### Chem 131B. Lec. 18. Molecular Structure & Statistical Mechanics (English) Lecture

UCI Chem 131B Molecular Structure & Statistical Mechanics (Winter 2013)

Lec 18. Molecular Structure & Statistical Mechanics -- Eigenstates & Eigenvalues.

View the complete course: __http://ocw.uci.edu/courses/chem_131b_molecular_structure_and_elementary_statistical_mechanics.html__

Instructor: Rachel Martin, Ph.D.

License: Creative Commons BY-NC-SA

Terms of Use: __http://ocw.uci.edu/info__.

More courses at __http://ocw.uci.edu__

Description: Principles of quantum mechanics with application to the elements of atomic structure and energy levels, diatomic molecular spectroscopy and structure determination, and chemical bonding in simple molecules.

Recorded on February 22, 2013.

Index of Topics:

00:30 - Eigenstates and Eigenvalues

01:19 - Matrix Representations

05:21 - Zeeman Basis

07:57 - Eigenstates and Eigenvalues, Slide 2

11:31 - Raising and Lowering Operators

15:09 - Eigenstates and Eigenvalues, Slide 3

17:01 - Superpositions

21:16 - Spin Operators and Eigenstates

22:20 - Rotation Operators

23:46 - Pulsed NMR

29:05 - NMR Probes

31:09 - Nutation Curves (Solenoid)

35:57 - RF Homogeneity

36:41 - Spin-Lattice Relaxation (T1)

41:09 - What Causes Longitudinal Relaxation?

42:02 - What Causes Longitudinal Relaxation, Slide 2

44:10 - Inversion Recovery (T1)

47:11 - Relaxation along the Z-Axis

Required attribution: Martin, Rachel. Molecular Structure & Statistical Mechanics 131B (UCI OpenCourseWare: University of California, Irvine), __http://ocw.uci.edu/courses/chem_131b_molecular_structure_and_elementary_statistical_mechanics.html__. [Access date]. License: __Creative Commons Attribution-ShareAlike 3.0 United States License.__

Rachel Martin Chemistry Dept. | Physical Sciences Sch. | University of California, Irvine

### Chem 131B. Lec. 19. Molecular Structure & Statistical Mechanics (English) Lecture

UCI Chem 131B Molecular Structure & Statistical Mechanics (Winter 2013)

Lec 19. Molecular Structure & Statistical Mechanics -- Spin Rotations T1 & T2.

View the complete course: __http://ocw.uci.edu/courses/chem_131b_molecular_structure_and_elementary_statistical_mechanics.html__

Instructor: Rachel Martin, Ph.D.

License: Creative Commons BY-NC-SA

Terms of Use: __http://ocw.uci.edu/info__.

More courses at __http://ocw.uci.edu__

Description: Principles of quantum mechanics with application to the elements of atomic structure and energy levels, diatomic molecular spectroscopy and structure determination, and chemical bonding in simple molecules.

Recorded on February 25, 2013.

Index of Topics:

03:49 - Inversion Recovery (T1)

04:59 - Relaxation Along the Z-Axis

05:50 - Moving Tube

05:58 - Relaxation Along the Z-Axis (revisited)

07:02 - Moving Tube (revisited)

08:24 - Moving Tube, Slide 2

09:20 - Spin-Spin Relaxation (T2)

12:29 - Spin Echo (T2)

14:04 - H NMR Spectroscopy: Spin-Spin Splitting

16:40 - Rules for Splitting Patterns

20:23 - Splitting is Generally Not Observed Between Protons Separated by More Than Three σ Bonds

21:18 - The n+1 Rule (For "Simple" Compounds)

23:49 - J-Coupling: Product Basis

26:20 - J-Coupling: Hamiltonian

29:09 - J-Coupling: Product Basis, Slide 2

32:13 - J-Coupling: Equivalent Spins

34:21 - H NMR-- Spin-Spin Splitting: An Example

34:31 - J-Coupling: Equivalent Spins (revisited)

35:11 - H NMR-- Spin-Spin Splitting: An Example (revisited)

36:26 - Standard Coupling Values (J, in Hz)

37:21 - Sample Spectrum

38:28 - More Complex Splitting Patterns: Nitrobenzene

39:14 - The Difference Between a Quartet and a Doublet of Doublets

39:56 - Another Example of Doublets of Doublets

40:17 - A Closer Look at the Splitting Pattern

40:42 - NMR Spectrum Example

42:24 - General 2D Pulse Sequence

44:53 - ^(13)C-^(15)N Correlation of Arginine

45:56 - H-N HSQC

Required attribution: Martin, Rachel. Molecular Structure & Statistical Mechanics 131B (UCI OpenCourseWare: University of California, Irvine), __http://ocw.uci.edu/courses/chem_131b_molecular_structure_and_elementary_statistical_mechanics.html__. [Access date]. License: __Creative Commons Attribution-ShareAlike 3.0 United States License.__

Rachel Martin Chemistry Dept. | Physical Sciences Sch. | University of California, Irvine

### Chem 131B. Lec. 20. Molecular Structure & Statistical Mechanics (English) Lecture

UCI Chem 131B Molecular Structure & Statistical Mechanics (Winter 2013)

Lec 20. Molecular Structure & Statistical Mechanics -- NMR Applications/Review.

View the complete course: __http://ocw.uci.edu/courses/chem_131b_molecular_structure_and_elementary_statistical_mechanics.html__

Instructor: Rachel Martin, Ph.D.

License: Creative Commons BY-NC-SA

Terms of Use: __http://ocw.uci.edu/info__.

More courses at __http://ocw.uci.edu__

Description: Principles of quantum mechanics with application to the elements of atomic structure and energy levels, diatomic molecular spectroscopy and structure determination, and chemical bonding in simple molecules.

Recorded on February 27, 2013.

