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Join Professor Raffi Hovasapian in his Physical Chemistry online course as he explains chemical systems using the laws of physics. Each lesson starts out with Raffi breaking down the complex theories into manageable ideas and ends with several fully worked-out example problems.

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I. Classical Thermodynamics Preliminaries

  The Ideal Gas Law 46:05
   Intro 0:00 
   Course Overview 0:16 
    Thermodynamics & Classical Thermodynamics 0:17 
    Structure of the Course 1:30 
   The Ideal Gas Law 3:06 
    Ideal Gas Law: PV=nRT 3:07 
    Units of Pressure 4:51 
    Manipulating Units 5:52 
    Atmosphere : atm 8:15 
    Millimeter of Mercury: mm Hg 8:48 
    SI Unit of Volume 9:32 
    SI Unit of Temperature 10:32 
    Value of R (Gas Constant): Pv = nRT 10:51 
   Extensive and Intensive Variables (Properties) 15:23 
    Intensive Property 15:52 
    Extensive Property 16:30 
    Example: Extensive and Intensive Variables 18:20 
   Ideal Gas Law 19:24 
    Ideal Gas Law with Intensive Variables 19:25 
   Graphing Equations 23:51 
    Hold T Constant & Graph P vs. V 23:52 
    Hold P Constant & Graph V vs. T 31:08 
    Hold V Constant & Graph P vs. T 34:38 
    Isochores or Isometrics 37:08 
    More on the V vs. T Graph 39:46 
    More on the P vs. V Graph 42:06 
    Ideal Gas Law at Low Pressure & High Temperature 44:26 
    Ideal Gas Law at High Pressure & Low Temperature 45:16 
  Math Lesson 1: Partial Differentiation 46:02
   Intro 0:00 
   Math Lesson 1: Partial Differentiation 0:38 
    Overview 0:39 
   Example I 3:00 
   Example II 6:33 
   Example III 9:52 
   Example IV 17:26 
   Differential & Derivative 21:44 
    What Does It Mean? 21:45 
    Total Differential (or Total Derivative) 30:16 
    Net Change in Pressure (P) 33:58 
    General Equation for Total Differential 38:12 
   Example 5: Total Differential 39:28 

II. Energy

  Energy & the First Law I 1:06:45
   Intro 0:00 
   Properties of Thermodynamic State 1:38 
    Big Picture: 3 Properties of Thermodynamic State 1:39 
    Enthalpy & Free Energy 3:30 
    Associated Law 4:40 
   Energy & the First Law of Thermodynamics 7:13 
    System & Its Surrounding Separated by a Boundary 7:14 
    In Other Cases the Boundary is Less Clear 10:47 
   State of a System 12:37 
    State of a System 12:38 
    Change in State 14:00 
    Path for a Change in State 14:57 
    Example: State of a System 15:46 
   Open, Close, and Isolated System 18:26 
    Open System 18:27 
    Closed System 19:02 
    Isolated System 19:22 
   Important Questions 20:38 
    Important Questions 20:39 
   Work & Heat 22:50 
    Definition of Work 23:33 
    Properties of Work 25:34 
    Definition of Heat 32:16 
    Properties of Heat 34:49 
    Experiment #1 42:23 
    Experiment #2 47:00 
   More on Work & Heat 54:50 
    More on Work & Heat 54:51 
   Conventions for Heat & Work 60:50 
    Convention for Heat 62:40 
    Convention for Work 64:24 
    Schematic Representation 65:00 
  Energy & the First Law II 1:06:33
   Intro 0:00 
   The First Law of Thermodynamics 0:53 
    The First Law of Thermodynamics 0:54 
   Example 1: What is the Change in Energy of the System & Surroundings? 8:53 
   Energy and The First Law II, cont. 11:55 
    The Energy of a System Changes in Two Ways 11:56 
    Systems Possess Energy, Not Heat or Work 12:45 
    Scenario 1 16:00 
    Scenario 2 16:46 
    State Property, Path Properties, and Path Functions 18:10 
   Pressure-Volume Work 22:36 
    When a System Changes 22:37 
    Gas Expands 24:06 
    Gas is Compressed 25:13 
    Pressure Volume Diagram: Analyzing Expansion 27:17 
    What if We do the Same Expansion in Two Stages? 35:22 
    Multistage Expansion 43:58 
    General Expression for the Pressure-Volume Work 46:59 
    Upper Limit of Isothermal Expansion 50:00 
    Expression for the Work Done in an Isothermal Expansion 52:45 
   Example 2: Find an Expression for the Maximum Work Done by an Ideal Gas upon Isothermal Expansion 56:18 
   Example 3: Calculate the External Pressure and Work Done 58:50 
  Energy & the First Law III 1:02:17
   Intro 0:00 
   Compression 0:20 
    Compression Overview 0:34 
    Single-stage compression vs. 2-stage Compression 2:16 
    Multi-stage Compression 8:40 
   Example I: Compression 14:47 
    Example 1: Single-stage Compression 14:47 
    Example 1: 2-stage Compression 20:07 
    Example 1: Absolute Minimum 26:37 
   More on Compression 32:55 
    Isothermal Expansion & Compression 32:56 
    External & Internal Pressure of the System 35:18 
   Reversible & Irreversible Processes 37:32 
    Process 1: Overview 38:57 
    Process 2: Overview 39:36 
    Process 1: Analysis 40:42 
    Process 2: Analysis 45:29 
    Reversible Process 50:03 
    Isothermal Expansion and Compression 54:31 
   Example II: Reversible Isothermal Compression of a Van der Waals Gas 58:10 
    Example 2: Reversible Isothermal Compression of a Van der Waals Gas 58:11 
  Changes in Energy & State: Constant Volume 1:04:39
   Intro 0:00 
   Recall 0:37 
    State Function & Path Function 0:38 
   First Law 2:11 
    Exact & Inexact Differential 2:12 
   Where Does (∆U = Q - W) or dU = dQ - dU Come from? 8:54 
    Cyclic Integrals of Path and State Functions 8:55 
    Our Empirical Experience of the First Law 12:31 
    ∆U = Q - W 18:42 
   Relations between Changes in Properties and Energy 22:24 
    Relations between Changes in Properties and Energy 22:25 
    Rate of Change of Energy per Unit Change in Temperature 29:54 
    Rate of Change of Energy per Unit Change in Volume at Constant Temperature 32:39 
    Total Differential Equation 34:38 
   Constant Volume 41:08 
    If Volume Remains Constant, then dV = 0 41:09 
    Constant Volume Heat Capacity 45:22 
    Constant Volume Integrated 48:14 
    Increase & Decrease in Energy of the System 54:19 
   Example 1: ∆U and Qv 57:43 
   Important Equations 62:06 
  Joule's Experiment 16:50
   Intro 0:00 
   Joule's Experiment 0:09 
    Joule's Experiment 1:20 
   Interpretation of the Result 4:42 
    The Gas Expands Against No External Pressure 4:43 
    Temperature of the Surrounding Does Not Change 6:20 
    System & Surrounding 7:04 
    Joule's Law 10:44 
    More on Joule's Experiment 11:08 
    Later Experiment 12:38 
    Dealing with the 2nd Law & Its Mathematical Consequences 13:52 
  Changes in Energy & State: Constant Pressure 43:40
   Intro 0:00 
   Changes in Energy & State: Constant Pressure 0:20 
    Integrating with Constant Pressure 0:35 
    Defining the New State Function 6:24 
    Heat & Enthalpy of the System at Constant Pressure 8:54 
    Finding ∆U 12:10 
    dH 15:28 
    Constant Pressure Heat Capacity 18:08 
   Important Equations 25:44 
    Important Equations 25:45 
    Important Equations at Constant Pressure 27:32 
   Example I: Change in Enthalpy (∆H) 28:53 
   Example II: Change in Internal Energy (∆U) 34:19 
  The Relationship Between Cp & Cv 32:23
   Intro 0:00 
   The Relationship Between Cp & Cv 0:21 
    For a Constant Volume Process No Work is Done 0:22 
    For a Constant Pressure Process ∆V ≠ 0, so Work is Done 1:16 
    The Relationship Between Cp & Cv: For an Ideal Gas 3:26 
    The Relationship Between Cp & Cv: In Terms of Molar heat Capacities 5:44 
    Heat Capacity Can Have an Infinite # of Values 7:14 
    The Relationship Between Cp & Cv 11:20 
   When Cp is Greater than Cv 17:13 
    2nd Term 18:10 
    1st Term 19:20 
   Constant P Process: 3 Parts 22:36 
    Part 1 23:45 
    Part 2 24:10 
    Part 3 24:46 
   Define : γ = (Cp/Cv) 28:06 
    For Gases 28:36 
    For Liquids 29:04 
    For an Ideal Gas 30:46 
  The Joule Thompson Experiment 39:15
   Intro 0:00 
   General Equations 0:13 
    Recall 0:14 
    How Does Enthalpy of a System Change Upon a Unit Change in Pressure? 2:58 
    For Liquids & Solids 12:11 
    For Ideal Gases 14:08 
    For Real Gases 16:58 
   The Joule Thompson Experiment 18:37 
    The Joule Thompson Experiment Setup 18:38 
    The Flow in 2 Stages 22:54 
    Work Equation for the Joule Thompson Experiment 24:14 
    Insulated Pipe 26:33 
    Joule-Thompson Coefficient 29:50 
    Changing Temperature & Pressure in Such a Way that Enthalpy Remains Constant 31:44 
   Joule Thompson Inversion Temperature 36:26 
    Positive & Negative Joule-Thompson Coefficient 36:27 
    Joule Thompson Inversion Temperature 37:22 
    Inversion Temperature of Hydrogen Gas 37:59 
  Adiabatic Changes of State 35:52
   Intro 0:00 
   Adiabatic Changes of State 0:10 
    Adiabatic Changes of State 0:18 
    Work & Energy in an Adiabatic Process 3:44 
    Pressure-Volume Work 7:43 
   Adiabatic Changes for an Ideal Gas 9:23 
    Adiabatic Changes for an Ideal Gas 9:24 
    Equation for a Fixed Change in Volume 11:20 
    Maximum & Minimum Values of Temperature 14:20 
   Adiabatic Path 18:08 
    Adiabatic Path Diagram 18:09 
    Reversible Adiabatic Expansion 21:54 
    Reversible Adiabatic Compression 22:34 
    Fundamental Relationship Equation for an Ideal Gas Under Adiabatic Expansion 25:00 
    More on the Equation 28:20 
   Important Equations 32:16 
    Important Adiabatic Equation 32:17 
    Reversible Adiabatic Change of State Equation 33:02 

