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A Textbook of Physical Chemistry – Volume I, , 352, ,  Photochemical Reactions (Hydrogen-Bromine & Hydrogen-Chlorine, Reactions), There are many chemical reactions which occur also when the reactants are exposed to light. These, reactions are called as photochemical reactions. Now before we discuss the nature and types of photochemical, reactions, we need to discuss two laws first; the first is Grotthuss-Draper law while the second one is StarkEinstein law., The first law of photochemistry was given by Theodor Grotthuss and John W. Draper, and therefore,, got its unique name., The first law of photochemistry states that when the light is allowed to strike the reactions mixture,, it can be partially transmitted, reflected and absorbed; and it is the absorbed portion of the incident light, which is responsible to carry out any chemical change., The second law of photochemistry was given by Johannes Stark and Albert Einstein, and therefore,, is popularly known as Stark-Einstein law., The second law of photochemistry states that one photon of light must be absorbed for one molecule, to get activated in a photochemical reaction by a chemical system., The quantum yield of a reaction is simply the ratio of number of molecules reacting in a given time to the, number of photons absorbed in the same time i.e., , LEGAL NOTICE, This document is an excerpt from the book entitled “A, Textbook of Physical Chemistry – Volume 1 by, Mandeep Dalal”, and is the intellectual property of the, Author/Publisher. The content of this document is, protected by international copyright law and is valid, only for the personal preview of the user who has, originally downloaded it from the publisher’s website, (www.dalalinstitute.com). Any act of copying (including, plagiarizing its language) or sharing this document will, result in severe civil and criminal prosecution to the, maximum extent possible under law., , Copyright © Mandeep Dalal

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LEGAL NOTICE, This document is an excerpt from the book entitled “A, Textbook of Physical Chemistry – Volume 1 by, Mandeep Dalal”, and is the intellectual property of the, Author/Publisher. The content of this document is, protected by international copyright law and is valid, only for the personal preview of the user who has, originally downloaded it from the publisher’s website, (www.dalalinstitute.com). Any act of copying (including, plagiarizing its language) or sharing this document will, result in severe civil and criminal prosecution to the, maximum extent possible under law., , This is a low resolution version only for preview purpose. If you, want to read the full book, please consider buying., , Buy the complete book with TOC navigation, high resolution, images and no watermark.

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Table of Contents, CHAPTER 1 ................................................................................................................................................ 11, Quantum Mechanics – I ........................................................................................................................ 11, , , Postulates of Quantum Mechanics .................................................................................................. 11, , , , Derivation of Schrodinger Wave Equation...................................................................................... 16, , , , Max-Born Interpretation of Wave Functions .................................................................................. 21, , , , The Heisenberg’s Uncertainty Principle.......................................................................................... 24, , , , Quantum Mechanical Operators and Their Commutation Relations............................................... 29, , , , Hermitian Operators – Elementary Ideas, Quantum Mechanical Operator for Linear Momentum,, Angular Momentum and Energy as Hermitian Operator ................................................................. 52, , , , The Average Value of the Square of Hermitian Operators ............................................................. 62, , , , Commuting Operators and Uncertainty Principle (x & p; E & t) .................................................... 63, , , , Schrodinger Wave Equation for a Particle in One Dimensional Box.............................................. 65, , , , Evaluation of Average Position, Average Momentum and Determination of Uncertainty in Position, and Momentum and Hence Heisenberg’s Uncertainty Principle..................................................... 70, , , , Pictorial Representation of the Wave Equation of a Particle in One Dimensional Box and Its, Influence on the Kinetic Energy of the Particle in Each Successive Quantum Level ..................... 75, , , , Lowest Energy of the Particle ......................................................................................................... 80, , , , Problems .......................................................................................................................................... 82, , , , Bibliography .................................................................................................................................... 83, , CHAPTER 2 ................................................................................................................................................ 84, Thermodynamics – I .............................................................................................................................. 84, , , Brief Resume of First and Second Law of Thermodynamics .......................................................... 84, , , , Entropy Changes in Reversible and Irreversible Processes ............................................................. 87, , , , Variation of Entropy with Temperature, Pressure and Volume ...................................................... 92, , , , Entropy Concept as a Measure of Unavailable Energy and Criteria for the Spontaneity of Reaction, ...........................................................................................................................................................94, , , , Free Energy, Enthalpy Functions and Their Significance, Criteria for Spontaneity of a Process ... 98, , , , Partial Molar Quantities (Free Energy, Volume, Heat Concept) ................................................... 104, , , , Gibb’s-Duhem Equation ................................................................................................................ 108, , , , Problems ........................................................................................................................................ 111, , , , Bibliography .................................................................................................................................. 112

