separation (d) between ions increases, the potential energy decreases until repulsive forces dominate where the potential energy rises exponentially

1. The Born-Mayer Equation calculates the minimum potential energy shown in Figure 18: $E_{p,min} = -A \times \frac{N_{A}||z_{1}z_{2}||}{4 \pi \epsilon_{0} d} (1 - \frac{d*}{d})$ (Eq.22)

2. d* is a constant dependent on the compressibility of the crystal.

3.2.2 Covalent Bonding

I covalent bond: a pair of electrons shared between two atoms

II coordinate covalent bond: when both electrons come from a single atom.

1. Note that this type of bonding is no different from a normal covalent bond.

2. Coordinate covalent bonds are also known as dative covalent bonds.

III Octet rule: atoms bond together to complete a full shell by sharing electron pairs

IV There are several "tips" in predicting the molecular arrangement of a given chemical formula:

1. In general, the central atom tends to be the element with the lowest ionization energy.

2. When desperate, try arranging the atoms symmetrically around the central atom.

   1. This rule has many exceptions, such as $N_{2}O$ ($NNO$).

V resonance: the blending of structures

1. resonance structure: one way to represent a molecule in terms of Lewis structures

2. resonance hybrid: the blend of resonance structures represents the actual molecule

3. A set of rules that determines the contribution of each resonance structure is:

   1. Each contributing structure must have its nuclei in the same positions

   2. Structures with the same energy contribute equally to the resonance

   3. low-energy structures contribute more than high-energy structures

VI Formal charge: the charge of an atom assuming that all electrons are shared equally

1. it is calculated by (V = valence electrons, L = lone pair e-, B = bonding pair e-) Formal charge = $V - (L + \frac{1} {2} B)$ (Eq. 23)

2. formal charge exaggerates the covalent character of bonding

3. The Lewis structure with formal charges closest to zero for all of its atoms in the molecule represents the lowest energy arrangement of atoms and electrons.

   1. For a molecule of water ($H_{2}O$), oxygen has 6 - (4 + 2) = 0.

VII Oxidation number: the charge on an atom assuming that the more electronegative atom possesses all of the electrons in a bond

1. For a molecule of water ($H_{2}O$), oxygen has 6 - 8 = -2.

VIII radical: species having electrons with unpaired spins

1. tends to be unstable and frequently causes chain reactions due to unpaired electrons

2. antioxidant: reacts rapidly with radicals to prevent further radical reactions

3. biradical: a molecule with two unpaired electrons

IX There are many exceptions to the octet rule:

1. Most reactive intermediates do not obey the octet rule.

2. Hypervalent molecules: A molecule which the center atom possesses more than eight electrons (an expanded valence shell)

X expanded valence shell: when the central atom expands its octet and accommodates more than eight electrons. Conditions for an “expanded valence shell” is:

1. The central atom must be sufficiently big enough to accommodate higher coordination.

   1. Period 2 elements are too small to have more than four bonding spaces

2. The central atom must have access to its d-orbitals.

3. the electronegativity of ligands (substituents) is also important

   1. $PH_{5}$ doesn't exist but $P Cl_{l5}$ does; the ligands must be electronegative enough to make sure the central atom does not have too high electron density