III. Energy Example Problems

  1st Law Example Problems I 42:40
   Intro 0:00 
   Fundamental Equations 0:56 
    Work 2:40 
    Energy (1st Law) 3:10 
    Definition of Enthalpy 3:44 
    Heat capacity Definitions 4:06 
    The Mathematics 6:35 
   Fundamental Concepts 8:13 
    Isothermal 8:20 
    Adiabatic 8:54 
    Isobaric 9:25 
    Isometric 9:48 
    Ideal Gases 10:14 
   Example I 12:08 
    Example I: Conventions 12:44 
    Example I: Part A 15:30 
    Example I: Part B 18:24 
    Example I: Part C 19:53 
   Example II: What is the Heat Capacity of the System? 21:49 
   Example III: Find Q, W, ∆U & ∆H for this Change of State 24:15 
   Example IV: Find Q, W, ∆U & ∆H 31:37 
   Example V: Find Q, W, ∆U & ∆H 38:20 
  1st Law Example Problems II 1:00:23
   Intro 0:00 
   Example I 0:11 
    Example I: Finding ∆U 1:49 
    Example I: Finding W 6:22 
    Example I: Finding Q 11:23 
    Example I: Finding ∆H 16:09 
    Example I: Summary 17:07 
   Example II 21:16 
    Example II: Finding W 22:42 
    Example II: Finding ∆H 27:48 
    Example II: Finding Q 30:58 
    Example II: Finding ∆U 31:30 
   Example III 33:33 
    Example III: Finding ∆U, Q & W 33:34 
    Example III: Finding ∆H 38:07 
   Example IV 41:50 
    Example IV: Finding ∆U 41:51 
    Example IV: Finding ∆H 45:42 
   Example V 49:31 
    Example V: Finding W 49:32 
    Example V: Finding ∆U 55:26 
    Example V: Finding Q 56:26 
    Example V: Finding ∆H 56:55 
  1st Law Example Problems III 44:34
   Intro 0:00 
   Example I 0:15 
    Example I: Finding the Final Temperature 3:40 
    Example I: Finding Q 8:04 
    Example I: Finding ∆U 8:25 
    Example I: Finding W 9:08 
    Example I: Finding ∆H 9:51 
   Example II 11:27 
    Example II: Finding the Final Temperature 11:28 
    Example II: Finding ∆U 21:25 
    Example II: Finding W & Q 22:14 
    Example II: Finding ∆H 23:03 
   Example III 24:38 
    Example III: Finding the Final Temperature 24:39 
    Example III: Finding W, ∆U, and Q 27:43 
    Example III: Finding ∆H 28:04 
   Example IV 29:23 
    Example IV: Finding ∆U, W, and Q 25:36 
    Example IV: Finding ∆H 31:33 
   Example V 32:24 
    Example V: Finding the Final Temperature 33:32 
    Example V: Finding ∆U 39:31 
    Example V: Finding W 40:17 
    Example V: First Way of Finding ∆H 41:10 
    Example V: Second Way of Finding ∆H 42:10 
  Thermochemistry Example Problems 59:07
   Intro 0:00 
   Example I: Find ∆H° for the Following Reaction 0:42 
   Example II: Calculate the ∆U° for the Reaction in Example I 5:33 
   Example III: Calculate the Heat of Formation of NH₃ at 298 K 14:23 
   Example IV 32:15 
    Part A: Calculate the Heat of Vaporization of Water at 25°C 33:49 
    Part B: Calculate the Work Done in Vaporizing 2 Mols of Water at 25°C Under a Constant Pressure of 1 atm 35:26 
    Part C: Find ∆U for the Vaporization of Water at 25°C 41:00 
    Part D: Find the Enthalpy of Vaporization of Water at 100°C 43:12 
   Example V 49:24 
    Part A: Constant Temperature & Increasing Pressure 50:25 
    Part B: Increasing temperature & Constant Pressure 56:20 

IV. Entropy

  Entropy 49:16
   Intro 0:00 
   Entropy, Part 1 0:16 
    Coefficient of Thermal Expansion (Isobaric) 0:38 
    Coefficient of Compressibility (Isothermal) 1:25 
    Relative Increase & Relative Decrease 2:16 
    More on α 4:40 
    More on κ 8:38 
   Entropy, Part 2 11:04 
    Definition of Entropy 12:54 
    Differential Change in Entropy & the Reversible Path 20:08 
    State Property of the System 28:26 
    Entropy Changes Under Isothermal Conditions 35:00 
    Recall: Heating Curve 41:05 
    Some Phase Changes Take Place Under Constant Pressure 44:07 
   Example I: Finding ∆S for a Phase Change 46:05 
  Math Lesson II 33:59
   Intro 0:00 
   Math Lesson II 0:46 
    Let F(x,y) = x²y³ 0:47 
    Total Differential 3:34 
    Total Differential Expression 6:06 
    Example 1 9:24 
   More on Math Expression 13:26 
    Exact Total Differential Expression 13:27 
    Exact Differentials 19:50 
    Inexact Differentials 20:20 
   The Cyclic Rule 21:06 
    The Cyclic Rule 21:07 
    Example 2 27:58 
  Entropy As a Function of Temperature & Volume 54:37
   Intro 0:00 
   Entropy As a Function of Temperature & Volume 0:14 
    Fundamental Equation of Thermodynamics 1:16 
    Things to Notice 9:10 
    Entropy As a Function of Temperature & Volume 14:47 
    Temperature-dependence of Entropy 24:00 
   Example I 26:19 
   Entropy As a Function of Temperature & Volume, Cont. 31:55 
    Volume-dependence of Entropy at Constant Temperature 31:56 
    Differentiate with Respect to Temperature, Holding Volume Constant 36:16 
    Recall the Cyclic Rule 45:15 
   Summary & Recap 46:47 
    Fundamental Equation of Thermodynamics 46:48 
    For Entropy as a Function of Temperature & Volume 47:18 
    The Volume-dependence of Entropy for Liquids & Solids 52:52 
  Entropy as a Function of Temperature & Pressure 31:18
   Intro 0:00 
   Entropy as a Function of Temperature & Pressure 0:17 
    Entropy as a Function of Temperature & Pressure 0:18 
    Rewrite the Total Differential 5:54 
    Temperature-dependence 7:08 
    Pressure-dependence 9:04 
    Differentiate with Respect to Pressure & Holding Temperature Constant 9:54 
    Differentiate with Respect to Temperature & Holding Pressure Constant 11:28 
   Pressure-Dependence of Entropy for Liquids & Solids 18:45 
    Pressure-Dependence of Entropy for Liquids & Solids 18:46 
   Example I: ∆S of Transformation 26:20 
  Summary of Entropy So Far 23:06
   Intro 0:00 
   Summary of Entropy So Far 0:43 
    Defining dS 1:04 
    Fundamental Equation of Thermodynamics 3:51 
    Temperature & Volume 6:04 
    Temperature & Pressure 9:10 
    Two Important Equations for How Entropy Behaves 13:38 
    State of a System & Heat Capacity 15:34 
    Temperature-dependence of Entropy 19:49 
  Entropy Changes for an Ideal Gas 25:42
   Intro 0:00 
   Entropy Changes for an Ideal Gas 1:10 
    General Equation 1:22 
    The Fundamental Theorem of Thermodynamics 2:37 
    Recall the Basic Total Differential Expression for S = S (T,V) 5:36 
    For a Finite Change in State 7:58 
    If Cv is Constant Over the Particular Temperature Range 9:05 
   Change in Entropy of an Ideal Gas as a Function of Temperature & Pressure 11:35 
    Change in Entropy of an Ideal Gas as a Function of Temperature & Pressure 11:36 
    Recall the Basic Total Differential expression for S = S (T, P) 15:13 
    For a Finite Change 18:06 
   Example 1: Calculate the ∆S of Transformation 22:02 