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CHAPTER 3 .............................................................................................................................................. 113, Chemical Dynamics – I ........................................................................................................................ 113, , , Effect of Temperature on Reaction Rates ...................................................................................... 113, , , , Rate Law for Opposing Reactions of Ist Order and IInd Order..................................................... 119, , , , Rate Law for Consecutive & Parallel Reactions of Ist Order Reactions ....................................... 127, , , , Collision Theory of Reaction Rates and Its Limitations ............................................................... 135, , , , Steric Factor................................................................................................................................... 141, , , , Activated Complex Theory ........................................................................................................... 143, , , , Ionic Reactions: Single and Double Sphere Models ..................................................................... 147, , , , Influence of Solvent and Ionic Strength ........................................................................................ 152, , , , The Comparison of Collision and Activated Complex Theory ..................................................... 157, , , , Problems ........................................................................................................................................ 158, , , , Bibliography .................................................................................................................................. 159, , CHAPTER 4 .............................................................................................................................................. 160, Electrochemistry – I: Ion-Ion Interactions ..................................................................................... 160, , , The Debye-Huckel Theory of Ion-Ion Interactions ....................................................................... 160, , , , Potential and Excess Charge Density as a Function of Distance from the Central Ion ................. 168, , , , Debye-Huckel Reciprocal Length ................................................................................................. 173, , , , Ionic Cloud and Its Contribution to the Total Potential ................................................................ 176, , , , Debye-Huckel Limiting Law of Activity Coefficients and Its Limitations ................................... 178, , , , Ion-Size Effect on Potential ........................................................................................................... 185, , , , Ion-Size Parameter and the Theoretical Mean - Activity Coefficient in the Case of Ionic Clouds with, Finite-Sized Ions ............................................................................................................................ 187, , , , Debye-Huckel-Onsager Treatment for Aqueous Solutions and Its Limitations ............................ 190, , , , Debye-Huckel-Onsager Theory for Non-Aqueous Solutions........................................................ 195, , , , The Solvent Effect on the Mobility at Infinite Dilution ................................................................ 196, , , , Equivalent Conductivity (Λ) vs Concentration C1/2 as a Function of the Solvent ......................... 198, , , , Effect of Ion Association Upon Conductivity (Debye-Huckel-Bjerrum Equation) ...................... 200, , , , Problems ........................................................................................................................................ 209, , , , Bibliography .................................................................................................................................. 210, , CHAPTER 5 .............................................................................................................................................. 211, Quantum Mechanics – II .................................................................................................................... 211, , , Schrodinger Wave Equation for a Particle in a Three Dimensional Box ...................................... 211

