Dr. Aniruddha Chakraborty

School of Basic Sciences

Indian Institute of Technology Mandi

Mandi, Himachal Pradesh 175001

India

ph: +(91)1905-237930

achakrab

Molecular Thermodynamics

In this course simple concept of probability will be used to predict the outcome of events e.g. why it is that chemical reactions approach equilibrium and why the natural unpredictability of random events makes equilibrium a dynamic state. But for understanding what is really going on, one has to start with the idea of energy. Although the concept of energy itself would not be enough to explain why some chemical reactions occur and some do not. For that we need to add the concept of entropy, which is a measure of all possible ways energy can be distributed. Entropy is actually the key to understanding, what is going on in real chemical processes. Unlike energy, Entropy is not conserved, and that fact alone drives natural processes in the direction “forward in time.”

**Module 1:Probability, Distributions, and Equilibrium**

Distributions, Relative Probability and Fluctuations, Equilibrium, Most Probable Distribution, Le Chˆatelier’s Principle, Equilibrium Amounts and Equilibrium Constants.

**Module 2:Energy Levels in Real Chemical Systems**

Real Chemical Reactions, The Quantized Nature of Energy, Distributions of Energy Quanta in Small Systems, Probability of a Particular Distribution of Energy, Most Probable Distribution, Energy Level Separation, Fraction of reactive Particles.

**Module 3:First Law of thermodynamics, - bonding and internal energy**

Internal Energy, Chemical Bond, Mean Bond Dissociation Energies and Internal Energy, Using Bond Dissociation Energies to Understand Chemical Reactions, The “High-Energy Phosphate Bond” and Other Anomalies, Beyond Covalent bond, Modern View of Bonding.

**Module 4: Entropy and the second law **

Energy Does Not Rule, Entropy Comparisons Are Informative, Standard Change in Entropy for a Chemical Reaction.

**Module 5: Enthalpy and the surroundings**

Enthalpy vs. Internal Energy, High Temperature Breaks Bonds.

**Module 6: Gibbs Energy and Equilibrium Constant**

The Second Law - Again, Concept of equilibrium, The “Low Enthalpy/High Entropy Rule”, Quantitative Look at Melting Points, Vapor Pressure, Barometric Pressure, and Boiling, Isomerization Reactions, Experimental Data Can Reveal Energy Level Information, Application to Real Chemical Reactions.

**Module 7: Applications of Gibbs Energy - Phase Changes**

Evaporation, Boiling, Sublimation, Vapor Deposition, Solubility, Impure Liquids.

**Module 8: Applications of Gibbs Energy - Electrochemistry**

Electrical Work Is Limited by the Gibbs Energy, Gibbs Energy and Cell Potential, Actual Cell Voltages and the Nernst Equation.

**Text Book: **

Introduction to Molecular Thermodynamics, R. M. Hanson and S. Green, University Science Books, 2008. Interactive guide: http://www.stolaf.edu/depts/chemistry/imt/concept/index.htm.

**Reference Books:**

Molecular Thermodynamics, D. A. Mcquarrie and J. D. Simon, University Science Books, 1999.

Molecular Thermodynamics, Richard E. Dickerson, W. A. Benjamin, 1969.

Molecular Thermodynamics: A Statistical Approach, James W. Whalen, 1991.

Molecular Thermodynamics: An Introduction to Statistical Mechanics for Chemists, J. H. Knox, 1978.

Molecular thermodynamics, James A. Fay, 1962.

**Distribution of Marks:**

Assignments* : 30%, Quiz 1: 10%, Quiz 2: 10%, Final Exam: 50%.

*One literature report, two regular assignments, one reading assignment & one interactive assignment.

**Lectures:**

Lecture 1: Course contents: Key Features & Highlights

Lecture 2: Probability is based on counting: AND Probability Multiplies, OR Probability Adds, AND and OR Probability Can Be Combined.

Lecture 3: Probability in general Can Be Interpreted Two Ways.

Lecture 4: Fundamentals of distributions.

Lecture 5: For Large Populations, We Approximate.

Lecture 6: Relative Probability and Fluctuations.

Lecture 7: Equilibrium and the Most Probable Distribution, Equilibrium Constants.