V. Entropy Example Problems

  Entropy Example Problems I 43:39
   Intro 0:00 
   Entropy Example Problems I 0:24 
    Fundamental Equation of Thermodynamics 1:10 
    Entropy as a Function of Temperature & Volume 2:04 
    Entropy as a Function of Temperature & Pressure 2:59 
    Entropy For Phase Changes 4:47 
    Entropy For an Ideal Gas 6:14 
    Third Law Entropies 8:25 
    Statement of the Third Law 9:17 
    Entropy of the Liquid State of a Substance Above Its Melting Point 10:23 
    Entropy For the Gas Above Its Boiling Temperature 13:02 
    Entropy Changes in Chemical Reactions 15:26 
    Entropy Change at a Temperature Other than 25°C 16:32 
   Example I 19:31 
    Part A: Calculate ∆S for the Transformation Under Constant Volume 20:34 
    Part B: Calculate ∆S for the Transformation Under Constant Pressure 25:04 
   Example II: Calculate ∆S fir the Transformation Under Isobaric Conditions 27:53 
   Example III 30:14 
    Part A: Calculate ∆S if 1 Mol of Aluminum is taken from 25°C to 255°C 31:14 
    Part B: If S°₂₉₈ = 28.4 J/mol-K, Calculate S° for Aluminum at 498 K 33:23 
   Example IV: Calculate Entropy Change of Vaporization for CCl₄ 34:19 
   Example V 35:41 
    Part A: Calculate ∆S of Transformation 37:36 
    Part B: Calculate ∆S of Transformation 39:10 
  Entropy Example Problems II 56:44
   Intro 0:00 
   Example I 0:09 
    Example I: Calculate ∆U 1:28 
    Example I: Calculate Q 3:29 
    Example I: Calculate Cp 4:54 
    Example I: Calculate ∆S 6:14 
   Example II 7:13 
    Example II: Calculate W 8:14 
    Example II: Calculate ∆U 8:56 
    Example II: Calculate Q 10:18 
    Example II: Calculate ∆H 11:00 
    Example II: Calculate ∆S 12:36 
   Example III 18:47 
    Example III: Calculate ∆H 19:38 
    Example III: Calculate Q 21:14 
    Example III: Calculate ∆U 21:44 
    Example III: Calculate W 23:59 
    Example III: Calculate ∆S 24:55 
   Example IV 27:57 
    Example IV: Diagram 29:32 
    Example IV: Calculate W 32:27 
    Example IV: Calculate ∆U 36:36 
    Example IV: Calculate Q 38:32 
    Example IV: Calculate ∆H 39:00 
    Example IV: Calculate ∆S 40:27 
    Example IV: Summary 43:41 
   Example V 48:25 
    Example V: Diagram 49:05 
    Example V: Calculate W 50:58 
    Example V: Calculate ∆U 53:29 
    Example V: Calculate Q 53:44 
    Example V: Calculate ∆H 54:34 
    Example V: Calculate ∆S 55:01 
  Entropy Example Problems III 57:06
   Intro 0:00 
   Example I: Isothermal Expansion 0:09 
    Example I: Calculate W 1:19 
    Example I: Calculate ∆U 1:48 
    Example I: Calculate Q 2:06 
    Example I: Calculate ∆H 2:26 
    Example I: Calculate ∆S 3:02 
   Example II: Adiabatic and Reversible Expansion 6:10 
    Example II: Calculate Q 6:48 
    Example II: Basic Equation for the Reversible Adiabatic Expansion of an Ideal Gas 8:12 
    Example II: Finding Volume 12:40 
    Example II: Finding Temperature 17:58 
    Example II: Calculate ∆U 19:53 
    Example II: Calculate W 20:59 
    Example II: Calculate ∆H 21:42 
    Example II: Calculate ∆S 23:42 
   Example III: Calculate the Entropy of Water Vapor 25:20 
   Example IV: Calculate the Molar ∆S for the Transformation 34:32 
   Example V 44:19 
    Part A: Calculate the Standard Entropy of Liquid Lead at 525°C 46:17 
    Part B: Calculate ∆H for the Transformation of Solid Lead from 25°C to Liquid Lead at 525°C 52:23 

VI. Entropy and Probability

  Entropy & Probability I 54:35
   Intro 0:00 
   Entropy & Probability 0:11 
    Structural Model 3:05 
    Recall the Fundamental Equation of Thermodynamics 9:11 
    Two Independent Ways of Affecting the Entropy of a System 10:05 
    Boltzmann Definition 12:10 
   Omega 16:24 
    Definition of Omega 16:25 
   Energy Distribution 19:43 
    The Energy Distribution 19:44 
    In How Many Ways can N Particles be Distributed According to the Energy Distribution 23:05 
   Example I: In How Many Ways can the Following Distribution be Achieved 32:51 
   Example II: In How Many Ways can the Following Distribution be Achieved 33:51 
   Example III: In How Many Ways can the Following Distribution be Achieved 34:45 
   Example IV: In How Many Ways can the Following Distribution be Achieved 38:50 
   Entropy & Probability, cont. 40:57 
    More on Distribution 40:58 
    Example I Summary 41:43 
    Example II Summary 42:12 
    Distribution that Maximizes Omega 42:26 
    If Omega is Large, then S is Large 44:22 
    Two Constraints for a System to Achieve the Highest Entropy Possible 47:07 
    What Happened When the Energy of a System is Increased? 49:00 
  Entropy & Probability II 35:05
   Intro 0:00 
   Volume Distribution 0:08 
    Distributing 2 Balls in 3 Spaces 1:43 
    Distributing 2 Balls in 4 Spaces 3:44 
    Distributing 3 Balls in 10 Spaces 5:30 
    Number of Ways to Distribute P Particles over N Spaces 6:05 
    When N is Much Larger than the Number of Particles P 7:56 
    Energy Distribution 25:04 
    Volume Distribution 25:58 
   Entropy, Total Entropy, & Total Omega Equations 27:34 
    Entropy, Total Entropy, & Total Omega Equations 27:35 

VII. Spontaneity, Equilibrium, and the Fundamental Equations

  Spontaneity & Equilibrium I 28:42
   Intro 0:00 
   Reversible & Irreversible 0:24 
    Reversible vs. Irreversible 0:58 
    Defining Equation for Equilibrium 2:11 
    Defining Equation for Irreversibility (Spontaneity) 3:11 
    TdS ≥ dQ 5:15 
   Transformation in an Isolated System 11:22 
    Transformation in an Isolated System 11:29 
   Transformation at Constant Temperature 14:50 
    Transformation at Constant Temperature 14:51 
   Helmholtz Free Energy 17:26 
    Define: A = U - TS 17:27 
    Spontaneous Isothermal Process & Helmholtz Energy 20:20 
    Pressure-volume Work 22:02 
  Spontaneity & Equilibrium II 34:38
   Intro 0:00 
   Transformation under Constant Temperature & Pressure 0:08 
    Transformation under Constant Temperature & Pressure 0:36 
    Define: G = U + PV - TS 3:32 
    Gibbs Energy 5:14 
    What Does This Say? 6:44 
    Spontaneous Process & a Decrease in G 14:12 
    Computing ∆G 18:54 
   Summary of Conditions 21:32 
    Constraint & Condition for Spontaneity 21:36 
    Constraint & Condition for Equilibrium 24:54 
   A Few Words About the Word Spontaneous 26:24 
    Spontaneous Does Not Mean Fast 26:25 
    Putting Hydrogen & Oxygen Together in a Flask 26:59 
    Spontaneous Vs. Not Spontaneous 28:14 
    Thermodynamically Favorable 29:03 
    Example: Making a Process Thermodynamically Favorable 29:34 
   Driving Forces for Spontaneity 31:35 
    Equation: ∆G = ∆H - T∆S 31:36 
    Always Spontaneous Process 32:39 
    Never Spontaneous Process 33:06 
    A Process That is Endothermic Can Still be Spontaneous 34:00 
  The Fundamental Equations of Thermodynamics 30:50
   Intro 0:00 
   The Fundamental Equations of Thermodynamics 0:44 
    Mechanical Properties of a System 0:45 
    Fundamental Properties of a System 1:16 
    Composite Properties of a System 1:44 
    General Condition of Equilibrium 3:16 
    Composite Functions & Their Differentiations 6:11 
    dH = TdS + VdP 7:53 
    dA = -SdT - PdV 9:26 
    dG = -SdT + VdP 10:22 
   Summary of Equations 12:10 
    Equation #1 14:33 
    Equation #2 15:15 
    Equation #3 15:58 
    Equation #4 16:42 
   Maxwell's Relations 20:20 
    Maxwell's Relations 20:21 
    Isothermal Volume-Dependence of Entropy & Isothermal Pressure-Dependence of Entropy 26:21 
  The General Thermodynamic Equations of State 34:06
   Intro 0:00 
   The General Thermodynamic Equations of State 0:10 
    Equations of State for Liquids & Solids 0:52 
    More General Condition for Equilibrium 4:02 
    General Conditions: Equation that Relates P to Functions of T & V 6:20 
    The Second Fundamental Equation of Thermodynamics 11:10 
    Equation 1 17:34 
    Equation 2 21:58 
    Recall the General Expression for Cp - Cv 28:11 
    For the Joule-Thomson Coefficient 30:44 
    Joule-Thomson Inversion Temperature 32:12 
  Properties of the Helmholtz & Gibbs Energies 39:18
   Intro 0:00 
   Properties of the Helmholtz & Gibbs Energies 0:10 
    Equating the Differential Coefficients 1:34 
    An Increase in T; a Decrease in A 3:25 
    An Increase in V; a Decrease in A 6:04 
    We Do the Same Thing for G 8:33 
    Increase in T; Decrease in G 10:50 
    Increase in P; Decrease in G 11:36 
    Gibbs Energy of a Pure Substance at a Constant Temperature from 1 atm to any Other Pressure. 14:12 
    If the Substance is a Liquid or a Solid, then Volume can be Treated as a Constant 18:57 
    For an Ideal Gas 22:18 
    Special Note 24:56 
   Temperature Dependence of Gibbs Energy 27:02 
    Temperature Dependence of Gibbs Energy #1 27:52 
    Temperature Dependence of Gibbs Energy #2 29:01 
    Temperature Dependence of Gibbs Energy #3 29:50 
    Temperature Dependence of Gibbs Energy #4 34:50 
  The Entropy of the Universe & the Surroundings 19:40
   Intro 0:00 
   Entropy of the Universe & the Surroundings 0:08 
    Equation: ∆G = ∆H - T∆S 0:20 
    Conditions of Constant Temperature & Pressure 1:14 
    Reversible Process 3:14 
    Spontaneous Process & the Entropy of the Universe 5:20 
    Tips for Remembering Everything 12:40 
    Verify Using Known Spontaneous Process 14:51 

