Its All about Pj Problem Strings (SiPjAjk) - 7 Spaces Of Interest (Si) and their associated Basic Sequences; 7 Pj Problems of Interest (PPI) and their Alleles (Ajk)

Expressions Of Pj Problems.

Pj Problems - Overview
Celestial Stars As Expressions Of Pj Problems
The Number Line As Expression Of Pj Problems
Geometries As Expressions Of Pj Problems
7 Spaces Of Interest - Overview
Triadic Unit Mesh
Creation As Expression Of Pj Problems
The Atom As Expression Of Pj Problems
Survival As Expression Of Pj Problems
Energy As Expression Of Pj Problems
Light As Expression Of Pj Problems
Heat As Expression Of Pj Problems
Sound As Expression Of Pj Problems
Music As Expression Of Pj Problems
Language As Expression of Pj Problems
Stories As Expressions of Pj Problems
Work As Expression Of Pj Problems
States Of Matter As Expressions Of Pj Problems
Buoyancy As Expression Of Pj Problems
Nuclear Reactions As Expressions Of Pj Problems
Molecular Shapes As Expressions Of Pj Problems
Electron Configurations As Expressions Of Pj Problems
Chemical Bonds As Expressions Of Pj Problems
Energy Conversion As Expression Of Pj Problems
Chemical Reactions As Expressions Of Pj Problems
Electromagnetism As Expression Of Pj Problems
Continuity As Expression Of Pj Problems
Growth As Expression Of Pj Problems
Human-cells As Expressions Of Pj Problems
Proteins As Expressions Of Pj Problems
Nucleic Acids As Expressions Of Pj Problems
COHN - Nature's Engineering Of The Human Body
The Human-Body Systems As Expressions Of Pj Problems
Vision As Expression Of Pj Problems
Walking As Expression Of Pj Problems
Behaviors As Expressions Of Pj Problems
Sensors' Sensings As Expressions Of Pj Problems
Beauty As Expression Of Pj Problems
Faith, Love, Charity As Expressions Of Pj Problems
Photosynthesis As Expressions Of Pj Problems
Weather As Expression Of Pj Problems
Systems As Expressions Of Pj Problems
Algorithms As Expressions Of Pj Problems
Tools As Expressions Of Pj Problems
Networks As Expressions Of Pj Problems
Search As Expressions Of Pj Problems
Differential Calculus As Expression Of Pj Problems
Antiderivative As Expression Of Pj Problems
Integral Calculus As Expression Of Pj Problems
Economies As Expresions Of Pj Problems
Inflation As Expression Of Pj Problems
Markets As Expressions Of Pj Problems
Money Supply As Expression Of Pj Problems
Painting As Expressions Of Pj Problems
Molecular Shape - Sigma (σ) Bonds - Pi (π) Bonds

1. Define the following: (a) Resonance Structures (b) Sigma Bonds (c) Pi Bonds
(d) Localized Electrons (e) Delocalized Electrons
2. Identify the bonds (sigma, or pi, or both) that formed each of the following compounds:
(a) H2 (Hydrogen) (b) HCl (hydrochloric acid) (c) C2H4 (Ethylene) (d) N2 (Nitrogen)
(e) H2CO (Formaldehyde) (f) C6H6 (Benzene).
3. What valence atomic orbitals formed the bonds of the compounds listed in problem (2)?
4. What compound listed in problem (2) has Pi (π) bonds that cannot be entirely described as localized Pi (π) bonds?
5. Write the general representative strings for Sigma (σ) bonds and Pi (π) bonds.

1(a) Resonance structures (also called resonance forms): the different Lewis structures that are equally acceptable descriptions of a single molecule.
(b) Sigma (σ) bond: a covalent bond in which the electron density is concentrated symmetrically about the line joining the nuclei (internuclear axis) of the bonded atoms. In other words, a covalent bond in which the internuclear axis passes through the middle of the region of orbital overlap (figure 9.16).
Sigma Bonds
Pi (π) bond: a covalent bond in which the electron density is concentrated above and below the internuclear axis of the bonded atoms. In other words, a covalent bond in which the line passing through the middle of the region of orbital overlap is perpendicular to the internuclear axis of the bonded atoms (figure 9.17).
Pi Bonds
Localized electrons: σ and π electrons totally associated with the atoms that form the bond. Such bonds are localized bonds.
Delocalized electrons: electrons not totally associated with the atoms that form the bond. Such bonds are delocalized bonds. Delocalized bonds are commomly encountered in molecules that have two or more resonance structures involving π bonds. Such bonds are called delocalzed π bonds.