Index of Topics:

06:48 - 19: NMR Applications/Review

10:26 - Going Through the Process

15:59 - Sidechain Correlations- TOCSY

17:13 - G18V Backbone Walk- H-N-CACB

17:54 - Mistic Structure

18:17 - Mistic Structure, Slide 2

18:59 - Relative Sizes of Interactions

19:40 - Quadrupolar Nuclei- Periodic Table

20:56 - Quadrupolar Nuclei

21:23 - Quadupolar Moment Interacts with the EFT Present at the Nucleus

24:31 - Quadrpolar Hamiltonian

25:19 - Spin 1

27:34 - Bicelles: Membrane Mimetics

29:39 - ^(2)H Spectra

31:59 - Multiple Lipid Phases

35:56 - NMR Spectroscopy Worksheet

Molecular Structure and Statistical Mechanics 131B is part of OpenChem.

http://ocw.uci.edu/openchem

Required attribution: Martin, Rachel. Molecular Structure & Statistical Mechanics 131B (UCI OpenCourseWare: University of California, Irvine), http://ocw.uci.edu/courses/chem_131b_molecular_structure_and_elementary_statistical_mechanics.html. [Access date]. License: Creative Commons Attribution-ShareAlike 3.0 United States License

Rachel Martin Chemistry Dept. | Physical Sciences Sch. | University of California, Irvine

### Chem 131B. Lec. 21. Molecular Structure & Statistical Mechanics (English) Lecture

UCI Chem 131B Molecular Structure & Statistical Mechanics (Winter 2013)

Lec 21. Molecular Structure & Statistical Mechanics -- Second Midterm Examination Review.

View the complete course: __http://ocw.uci.edu/courses/chem_131b_molecular_structure_and_elementary_statistical_mechanics.html__

Instructor: Rachel Martin, Ph.D.

Terms of Use: __http://ocw.uci.edu/info__.

More courses at __http://ocw.uci.edu__

Recorded on March 4, 2013.

Index of Topics:

01:33 - IR Spectrum of Carbon Monoxide

04:39 - Is Carbon Monoxide a Perfect Rigid Rotor?

07:14 - How Would the Raman Spectrum of CO Look Different?

10:36 - Electronic Spectroscopy

15:17 - Franck-Condon Factors

19:34 - Term Symbols and Electronic Transitions

25:05 - NMR Spectroscopy

33:21- NMR Spectroscopy, Continued

Required attribution: Martin, Rachel. Molecular Structure & Statistical Mechanics 131B (UCI OpenCourseWare: University of California, Irvine), __http://ocw.uci.edu/courses/chem_131b_molecular_structure_and_elementary_statistical_mechanics.html__. [Access date]. License: __Creative Commons Attribution-ShareAlike 3.0 United States License.__

Rachel Martin Chemistry Dept. | Physical Sciences Sch. | University of California, Irvine

### Chem 131B. Lec. 22. Molecular Structure & Statistical Mechanics. The Boltzmann Distribution (English) Lecture

UCI Chem 131B Molecular Structure & Statistical Mechanics (Winter 2013)

Lec 22. Molecular Structure & Statistical Mechanics -- The Boltzmann Distribution.

View the complete course: __http://ocw.uci.edu/courses/chem_131b_molecular_structure_and_elementary_statistical_mechanics.html__

Instructor: Rachel Martin, Ph.D.

Terms of Use: __http://ocw.uci.edu/info__.

More courses at __http://ocw.uci.edu__

Recorded on March 6, 2013.

Index of Topics:

03:27 - 20: The Boltzmann Distribution

05:23 - NMR Population Differences

06:14 - What is the Population Difference?

10:34 - Statistical Mechanics

12:38 - Statistical Mechanics: Ensemble

15:32 - Statistical Mechanics: Ensemble, Slide 2

17:14 - Conformational Ensemble

18:09 - Conformational Ensemble, Slide 2

18:47 - Statistical Mechanics

21:08 - Statistical Mechanics, Slide 2

24:26 - Weights of Configurations

27:47 - Weights of Configurations, Slide 2

30:07 - Dominant Configuration

33:59 - Dominant Configuration, Slide 2

34:58 - Dominant Configuration, Slide 3

38:18 - Dominant Configuration, Slide 4

39:48 - Dominant Configuration, Slide 5

41:17 - Relative Populations

43:05 - Rotational Spectrum of HCl

__http://ocw.uci.edu/courses/chem_131b_molecular_structure_and_elementary_statistical_mechanics.html__. [Access date]. License: __Creative Commons Attribution-ShareAlike 3.0 United States License.__

Rachel Martin Chemistry Dept. | Physical Sciences Sch. | University of California, Irvine

### Chem 131B. Lec. 23. Molecular Structure & Statistical Mechanics. Partition Functions Pt. 1 (English) Lecture

UCI Chem 131B Molecular Structure & Statistical Mechanics (Winter 2013)

Lec 23. Molecular Structure & Statistical Mechanics -- Partition Functions -- Part 1.

View the complete course: __http://ocw.uci.edu/courses/chem_131b_molecular_structure_and_elementary_statistical_mechanics.html__

Instructor: Rachel Martin, Ph.D.

Terms of Use: __http://ocw.uci.edu/info__.

More courses at __http://ocw.uci.edu__

Recorded on March 8, 2013.

Index of Topics:

02:11 - 21: Partition Functions

02:51 - Rotational Spectrum of HCl

03:53 - Molecular Partition Function

07:17 - Rotational Spectrum of HCl, Slide 2

16:05 - Partition Function and Temperature

22:25 - 2-Level System Partition Function

27:09 - Contributions to the Partition Function

31:12 - Particle in a Box Partition Function

32:36 - Particle in a Box Partition Function, Slide 2

35:20 - Particle in a Box Partition Function, Slide 3

38:12 - Harmonic Oscillator Partition Function

43:08 - Partition Function Example 1

__http://ocw.uci.edu/courses/chem_131b_molecular_structure_and_elementary_statistical_mechanics.html__. [Access date]. License: __Creative Commons Attribution-ShareAlike 3.0 United States License.__

Rachel Martin Chemistry Dept. | Physical Sciences Sch. | University of California, Irvine

### Chem 131B. Lec. 24. Molecular Structure & Statistical Mechanics. Partition Functions Pt. 2 (English) Lecture

UCI Chem 131B Molecular Structure & Statistical Mechanics (Winter 2013)

Lec 24. Molecular Structure & Statistical Mechanics -- Partition Functions -- Part 2.

View the complete course: __http://ocw.uci.edu/courses/chem_131b_molecular_structure_and_elementary_statistical_mechanics.html__

Instructor: Rachel Martin, Ph.D.

Terms of Use: __http://ocw.uci.edu/info__.

More courses at __http://ocw.uci.edu__

Recorded on March 12, 2013.

