Expressions Of Pj Problems

Pj Problems - Overview

Celestial Stars

The Number Line

Geometries

7 Spaces Of Interest - Overview

Triadic Unit Mesh

Creation

The Atom

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COHN - Natures Engineering Of The Human Body

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Differential Calculus

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Painting

Acid - Base Definitions

Tika is a bright chemistry student. She posits that the formation of a complex ion is an acid-base reaction in which the complex ion is the acid and the ligand is the base. What acid-base definition did Tika used to arrive at this conclusion?

**The strings**:

S_{7}P_{2}A_{22} (Identity - Chemical Property).
**The math**:

Pj Problem of Interest is of type *identity* (chemical property). Definition problems are of type *identity*.

**Arrhenius acid -base definition**:
*Acids* are substances that ionize in water solution to produce hydrogen ions, H^{+}, or free protons.
*Bases* are substances that ionize in water solution to produce hydroxide ions, OH^{-}.

For example:

HCl -------> H^{+} + Cl^{-} ----(1)

NaOH -------> Na^{+} + OH^{-} ----(2)

In reaction (1), hydrochloric acid (hydrogen chloride gas dissolved in water) ionizes into positive hydrogen ion and negative chlorine ion.

In reaction (2), Sodium hydroxide crystals dissolved in water and dissociates into positive sodium ion and negative hydroxide ion.

Reaction (2) is a *dissociation* instead of an *ionization* because the ions already exist in the crystal. These ions separate when the crystal is dissolved in water.

**Bronsted-Lowry's acid -base definition**:
*Acids* are proton donors
*Bases* are proton acceptors.

For example:

NH_{3} + H_{2}O -------> [NH_{4}]^{+} + OH^{-} ----(3)

In reaction (3), water is the acid because it donates a proton and ammonia is the base because it accepts the proton.

In general, an acid-base reaction is described as:

acid + base -------> conjugate base + conjugate acid

The *conjugate base* of an acid is the particle that remains after a proton has been released by the acid.

The *conjugate acid* results when the base acquires a proton from the acid.
**Lewis' acid -base definition**:
*Acids* are electron-pair acceptors
*Bases* are electron-pair donors.

The Lewis acid-base definition is broader in the sense that they apply to reactions and solutions that do not involve hydrogen or hydrogen ions. Applying the Lewis definitions to reaction (3) results in ammonia being the base and the hydrogen atom attached to the oxygen of the water molecule being the acid.

Tika used the Lewis acid-base definition.

A *complex ion* is formed when polar molecules (negative ions) cluster around a central positive ion.

The polar molecules are called *ligands*.

Math

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.

Derivation Of The Area Of A Circle, A Sector Of A Circle And A Circular Ring

Derivation Of The Area Of A Trapezoid, A Rectangle And A Triangle

Derivation Of The Area Of An Ellipse

Derivation Of Volume Of A Cylinder

Derivation Of Volume Of A Sphere

Derivation Of Volume Of A Cone

Derivation Of Volume Of A Torus

Derivation Of Volume Of A Paraboloid

Volume Obtained By Revolving The Curve y = x^{2} About The X Axis

Single Variable Functions

Absolute Value Functions

Conics

Real Numbers

Vector Spaces

Equation Of The Ascent Path Of An Airplane

Calculating Capacity Of A Video Adapter Board Memory

Probability Density Functions

Boolean Algebra - Logic Functions

Ordinary Differential Equations (ODEs)

Infinite Sequences And Series

Introduction To Group Theory

Advanced Calculus - Partial Derivatives

Advanced Calculus - General Charateristics Of Partial Differential Equations

Advanced Calculus - Jacobians

Advanced Calculus - Solving PDEs By The Method Of Separation Of Variables

Advanced Calculus - Fourier Series

Advanced Calculus - Multiple Integrals

Production Schedule That Maximizes Profit Given Constraint Equation

Separation Of Variables As Solution Method For Homogeneous Heat Flow Equation

Newton And Fourier Cooling Laws Applied To Heat Flow Boundary Conditions

Fourier Series

Derivation Of Heat Equation For A One-Dimensional Heat Flow

Homogenizing-Non-Homogeneous-Time-Varying-IBVP-Boundary-Condition

The Universe is composed of *matter* and *radiant energy*. *Matter* is any kind of *mass-energy* that moves with velocities less than the velocity of light. *Radiant energy* is any kind of *mass-energy* that moves with the velocity of light.

Periodic Table

Composition And Structure Of Matter

How Matter Gets Composed

How Matter Gets Composed (2)

Molecular Structure Of Matter

Molecular Shapes: Bond Length, Bond Angle

Molecular Shapes: Valence Shell Electron Pair Repulsion

Molecular Shapes: Orbital Hybridization

Molecular Shapes: Sigma Bonds Pi Bonds

Molecular Shapes: Non ABn Molecules

Molecular Orbital Theory

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