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Articles 1 - 30 of 56
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On The Exact Helium Wave Function Expansion, Ii, An Exponential Modulated Form, Carl W. David
On The Exact Helium Wave Function Expansion, Ii, An Exponential Modulated Form, Carl W. David
Chemistry Education Materials
A 11S wave function’s expansion for 2 electron atoms and ions is proposed employing an appropriate exponential factor and Fock’s logarithmic terms. The leading coefficient’s are presented.
On The Exact Helium Wave Function Expansion, Carl W. David
On The Exact Helium Wave Function Expansion, Carl W. David
Chemistry Education Materials
A 1S wave function’s expansion for 2 electron atoms and ions is obtained and the leading coefficients are reported.
The Phase Diagram Of A Non-Ideal Mixture’S P − V − X 2-Component Gas=Liquid Representation, Including Azeotropes, Carl W. David
The Phase Diagram Of A Non-Ideal Mixture’S P − V − X 2-Component Gas=Liquid Representation, Including Azeotropes, Carl W. David
Chemistry Education Materials
The liquid=vapor two phase p−v−x diagram is constructed for non-ideal solutions including azeotropes.
The Van Der Waals Mixture Construct Of A P-X Two-Component Gas=Liquid Phase Diagram, Carl W. David
The Van Der Waals Mixture Construct Of A P-X Two-Component Gas=Liquid Phase Diagram, Carl W. David
Chemistry Education Materials
The van der Waals model, when applied to a mixture, is used to construct tie-line points on a liquid=vapor two phase p-x diagram.
H-Atom Ladder Operator Revisited, Carl W. David
H-Atom Ladder Operator Revisited, Carl W. David
Chemistry Education Materials
An error laden note (Am. J. Phys., 34, 984,(1966)) concerning the ladder operator solution to the hydrogen atom electronic energy levels is corrected.
The Van Der Waals Fluid’S Liquid Vapor Coexistence Locus, Using Maxima/Gnuplot, Carl W. David
The Van Der Waals Fluid’S Liquid Vapor Coexistence Locus, Using Maxima/Gnuplot, Carl W. David
Chemistry Education Materials
The Maxima/Gnuplot code for plotting the van der Waals locus of liquid and vapor molar volumes as a function of pressure and temperature (all reduced) is presented.
Heat And Work, The First Law Of Thermodynamics From The Boltzmann Pov, Carl W. David
Heat And Work, The First Law Of Thermodynamics From The Boltzmann Pov, Carl W. David
Chemistry Education Materials
The First Law of Thermodynamics is discussed in terms of the Boltzmann distribution.
Spontaneity, Carl W. David
Spontaneity, Carl W. David
Chemistry Education Materials
An attempt is made to better understand thermodynamic spontaneity.
The Legendre Transformation For Beginning Thermodynamics Students, Carl W. David
The Legendre Transformation For Beginning Thermodynamics Students, Carl W. David
Chemistry Education Materials
The Legendre Transform, as traditionally taught in introductory Physical Chemistry classes, can be better understood with some simple examples, which are discussed herein.
Infra-Red Microwave Spectra, Overtones, Degeneracy And Thermal Populations All In One Diagram, Carl W. David
Infra-Red Microwave Spectra, Overtones, Degeneracy And Thermal Populations All In One Diagram, Carl W. David
Chemistry Education Materials
An old drawing, which had an error in it, is re-presented (corrected) for understanding the relationships in diatomic vibrational-rotational interactions at the introductory level.
The Commutator Of The Runge Lenz Vector With Other Operators Of The H-Atoms Physics Using Maxima, Carl W. David
The Commutator Of The Runge Lenz Vector With Other Operators Of The H-Atoms Physics Using Maxima, Carl W. David
Chemistry Education Materials
Commutators of components of the Runge-Lenz vector and constants of the motion and ladder operators for the H-atom problem are evaluated using brute force calculus and Maxima.
Errata For Manuscript #34, Carl W. David, Jan Siroky
Errata For Manuscript #34, Carl W. David, Jan Siroky
Chemistry Education Materials
An error in manuscript 34 of this collection concerning the Laplacian in spherical polar coordinates is corrected.