2(a) The valence-shell configuration of H = 1s1. Two s orbitals overlap to form H2. The internuclear axis of the atoms passes through the middle of the orbital overlap. So, H2 is formed by a sigma (σ) bond (figure 9.19).
Hydrogren Bonds
(b) The valence-shell configuration of H = 1s1. The valence-shell configuration of Cl = 1s22s22p63s23p5. The s orbital of H overlaps with the p orbital of Cl to form HCl. The internuclear axis of the atoms passes through the middle of the orbital overlap. So, HCl is formed by a sigma (σ) bond (figure 9.20).
HCl Bonds
(c) Molecular geometry of C2H4 is trigonal planar. This geometry implies the sp2 hybrid orbitals on C. The valence-shell configuration of H = 1s1. The valence-shell configuration of C = 1s22s22p2. One 2s electron is promoted to the third 2p orbital. This 2s orbital then merges with two 2p orbitals to form 3 sp2 hybrid orbitals. Each C atom uses its 3 sp2 hybrid orbitals to form σ bonds with the other C atom and two H atoms (a total of 5 σ bonds). The 2 valence electrons in the unhybridized 2p orbitals of the two C atoms form a π bond. Hence the double bond between the two C atoms (one σ bond and one π bond). In total, five σ bonds and one π bond form C2H4 (figure 9.21). Ethylene Bonds
(d) The valence-shell configuration of N = 1s22s22p3. N2 is formed by one σ bond and two π bonds. A total of 3 pairs of 2p orbitals formed the bonds. a pair of 2p orbitals form the sigma bond and 2 pairs of 2p orbitals form the pi bonds (figure 9.22).
Nitrogen Bonds
(e) Molecular geometry of H2CO is trigonal planar. This geometry implies the sp2 hybrid orbitals on C. The valence-shell configuration of H = 1s1. The valence-shell configuration of C = 1s22s22p2. One 2s electron is promoted to the third 2p orbital. This 2s orbital then merges with two 2p orbitals to form 3 sp2 hybrid orbitals. The C atom uses its 3 sp2 hybrid orbitals to form σ bonds with two H atoms and one O atom. The remaining electron is in an unhybridized 2p orbital. The O atom has three electron domains around it which implies that it has sp2 hybrid orbitals. One of the sp2 hybrid orbital is used to form the C-O σ bond; the other two hold the two nonbonding elctron pairs of the O atom. The remaining electron is in an unhybridized 2p orbital. The unhybridized 2p orbital of the C atom and the unhybridized 2p orbital of the O atom formed the π bond between the C atom and the O atom. So, in H2CO, there 3 σ bonds and 1 π bond (figure 9.23).
Formaldehyde Bonds
(f) Molecular geometry of C6H6 (Benzene) indicates that each carbon atom is surrounded by three atoms at 120o angles. This geometry implies three sp2 hybrid orbitals on each C atom of benzene. Consequently, six C-C σ bonds and C-H σ bonds are formed from the sp2 hybrid orbital set. Each C atom has an unhybridized 2p orbital. So, benzene has a total of six unhybridized carbon 2p orbitals in a ring arrangement which form the three π bonds responsible for the resonance structures of the benzene molecule (figure 9.24).
Benzene Bonds

3(a) overlap of two s orbitals (b) overlap of an s orbital and a p orbital (c) overlap of four s orbitala and four sp2 hybrid orbitals, overlap of two sp2 hybrid orbitals, overlap of two unhybridized p orbitals (d) overlap of p orbitals (e) overlap of two s orbitals and two sp2 hybrid orbitals, overlap of two sp2 hybrid orbitals, overlap of two unhybridized p orbitals (f) overlap of six s orbitals and six sp2 hybrid orbitals, overlap of twelve sp2 hybrid orbitals, overlap of six unhybridized p orbitals.

4.C6H6 (Benzene) is the compound in the list of compounds in problem (2) whose pi (π) bonds cannot be entirely described as localized π bonds. There are three resonance structures presented by the benzene molecule. Two of the resonance structures have localized π bonds while one has delocalized π bonds (figure 9.25).
Benzene Bonds

5. Sigma (σ) and Pi (π) bonds are covalent bonds. The regions where the bondings occur are the valence orbital overlaps. So Sigma (σ) bonds and Pi (π) bonds have: S7P6A64 (multi-criteria permutation), S7P3A31 (force - pull) and S7P6A66 (chemical interaction) as their general representative strings.



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