VIII. Free Energy Example Problems

  Free Energy Example Problems I 54:16
   Intro 0:00 
   Example I 0:11 
    Example I: Deriving a Function for Entropy (S) 2:06 
    Example I: Deriving a Function for V 5:55 
    Example I: Deriving a Function for H 8:06 
    Example I: Deriving a Function for U 12:06 
   Example II 15:18 
   Example III 21:52 
   Example IV 26:12 
    Example IV: Part A 26:55 
    Example IV: Part B 28:30 
    Example IV: Part C 30:25 
   Example V 33:45 
   Example VI 40:46 
   Example VII 43:43 
    Example VII: Part A 44:46 
    Example VII: Part B 50:52 
    Example VII: Part C 51:56 
  Free Energy Example Problems II 31:17
   Intro 0:00 
   Example I 0:09 
   Example II 5:18 
   Example III 8:22 
   Example IV 12:32 
   Example V 17:14 
   Example VI 20:34 
    Example VI: Part A 21:04 
    Example VI: Part B 23:56 
    Example VI: Part C 27:56 
  Free Energy Example Problems III 45:00
   Intro 0:00 
   Example I 0:10 
   Example II 15:03 
   Example III 21:47 
   Example IV 28:37 
    Example IV: Part A 29:33 
    Example IV: Part B 36:09 
    Example IV: Part C 40:34 
  Three Miscellaneous Example Problems 58:05
   Intro 0:00 
   Example I 0:41 
    Part A: Calculating ∆H 3:55 
    Part B: Calculating ∆S 15:13 
   Example II 24:39 
    Part A: Final Temperature of the System 26:25 
    Part B: Calculating ∆S 36:57 
   Example III 46:49 

IX. Equation Review for Thermodynamics

  Looking Back Over Everything: All the Equations in One Place 25:20
   Intro 0:00 
   Work, Heat, and Energy 0:18 
    Definition of Work, Energy, Enthalpy, and Heat Capacities 0:23 
    Heat Capacities for an Ideal Gas 3:40 
    Path Property & State Property 3:56 
    Energy Differential 5:04 
    Enthalpy Differential 5:40 
    Joule's Law & Joule-Thomson Coefficient 6:23 
    Coefficient of Thermal Expansion & Coefficient of Compressibility 7:01 
    Enthalpy of a Substance at Any Other Temperature 7:29 
    Enthalpy of a Reaction at Any Other Temperature 8:01 
   Entropy 8:53 
    Definition of Entropy 8:54 
    Clausius Inequality 9:11 
    Entropy Changes in Isothermal Systems 9:44 
    The Fundamental Equation of Thermodynamics 10:12 
    Expressing Entropy Changes in Terms of Properties of the System 10:42 
    Entropy Changes in the Ideal Gas 11:22 
    Third Law Entropies 11:38 
    Entropy Changes in Chemical Reactions 14:02 
    Statistical Definition of Entropy 14:34 
    Omega for the Spatial & Energy Distribution 14:47 
   Spontaneity and Equilibrium 15:43 
    Helmholtz Energy & Gibbs Energy 15:44 
    Condition for Spontaneity & Equilibrium 16:24 
    Condition for Spontaneity with Respect to Entropy 17:58 
    The Fundamental Equations 18:30 
    Maxwell's Relations 19:04 
    The Thermodynamic Equations of State 20:07 
    Energy & Enthalpy Differentials 21:08 
    Joule's Law & Joule-Thomson Coefficient 21:59 
    Relationship Between Constant Pressure & Constant Volume Heat Capacities 23:14 
    One Final Equation - Just for Fun 24:04 

X. Quantum Mechanics Preliminaries

  Complex Numbers 34:25
   Intro 0:00 
   Complex Numbers 0:11 
    Representing Complex Numbers in the 2-Dimmensional Plane 0:56 
    Addition of Complex Numbers 2:35 
    Subtraction of Complex Numbers 3:17 
    Multiplication of Complex Numbers 3:47 
    Division of Complex Numbers 6:04 
    r & θ 8:04 
    Euler's Formula 11:00 
    Polar Exponential Representation of the Complex Numbers 11:22 
   Example I 14:25 
   Example II 15:21 
   Example III 16:58 
   Example IV 18:35 
   Example V 20:40 
   Example VI 21:32 
   Example VII 25:22 
  Probability & Statistics 59:57
   Intro 0:00 
   Probability & Statistics 1:51 
    Normalization Condition 1:52 
    Define the Mean or Average of x 11:04 
   Example I: Calculate the Mean of x 14:57 
   Example II: Calculate the Second Moment of the Data in Example I 22:39 
   Define the Second Central Moment or Variance 25:26 
    Define the Second Central Moment or Variance 25:27 
    1st Term 32:16 
    2nd Term 32:40 
    3rd Term 34:07 
   Continuous Distributions 35:47 
    Continuous Distributions 35:48 
   Probability Density 39:30 
    Probability Density 39:31 
    Normalization Condition 46:51 
   Example III 50:13 
    Part A - Show that P(x) is Normalized 51:40 
    Part B - Calculate the Average Position of the Particle Along the Interval 54:31 
   Important Things to Remember 58:24 
  Schrӧdinger Equation & Operators 42:05
   Intro 0:00 
   Schrӧdinger Equation & Operators 0:16 
    Relation Between a Photon's Momentum & Its Wavelength 0:17 
    Louis de Broglie: Wavelength for Matter 0:39 
    Schrӧdinger Equation 1:19 
    Definition of Ψ(x) 3:31 
    Quantum Mechanics 5:02 
    Operators 7:51 
   Example I 10:10 
   Example II 11:53 
   Example III 14:24 
   Example IV 17:35 
   Example V 19:59 
   Example VI 22:39 
   Operators Can Be Linear or Non Linear 27:58 
    Operators Can Be Linear or Non Linear 28:34 
   Example VII 32:47 
   Example VIII 36:55 
   Example IX 39:29 
  Schrӧdinger Equation as an Eigenvalue Problem 30:26
   Intro 0:00 
   Schrӧdinger Equation as an Eigenvalue Problem 0:10 
    Operator: Multiplying the Original Function by Some Scalar 0:11 
    Operator, Eigenfunction, & Eigenvalue 4:42 
    Example: Eigenvalue Problem 8:00 
    Schrӧdinger Equation as an Eigenvalue Problem 9:24 
    Hamiltonian Operator 15:09 
   Quantum Mechanical Operators 16:46 
    Kinetic Energy Operator 19:16 
    Potential Energy Operator 20:02 
    Total Energy Operator 21:12 
    Classical Point of View 21:48 
    Linear Momentum Operator 24:02 
   Example I 26:01 
  The Plausibility of the Schrӧdinger Equation 21:34
   Intro 0:00 
   The Plausibility of the Schrӧdinger Equation 1:16 
    The Plausibility of the Schrӧdinger Equation, Part 1 1:17 
    The Plausibility of the Schrӧdinger Equation, Part 2 8:24 
    The Plausibility of the Schrӧdinger Equation, Part 3 13:45 