Index of Topics:

01:49 - 22: Partition Functions

01:59 - Quiz

02:18 - Rotational Partition Function

03:45 - Rotational Partition Functions

05:42 - Rotational Partition Functions, Slide 2

08:13 - Rotational Temperature

12:51 - Symmetric Linear Molecule

17:01 - Rotational Raman for H2

23:30 - Strokes Lines for H2

29:11 - The Mean Energy

31:30 - Partition Function and Temperature

32:42 - The Canonical Ensemble

36:38 - The Canonical Ensemble, Slide 2

__http://ocw.uci.edu/courses/chem_131b_molecular_structure_and_elementary_statistical_mechanics.html__. [Access date]. License: __Creative Commons Attribution-ShareAlike 3.0 United States License.__

Rachel Martin Chemistry Dept. | Physical Sciences Sch. | University of California, Irvine

### Chem 131B. Lec. 25. Molecular Structure & Statistical Mechanics. Partition Functions (English) Lecture

UCI Chem 131B Molecular Structure & Statistical Mechanics (Winter 2013)

Lec 25. Molecular Structure & Statistical Mechanics -- Partition Functions -- Part 3.

View the complete course: http://ocw.uci.edu/courses/chem_131b_molecular_structure_and_elementary_statistical_mechanics.html

Instructor: Rachel Martin, Ph.D.

License: Creative Commons BY-NC-SA

Terms of Use: http://ocw.uci.edu/info.

More courses at http://ocw.uci.edu

Recorded on March 13, 2013.

Index of Topics:

01:02 - Simulation

06:32 - 23: Statistical Mechanics Examples

06:38 - Langrange Multipliers: Motivation

09:24 - Math Review: Langrange Multipliers

11:22 - Langrange Multipliers: Example 1

13:38 - Langrange Multipliers: Example 2

16:30 - Multiple Constraints

18:50 - Partition Function Example 1, Speed Distribution

20:00 - Partition Function Example 1, Maxwell-Boltzmann Distribution of Particle Velocities

21:32 - Partition Function Example 1, Simplifying Further

22:43 - Partition Function Example 1, The Mean- Square Velocity Define the Width of the Distribution

26:33 - Partition Function Example 1, Ideal Gas

27:06 - Partition Function Example 1, Temperature Dependence of Velocity Distribution

27:42 - Partition Function Example 2, Curie's law of Paramagnetism

32:40 - Partition Function Example 2, Calculate the Average Magnetization as a Function of T

34:52 - Partition Function Example 2, Using the Taylor Series Expansion

38:36 - Curie's Law

39:17 - Partition Function Example 3, Consider the Microstates

42:19 - Partition Function Example 3, Assume the Beads Have an Attractive Force

Required attribution: Martin, Rachel. Molecular Structure & Statistical Mechanics 131B (UCI OpenCourseWare: University of California, Irvine), http://ocw.uci.edu/courses/chem_131b_molecular_structure_and_elementary_statistical_mechanics.html. [Access date]. License: Creative Commons Attribution-ShareAlike 3.0 United States License.

Rachel Martin Chemistry Dept. | Physical Sciences Sch. | University of California, Irvine

### Chem 131B. Lec. 26. Molecular Structure & Statistical Mechanics. Final Exam Review (English) Lecture

UCI Chem 131B Molecular Structure & Statistical Mechanics (Winter 2013)

Lec 26. Molecular Structure & Statistical Mechanics -- Final Exam Review.

View the complete course: __http://ocw.uci.edu/courses/chem_131b_molecular_structure_and_elementary_statistical_mechanics.html__

Instructor: Rachel Martin, Ph.D.

Terms of Use: __http://ocw.uci.edu/info__.

More courses at __http://ocw.uci.edu__

Recorded on March 16, 2013.

Index of Topics:

04:08 - Final Exam Review

04:15 - The Canonical Ensemble

05:17 - The Canonical Ensemble, Slide 2

08:40 - Point Groups: Flow Chart

09:34 - Example: OCl2

11:27 - Group Theory- Molecular Motion

13:08 - Group Theory- Molecular Motion, Slide 2

15:03 - Group Theory- Molecular Motion, Slide 3

16:05 - Big Picture: Spectroscopy

17:13 - Raman Spectroscopy

17:48 - Vibration and Rotational Energy Levels

18:37 - IR Spectrum of HCl

18:56 - Bond Length of HCl

19:43 - Vibrational Spectroscopy: Use the Spectrum to Estimate the Force Constant

20:51 - Vibrational Spectroscopy: Why is There No Peak in the Center of These Spectra?

22:32 - Vibrational Spectroscopy: Summary of Example

23:52 - Degeneracy

24:52 - Vibrational Raman Spectroscopy

24:58 - Term Symbols for Atoms

25:57 - Hund's Rule

26:33 - Term Symbols for Linear Molecules

30:48 - Selection Rules

33:41 - Electronic Spectroscopy

34:54 - Nuclear Zeeman Effect

26:30 - Spin Quantum Number

37:06 - Zeeman Basis

38:48 - Raising and Lowering Operators

40:17 - Eigenstates and Eigenvalues

40:35 - ^(1)H NMR Spectroscopy is a Powerful tool for Structure Elucidation

41:54 - J-Coupling: Product Basis

42:15 - NMR Spectra

42:59 - Statistical Mechanics

43:48 - Relative Populations

44:13 - Molecular Partition Function

45:00 - 2-Level System Partition Function

Required attribution: Martin, Rachel. Molecular Structure & Statistical Mechanics 131B (UCI OpenCourseWare: University of California, Irvine), __http://ocw.uci.edu/courses/chem_131b_molecular_structure_and_elementary_statistical_mechanics.html__. [Access date]. License: __Creative Commons Attribution-ShareAlike 3.0 United States License__.

Rachel Martin Chemistry Dept. | Physical Sciences Sch. | University of California, Irvine

### Chem 131C. Lec. 01. Thermodynamics and Chemical Dynamics: Syllabus, Homework, & Lectures. (English) Lecture

UCI Chem 131C Thermodynamics and Chemical Dynamics (Spring 2012)

Lec 01. Thermodynamics and Chemical Dynamics -- Syllabus, Homework, & Lectures --

View the complete course: http://ocw.uci.edu/courses/chem_131c_thermodynamics_and_chemical_dynamics.html

Instructor: Reginald Penner, Ph.D.