Lecture 8: Le Chˆ atelier’s Principle Is Based on Probability.

Lecture 9: Energy Distributions in relatively smaller systems.

Lecture 10: Energy Distributions in relatively larger systems.

Lecture 11: Some distributions of energy are more probable than others.

Lecture 12: The most probable distribution is the most disordered.

Lecture 13: The most probable distribution is the one we expect to observe.

Lecture 14: Energy distribution changes with temperature.

Lecture 15: Internal Energy and the First Law of Thermodynamics.

Lecture 16: Macroscopic Heat & Heat Capacity.

Lecture 17: Macroscopic Work.

Lecture 18: In Chemical Reactions - work can be ignored.

Lecture 19: Direct Measurement of Internal energy change - Calorimetry.

Lecture 20: Effect of surroundings !

Lecture 21: Converting heat to work : Biology application.

Lecture 22: Chemical Bond & internal energy.

Lecture 23: Bond Dissociation Energy and Internal Energy.

Lecture 24: Modern View of Chemical Bonding.

Lecture 25: Effect of Temperature on Equilibrium.

Lecture 26: Experimental Data can reveal energy level information.

Lecture 27: Entropy & The Second Law of Thermodynamics.

Lecture 28: Entropy comparisons are informative.

Lecture 29: Effect of pressure & concentration on Entropy.

Lecture 30: Evaporation of Liquid water.

Lecture 31: Microscopic picture of pressure effect on entropy.

Lecture 32: Enthalpy and the surroundings.

Lecture 33: High Temperature breaks bonds.

Lecture 34: Gibbs Energy - The Second Law of Thermodynamics again.

Lecture 35: Definition of equilibrium.

Lecture 36: The equilibrium constant - effect of temperature.

Lecture 37: A qualitative picture of the approach to equilibrium.

Lecture 38: Evaporation, Boiling, sublimation & vapor deposition.

Lecture 39: Triple points

Lecture 40: Critical points & phase diagram.

Lecture 41: Electrical work is limited by the Gibbs energy.

Lecture 42: Gibbs energy and cell potential.

**Assignment 1: Regular Assignment**

A system initially containing 400 molecules of H2 and 100 molecule of D2 is allowed to equilibrate, forming HD. The most probable distribution in this case is 320 H2 + 20 D2 + 160 HD. The question is how probable is this most probable distribution?

*Suggested Method:* List all the 101 distributions and determine the number of ways of getting each one. Adding all these ways together, we have the total number of ways possible. Then divide the number of ways of getting the most probable distribution by the total number of ways possible.

**Assignment 2: Literature Report **

List all Nobel laureates in Thermodynamics, along with their Nobel winning research work. Please mention which research work was in the regime of 'equilibrium thermodynamics' and which one was in the regime of 'non-equilibrium thermodynamics'.

**Assignment 3: Interactive Assignment**

"The most probable distribution of energy is the Boltzmann Distribution" - Justify.

**Assignment 4: Regular Assignment **

Write a short note on "Negative Temperature".

Key Points: zero temperature & negative temperatures - theoretical vs. experimental possibility, is negative temperature more "hotter" than positive temperature ?.

**Assignment 5: Reading Assignment**

Measuring the heat associated with a chemical reaction experimentally requires carrying out the reaction in a device called Calorimeter. Study how the change in temperature of the calorimeter along with its heat capacity can be used to determine change in internal energy for a chemical reaction.

**Quiz 1: Questions**

1. (a) Write out all the ways (microstates) to distribute 2 quanta of energy to 4 paricles, grouping these microstates into distinct distributions.

(b) How much more probable is to find two particles each with one quantum of energy than finding a single particle with both quanta?

2. A jar contains one blue ball, one green ball, one red ball, and three orange balls. What is the probability that a ball drawn at random

(a) will be green? (b) will be orange? (c) will not be blue?

3. A system initially containing 2.0 mol. of H2O, 1.0 mol. of D2O, and 2.0 mol. of HDO is allowed to exchange Hydrogen for Deuterium. Determine the amounts of H2O, D2O and HDO expected at equilibrium?