XI. The Particle in a Box

  The Particle in a Box Part I 56:22
   Intro 0:00 
   Free Particle in a Box 0:28 
    Definition of a Free Particle in a Box 0:29 
    Amplitude of the Matter Wave 6:22 
    Intensity of the Wave 6:53 
    Probability Density 9:39 
    Probability that the Particle is Located Between x & dx 10:54 
    Probability that the Particle will be Found Between o & a 12:35 
    Wave Function & the Particle 14:59 
    Boundary Conditions 19:22 
    What Happened When There is No Constraint on the Particle 27:54 
    Diagrams 34:12 
    More on Probability Density 40:53 
   The Correspondence Principle 46:45 
    The Correspondence Principle 46:46 
   Normalizing the Wave Function 47:46 
    Normalizing the Wave Function 47:47 
    Normalized Wave Function & Normalization Constant 52:24 
  The Particle in a Box Part II 45:24
   Intro 0:00 
   Free Particle in a Box 0:08 
    Free Particle in a 1-dimensional Box 0:09 
    For a Particle in a Box 3:57 
   Calculating Average Values & Standard Deviations 5:42 
    Average Value for the Position of a Particle 6:32 
    Standard Deviations for the Position of a Particle 10:51 
    Recall: Energy & Momentum are Represented by Operators 13:33 
    Recall: Schrӧdinger Equation in Operator Form 15:57 
    Average Value of a Physical Quantity that is Associated with an Operator 18:16 
    Average Momentum of a Free Particle in a Box 20:48 
   The Uncertainty Principle 24:42 
    Finding the Standard Deviation of the Momentum 25:08 
    Expression for the Uncertainty Principle 35:02 
    Summary of the Uncertainty Principle 41:28 
  The Particle in a Box Part III 48:43
   Intro 0:00 
   2-Dimension 0:12 
    Dimension 2 0:31 
    Boundary Conditions 1:52 
    Partial Derivatives 4:27 
   Example I 6:08 
   The Particle in a Box, cont. 11:28 
    Operator Notation 12:04 
    Symbol for the Laplacian 13:50 
    The Equation Becomes… 14:30 
    Boundary Conditions 14:54 
    Separation of Variables 15:33 
    Solution to the 1-dimensional Case 16:31 
    Normalization Constant 22:32 
   3-Dimension 28:30 
    Particle in a 3-dimensional Box 28:31 
    In Del Notation 32:22 
    The Solutions 34:51 
    Expressing the State of the System for a Particle in a 3D Box 39:10 
    Energy Level & Degeneracy 43:35 

XII. Postulates and Principles of Quantum Mechanics

  The Postulates & Principles of Quantum Mechanics, Part I 46:18
   Intro 0:00 
   Postulate I 0:31 
    Probability That The Particle Will Be Found in a Differential Volume Element 0:32 
   Example I: Normalize This Wave Function 11:30 
   Postulate II 18:20 
    Postulate II 18:21 
    Quantum Mechanical Operators: Position 20:48 
    Quantum Mechanical Operators: Kinetic Energy 21:57 
    Quantum Mechanical Operators: Potential Energy 22:42 
    Quantum Mechanical Operators: Total Energy 22:57 
    Quantum Mechanical Operators: Momentum 23:22 
    Quantum Mechanical Operators: Angular Momentum 23:48 
    More On The Kinetic Energy Operator 24:48 
   Angular Momentum 28:08 
    Angular Momentum Overview 28:09 
    Angular Momentum Operator in Quantum Mechanic 31:34 
    The Classical Mechanical Observable 32:56 
    Quantum Mechanical Operator 37:01 
    Getting the Quantum Mechanical Operator from the Classical Mechanical Observable 40:16 
   Postulate II, cont. 43:40 
    Quantum Mechanical Operators are Both Linear & Hermetical 43:41 
  The Postulates & Principles of Quantum Mechanics, Part II 39:28
   Intro 0:00 
   Postulate III 0:09 
    Postulate III: Part I 0:10 
    Postulate III: Part II 5:56 
    Postulate III: Part III 12:43 
    Postulate III: Part IV 18:28 
   Postulate IV 23:57 
    Postulate IV 23:58 
   Postulate V 27:02 
    Postulate V 27:03 
   Average Value 36:38 
    Average Value 36:39 
  The Postulates & Principles of Quantum Mechanics, Part III 35:32
   Intro 0:00 
   The Postulates & Principles of Quantum Mechanics, Part III 0:10 
    Equations: Linear & Hermitian 0:11 
    Introduction to Hermitian Property 3:36 
    Eigenfunctions are Orthogonal 9:55 
    The Sequence of Wave Functions for the Particle in a Box forms an Orthonormal Set 14:34 
    Definition of Orthogonality 16:42 
    Definition of Hermiticity 17:26 
    Hermiticity: The Left Integral 23:04 
    Hermiticity: The Right Integral 28:47 
    Hermiticity: Summary 34:06 
  The Postulates & Principles of Quantum Mechanics, Part IV 29:55
   Intro 0:00 
   The Postulates & Principles of Quantum Mechanics, Part IV 0:09 
    Operators can be Applied Sequentially 0:10 
    Sample Calculation 1 2:41 
    Sample Calculation 2 5:18 
    Commutator of Two Operators 8:16 
    The Uncertainty Principle 19:01 
    In the Case of Linear Momentum and Position Operator 23:14 
    When the Commutator of Two Operators Equals to Zero 26:31 

XIII. Postulates and Principles Example Problems, Including Particle in a Box

  Example Problems I 54:25
   Intro 0:00 
   Example I: Three Dimensional Box & Eigenfunction of The Laplacian Operator 0:37 
   Example II: Positions of a Particle in a 1-dimensional Box 15:46 
   Example III: Transition State & Frequency 29:29 
   Example IV: Finding a Particle in a 1-dimensional Box 35:03 
   Example V: Degeneracy & Energy Levels of a Particle in a Box 44:59 
  Example Problems II 46:58
   Intro 0:00 
   Review 0:25 
    Wave Function 0:26 
    Normalization Condition 2:28 
    Observable in Classical Mechanics & Linear/Hermitian Operator in Quantum Mechanics 3:36 
    Hermitian 6:11 
    Eigenfunctions & Eigenvalue 8:20 
    Normalized Wave Functions 12:00 
    Average Value 13:42 
    If Ψ is Written as a Linear Combination 15:44 
    Commutator 16:45 
   Example I: Normalize The Wave Function 19:18 
   Example II: Probability of Finding of a Particle 22:27 
   Example III: Orthogonal 26:00 
   Example IV: Average Value of the Kinetic Energy Operator 30:22 
   Example V: Evaluate These Commutators 39:02 
  Example Problems III 44:11
   Intro 0:00 
   Example I: Good Candidate for a Wave Function 0:08 
   Example II: Variance of the Energy 7:00 
   Example III: Evaluate the Angular Momentum Operators 15:00 
   Example IV: Real Eigenvalues Imposes the Hermitian Property on Operators 28:44 
   Example V: A Demonstration of Why the Eigenfunctions of Hermitian Operators are Orthogonal 35:33 

XIV. The Harmonic Oscillator

  The Harmonic Oscillator I 35:33
   Intro 0:00 
   The Harmonic Oscillator 0:10 
    Harmonic Motion 0:11 
    Classical Harmonic Oscillator 4:38 
    Hooke's Law 8:18 
    Classical Harmonic Oscillator, cont. 10:33 
    General Solution for the Differential Equation 15:16 
    Initial Position & Velocity 16:05 
    Period & Amplitude 20:42 
    Potential Energy of the Harmonic Oscillator 23:20 
    Kinetic Energy of the Harmonic Oscillator 26:37 
    Total Energy of the Harmonic Oscillator 27:23 
    Conservative System 34:37 
  The Harmonic Oscillator II 43:04
   Intro 0:00 
   The Harmonic Oscillator II 0:08 
    Diatomic Molecule 0:10 
    Notion of Reduced Mass 5:27 
    Harmonic Oscillator Potential & The Intermolecular Potential of a Vibrating Molecule 7:33 
    The Schrӧdinger Equation for the 1-dimensional Quantum Mechanic Oscillator 14:14 
    Quantized Values for the Energy Level 15:46 
    Ground State & the Zero-Point Energy 21:50 
    Vibrational Energy Levels 25:18 
    Transition from One Energy Level to the Next 26:42 
    Fundamental Vibrational Frequency for Diatomic Molecule 34:57 
    Example: Calculate k 38:01 
  The Harmonic Oscillator III 26:30
   Intro 0:00 
   The Harmonic Oscillator III 0:09 
    The Wave Functions Corresponding to the Energies 0:10 
    Normalization Constant 2:34 
    Hermite Polynomials 3:22 
    First Few Hermite Polynomials 4:56 
    First Few Wave-Functions 6:37 
    Plotting the Probability Density of the Wave-Functions 8:37 
    Probability Density for Large Values of r 14:24 
    Recall: Odd Function & Even Function 19:05 
    More on the Hermite Polynomials 20:07 
    Recall: If f(x) is Odd 20:36 
    Average Value of x 22:31 
    Average Value of Momentum 23:56 