License: Creative Commons BY-NC-SA

Terms of Use: http://ocw.uci.edu/info.

More courses at http://ocw.uci.edu

Description: In Chemistry 131C, students will study how to calculate macroscopic chemical properties of systems. This course will build on the microscopic understanding (Chemical Physics) to reinforce and expand your understanding of the basic thermo-chemistry concepts from General Chemistry (Physical Chemistry.) We then go on to study how chemical reaction rates are measured and calculated from molecular properties. Topics covered include: Energy, entropy, and the thermodynamic potentials; Chemical equilibrium; and Chemical kinetics.

Thermodynamics and Chemical Dynamics (Chem 131C) is part of OpenChem: http://ocw.uci.edu/openchem/

This video is part of a 27-lecture undergraduate-level course titled "Thermodynamics and Chemical Dynamics" taught at UC Irvine by Professor Reginald M. Penner.

Recorded on April 11, 2012.

Index of Topics:

00:20 - Introduction

00:32 - Curvature of the Conical Intersection Seam: An Approximate Second-Order Analysis

01:15 - Announcements

02:24 - Syllabus

13:50 - Lectures

15:58 - Results

17:41 - More Information about Lecture Format ("I use powerpoint...")

18:47 - Example of Lecture Format

19:23 - Each Week-Three Inputs (Lecture Format)

21:36 - What Are We Going to Learn This Quarter?

25:50 - What's in this Lecture?

25:58 - Quantum Mechanics is Discovered (Timeline)

26:20 - Pioneers in Quantum Mechanics (Timeline)

31:26 - James Clerk Maxwell

31:44 - Maxwell Invented Free Color Photography

31:57 - First color photograph Example

32:25 - Ludwig Boltzmann

33:11 - Boltzmann's Grave in Vienna

33:23 - Willard Gibbs:

35:05 - Grove Street Cemetery:

35:35 - Statistical Mechanics: Why do We Need it?

36:40 - Using Thermodynamics

37:15 - Statistical Mechanics Establishes this Connection

37:54 - The Free Energy of Ammonia

38:32 - "Elements of Statistical Thermodynamics" Book (by Leonard K. Nash)

39:32 - Books to Buy:

40:16 - ...Consider a Molecule Having Evenly Spaced Energy Levels

40:42 - We can approximate its state distribution as shown here:

40:54 - The quantum numbers of these evenly spaced (by hv...)

40:58 - ...now imagine that you have a 3-dimensional array molecules...

42:06 - Now let's add three quanta of energy to these three molecules.

43:30 - Microstate

43:38 - Ten microstates in total:

43:42 - The 10 microstates exist in just three configurations.

44:46 - Examples of Notations (Example II)

45:08 - Examples of Configurations (I, II, III)

45:20 - Counting the Microstates Associated with Each Configuration

49:14 - Formula for Determining Total Number of Microstates

Required attribution: Penner, Reginald Thermodynamics and Chemical Dynamics 131C (UCI OpenCourseWare: University of California, Irvine), http://ocw.uci.edu/courses/chem_131c_thermodynamics_and_chemical_dynamics.html. [Access date]. License: Creative Commons Attribution-ShareAlike 3.0 United States License.

Reginald Penner Chemistry Dept. | Physical Sciences Sch. | University of California, Irvine

### Chem 131C. Lec. 02. Thermodynamics and Chemical Dynamics. The Boltzmann distribution law (English) Lecture

UCI Chem 131C Thermodynamics and Chemical Dynamics (Spring 2012)

Lec 02. Thermodynamics and Chemical Dynamics -- The Boltzmann Distribution Law --

View the complete course: http://ocw.uci.edu/courses/chem_131c_thermodynamics_and_chemical_dynamics.html

Instructor: Reginald Penner, Ph.D.

License: Creative Commons BY-NC-SA

Terms of Use: http://ocw.uci.edu/info.

More courses at http://ocw.uci.edu

Description: In Chemistry 131C, students will study how to calculate macroscopic chemical properties of systems. This course will build on the microscopic understanding (Chemical Physics) to reinforce and expand your understanding of the basic thermo-chemistry concepts from General Chemistry (Physical Chemistry.) We then go on to study how chemical reaction rates are measured and calculated from molecular properties. Topics covered include: Energy, entropy, and the thermodynamic potentials; Chemical equilibrium; and Chemical kinetics. This video is part of a 27-lecture undergraduate-level course titled "Thermodynamics and Chemical Dynamics" taught at UC Irvine by Professor Reginald M. Penner.

Thermodynamics and Chemical Dynamics (Chem 131C) is part of OpenChem: http://ocw.uci.edu/openchem/.

Recorded on April 4, 2012.

Index of Topics:

01:48 - About Quiz I

04:17 - The Boltzmann Distribution Law

04:21 - What's in This Lecture?

04:44 - Consider a Harmonic Oscillator-Like State Distribution

05:04 - Now imagine that you have a 3-dimensional array of these "molecules"

06:28 - now let's add three quanta of energy to these three molecules.

06:52 - One option is to put all three quanta into one molecule.

07:40 - We shall refer to ech of these possibilities as a microstate;

07:44 - Notation for Specifying a particular configuration (families of microstates)

08:50 - Configuration Example

09:04 - Configuration Example (I, II, III)

09:59 - Configuration II Example

11:11 - Configuration I Example

14:13 - Configuration III Example

14:41 - Formula - The Number of Microstates, W, for a Particular Configuration

15:09 - Example: Consider a system of eight molecules containing four energy quota...

17:16 - How about 5 quanta in ten "molecules" (example)?

19:07 - How about 5 quanta in ten "molecules" (example II)?

20:27 - Curious: configuration VI is favored by more than 2:1 compared the others...

21:31 - Now what happens as we increase the number of molecules?

22:14 - Flipping a Coin Example

22:55 - Flipping a Coin Outcomes and Possibilities

23:24 - N coin flips, the preference of the system for the most probably configuration increases with N...

27:32 - Question: What does the big "N" stand for on Cornhuskers Stadium?

27:57 - Knowledge of this highly preferred configuration equates to knowledge of the system as a whole!

28:17 - Configuration VI is favored by more than 2:1 compared with any other...

28:21 - ...two ways to find this highly preferred configuration...

28:41 - Knowledge of this highly preferred configuration equates to knowledge of the system as a whole!

29:48 - Consider an isolated (N & Q constant) macroscopic (N large etc.) assembly of N...