4. Simple probability governs the equilibirium positions of chemical systems and the number of heads and tails you can toss with a coin. Why does normal chemical system never seem to fluctuate from its equilibrium position but if you flip a coin 100 times you expect that you might not get exactly 50 heads and 50 tails?

5. “Determining equilibirium amounts based solely on probability has the advantage that we do not have to worry about there being more then one equilibrium at work ”- Justify.

6. “Equilibrium constants describe the most probable distribution ” - Justify.

7. “Le Chatelier’s principle is based on probability” - Justify.

8. How probable is the most probable distribution? Explain with examples.

**Quiz 2: Questions**

1. State the two major conditions required for the Boltzmann distribution to be the most probable distribution.

2. For a certain reaction to occure the system has to have an energy of at least 3.0 x 10^(-20) J above the ground state. What fraction of the particles will have enough energy to react - (a) at 100K ? (b) at 500K ?

3. He has more widely spaced translational energy levels then H - Argue for or against.

4. Which type of energy (electronic, vibrational, rotational, and/or translational). (a) are unique to molecules? (b) are not found in solids?

(c) have the largest energy separations between levels? (d) have the smallest energy separations between levels?

5. Using diagram, indicate with a vertical arrow an absorption that might involve this molecule in its overall ground state becoming

(a) vibrationally but not rotationally excited, (b) electronically but not vibrationally excited, (c) both electronically and vibrationally excited, but not rotationally excited, (d) rotationally excited but not vibrationally excited.

6. Explain why state functions, such as U and T, are frequently referred to as path-independent functions while Q and W are referred to as path-dependent functions.

7. Give one Specific real-world examples of each of the following: (a) a situation where putting heat into a system raises its temperature,

(b) a situation where putting heat into a system does not raise its temperature & (c) a situation where a system's temperature is changed even though no heat is added or removed.

8. Why chemical reactions continue until they ``reach equilibrium"? What factors determine, which side of a reaction is favoured at low temperature? What factors determine whether the equilibirium constant will increase or decrease with increase in temperature? What factors determine the limit of the equilibrium constant at very high temperature?

**Final Exam. Questions**

1. Show that the Clausius’s definition of entropy change in terms of heat and temperature can be derived from probability.

2. “The entropy of liquid water is increased when substance ‘A’ is added to it” – explain with appropriate equation.

3. Explain the thermodynamic definition of ‘activity’ and ‘activity coefficient’.

4. Explain in terms of particles, energy levels and temperature, why curves on G-T plots generally got steeper as T increases. Discuss the limitations of G-T plot.

5. How can one calculate the entropy change of ‘surroundings’?

6. Why solids and liquids do not appear in the reaction quotient?

7. Discuss the concept of reaction coordinate with example.

8. “It is certainly possible to not have a Boltzmann distribution” – Justify.

9. Explain the phenomena of ‘freezing point depression’ and ‘boiling point elevation’ using the concept of molecular thermodynamics.

10. How can one estimate the value of D _{r }H^{0} and D _{r }S^{0 }experimentally?

11. We have DS_{sur} = q_{sur}/T. But heat is not a state function. Then how can the change in entropy of surroundings be independent of the ‘path’?

12. “The amount of electrical work is limited by the Gibb’s energy” – Justify.

13. What is supercritical fluid?

14. “When dG is positive for a chemical reaction, the minimum amount of electrical work that must be added to get the reaction to go is dG” – explain.

15. Discuss the concept of stationary state in quantum mechanics with appropriate equations.

16. Can experimental data reveal energy level information? Explain.

17. Why is ‘w’ necessarily zero for a reaction that proceeds in a bomb calorimeter?

18. “In chemical reactions work can be ignored” – Justify.

19. How to make a distinction between “heating a system” and “adding heat”?

20. How can one use bond dissociation energies to understand chemical reactions?

21. “We almost never measure the temperature of the system itself, especially if that ‘system’ is a chemical reaction.” – Explain.

22. Why diamond has the lowest standard molar entropy?

23. Many chemical reactions seem to stop before they are complete. They just seem to never use all of their limiting reactant, why is that? How can we predict what is going to happen? How can we make chemistry work in our favor?

24. What make chemicals react? Do substances react to give more stable product? Is it the release of heat that drives chemical processes? Or is it something else?