XV. The Rigid Rotator

  The Rigid Rotator I 41:10
   Intro 0:00 
   Possible Confusion from the Previous Discussion 0:07 
    Possible Confusion from the Previous Discussion 0:08 
   Rotation of a Single Mass Around a Fixed Center 8:17 
    Rotation of a Single Mass Around a Fixed Center 8:18 
    Angular Velocity 12:07 
    Rotational Inertia 13:24 
    Rotational Frequency 15:24 
    Kinetic Energy for a Linear System 16:38 
    Kinetic Energy for a Rotational System 17:42 
   Rotating Diatomic Molecule 19:40 
    Rotating Diatomic Molecule: Part 1 19:41 
    Rotating Diatomic Molecule: Part 2 24:56 
    Rotating Diatomic Molecule: Part 3 30:04 
   Hamiltonian of the Rigid Rotor 36:48 
    Hamiltonian of the Rigid Rotor 36:49 
  The Rigid Rotator II 30:32
   Intro 0:00 
   The Rigid Rotator II 0:08 
    Cartesian Coordinates 0:09 
    Spherical Coordinates 1:55 
    r 6:15 
    θ 6:28 
    φ 7:00 
    Moving a Distance 'r' 8:17 
    Moving a Distance 'r' in the Spherical Coordinates 11:49 
    For a Rigid Rotator, r is Constant 13:57 
    Hamiltonian Operator 15:09 
    Square of the Angular Momentum Operator 17:34 
    Orientation of the Rotation in Space 19:44 
    Wave Functions for the Rigid Rotator 20:40 
    The Schrӧdinger Equation for the Quantum Mechanic Rigid Rotator 21:24 
    Energy Levels for the Rigid Rotator 26:58 
  The Rigid Rotator III 35:19
   Intro 0:00 
   The Rigid Rotator III 0:11 
    When a Rotator is Subjected to Electromagnetic Radiation 1:24 
    Selection Rule 2:13 
    Frequencies at Which Absorption Transitions Occur 6:24 
    Energy Absorption & Transition 10:54 
    Energy of the Individual Levels Overview 20:58 
    Energy of the Individual Levels: Diagram 23:45 
    Frequency Required to Go from J to J + 1 25:53 
    Using Separation Between Lines on the Spectrum to Calculate Bond Length 28:02 
   Example I: Calculating Rotational Inertia & Bond Length 29:18 
    Example I: Calculating Rotational Inertia 29:19 
    Example I: Calculating Bond Length 32:56 

XVI. Oscillator and Rotator Example Problems

  Example Problems I 33:48
   Intro 0:00 
   Equations Review 0:11 
    Energy of the Harmonic Oscillator 0:12 
    Selection Rule 3:02 
    Observed Frequency of Radiation 3:27 
    Harmonic Oscillator Wave Functions 5:52 
    Rigid Rotator 7:26 
    Selection Rule for Rigid Rotator 9:15 
    Frequency of Absorption 9:35 
    Wave Numbers 10:58 
   Example I: Calculate the Reduced Mass of the Hydrogen Atom 11:44 
   Example II: Calculate the Fundamental Vibration Frequency & the Zero-Point Energy of This Molecule 13:37 
   Example III: Show That the Product of Two Even Functions is even 19:35 
   Example IV: Harmonic Oscillator 24:56 
  Example Problems II 46:43
   Intro 0:00 
   Example I: Harmonic Oscillator 0:12 
   Example II: Harmonic Oscillator 23:26 
   Example III: Calculate the RMS Displacement of the Molecules 38:12 

XVII. The Hydrogen Atom

  The Hydrogen Atom I 40:00
   Intro 0:00 
   The Hydrogen Atom I 1:31 
    Review of the Rigid Rotator 1:32 
    Hydrogen Atom & the Coulomb Potential 2:50 
    Using the Spherical Coordinates 6:33 
    Applying This Last Expression to Equation 1 10:19 
    Angular Component & Radial Component 13:26 
    Angular Equation 15:56 
    Solution for F(φ) 19:32 
    Determine The Normalization Constant 20:33 
    Differential Equation for T(a) 24:44 
    Legendre Equation 27:20 
    Legendre Polynomials 31:20 
    The Legendre Polynomials are Mutually Orthogonal 35:40 
    Limits 37:17 
    Coefficients 38:28 
  The Hydrogen Atom II 35:58
   Intro 0:00 
   Associated Legendre Functions 0:07 
    Associated Legendre Functions 0:08 
    First Few Associated Legendre Functions 6:39 
    s, p, & d Orbital 13:24 
    The Normalization Condition 15:44 
   Spherical Harmonics 20:03 
    Equations We Have Found 20:04 
    Wave Functions for the Angular Component & Rigid Rotator 24:36 
    Spherical Harmonics Examples 25:40 
   Angular Momentum 30:09 
    Angular Momentum 30:10 
    Square of the Angular Momentum 35:38 
    Energies of the Rigid Rotator 38:21 
  The Hydrogen Atom III 36:18
   Intro 0:00 
   The Hydrogen Atom III 0:34 
    Angular Momentum is a Vector Quantity 0:35 
    The Operators Corresponding to the Three Components of Angular Momentum Operator: In Cartesian Coordinates 1:30 
    The Operators Corresponding to the Three Components of Angular Momentum Operator: In Spherical Coordinates 3:27 
    Z Component of the Angular Momentum Operator & the Spherical Harmonic 5:28 
    Magnitude of the Angular Momentum Vector 20:10 
    Classical Interpretation of Angular Momentum 25:22 
    Projection of the Angular Momentum Vector onto the xy-plane 33:24 
  The Hydrogen Atom IV 33:55
   Intro 0:00 
   The Hydrogen Atom IV 0:09 
    The Equation to Find R( r ) 0:10 
    Relation Between n & l 3:50 
    The Solutions for the Radial Functions 5:08 
    Associated Laguerre Polynomials 7:58 
    1st Few Associated Laguerre Polynomials 8:55 
    Complete Wave Function for the Atomic Orbitals of the Hydrogen Atom 12:24 
    The Normalization Condition 15:06 
    In Cartesian Coordinates 18:10 
    Working in Polar Coordinates 20:48 
    Principal Quantum Number 21:58 
    Angular Momentum Quantum Number 22:35 
    Magnetic Quantum Number 25:55 
    Zeeman Effect 30:45 
  The Hydrogen Atom V: Where We Are 51:53
   Intro 0:00 
   The Hydrogen Atom V: Where We Are 0:13 
    Review 0:14 
    Let's Write Out ψ₂₁₁ 7:32 
    Angular Momentum of the Electron 14:52 
    Representation of the Wave Function 19:36 
    Radial Component 28:02 
    Example: 1s Orbital 28:34 
    Probability for Radial Function 33:46 
    1s Orbital: Plotting Probability Densities vs. r 35:47 
    2s Orbital: Plotting Probability Densities vs. r 37:46 
    3s Orbital: Plotting Probability Densities vs. r 38:49 
    4s Orbital: Plotting Probability Densities vs. r 39:34 
    2p Orbital: Plotting Probability Densities vs. r 40:12 
    3p Orbital: Plotting Probability Densities vs. r 41:02 
    4p Orbital: Plotting Probability Densities vs. r 41:51 
    3d Orbital: Plotting Probability Densities vs. r 43:18 
    4d Orbital: Plotting Probability Densities vs. r 43:48 
   Example I: Probability of Finding an Electron in the 2s Orbital of the Hydrogen 45:40 
  The Hydrogen Atom VI 51:53
   Intro 0:00 
   The Hydrogen Atom VI 0:07 
    Last Lesson Review 0:08 
    Spherical Component 1:09 
    Normalization Condition 2:02 
   Complete 1s Orbital Wave Function 4:08 
    1s Orbital Wave Function 4:09 
    Normalization Condition 6:28 
    Spherically Symmetric 16:00 
    Average Value 17:52 
   Example I: Calculate the Region of Highest Probability for Finding the Electron 21:19 
   2s Orbital Wave Function 25:32 
    2s Orbital Wave Function 25:33 
    Average Value 28:56 
    General Formula 32:24 
  The Hydrogen Atom VII 34:29
   Intro 0:00 
   The Hydrogen Atom VII 0:12 
    p Orbitals 1:30 
    Not Spherically Symmetric 5:10 
    Recall That the Spherical Harmonics are Eigenfunctions of the Hamiltonian Operator 6:50 
    Any Linear Combination of These Orbitals Also Has The Same Energy 9:16 
    Functions of Real Variables 15:53 
    Solving for Px 16:50 
    Real Spherical Harmonics 21:56 
    Number of Nodes 32:56 

XVIII. Hydrogen Atom Example Problems

  Hydrogen Atom Example Problems I 43:49
   Intro 0:00 
   Example I: Angular Momentum & Spherical Harmonics 0:20 
   Example II: Pair-wise Orthogonal Legendre Polynomials 16:40 
   Example III: General Normalization Condition for the Legendre Polynomials 25:06 
   Example IV: Associated Legendre Functions 32:13 
  The Hydrogen Atom Example Problems II 1:01:57
   Intro 0:00 
   Example I: Normalization & Pair-wise Orthogonal 0:13 
    Part 1: Normalized 0:43 
    Part 2: Pair-wise Orthogonal 16:53 
   Example II: Show Explicitly That the Following Statement is True for Any Integer n 27:10 
   Example III: Spherical Harmonics 29:26 
   Angular Momentum Cones 56:37 
    Angular Momentum Cones 56:38 
    Physical Interpretation of Orbital Angular Momentum in Quantum mechanics 60:16 
  The Hydrogen Atom Example Problems III 48:33
   Intro 0:00 
   Example I: Show That ψ₂₁₁ is Normalized 0:07 
   Example II: Show That ψ₂₁₁ is Orthogonal to ψ₃₁₀ 11:48 
   Example III: Probability That a 1s Electron Will Be Found Within 1 Bohr Radius of The Nucleus 18:35 
   Example IV: Radius of a Sphere 26:06 
   Example V: Calculate <r> for the 2s Orbital of the Hydrogen-like Atom 36:33 
  The Hydrogen Atom Example Problems IV 48:33
   Intro 0:00 
   Example I: Probability Density vs. Radius Plot 0:11 
   Example II: Hydrogen Atom & The Coulombic Potential 14:16 
   Example III: Find a Relation Among <K>, <V>, & <E> 25:47 
   Example IV: Quantum Mechanical Virial Theorem 48:32 
   Example V: Find the Variance for the 2s Orbital 54:13 
  The Hydrogen Atom Example Problems V 48:33
   Intro 0:00 
   Example I: Derive a Formula for the Degeneracy of a Given Level n 0:11 
   Example II: Using Linear Combinations to Represent the Spherical Harmonics as Functions of the Real Variables θ & φ 8:30 
   Example III: Using Linear Combinations to Represent the Spherical Harmonics as Functions of the Real Variables θ & φ 23:01 
   Example IV: Orbital Functions 31:51 