31:41 - Graphic Representation

33:28 - Number of Microstates Before and After

35:46 - ...substituting from the expressions for energy defined earlier we have...

37:25 - ...this means that the left and right sides of this equality are constants, call this constant B (beta)

39:31 - The Boltzmann Distribution Law (Formula)

41:45 - Example (Solving for N)

43:07 - Molecular Partition Function, q: Two Versions (Figure)

44:17 - Example: What are the relative populations of the states of a two level system...

47:33 - Example: A certain atom has a threefold degenerate ground level...

52:33 - How much Thermal Energy is in the System? (Figure)

Required attribution: Penner, Reginald Thermodynamics and Chemical Dynamics 131C (UCI OpenCourseWare: University of California, Irvine), http://ocw.uci.edu/courses/chem_131c_thermodynamics_and_chemical_dynamics.html. [Access date]. License: Creative Commons Attribution-ShareAlike 3.0 United States License.

Reginald Penner Chemistry Dept. | Physical Sciences Sch. | University of California, Irvine

### Chem 131C. Lec. 03. Thermodynamics and Chemical Dynamics. Energy & q (the partition function) (English) Lecture

UCI Chem 131C Thermodynamics and Chemical Dynamics (Spring 2012)

Lec 03. Thermodynamics and Chemical Dynamics -- Energy and q (The Partition Function) --

View the complete course: http://ocw.uci.edu/courses/chem_131c_thermodynamics_and_chemical_dynamics.html

Instructor: Reginald Penner, Ph.D.

Terms of Use: http://ocw.uci.edu/info.

More courses at http://ocw.uci.edu

Description: In Chemistry 131C, students will study how to calculate macroscopic chemical properties of systems. This course will build on the microscopic understanding (Chemical Physics) to reinforce and expand your understanding of the basic thermo-chemistry concepts from General Chemistry (Physical Chemistry.) We then go on to study how chemical reaction rates are measured and calculated from molecular properties. Topics covered include: Energy, entropy, and the thermodynamic potentials; Chemical equilibrium; and Chemical kinetics. This video is part of a 27-lecture undergraduate-level course titled "Thermodynamics and Chemical Dynamics" taught at UC Irvine by Professor Reginald M. Penner.

Thermodynamics and Chemical Dynamics (Chem 131C) is part of OpenChem: http://ocw.uci.edu/openchem/

Recorded on April 6, 2012.

Index of Topics:

00:19 - Example-A certain atom has a threefold degenerate ground level...

01:02 - Function for Calculating Degeneracy of Energy Levels

01:24 - Sum of Three Energy Levels

03:35 - We need to calculate the thermal energy kT, in units...

04:22 - Energy Level Diagram

07:20 - Example: The four lowest electronic energy levels of atomic C have energies and degeneracies as follows...

07:51 - Equation: Partition Function

08:32 - In this case, q will have four terms - one for each state

08:49 - How to Calculate the Four Terms

09:59 - Example: 9.27 of 14 total states in C...

10:24 - does this makes sense (calculating thermal energy again)

10:56 - Diagram-Electronic States of Carbon

12:53 - now find the fractional population of each level for C...

14:51 - Diagram: ...now, it will be obvious to you that W must depend on energy...

15:45 - Partition Function (W must depend on energy, but how?)

20:03 - Example: the NO molecule has a doubly degenerate excited electronic level...

21:03 - Diagram--Wave Numbers

22:05 - Example - The NO molecule has a doubly degenerate excited electronic level... (continued)

22:40 - Plot (Diagram)

23:38 - Calculating Term Populations

Required attribution: Penner, Reginald Thermodynamics and Chemical Dynamics 131C (UCI OpenCourseWare: University of California, Irvine), http://ocw.uci.edu/courses/chem_131c_thermodynamics_and_chemical_dynamics.html. [Access date]. License: Creative Commons Attribution-ShareAlike 3.0 United States License.

Reginald Penner Chemistry Dept. | Physical Sciences Sch. | University of California, Irvine

### Chem 131C. Lec. 04. Thermodynamics and Chemical Dynamics. Entropy (English) Lecture

UCI Chem 131C Thermodynamics and Chemical Dynamics (Spring 2012)

Lec 04. Thermodynamics and Chemical Dynamics -- Entropy --

View the complete course: http://ocw.uci.edu/courses/chem_131c_thermodynamics_and_chemical_dynamics.html

Instructor: Reginald Penner, Ph.D.

Terms of Use: http://ocw.uci.edu/info.

More courses at http://ocw.uci.edu

Description: In Chemistry 131C, students will study how to calculate macroscopic chemical properties of systems. This course will build on the microscopic understanding (Chemical Physics) to reinforce and expand your understanding of the basic thermo-chemistry concepts from General Chemistry (Physical Chemistry.) We then go on to study how chemical reaction rates are measured and calculated from molecular properties. Topics covered include: Energy, entropy, and the thermodynamic potentials; Chemical equilibrium; and Chemical kinetics. This video is part of a 27-lecture undergraduate-level course titled "Thermodynamics and Chemical Dynamics" taught at UC Irvine by Professor Reginald M. Penner.

Thermodynamics and Chemical Dynamics (Chem 131C) is part of OpenChem: http://ocw.uci.edu/openchem/

Recorded on April 9, 2012.

Index of Topics:

00:05 - Intro Slide: Entropy

00:15 - Announcements

01:00 - Quiz I histogram

01:03 - What's in this Lecture?

01:17 - Six things we have learned about Statistical Mechanics

04:17 - Boltzman Distribution Law Diagram and Definition

04:21 - Things we Have Learned About Statistical Mechanics so Far

04:32 - The Boltzmann Distribution Law Formula (Diagram)

06:34 - Formula/Equation Diagram (the average internal energy of each of N molecules)

08:11 - Equation Diagram ("so q contains information about the averge internal energy of our system.")

09:13 - Diagram: (The NO molecule)

10:01 - Graph (b) the electronic contribution to the molar internal energy at 300K.

11:20 - Graph (b) - Evaluating formula

13:58 - (Does formula and solution make sense?)

15:37 - Chart (On p. 429 of your book, three types of ensembles are discussed as follows:)

16:24 - Chart: Microcanonical Ensembles

16:34 - About Microcanonical Ensembles

17:14 - Graph: Example: NO - it's obvious we're talking about one molecule here...

