1. Chap 7: The 2nd and 3rd Laws Entropy and Gibbs Free Energy Why do things fall apart? Why doe some things happen spontaneously? Why does anything worthwhile take work? –I’m not sure that our discussions will completely answer this, but we’ll give it a go.

2. 7.1 Spontaneous Change Last chapter, we learned about work, heat and enthalpy (at least I hope we did, it will be on the final…) We learned that all energy in the universe is conserved and constant –But that’s not really very useful –We want to predict the behaviour of the universe around us.

3. Spontaneous Changes We know from our own experiences that some things will happen spontaneously Metal coolsGas expands We can make the reverse happen (heat a metal cube up, partition a gas), but that takes work (energy)

4. Spontaneity in Processes A process is spontaneous if it has the tendency to occur without being driven by an external influence –Don’t confuse ‘spontaneous’ with ‘speedy’ or ‘rapid’!

5. 7.2: Entropy and Disorder If we think about the universe around us and look at all of the spontaneous changes we have observed over our lifetimes, one thing is certain: Energy and Matter tend to disperse in a disorderly fashion Gas molecules don’t pile up on one side of a flask Buildings fall apart Thing left untended will get worse

6. The 2nd Law of Thermodynamics The entropy of an isolated system increases in the course of any spontaneous change We can summarize this law mathematically as:

7. The 2nd Law What does this mean? –If a lot of heat energy is transferred, there is a large increase in entropy –This change in entropy is more noticeable at lower temperatures than higher temperatures (relatively) Temperature must be in Kelvin and heat must be in Joules 

8. Entropy Entropy is a measure of disorder, according to the second law of thermodynamics The entropy of an isolated system increases in any spontaneous reaction Entropy is a state function

9. Changes in Entropy The equation we obtained from the second law is valid for isothermal situations (change of state, gas expansion) but we frequently want to be able to determine the entropy as temperature changes… 

10. Entropy Change as a Function of Temperature at Constant Volume If T 2 > T 1, then the logarithm is ‘+’ and entropy increases –Makes sense since we are raising the temperature and thermal motion will increase The greater (higher) the heat capacity, the higher the entropy change

11. Entropy Change as a Function of Changing Volume We can use a similar logic to derive the change in entropy when the volume changes: When V 2 > V 1, the entropy increases Note: Units are still J/K 

12. Entropy Change as a Function of Pressure Remember Boyle’s Law? We can substitute this relationship into the equation for entropy change as a function of volume to get: Entropy decreases for a sample that has been compressed isothermally (P 1 >P 2 ) 

13. Entropy Changes Occurring as a Function of Physical State Changes What happens to the entropy of a system as we change state? Remember: Melting point temp = T f Boiling Point temp = T b Temperature doesn’t change as we heat a sample to cause a phase change Let’s look at liquid water --> water vapor

14. Boiling Water and Entropy Let’s get 3 facts straight: 1.At a transition temperature (T f or T b ), the temperature remains constant until the phase change is complete 2.At the transition temperature, the transfer of heat is reversible 3.Because we are at constant pressure, the heat supplied is equal to the enthalpy

15. Water Boiling and Entropy We use the ‘ º ’ superscript to denote the standard entropy (the entropy at 1 bar of pressure) (at the boiling temperature)

16. Ice Melting and Entropy We use the same logic to determine the entropy of fusion,  S fus

17. Trouton’s Rule Because the entropy increases so much in going from liquid to a gas, many liquids have similar  S° vap values

18. Trouton’s Rule Why is this? –Positional disorder of a gas versus a solid or liquid (which are pretty close to the same thing) Exceptions: Molecules with very weak or very strong intermolecular forces –Helium, Water and Methanol

19. 7.5: A Molecular Interpretation of Entropy We’ve looked at the changes to the entropy of a system, but now let’s look at the absolute entropy of the system itself If we had a perfect crystal, the positional disorder would be ____ If the temperature was 0K, the would be ___ thermal disorder, so the entropy would be ___

20. The 3rd Law The entropies of all perfect crystals approach zero as the absolute temperature approaches zero.

21. The Boltzmann Formula W is a reflection of the ensemble, the collection of molecules in the system This entropy value is called the statistical entropy S = k lnW Where: k = Boltzmann’s constant = 1.381 x10 -23 J/K W=# of ways atoms or molecules in the system can be arranged and still give the same total energy

22. The Boltzmann Formula Let’s think about W (Wahrscheinlichkeit) for a moment –Word translates as “probability” or “likelihood” If we could only arrange the atoms/molecules in the system one way, there would be ___ entropy since ln(1) = __ As we start to increase the population of the system, we can arrange the members of the system in different ways and still have the same total energy, so W increases.

23. The Boltzmann Formula Each molecule can be oriented 2 ways W = 2 x 2 x 2 x 2 = 16 Example 7.7

24. Residual Entropy We know Boltzmann’s concept of the ensemble is correct from observations of molecules at low temperature (and using logic with some cynicism) As we get near absolute zero, the entropy within the crystal becomes increasingly a function of the positional entropy within the ensemble cause by the packing of the components Let’s think about this for a minute…

25. Residual Entropy The entropy of 1 mole of FClO 3 at T = 0 K is 10.1 J/K. Suggest and interpretation. How many molecules do we have? How many ways can each molecule be arranged? What is the residual entropy? Pretty close!