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, , The Concept of Degeneracy Among Energy Levels for a Particle in Three Dimensional Box .... 215, , , , Schrodinger Wave Equation for a Linear Harmonic Oscillator & Its Solution by Polynomial Method, .........................................................................................................................................................217, , , , Zero Point Energy of a Particle Possessing Harmonic Motion and Its Consequence ................... 229, , , , Schrodinger Wave Equation for Three Dimensional Rigid Rotator .............................................. 231, , , , Energy of Rigid Rotator ................................................................................................................ 241, , , , Space Quantization ........................................................................................................................ 243, , , , Schrodinger Wave Equation for Hydrogen Atom: Separation of Variable in Polar Spherical, Coordinates and Its Solution ......................................................................................................... 247, , , , Principal, Azimuthal and Magnetic Quantum Numbers and the Magnitude of Their Values ....... 268, , , , Probability Distribution Function .................................................................................................. 276, , , , Radial Distribution Function ......................................................................................................... 278, , , , Shape of Atomic Orbitals (s, p & d) .............................................................................................. 281, , , , Problems ........................................................................................................................................ 287, , , , Bibliography .................................................................................................................................. 288, , CHAPTER 6 .............................................................................................................................................. 289, Thermodynamics – II ........................................................................................................................... 289, , , Clausius-Clapeyron Equation ........................................................................................................ 289, , , , Law of Mass Action and Its Thermodynamic Derivation ............................................................. 293, , , , Third Law of Thermodynamics (Nernst Heat Theorem, Determination of Absolute Entropy,, Unattainability of Absolute Zero) And Its Limitation ................................................................... 296, , , , Phase Diagram for Two Completely Miscible Components Systems ........................................... 304, , , , Eutectic Systems (Calculation of Eutectic Point) .......................................................................... 311, , , , Systems Forming Solid Compounds AxBy with Congruent and Incongruent Melting Points ....... 321, , , , Phase Diagram and Thermodynamic Treatment of Solid Solutions.............................................. 332, , , , Problems ........................................................................................................................................ 342, , , , Bibliography .................................................................................................................................. 343, , CHAPTER 7 .............................................................................................................................................. 344, Chemical Dynamics – II ...................................................................................................................... 344, , , Chain Reactions: Hydrogen-Bromine Reaction, Pyrolysis of Acetaldehyde, Decomposition of, Ethane ............................................................................................................................................ 344, , , , Photochemical Reactions (Hydrogen-Bromine & Hydrogen-Chlorine Reactions) ....................... 352, , , , General Treatment of Chain Reactions (Ortho-Para Hydrogen Conversion and Hydrogen-Bromine, Reactions) ....................................................................................................................................... 358

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, , Apparent Activation Energy of Chain Reactions .......................................................................... 362, , , , Chain Length ................................................................................................................................. 364, , , , Rice-Herzfeld Mechanism of Organic Molecules Decomposition (Acetaldehyde) ...................... 366, , , , Branching Chain Reactions and Explosions (H2-O2 Reaction) ..................................................... 368, , , , Kinetics of (One Intermediate) Enzymatic Reaction: Michaelis-Menten Treatment .................... 371, , , , Evaluation of Michaelis's Constant for Enzyme-Substrate Binding by Lineweaver-Burk Plot and, Eadie-Hofstee Methods ................................................................................................................. 375, , , , Competitive and Non-Competitive Inhibition ............................................................................... 378, , , , Problems ........................................................................................................................................ 388, , , , Bibliography .................................................................................................................................. 389, , CHAPTER 8 .............................................................................................................................................. 390, Electrochemistry – II: Ion Transport in Solutions ....................................................................... 390, , , Ionic Movement Under the Influence of an Electric Field ............................................................ 390, , , , Mobility of Ions ............................................................................................................................. 393, , , , Ionic Drift Velocity and Its Relation with Current Density .......................................................... 394, , , , Einstein Relation Between the Absolute Mobility and Diffusion Coefficient .............................. 398, , , , The Stokes-Einstein Relation ........................................................................................................ 401, , , , The Nernst-Einstein Equation ....................................................................................................... 403, , , , Walden’s Rule ............................................................................................................................... 404, , , , The Rate-Process Approach to Ionic Migration ............................................................................ 406, , , , The Rate-Process Equation for Equivalent Conductivity .............................................................. 410, , , , Total Driving Force for Ionic Transport: Nernst-Planck Flux Equation ....................................... 412, , , , Ionic Drift and Diffusion Potential ................................................................................................ 416, , , , The Onsager Phenomenological Equations ................................................................................... 418, , , , The Basic Equation for the Diffusion ............................................................................................ 419, , , , Planck-Henderson Equation for the Diffusion Potential ............................................................... 422, , , , Problems ........................................................................................................................................ 425, , , , Bibliography .................................................................................................................................. 426, , INDEX ......................................................................................................................................................... 427