17:54 - Diagram: The Boltzmann Distribution Law in terms of the molecular partition function, q

18:14 - so q asks the question:

18:47 - Canonical Ensembles

19:38 - Well, consider just two molecules, call them a and b...

21:28 - this is the appropriate expression when the N units are distinguishable.

22:48 - Equations for two States (for two distinguishable units, we CAN tell the difference...)

24:35 - Chart: What if we had three molecules, a, b,c...

25:53 - Chart: Ensemble name| What's Constant | Its Partition Function

27:01 - Experiment: Place 100 nickels into a shoes box, all heads up

29:00 - Experiment: 1. Place 100 nickels into a shoes box, ALL heads up...

30:34 - Experiment Conclusion: "For any isolated assembly, we can always predict...

31:00 - For any isolated assembly...

31:55 - Formula: S = k In W

Reginald Penner Chemistry Dept. | Physical Sciences Sch. | University of California, Irvine

### Chem 131C. Lec. 05. Thermodynamics and Chemical Dynamics. The Equipartition theorem (English) Lecture

UCI Chem 131C Thermodynamics and Chemical Dynamics (Spring 2012)

Lec 05. Thermodynamics and Chemical Dynamics -- The Equipartition Theorum --

View the complete course: http://ocw.uci.edu/courses/chem_131c_thermodynamics_and_chemical_dynamics.html

Instructor: Reginald Penner, Ph.D.

Terms of Use: http://ocw.uci.edu/info.

More courses at http://ocw.uci.edu

Description: In Chemistry 131C, students will study how to calculate macroscopic chemical properties of systems. This course will build on the microscopic understanding (Chemical Physics) to reinforce and expand your understanding of the basic thermo-chemistry concepts from General Chemistry (Physical Chemistry.) We then go on to study how chemical reaction rates are measured and calculated from molecular properties. Topics covered include: Energy, entropy, and the thermodynamic potentials; Chemical equilibrium; and Chemical kinetics. This video is part of a 27-lecture undergraduate-level course titled "Thermodynamics and Chemical Dynamics" taught at UC Irvine by Professor Reginald M. Penner.

Thermodynamics and Chemical Dynamics (Chem 131C) is part of OpenChem: http://ocw.uci.edu/openchem/

Recorded on April 11, 2012.

Index of Topics:

00:21 - Announcements

02:34 - Diagram: in real molecules, the situation is considerably more complex than the Harmonic Oscillator

03:20 - We have a very high density of translational states that are not, in reality...

03:36 - Diagram: these translational states are nested within rotational states

03:58 - Diagrams (many rotational states)

04:23 - ...we can treat each of these energetic manifolds...

05:45 - What's in this Lecture

05:51 - Your book mainly focuses attention on...

07:27 - Graph 5-13: Here is what happens to Cv as a function of T for a diatomic molecule:

10:04 - Graph 5-13 These are the rotation temperature...

11:08 - Graph 5-13 Here is what happens to Cv as a function of T...

11:37 - The Equipartition Theorum

12:10 - The Equipartition Theorum (with diagram)

13:17 - consider the classical Hamiltonian for a I D harmonic oscillator:

14:16 - now you'll recall that the heat capacity...

15:03 - Example: Formula

15:50 - Graph

16:13 - ...this is also the heat capacity for all monoatomic gases...

18:29 - For a linear molecule...

19:41 - Graph (Translation + Rotation)

20:26 - For a nonlinear molecule...

20:54 - What about for higher temperatures?

22:08 - so following through with the predictions of the equipartition theorem...

23:05 - so for a diatomic molecule...

24:24 - Example: Use the equipartition theorem to estimate...

31:18 - Example: Use the equipartition theorum to estimate... (Part B)

34:36 - Example: (Chart) "Use the equipartition theorum to estimate... (Part C)

38:55 - Calculate Each Term

39:18 - We'll Start with Translation...

39:40 - The translational energy of a classical gas molecule is:

40:15 - ...And a quantum mechanical gas has energies given by the particle-in-a-box model.

40:23 - we'll concentrate attention now on ideal monoatomic gases...

41:27 - consider first a monoatomic gas in one dimension.

43:59 - ...now these energies are very closely spaced. Consider, for example, an argon atom in a box...

45:25 - Log Scale

45:52 - ...if these states are quasi-continuous, we can rewrite this summation...

46:54 - so after integration we have...

47:05 - Example "Calculate..."

48:26 - What would...three dimensional cube?

49:36 - ...in terms of...now we calculate its transitional energy.

50:03 - ...and this yields a very simple expression:

Reginald Penner Chemistry Dept. | Physical Sciences Sch. | University of California, Irvine

### Chem 131C. Lec. 06. Thermodynamics and Chemical Dynamics. The Rotational partition function (English) Lecture

UCI Chem 131C Thermodynamics and Chemical Dynamics (Spring 2012)

Lec 06. Thermodynamics and Chemical Dynamics -- The Rotational Partition Function --

View the complete course: http://ocw.uci.edu/courses/chem_131c_thermodynamics_and_chemical_dynamics.html

Instructor: Reginald Penner, Ph.D.

Terms of Use: http://ocw.uci.edu/info.

More courses at http://ocw.uci.edu

Description: In Chemistry 131C, students will study how to calculate macroscopic chemical properties of systems. This course will build on the microscopic understanding (Chemical Physics) to reinforce and expand your understanding of the basic thermo-chemistry concepts from General Chemistry (Physical Chemistry.) We then go on to study how chemical reaction rates are measured and calculated from molecular properties. Topics covered include: Energy, entropy, and the thermodynamic potentials; Chemical equilibrium; and Chemical kinetics. This video is part of a 27-lecture undergraduate-level course titled "Thermodynamics and Chemical Dynamics" taught at UC Irvine by Professor Reginald M. Penner.

Thermodynamics and Chemical Dynamics (Chem 131C) is part of OpenChem: http://ocw.uci.edu/openchem/

Recorded on April 13, 2012.

Index of Topics:

00:05 - Introduction

00:19 - Announcements

01:10 - What's in this Lecture?

01:25 - Neglecting electronic energy levels...

01:41 - Vibration, Rotation, Translation Diagrams

02:19 - but we're lucky. We can treat each of these energetic manifolds separately...

02:51 - ...consider first a monoatomic gas in one dimension...