25. “All Chemical reactions proceed because they are going from a less probable state to a more probable state” – can we apply this argument to all natural processes and say that all natural processes are simply a result of chance? Explain.

**Few Interesting Questions**

****

1. What makes chemicals react ?

2. Do substance react to get the most stable product ?

3. Is it the release of heat that drives the chemical processes ?

4. Do you know that if you add salt to ice water, it gets really cold ? Why is that ?

5. Most Chemical reactions seem to stop before they are complete. They just seem to never use all of their limiting reactant. Why is that ?

6. How can one predict what is going to happen, and how can we make chemistry work in our favour ?

7. Any living thing is a complex mixture of chemicals. Is there a special life force that that governs the chemistry in any living thing, or is it, like all nonliving things, govern by the force of nature ?

8. Why does a drop of food coloring in a glass of water spread until the entire solution is colored ?

9. Why does ice melt in a glass of lemonade ?

10.Imagine watching a movie where a glass of green liquid suddenly separates into half blue on the left and half yellow on the right. Would you believe it ? Justify your answer.

11. What if a puddle of water suddenly came together and formed an ice sculpture ?

12. How can it be that all natural processes are simply a result of chance? What about free will ?

** Few Interesting Problems**

1. Simple probability governs the equilibrium positions of chemical systems and the number of heads and tails you can toss with a coin. Why does 'normal' chemical system never seem to fluctuate from it's equilibrium position, but if you flip a coin 100 times you expect that you might not get exactly 50 heads and 50 tails ?

2. Write out all the ways (microstates) 2 quanta of energy to 5 particles, grouping these microstates into distinct distributions. How much more probable is it to find two particles each with one quantum of energy than finding a single particle with both quanta ?

3. Give two specific real-world examples of each of the following : (a) a situation where putting heat into a system raises its temperature, (b) a situation where putting heat into a system does not raise it's temperature, and (c) a situation where a system's temperature is changes even though no heat is added or removed.

4. Explain why state functions, such as U and T, are frequently refereed to as path-independent functions while q and w are refererred to as path-depended functions. Give a real world example of a changethat can occur by two different paths, leading to different values of q in each case.

5. Use Hess's law and the fact that going from Delhi to Mandi involves an increase in altitude of 999 ft to determine the change in altitude in going from Goa to Mandi.

6. What factors determine which side of a reaction is favoured at low temperature ? What factors determine whether K will increase or decrease with increasing temperature ? What factors determine the limit of K at very high temperature ?

7. Intensive properties, such as temperature, are those that are independent of the amount of the substance present. Extensive properties, such as entropy, are those that do depend on the amount of substance present. List three intensive and three extensive properties, that are not discussed in the class.

8. Explain why it is that the reaction quotient Q is a unitless quantity.

9. Consider a thunderstorn that produced an inch of rain over a 200 square mile area in a period of one hour - how much energy was released during this storm ?

10. Is the difference in melting points between water and sodium chloride is due primarily to differences in enthalpy or entropy ?

11. The concentration of K+ in blood plasma is about 0.005 M, but the concentration of K+ in muscle cell fluid is much higher at about 0.15 M. The plasma and intercelluler fluid are separated by the cell membrane. Argue that the free energy change for the reaction K+ (plasma) -> K+ (muscle) must be positive. How might a cell make this reaction happen ? How might the body use the difference in concentration outside and inside the cell to drive other reactions ?

12. Explain how frost forms on a still night, when the air is stable, humidity is fairly low (but not too low) and the temperature slowly drops.

**Related Links**

1. Biograpphy of Ludwig Boltzmann. www-history.mcs.st-and.ac.uk/Biographies/Boltzmann.html.

2. The Chemical Bond Potential Energy Function. www.dartmouth.edu/~pchem/72/thps/morse.html

For IIT Mandi Students (B.Tech./M.Tech./M.S./M.Sc./Ph.D.) - You are always welcome to inquire about working on a project (irrespective of your discipline). For more details - visit my office!

Dr. Aniruddha Chakraborty

School of Basic Sciences

Indian Institute of Technology Mandi

Mandi, Himachal Pradesh 175001

India

ph: +(91)1905-237930

achakrab