XIX. Spin Quantum Number and Atomic Term Symbols

  Spin Quantum Number: Term Symbols I 59:18
   Intro 0:00 
   Quantum Numbers Specify an Orbital 0:24 
    n 1:10 
    l 1:20 
    m 1:35 
    4th Quantum Number: s 2:02 
   Spin Orbitals 7:03 
    Spin Orbitals 7:04 
    Multi-electron Atoms 11:08 
   Term Symbols 18:08 
    Russell-Saunders Coupling & The Atomic Term Symbol 18:09 
   Example: Configuration for C 27:50 
    Configuration for C: 1s²2s²2p² 27:51 
    Drawing Every Possible Arrangement 31:15 
    Term Symbols 45:24 
    Microstate 50:54 
  Spin Quantum Number: Term Symbols II 34:54
   Intro 0:00 
   Microstates 0:25 
    We Started With 21 Possible Microstates 0:26 
    ³P State 2:05 
    Microstates in ³P Level 5:10 
    ¹D State 13:16 
    ³P State 16:10 
    ²P₂ State 17:34 
    ³P₁ State 18:34 
    ³P₀ State 19:12 
    9 Microstates in ³P are Subdivided 19:40 
    ¹S State 21:44 
    Quicker Way to Find the Different Values of J for a Given Basic Term Symbol 22:22 
    Ground State 26:27 
   Hund's Empirical Rules for Specifying the Term Symbol for the Ground Electronic State 27:29 
    Hund's Empirical Rules: 1 28:24 
    Hund's Empirical Rules: 2 29:22 
    Hund's Empirical Rules: 3 - Part A 30:22 
    Hund's Empirical Rules: 3 - Part B 31:18 
    Example: 1s²2s²2p² 31:54 
  Spin Quantum Number: Term Symbols III 38:03
   Intro 0:00 
   Spin Quantum Number: Term Symbols III 0:14 
    Deriving the Term Symbols for the p² Configuration 0:15 
    Table: MS vs. ML 3:57 
    ¹D State 16:21 
    ³P State 21:13 
    ¹S State 24:48 
    J Value 25:32 
    Degeneracy of the Level 27:28 
    When Given r Electrons to Assign to n Equivalent Spin Orbitals 30:18 
    p² Configuration 32:51 
    Complementary Configurations 35:12 
  Term Symbols & Atomic Spectra 57:49
   Intro 0:00 
   Lyman Series 0:09 
    Spectroscopic Term Symbols 0:10 
    Lyman Series 3:04 
   Hydrogen Levels 8:21 
    Hydrogen Levels 8:22 
   Term Symbols & Atomic Spectra 14:17 
    Spin-Orbit Coupling 14:18 
    Selection Rules for Atomic Spectra 21:31 
    Selection Rules for Possible Transitions 23:56 
    Wave Numbers for The Transitions 28:04 
   Example I: Calculate the Frequencies of the Allowed Transitions from (4d) ²D →(2p) ²P 32:23 
   Helium Levels 49:50 
    Energy Levels for Helium 49:51 
   Transitions & Spin Multiplicity 52:27 
    Transitions & Spin Multiplicity 52:28 

XX. Term Symbols Example Problems

  Example Problems I 1:01:20
   Intro 0:00 
   Example I: What are the Term Symbols for the np¹ Configuration? 0:10 
   Example II: What are the Term Symbols for the np² Configuration? 20:38 
   Example III: What are the Term Symbols for the np³ Configuration? 40:46 
  Example Problems II 56:34
   Intro 0:00 
   Example I: Find the Term Symbols for the nd² Configuration 0:11 
   Example II: Find the Term Symbols for the 1s¹2p¹ Configuration 27:02 
   Example III: Calculate the Separation Between the Doublets in the Lyman Series for Atomic Hydrogen 41:41 
   Example IV: Calculate the Frequencies of the Lines for the (4d) ²D → (3p) ²P Transition 48:53 

XXI. Equation Review for Quantum Mechanics

  Quantum Mechanics: All the Equations in One Place 18:24
   Intro 0:00 
   Quantum Mechanics Equations 0:37 
    De Broglie Relation 0:38 
    Statistical Relations 1:00 
    The Schrӧdinger Equation 1:50 
    The Particle in a 1-Dimensional Box of Length a 3:09 
    The Particle in a 2-Dimensional Box of Area a x b 3:48 
    The Particle in a 3-Dimensional Box of Area a x b x c 4:22 
    The Schrӧdinger Equation Postulates 4:51 
    The Normalization Condition 5:40 
    The Probability Density 6:51 
    Linear 7:47 
    Hermitian 8:31 
    Eigenvalues & Eigenfunctions 8:55 
    The Average Value 9:29 
    Eigenfunctions of Quantum Mechanics Operators are Orthogonal 10:53 
    Commutator of Two Operators 10:56 
    The Uncertainty Principle 11:41 
    The Harmonic Oscillator 13:18 
    The Rigid Rotator 13:52 
    Energy of the Hydrogen Atom 14:30 
    Wavefunctions, Radial Component, and Associated Laguerre Polynomial 14:44 
    Angular Component or Spherical Harmonic 15:16 
    Associated Legendre Function 15:31 
    Principal Quantum Number 15:43 
    Angular Momentum Quantum Number 15:50 
    Magnetic Quantum Number 16:21 
    z-component of the Angular Momentum of the Electron 16:53 
    Atomic Spectroscopy: Term Symbols 17:14 
    Atomic Spectroscopy: Selection Rules 18:03 

XXII. Molecular Spectroscopy

  Spectroscopic Overview: Which Equation Do I Use & Why 50:02
   Intro 0:00 
   Spectroscopic Overview: Which Equation Do I Use & Why 1:02 
    Lesson Overview 1:03 
    Rotational & Vibrational Spectroscopy 4:01 
    Frequency of Absorption/Emission 6:04 
    Wavenumbers in Spectroscopy 8:10 
    Starting State vs. Excited State 10:10 
    Total Energy of a Molecule (Leaving out the Electronic Energy) 14:02 
    Energy of Rotation: Rigid Rotor 15:55 
    Energy of Vibration: Harmonic Oscillator 19:08 
    Equation of the Spectral Lines 23:22 
   Harmonic Oscillator-Rigid Rotor Approximation (Making Corrections) 28:37 
    Harmonic Oscillator-Rigid Rotor Approximation (Making Corrections) 28:38 
    Vibration-Rotation Interaction 33:46 
    Centrifugal Distortion 36:27 
    Anharmonicity 38:28 
    Correcting for All Three Simultaneously 41:03 
    Spectroscopic Parameters 44:26 
   Summary 47:32 
    Harmonic Oscillator-Rigid Rotor Approximation 47:33 
    Vibration-Rotation Interaction 48:14 
    Centrifugal Distortion 48:20 
    Anharmonicity 48:28 
    Correcting for All Three Simultaneously 48:44 
  Vibration-Rotation 59:47
   Intro 0:00 
   Vibration-Rotation 0:37 
    What is Molecular Spectroscopy? 0:38 
    Microwave, Infrared Radiation, Visible & Ultraviolet 1:53 
    Equation for the Frequency of the Absorbed Radiation 4:54 
    Wavenumbers 6:15 
    Diatomic Molecules: Energy of the Harmonic Oscillator 8:32 
    Selection Rules for Vibrational Transitions 10:35 
    Energy of the Rigid Rotator 16:29 
    Angular Momentum of the Rotator 21:38 
    Rotational Term F(J) 26:30 
    Selection Rules for Rotational Transition 29:30 
    Vibration Level & Rotational States 33:20 
    Selection Rules for Vibration-Rotation 37:42 
    Frequency of Absorption 39:32 
    Diagram: Energy Transition 45:55 
    Vibration-Rotation Spectrum: HCl 51:27 
    Vibration-Rotation Spectrum: Carbon Monoxide 54:30 
  Vibration-Rotation Interaction 46:22
   Intro 0:00 
   Vibration-Rotation Interaction 0:13 
    Vibration-Rotation Spectrum: HCl 0:14 
    Bond Length & Vibrational State 4:23 
    Vibration Rotation Interaction 10:18 
    Case 1 12:06 
    Case 2 17:17 
   Example I: HCl Vibration-Rotation Spectrum 22:58 
    Rotational Constant for the 0 & 1 Vibrational State 26:30 
    Equilibrium Bond Length for the 1 Vibrational State 39:42 
    Equilibrium Bond Length for the 0 Vibrational State 42:13 
    Bₑ & αₑ 44:54 
  The Non-Rigid Rotator 29:24
   Intro 0:00 
   The Non-Rigid Rotator 0:09 
    Pure Rotational Spectrum 0:54 
    The Selection Rules for Rotation 3:09 
    Spacing in the Spectrum 5:04 
    Centrifugal Distortion Constant 9:00 
    Fundamental Vibration Frequency 11:46 
    Observed Frequencies of Absorption 14:14 
    Difference between the Rigid Rotator & the Adjusted Rigid Rotator 16:51 
    Adjusted Rigid Rotator 21:31 
    Observed Frequencies of Absorption 26:26 
  The Anharmonic Oscillator 30:53
   Intro 0:00 
   The Anharmonic Oscillator 0:09 
    Vibration-Rotation Interaction & Centrifugal Distortion 0:10 
    Making Corrections to the Harmonic Oscillator 4:50 
    Selection Rule for the Harmonic Oscillator 7:50 
    Overtones 8:40 
    True Oscillator 11:46 
    Harmonic Oscillator Energies 13:16 
    Anharmonic Oscillator Energies 13:33 
    Observed Frequencies of the Overtones 15:09 
    True Potential 17:22 
    HCl Vibrational Frequencies: Fundamental & First Few Overtones 21:10 
   Example I: Vibrational States & Overtones of the Vibrational Spectrum 22:42 
    Example I: Part A - First 4 Vibrational States 23:44 
    Example I: Part B - Fundamental & First 3 Overtones 25:31 
   Important Equations 27:45 
    Energy of the Q State 29:14 
    The Difference in Energy between 2 Successive States 29:23 
    Difference in Energy between 2 Spectral Lines 29:40 
  Electronic Transitions 1:01:33
   Intro 0:00 
   Electronic Transitions 0:16 
    Electronic State & Transition 0:17 
    Total Energy of the Diatomic Molecule 3:34 
    Vibronic Transitions 4:30 
    Selection Rule for Vibronic Transitions 9:11 
    More on Vibronic Transitions 10:08 
    Frequencies in the Spectrum 16:46 
    Difference of the Minima of the 2 Potential Curves 24:48 
    Anharmonic Zero-point Vibrational Energies of the 2 States 26:24 
    Frequency of the 0 → 0 Vibronic Transition 27:54 
    Making the Equation More Compact 29:34 
    Spectroscopic Parameters 32:11 
    Franck-Condon Principle 34:32 
   Example I: Find the Values of the Spectroscopic Parameters for the Upper Excited State 47:27 
   Table of Electronic States and Parameters 56:41 