03:43 - ...so its molecular partition function, q, is:

04:29 - Diagram: Calculation of Ground State and Excited State

05:02 - Diagram: ...looking at the energy spacing of the first 100 states...

05:40 - ...If these states are quasi-continuous, we can rewrite this summation...

06:08 - Diagram: ...so after integration we have:

06:13 - Example: Calculate...

07:22 - Diagram: ...is related to the molecular properties through the mass...

08:28 - In terms of...

09:24 - Diagram: the enthalpy, H...

09:52 - Chart: so we can calculate everything for ideal, monoatomic gases...

11:10 - ...this begins to fulfill the promise of Statistical Mechanics:

11:41 - ...works for all ideal molecules.

11:51 - we have a manifold of rotational states that looks like this...

12:20 - ...and the energies of these states are given by the expression...

14:13 - ...B here has units of joules:

14:53 - ...I'm easily confused, so I try to stick to Joules:

15:26 - so let's work out the expression for...

16:01 - our usual expression for q applies for each of these three orthogonal axes:

16:27 - ...so if we write out this series, here's what it is:

18:36 - when B is expressed in Joules, these are the equations for the rotational partition function that apply:

19:43 - what's a symmetry number?

21:14 - huh? what axis?

21:59 - Ammonia

22:36 - Number of Symmetries:

26:55 - Example: Exercise 17.4a What is the symmetry of:

31:11 - Example: What is the symmetry number of:

Reginald Penner Chemistry Dept. | Physical Sciences Sch. | University of California, Irvine

### Chem 131C. Lec. 07. Thermodynamics and Chemical Dynamics. Vibrational partitional functions (English) Lecture

UCI Chem 131C Thermodynamics and Chemical Dynamics (Spring 2012)

Lec 07. Thermodynamics and Chemical Dynamics -- Vibrational Partition Functions --

View the complete course: http://ocw.uci.edu/courses/chem_131c_thermodynamics_and_chemical_dynamics.html

Instructor: Reginald Penner, Ph.D.

Terms of Use: http://ocw.uci.edu/info.

More courses at http://ocw.uci.edu

Thermodynamics and Chemical Dynamics (Chem 131C) is part of OpenChem: http://ocw.uci.edu/openchem/

Recorded on April 16, 2013.

Index of Topics:

00:05 - Introduction: Vibrational Partition Functions

00:17 - Quiz 2 Histogram

00:41 - The Symmetry Number

04:14 - We also get this answer using my approach.

07:09 - Aluminum Chloride Atoms Example

09:45 - We also get this answer using my approach (Diagram example)

13:03 - What is the symmetry number of: benzene?

15:43 - Estimate the rotational partition function for HCl...

16:09 - Linear molecules lacking a center of symmetry:

16:41 - Estimate the rotational...(formula)

19:12 - Calculate the rotational partition function for methane.

22:02 - Vibrational States

23:23 - ...including the zero point energy, we have...

24:52 - this geometric series has the form:

25:40 - how big is...

28:04 - Example: The triatomic molecule, chlorine dioxide (OCIO) has three vibrational modes...

31:42 - Graph: What Does the T-dependence...look like?

32:45 - Of course, molecular dissociation would occur before...

32:58 - thinking about the partition functions at room temperature, we conclude...

33:24 - What about vibrational energy?

35:13 - E=RT, Equipartition Theorum

36:13 - Here's a midterm exam question from a couple of years ago:

37:55 - Midterm exam solution

39:10 - Equations Page of Exam

41:03 - Calculations and Solution

41:40 - If you are asked: calculate the fractions of molecules for which...

42:25 - Calculations: ("now one mole of...)

44:47 - Example

45:07 - B. Now one mole of...

45:18 - Example (as in 44:47)

Reginald Penner Chemistry Dept. | Physical Sciences Sch. | University of California, Irvine

### Chem 131C. Lec. 08. Thermodynamics and Chemical Dynamics. The First Law (English) Lecture

UCI Chem 131C Thermodynamics and Chemical Dynamics (Spring 2012)

Lec 08. Thermodynamics and Chemical Dynamics -- The First Law --

View the complete course: http://ocw.uci.edu/courses/chem_131c_thermodynamics_and_chemical_dynamics.html

Instructor: Reginald Penner, Ph.D.

Terms of Use: http://ocw.uci.edu/info.

More courses at http://ocw.uci.edu

Thermodynamics and Chemical Dynamics (Chem 131C) is part of OpenChem: http://ocw.uci.edu/openchem/

Recorded on April 18, 2012.

Index of Topics:

00:01 - Announcements

00:58 - Example: the triatomic molecule, chlorine dioxide...

04:27 - Plot of equation (Diagram)

09:40 - Thermodynamics

11:39 - Energy

14:24 - In Thermodynamics, we divide the universe into the system...

15:30 - Diagram: Now there are three flavors of systems:

17:32 - Glossary of Thermodynamic Jargon (Types of Equilibrium)

18:15 - We'll be talking about closed systems until further notice.

20:23 - now, we know what heat is, but what is work?

21:28 - let's think about mechanical work...

23:54 - the external force is:

25:57 - now what happens to the volume?

28:27 - Example: Calculate the work required to compress...

30:15 - Our equation for work...

31:45 - Answer: Graphically, this experiment is as shown below...

34:23 - So instead of compressing the piston using the entire mass necessary...

35:01 - Diagram: Step 1

35:18 - Step 2

36:22 - Conclusion:

36:24 - Diagram: so, more steps means less work.

36:52 - In the thermodynamics, a reversible process is any process the direction of which can be reversed by...

38:54 - Diagram: so instead of dividing the mass into two parts...

40:07 - ...add one granule at a time to the piston

40:50 - So as an example...

43:38 - Chart: Summary:

44:37 - Let me just point out that both of these equations conform...

45:47 - other flavors of work...

46:27 - that's w, what about q?

Reginald Penner Chemistry Dept. | Physical Sciences Sch. | University of California, Irvine

### Chem 131C. Lec. 09. Thermodynamics and Chemical Dynamics. The 1st law (review) & adiabatic processes part II (English) Lecture

UCI Chem 131C Thermodynamics and Chemical Dynamics (Spring 2012)

Lec 09. Thermodynamics and Chemical Dynamics -- The First Law (review) & Adiabatic Processes Part II --

View the complete course: http://ocw.uci.edu/courses/chem_131c_thermodynamics_and_chemical_dynamics.html

Instructor: Reginald Penner, Ph.D.

