Pj Problems - Overview
The Number Line
7 Spaces Of Interest - Overview
Triadic Unit Mesh
States Of Matter
COHN - Natures Engineering Of The Human Body
The Human-Body Systems
Faith, Love, Charity
The activation energy for a process is 55,000 cal/mole. The rate of this process is known at 400oC.
What is the incremental temperature needed to double the rate?
S7P5A52 (Change - Chemical Change)
Pj Problem of Interest is of type change (chemical change). The rate of the chemical reaction is being changed by changing the temperature.
Temperature is a primary influencer of the rate of a chemical reaction. Concentrations of reactants is also a primary influencer of chemical reactions. In biochemical systems, enzymes are important influencer of biochemical reactions.
In 1893 A.D. Svante Arrhenius proposed an equation (now known as Arrhenius equation) that relates the rate of a chemical reaction with temperature. Arrhenius was also a pioneer in modern electrolyte theory.
Arrhenius Rate Equation
φ = Ae (-Ea/kT) -------------(1)
where A is a constant, e is natural logarithm,
Ea is activation energy
k is Boltzman's constant = 3.30 x 10-24 (cal/oK)/atom.
T is temperature degrees Kelvin.
If the activation energy is expressed in cal/mole, k is replaced by the universal gas constant R = 1.987 (cal/oK)/mole.
Now, 400oC = 673oK
So, at 400oC, rate = Ae (-Ea/673R)
At temperature T, rate is doubled
So, 2Ae (-Ea/673R) = Ae (-Ea/RT)
Taking natural logarithm:
So, ln2 - Ea/673R = -Ea/RT
So, ln2 = (Ea/R)[1/673 - 1/T]
so, Rln2/Ea = [1/673 - 1/T]
So, (1.987 x 0.693)/55000 = 0.001486 - 1/T
So, 0.0000250 = 0.0014858 - 1/T
So, 1/T = 0.0014858 - 0.0000250 = 0.001461
So, T = 684.5oK
So, rate at 400oC will be doubled if temperature is raised by 11.5oC.
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
Single Variable Functions
Absolute Value Functions
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
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
Derivation Of Heat Equation For A One-Dimensional Heat Flow
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.
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