The Van Der Waals Fluid's Liquid Vapor Coexistence Locus, Carl W. David
The Van Der Waals Fluid's Liquid Vapor Coexistence Locus, Carl W. David
Chemistry Education Materials
The liquid vapor coexistence locus is plotted from the analytical solution to the Maxwell construction for the van der Waals fluid.
Avoiding The Cubic Equation In Finding The Van Der Waals Fluid's Vapor Pressures, Carl W. David
Avoiding The Cubic Equation In Finding The Van Der Waals Fluid's Vapor Pressures, Carl W. David
Chemistry Education Materials
The van der Waals coexistence curve of liquid and vapor volumes as functions of the temperature (all in reduced coordinates) as well as the correspponding vapor pressures at these temperatures, is obtained using SageMath, a symbolic calculus/algebra computer programming language.The lack of correspondence of the coexistence locus’ analytical form as obtained herein and those of Lekner remains disconcerting.
Revisiting The Fenceplot For The Maxwell Construction Of A Van Der Waals Fluid, Carl W. David
Revisiting The Fenceplot For The Maxwell Construction Of A Van Der Waals Fluid, Carl W. David
Chemistry Education Materials
An earlier published plot intended to better explain the Maxwell construction of the vapor pressure construct for van der Waals fluids is improved using Inkscape.
Verwiebe's "3-D" Ice Phase Diagram Reworked, Carl W. David
Verwiebe's "3-D" Ice Phase Diagram Reworked, Carl W. David
Chemistry Education Materials
The two dimensional phase diagrams of the various forms of ice are difficult to read and understand. A ``3D'' versions appearing ~80 years ago helps understanding of the phases and their inter-conversion into other phases.
Is The Maxwell Construction Correct In Predicting The Van Der Waals Fluid's Vapor Pressure?, Carl W. David
Is The Maxwell Construction Correct In Predicting The Van Der Waals Fluid's Vapor Pressure?, Carl W. David
Chemistry Education Materials
The Maxwell construction yields a pressure value which traditionally been associated with the vapor pressure. Here, the question is answered whether or not the two phases represented by the construct are indeed in equilibrium.
Fugacity Examples 2: The Fugacity Of A “Hard-Sphere” Semi-Ideal Gas And The Van Der Waals Gas, Carl W. David
Fugacity Examples 2: The Fugacity Of A “Hard-Sphere” Semi-Ideal Gas And The Van Der Waals Gas, Carl W. David
Chemistry Education Materials
The fugacity of the van der Waals gas is obtained after a review of the concept itself.
Errata For Tensor Of Moment Of Inertia (52) Manuscript, Carl W. David
Errata For Tensor Of Moment Of Inertia (52) Manuscript, Carl W. David
Chemistry Education Materials
An error in the manuscript (52) of this series is noted
Plotting The Van Der Waals Fluid In Pseudo-3d And The Maxwell Construction, Carl W. David
Plotting The Van Der Waals Fluid In Pseudo-3d And The Maxwell Construction, Carl W. David
Chemistry Education Materials
The van der Waals (from his thesis of 1873) equation is a cubic in the molar volume. Plotting the equation in pseudo 3 dimensions is quite simple to do, but including tie lines is quite difficult. Employing the solutions to the cubic van der Waals equation, the tie lines are readily available and can be easily incorporated into the aforementioned 3D plots.