XXIII. Molecular Spectroscopy Example Problems

  Example Problems I 33:47
   Intro 0:00 
   Example I: Calculate the Bond Length 0:10 
   Example II: Calculate the Rotational Constant 7:39 
   Example III: Calculate the Number of Rotations 10:54 
   Example IV: What is the Force Constant & Period of Vibration? 16:31 
   Example V: Part A - Calculate the Fundamental Vibration Frequency 21:42 
   Example V: Part B - Calculate the Energies of the First Three Vibrational Levels 24:12 
   Example VI: Calculate the Frequencies of the First 2 Lines of the R & P Branches of the Vib-Rot Spectrum of HBr 26:28 
  Example Problems II 1:01:05
   Intro 0:00 
   Example I: Calculate the Frequencies of the Transitions 0:09 
   Example II: Specify Which Transitions are Allowed & Calculate the Frequencies of These Transitions 22:07 
   Example III: Calculate the Vibrational State & Equilibrium Bond Length 34:31 
   Example IV: Frequencies of the Overtones 49:28 
   Example V: Vib-Rot Interaction, Centrifugal Distortion, & Anharmonicity 54:47 
  Example Problems III 33:31
   Intro 0:00 
   Example I: Part A - Derive an Expression for ∆G( r ) 0:10 
   Example I: Part B - Maximum Vibrational Quantum Number 6:10 
   Example II: Part A - Derive an Expression for the Dissociation Energy of the Molecule 8:29 
   Example II: Part B - Equation for ∆G( r ) 14:00 
   Example III: How Many Vibrational States are There for Br₂ before the Molecule Dissociates 18:16 
   Example IV: Find the Difference between the Two Minima of the Potential Energy Curves 20:57 
   Example V: Rotational Spectrum 30:51 

XXIV. Statistical Thermodynamics

  Statistical Thermodynamics: The Big Picture 1:01:15
   Intro 0:00 
   Statistical Thermodynamics: The Big Picture 0:10 
    Our Big Picture Goal 0:11 
    Partition Function (Q) 2:42 
    The Molecular Partition Function (q) 4:00 
    Consider a System of N Particles 6:54 
    Ensemble 13:22 
    Energy Distribution Table 15:36 
    Probability of Finding a System with Energy 16:51 
    The Partition Function 21:10 
    Microstate 28:10 
    Entropy of the Ensemble 30:34 
    Entropy of the System 31:48 
   Expressing the Thermodynamic Functions in Terms of The Partition Function 39:21 
    The Partition Function 39:22 
    Pi & U 41:20 
    Entropy of the System 44:14 
    Helmholtz Energy 48:15 
    Pressure of the System 49:32 
    Enthalpy of the System 51:46 
    Gibbs Free Energy 52:56 
    Heat Capacity 54:30 
   Expressing Q in Terms of the Molecular Partition Function (q) 59:31 
    Indistinguishable Particles 62:16 
    N is the Number of Particles in the System 63:27 
    The Molecular Partition Function 65:06 
    Quantum States & Degeneracy 67:46 
    Thermo Property in Terms of ln Q 70:09 
    Example: Thermo Property in Terms of ln Q 73:23 
  Statistical Thermodynamics: The Various Partition Functions I 47:23
   Intro 0:00 
   Lesson Overview 0:19 
   Monatomic Ideal Gases 6:40 
    Monatomic Ideal Gases Overview 6:42 
    Finding the Parition Function of Translation 8:17 
    Finding the Parition Function of Electronics 13:29 
    Example: Na 17:42 
    Example: F 23:12 
    Energy Difference between the Ground State & the 1st Excited State 29:27 
    The Various Partition Functions for Monatomic Ideal Gases 32:20 
    Finding P 43:16 
    Going Back to U = (3/2) RT 46:20 
  Statistical Thermodynamics: The Various Partition Functions II 54:09
   Intro 0:00 
   Diatomic Gases 0:16 
    Diatomic Gases 0:17 
    Zero-Energy Mark for Rotation 2:26 
    Zero-Energy Mark for Vibration 3:21 
    Zero-Energy Mark for Electronic 5:54 
    Vibration Partition Function 9:48 
    When Temperature is Very Low 14:00 
    When Temperature is Very High 15:22 
    Vibrational Component 18:48 
    Fraction of Molecules in the r Vibration State 21:00 
    Example: Fraction of Molecules in the r Vib. State 23:29 
    Rotation Partition Function 26:06 
    Heteronuclear & Homonuclear Diatomics 33:13 
    Energy & Heat Capacity 36:01 
    Fraction of Molecules in the J Rotational Level 39:20 
    Example: Fraction of Molecules in the J Rotational Level 40:32 
    Finding the Most Populated Level 44:07 
   Putting It All Together 46:06 
    Putting It All Together 46:07 
    Energy of Translation 51:51 
    Energy of Rotation 52:19 
    Energy of Vibration 52:42 
    Electronic Energy 53:35 

XXV. Statistical Thermodynamics Example Problems

  Example Problems I 48:32
   Intro 0:00 
   Example I: Calculate the Fraction of Potassium Atoms in the First Excited Electronic State 0:10 
   Example II: Show That Each Translational Degree of Freedom Contributes R/2 to the Molar Heat Capacity 14:46 
   Example III: Calculate the Dissociation Energy 21:23 
   Example IV: Calculate the Vibrational Contribution to the Molar heat Capacity of Oxygen Gas at 500 K 25:46 
   Example V: Upper & Lower Quantum State 32:55 
   Example VI: Calculate the Relative Populations of the J=2 and J=1 Rotational States of the CO Molecule at 25°C 42:21 
  Example Problems II 57:30
   Intro 0:00 
   Example I: Make a Plot of the Fraction of CO Molecules in Various Rotational Levels 0:10 
   Example II: Calculate the Ratio of the Translational Partition Function for Cl₂ and Br₂ at Equal Volume & Temperature 8:05 
   Example III: Vibrational Degree of Freedom & Vibrational Molar Heat Capacity 11:59 
   Example IV: Calculate the Characteristic Vibrational & Rotational temperatures for Each DOF 45:03 

Duration: 67 hours, 52 minutes

Number of Lessons: 92

This course is perfect for the college student taking Physical Chemistry and is looking for time-saving clear explanations and tons of step-by-step example problems. Almost every topic imaginable is covered in detail in one of Educator’s most comprehensive courses.

Additional Features:

  • Free Sample Lessons
  • Closed Captioning (CC)
  • Downloadable Lecture Slides
  • Instructor Comments

Topics Include:

  • Joule’s Experiment
  • 1st Law of Thermodynamics
  • Entropy
  • Spontaneity & Equilibrium
  • Free Energy
  • Schrodinger Equation
  • Particle in a Box
  • Quantum Mechanics
  • Harmonic Oscillator
  • Rigid Rotator
  • Hydrogen Atom
  • Quantum Numbers
  • Molecular Spectroscopy
  • Statistical Thermodynamics

Professor Hovasapian combines his triple degrees in Mathematics, Chemistry, and Classics with his 15+ years of teaching experience to help students understand difficult math and science concepts.

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