*Its All about Pj Problem Strings (S _{i}P_{j}A_{jk}) -
7 Spaces Of Interest (S_{i}) and their associated Basic Sequences; 7 Pj Problems of Interest (PPI) and their Alleles (A_{jk})*

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 - Valence Bond Theory - Orbital Hybridization

1. Define the following: (a) Electron Orbital (b) Orbital Overlap (c) Electron Promotion

(d) Hund's Rule (e) Hybrid Orbitals (f) Valence Bond Theory

2. Indicate the hybridization and bond angles associated with each of the following electron-domain geometries:
(a) linear (b) trigonal planar (c) tetrahedral (d) trigonal bipyramidal (e) octahedral.

3(a) Describe the steps needed to construct the hybrid orbitals that appropriately explains the bonding in BF_{3}?

(b) Name the hybrid orbitals constructed in (a) and sketch on one origin, the large lobes of the hybrid orbitals.

(c) If there are any unhybridized valence atomic orbitals of B in BF_{3} how are they oriented relative to the hybridized orbitals?

4. Indicate the hybridization of the central atom in:

(a) BCl_{3} (b) AlCl_{4}^{-} (c) PF_{6}^{-}

5. Write general representative strings for orbital hybridization.

1(a) *Electron Orbital*: a region of space around the nucleus of an atom where an electron is very likely to be found according to the quantum mechanics model of the atom.

1(b) *Orbital Overlapp*: The region of space between the nuclei of the two atoms involved in a covalent bond that can be shared by their respective valence atomic orbitals. This region of space results from the overlap of the valence atomic orbitals.

1(c)
*Electron-promotion*: the transfer of an electron from a valence atomic orbital of a subshell of a valence shell to an empty valence atomic orbital of the next subshell of the same valence shell.

1(d) *Hund's Rule*: The pairing of electrons in orbitals occurs only after each orbital has had one electron placed in it.

1(e) *Hybrid Orbitals*: the set of orbitals derived from the *mixing* of two or more valence atomic orbitals. The *mixing* process is called *hybridization*.

There are five basic types of hybrid orbitals (figure 9.4):
*sp hybrid orbitals*, *sp ^{2} hybrid orbitals*,

1(f)

2(a) A *linear* electron domain geometry is derived from 2 bonding domains and zero non bonding domains. Consequently, *two s,p* hybrid orbital set resulting from the hybridization of the *s,p* atomic orbital set are associated with a *linear* electron domain geometry. Bond angle = 180^{o}.

(b) A *trigonal planar* electron domain geometry is derived from 3 bonding domains and zero non bonding domains. Consequently, *three s,p ^{2}* hybrid orbital set resulting from the hybridization of the

(c) A

(d) A

(e) A

3(a) Electron configuration of B (Boron) = 1s^{2}2s^{2}2p^{1}.
One 2s electron is promoted to a 2p orbital. So there are 3 unpaired electrons: 1 in the 2s orbital, 2 in two 2p orbitals. So, the hybridization results in 3 sp^{2} hybrid orbitals which form a trigonal planar electron domain geometry with a bond angle of 120^{o}.

(b) sp^{2} hybrid orbitals.

(c) One 2p orbital is unhybridized. Its orientation is perpendicular to the trigonal plane of the sp^{2} hybrid orbitals.

4(a) Central atom = B; valence-shell configuration = 2s^{2}2p^{1}; one 2s electron is promoted to a 2p orbital; hybridization results in 3 sp^{2} hybrid orbitals.

(b) Central atom = Al; valence-shell configuration = 3s^{2}3p^{1}; one 3s electron is promoted to a 3p orbital.; excess electron is at third 3p 0rbital; hybridization results in four sp^{3} hybrid orbitals.

(c) Central atom = P; valence-shell configuration = 3s^{2}3p^{3}; third 3p electron is promoted to a first 3d orbital; one 3s electron is promoted to a 3p orbital; excess electron is at second 3d orbital; hybridization results in six sp^{3}d^{2} hybrid orbitals.

5. Orbital Hybridization has:S_{7}P_{6}A_{64} (multi-criteria permutation) and S_{7}P_{6}A_{66} (chemical interaction) as its general representative strings.

Mind Warm Ups

The *point* "**.**" is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

*Problems by Peter O. Sagay*