The Van Der Waals Equation As A Cubic, Carl W. David
The Van Der Waals Equation As A Cubic, Carl W. David
Chemistry Education Materials
The van der Waals (from his thesis of 1873) equation is a cubic in the molar volume. Since this is the first equation of state studied in chemistry more complicated than the ideal gas equation, it is noteworthy that the solution of this cubic is rarely if ever addressed. When (lowering the temperature) the two imaginary roots coalesce with the real root of the van der Waals equation we have the critical point. At Kelvin temperatures below Tc. the equation has three real roots; we explore obtaining those roots to aid in the Maxwell construction required to obtain the vapor …
Transition Metals As Tools To Probe The Electronic Properties Of Porphyrinoids, Jillian Worlinsky
Transition Metals As Tools To Probe The Electronic Properties Of Porphyrinoids, Jillian Worlinsky
Chemistry Education Materials
This thesis describes in a number of separate chapters a range of studies that measure the variation of specific physical properties with structural modification of the macrocycles, with a particular focus also on using their coordinated metals as probes. Specifically, the transition metal ions are used as tools for interrogation of the electronic properties of porphyrins and pyrrole-modified porphyrins. With the aim of better understanding the electronic and structural factors that govern the optical responses, axial binding strengths, fragmentation patterns and carbonyl stretching frequencies of meso-tetraarylporphyrins, a rational design of pyrrole-modified metalloporphyrins with designed optical properties is derived.
Hierarchical Subject Inter-Relations In Physical Chemistry, Carl W. David
Hierarchical Subject Inter-Relations In Physical Chemistry, Carl W. David
Chemistry Education Materials
Students mystified by the progression of topics in Physical Chemistry may gain insight into their path through the material if acquainted with the diagrams presented and discussed herein.
Constructed Response Answers In A Multiple-Choice Universe, Carl W. David
Constructed Response Answers In A Multiple-Choice Universe, Carl W. David
Chemistry Education Materials
A scheme is introduced which allows computer readable multiple choice forms used in traditional examinations to be employed for constructed response items.
Guessing Harmonic Oscillator Wavefunctions Using Maple, Carl W. David
Guessing Harmonic Oscillator Wavefunctions Using Maple, Carl W. David
Chemistry Education Materials
The guessing of eigenfunctions is not trivial at higher quantum numbers, no matter what the system being considered. Instead of guessing, one can employ a symbolic calculus progam (Maple in this case) to aid in the reasoning process.
The Driven Harmonic Oscillator In Chemistry, Carl W. David
The Driven Harmonic Oscillator In Chemistry, Carl W. David
Chemistry Education Materials
The molecular dynamical simulation of the normal vibrational mode of water which involves H-O-H angle deformation, when driven by an external force, can be used to see how a driven harmonic oscillator, classically, is associated with the infra-red spectrum of water (and the absorption for this particular normal mode).
Using The Morse Potential To Understand Reaction Coördinates Using Maple, Carl W. David
Using The Morse Potential To Understand Reaction Coördinates Using Maple, Carl W. David
Chemistry Education Materials
The interactions employed in the “linear” reaction A(g)+BC(g) -> AB(g) + C(g) in a “one dimensional world” can be used to illustrate the “reaction coördinate”, using Maple, in a manner which allows students to inspect potential energy surfaces, make contour maps of those surfaces, and conceptually construct the “reaction coördinate” by tracing the local minimum path on the surface created.“one dimensional world” can be used to illustrate the “reaction coördinate”, using Maple, in a manner which allows students to inspect potential energy surfaces, make contour maps of those surfaces, and conceptually construct the “reaction coördinate” by tracing the local minimum …
Frobenius Solution For Legendre's Equation, Rodrigue's Formula And Normalization, Carl W. David
Frobenius Solution For Legendre's Equation, Rodrigue's Formula And Normalization, Carl W. David
Chemistry Education Materials
The Frobenius solution to Legendre/s equation is developed in detail as is Rodrigue's formula, which is employed to normalize Legendre polynomials.
1s_A 1s_B Overlap Integrals, Analytic And Maple Approches, Carl W. David
1s_A 1s_B Overlap Integrals, Analytic And Maple Approches, Carl W. David
Chemistry Education Materials
The calculation of overlap between adjacent orbitals (not on the same center) requires a slight facility with calculus which is quite instructive. That calculation is presented here.
Rationale For Studying Physical Chemistry, Carl W. David
Rationale For Studying Physical Chemistry, Carl W. David
Chemistry Education Materials
The various rationales for studying physical chemistry, and specifically the theoretical component thereof are presented in what is hoped in a coherent package.