Terms of Use: http://ocw.uci.edu/info.

More courses at http://ocw.uci.edu

Thermodynamics and Chemical Dynamics (Chem 131C) is part of OpenChem: http://ocw.uci.edu/openchem/

Recorded on April 20, 2012.

Index of Topics:

00:07 - In Today's Lecture

00:20 - heat, q, and work, w

00:51 - The Sign Convention

01:16 - Formula and Diagram ("surroundings")

03:19 - Diagram: (heat, q...)

04:11 - Other Flavors of Work:

04:30 - That's w, what about q?

05:27 - Since chemical reactions are typically carried out at a constant...

06:01 - Formula: it's convenient to give the quantities in parentheses a name...

06:33 - "Two forms of.." Calcite and Aragonite photo

06:55 - Problem: The change in U when 1.0 mole of calcite is...

09:43 - The heat capacity is the slope of the U (or H)

11:14 - Problem: a common method for measuring heat capacities...

13:31 - "Heat capacity over constant pressure..." (formulas and solutions)

14:16 - Problem: Find ΔH for the heating of 2.0000 moles...

16:47 - Adiabatic Processes

20:58 - Graph ("Isotherm...")

23:18 - Problem: 2.0 moles of neon that expands adiabatically...

Gianmarc Johns Chemistry Dept. | Physical Sciences Sch. | University of California, Irvine

### Chem 131C. Lec. 10. Thermodynamics and Chemical Dynamics. Jim Joule (English) Lecture

UCI Chem 131C Thermodynamics and Chemical Dynamics (Spring 2012)

Lec 10. Thermodynamics and Chemical Dynamics -- Jim Joule --

View the complete course: http://ocw.uci.edu/courses/chem_131c_thermodynamics_and_chemical_dynamics.html

Instructor: Reginald Penner, Ph.D.

Terms of Use: http://ocw.uci.edu/info.

More courses at http://ocw.uci.edu

Thermodynamics and Chemical Dynamics (Chem 131C) is part of OpenChem: http://ocw.uci.edu/openchem/

Recorded on April 25, 2012.

Index of Topics:

04:13 - In an adiabatic process, q=0 for the process...

07:51 - note: The change in P with an expansion is larger...

08:04 - Isotherm Graph

10:21 - ...now it's not obvious from these equations...

13:27 - About Jim Joule

14:20 - Joule's dad was a brewer

18:24 - Now, you should know that Joule was quite an experimentalist.

20:09 - Diagram: He actually did this experiment quantitatively

21:04 - The quantity of work that must be expended at sea-level...

22:35 - 77255 and California DMV

22:58 - Diagram: ...so in 1853, he did the following experiment

23:44 - So why did Joule expect a temperature change?

23:49 - ...this is the Leonard-Jones 6-12 potential.

27:29 - For an ideal gas, the intermolecular potential...

27:38 - Diagram: At high pressures, you're here.

28:17 - Diagram: At "normal" pressures, you're here.

28:43 - Well, recall that for a real gas, the compressibility factor...

29:09 - The compressibility factor, Z, for a real gas...

30:29 - The compressibility factor, Z, for a real gas reflects these two manifolds...

31:00 - (Diagram) Now, let's do a thought experiment...

32:33 - question: where does the energy come from?

34:03 - 1853: Jim Joule tried to measure...

35:05 - 1854: Joule teams up with a new friend, William Thompson (AKA Lord Kelvin)

36:40 - The Joule-Thompson Effect...

39:43 - so, the Joule-Thompson process occurs at constant enthalpy.

41:12 - but Joule and Thompson were delighted to find that for real gases...

41:52 - Problem: The Joule-Thompson coefficient of air at 300K and 25 atm...

45:13 - "Plot from your Chapter 14...temperature as a function of pressure."

45:54 - note that real gases have two inversion temperatures at each pressure value:

47:13 - The Linde Refrigerator: A mechanical heat pump...

Reginald Penner Chemistry Dept. | Physical Sciences Sch. | University of California, Irvine

### Chem 131C. Lec. 11. Thermodynamics and Chemical Dynamics. Midterm 1 review (English) Lecture

UCI Chem 131C Thermodynamics and Chemical Dynamics (Spring 2012)

Lec 11. Thermodynamics and Chemical Dynamics -- Midterm 1 Review --

View the complete course: http://ocw.uci.edu/courses/chem_131c_thermodynamics_and_chemical_dynamics.html

Instructor: Reginald Penner, Ph.D.

Terms of Use: http://ocw.uci.edu/info.

More courses at http://ocw.uci.edu

Thermodynamics and Chemical Dynamics (Chem 131C) is part of OpenChem: http://ocw.uci.edu/openchem/

Recorded on April 25, 2012.

Index of Topics:

00:05 - Announcements

00:28 - Midterm Exam

00:52 - Partition Functions: Enjoy in any of Four Flavors...

01:51 - Example: The NO molecule has a doubly degenerate...

03:24 - Plot It:

05:01 - ...(b) the electronic contribution to the molar internal energy...

05:08 - Equations

05:22 - More Equations

05:38 - (Diagram) The electronic contribution to the molar internal energy...

06:32 - Here's a midterm exam question from a couple of years ago.

08:42 - Which equation(s) do I need?

10:31 - If you are asked: calculate the fraction of molecules...

10:48 - so what were we asked again? B. Now one mole of...

12:06 - The equipartition theorem:

13:33 - now you'll recall that the heat capacity...

14:15 - Formula: the equipartition theorem tells us...

14:17 - the equipartition theorem tells us that translation contributes...

14:41 - Graph: the contribution of molecular translation...

14:55 - Formula: ...this is also the heat capacity for all monoatomic gases

16:01 - For a linear molecule:

16:44 - Graph: translation + rotation

16:53 - For nonlinear molecule:

17:45 - ...well, let's go back to the classical Hamiltonian again.

18:12 - so following through with the predictions of the equipartition...

18:58 - Formula: in the specific case of a diatomic, we get:

19:02 - Formula Graph:

19:10 - Example: Use the equipartition theorem to estimate...

20:05 - Too subjective, let's use this rule of thumb:

Reginald Penner Chemistry Dept. | Physical Sciences Sch. | University of California, Irvine