Expressions Of Pj Problems

Pj Problems - Overview

Celestial Stars

The Number Line

Geometries

7 Spaces Of Interest - Overview

Triadic Unit Mesh

Creation

The Atom

Survival

Energy

Light

Heat

Sound

Music

Language

Stories

Work

States Of Matter

Buoyancy

Nuclear Reactions

Molecular Shapes

Electron Configurations

Chemical Bonds

Energy Conversion

Chemical Reactions

Electromagnetism

Continuity

Growth

Human-cells

Proteins

Nucleic Acids

COHN - Natures Engineering Of The Human Body

The Human-Body Systems

Vision

Walking

Behaviors

Sensors Sensings

Beauty

Faith, Love, Charity

Photosynthesis

Weather

Systems

Algorithms

Tools

Networks

Search

Differential Calculus

Antiderivative

Integral Calculus

Economies

Inflation

Markets

Money Supply

Painting

How Matter Gets Composed (2)

(1). A previous problem indicated how *catalysts* accelerate the rate of chemical reactions. The following strings represent the other three primary influencers of the rate of chemical reactions. Describe them.

(a) S_{2}P_{2}A_{21}; S_{2}P_{2}A_{22}.

(b) (S_{7}P_{1}A_{15})_{solute}/(S_{7}P_{1}A_{14})_{solution}.

(c) (S_{7}P_{4}A_{41})_{K.E}.

2. Consider the following chemical equation:

*a*A + *b*B <-------> *c*C + *d*D ----(eq 1)

The reactants are A and B and the products are C and D for a given temperature. The coefficients *a*, *b*, *c* and *d* balance the equation.

(a) Describe all primary strings implicit in (eq 1).

(b) Write the *equilibrium expression* for (eq 1) and its string representations.

**The strings**:

(a) S_{2}P_{2}A_{21}; S_{2}P_{2}A_{22}.

(b) (S_{7}P_{1}A_{15})_{solute}/(S_{7}P_{1}A_{14})_{solution}.

(c) (S_{7}P_{4}A_{41})_{K.E}.

2(a) S_{7}P_{6}A_{66} (chemical process), S_{7}P_{5}A_{52} (chemical change) and S_{7}P_{7}A_{72} (dynamic equilibrium).
**The math**:

Several strings play important roles in the composition of matter. The bonding force represented by S_{7}P_{3}A_{31} is central to the composition of matter. Other important strings are as follows:
1(a). The strings S_{2}P_{2}A_{21} and S_{2}P_{2}A_{22} represent the physical properties and chemical properties (*identity*) of the reactants. The *identities* of the reactants of a chemical reaction play an important role in the determination of the magnitude of the reaction's *activation energy*.

(b) The string ratio (S_{7}P_{1}A_{15})_{solute}/(S_{7}P_{1}A_{14})_{solution} represents the *concentration* of each of the reactants. There are several formal words used to indicate *concentration*. Two commonly used words are *Molarity* (M) and *Molality* (m). *Molarity* expresses *concentration* in (moles of solute)/(Liter of solution). Where *moles of solute* = *(mass of solute)/(molecular weight of solute)*. *Molality* expresses *concentration* in (moles of solute)/(kilogram of solvent). *Molality* is in essence a *mass*/*mass* ratio that is independent of temperature changes and as a result a more desired form of expressing *concentration* in chemical scenarios where constancy of reactants' *concentration* is desired.
*Chemical reactions are faster when the concentrations of the reactants are increased*. According to *Collision Theory*, more mlecules in a given volume results in more collisions which increase the rate of a chemical reaction.

(c)The string (S_{7}P_{4}A_{41})_{K.E} represents *kinetic energy* explicitly and *temperature* implicitly. *Kinectic Energy* is energy due to motion and *temperature* is a measure of the average kinetic energy of the particles composing a substance. *Chemical reactions are faster when the temperature is increased*. Increase in temperature increases kinetic energy and consequently, molecular speeds of reactants. Increased speed causes the average energy of a collision to increase . As a result, average energy of collisions is more likely to exceed *activation energy*.

2(a) All strings in problem 1 are implicit in (eq 1). Additionally, the following strings are also implicit in (eq 1): S_{7}P_{6}A_{66} (chemical process), S_{7}P_{5}A_{52} (chemical change) and S_{7}P_{7}A_{72} (dynamic equilibrium).

(b) K = {[C]^{c}[D]^{d}}/{[A]^{a}[B]^{b}}.

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

More Pj Problem Strings