1. Entropy and Free Energy
Chapter 18

2. Learning Objectives Students understand
The concept of entropy and its relationship to reaction spontaneity.
The relationship between enthalpy, entropy, and free energy changes for a reaction.

3. Learning Objectives Students will be able to
Calculate the change in entropy to determine spontaneity
Use the change in Gibbs free energy to predict spontaneity
Calculate standard free energy change from data
Calculate an equilibrium constant for a process from free energy

4. Spontaneous Change and Equilibrium
reactions proceed until equilibrium is reached
some favor reactants, some favor products
spontaneous changes occur without outside intervention in the direction that leads to equilibrium
doesn’t mean quickly!

5. 18.1 Heat and Spontaneity
many exothermic reactions are product-favored, but heat release alone does not determine spontaneity
gas fills available space (energy neutral)
ice melts (endothermic) above 0oC
energy transfer as heat

6. 18.2 Dispersal of Energy: Entropy
Entropy, S, measures disorder or chaos and quantifies the dispersal of energy
positional entropy describes positions in a given state (more positional entropy increases from solid liquid gas)
energy goes from being more concentration to being more dispersed

7. Second Law of Thermodynamics
In any spontaneous process there is always an increase in the entropy of the universe.

8. Entropy Thermal energy is caused by the random motion of particles.
Potential energy is dispersed when it is converted to thermal energy (when energy is transferred as heat).

9. Calculating Entropy ΔS = qrev/T
where qrev is heat transfer under reversible conditions and T is the Kelvin temp at which change occurs
Reversible process: after carrying out a change along a given path, it must be possible to return to the starting point by the same path without altering surroundings.

10. 18.3 Dispersal of Energy
Boltzmann proposed that the entropy of a system (dispersal of energy at a given temperature) results from the number of microstates (ways to distribute energy) available.
As the number of microstates increases, so does the entropy of the system.

11. Dispersal of Matter
Gas expansion (dispersion of matter) leads to the dispersal of energy. If O2 and N2 are connected by a valve, they diffuse together leading to an even distribution. The mixture will never separate into separate samples on its own!

12. Homework
After reading sections , you should be able to do the following problems…
P. 711 (1-8)

13. 18.4 Entropy Measurements and Values
For any substance under certain conditions, a numerical value for entropy can be determined
The Third Law of Thermodynamics states that there is no disorder in a perfect crystal at 0 K; S = 0.

14. Entropy
Entropy of a substance will increase in going from a solid to a liquid to a gas.
Larger and more complex molecules have higher entropies than smaller and more simple molecules.
Entropy increases as temperature is raised.
Entropy of a gas increases with an increase in volume.

15. Third Law of Thermodynamics
ΔSsurr = -ΔHsys/T
Sign is positive when exothermic; heat flows to surroundings
Sign is negative when endothermic

16. Standard Entropy Values, So
Change can also be calculated from tables
ΔSorxn = ΣSoproducts - ΣSoreactants

17. Practice Problem
Calculate the standard entropy changes for the following processes using entropy values in Appendix L. Do the calculated values of ΔSo match predictions?
Dissolving 1.0 mol of NH4Cl(s) in water: NH4Cl(s)  NH4Cl(aq)
The formation of 2.0 mol of NH3(g) from N2(g) and H2(g): N2(g) + 3H2(g)  2NH3(g)

18. 18.5 Entropy Changes
Change in entropy is equal to the change in the entropy of the system AND the change in entropy of surroundings.
ΔSouniv = ΔSosys + ΔSosurr
Spontaneous when ΔSuniv > 0, positive
Not spontaneous when ΔSuniv < 0, negative

19. Calculating ΔSo ΔSosys = ΣSoproducts – ΣSoreactants
ΔSsurr = - ΔHosys/T
ΔSouniv = ΔSosys + ΔSosurr

20. Practice Problem
Predict whether these reactions are spontaneous – see table 18.1 p. 694
CH4(g) + 2O2(g)  H2O(l) + CO2(g) ΔHrxn = kJ ΔSsys = J/K
2Fe2O3(s) + 3C(graphite)  4Fe(s) + 3CO2(g)
ΔHrxn = kJ ΔSsys = J/K
C(graphite) + O2(g)  CO2(g)
ΔHrxn = kJ ΔSsys = +3.1J/K
N2(g) + 3F2(g)  2NF3(g)
ΔHrxn = kJ ΔSsys = J/K

21. Practice Problem
Is the reaction of hydrogen and chlorine to give hydrogen chloride gas predicted to be spontaneous?
H2(g) + Cl2(g)  2HCl(g)
Calculate the values for ΔSsys and ΔSsurr

22. Practice Problem 2Fe2O3(s) + 3C(graphite)  4Fe(s) + 3CO2(g)
ΔHrxn = kJ and ΔSrxn = J/K
Show that it is necessary that this reaction be carried out at high temperatures.

23. Homework
After reading sections 18.4 and 18.5, you should be able to do the following…
P. 711 (9-14)

24. 18.6 Free Energy
Free energy, G, describes whether or not a reaction is spontaneous. Gibbs free energy is dependent on change in enthalpy, change in entropy, and temperature of the system.
ΔG = ΔH – TΔS
where T is Kelvin

25. ΔGo and Spontaneity
If the value of ΔGrxn is negative, a reaction is spontaneous.
If ΔGrxn = 0, the reaction is at equilibrium.
If the value of ΔGrxn is positive, the reaction is not spontaneous.

26. Free Energy and Equilibrium
At equilibrium, no net change in concentration of reactants and products occur, so free energy and the equilibrium constant have the following relationship: ΔG = -RTlnK

27. Free Energy and Equilibrium
When ΔG is negative, K is greater than 1 and the reaction is product favored. K>Q
When ΔG is positive, K is less than 1 and the reaction is reactant favored. K<Q
When ΔG = 0, the reaction is at equilibrium. Q = K

28. What is “Free” Energy?
The “free” energy is the sum of the energies available from the enthalpy term (dispersal of energy) and the entropy term (dispersal of matter).

29. Dependence of Spontaneity on TemperatureΔH ΔG + -
Spontaneous at all temps
Spontaneous at high temps
Spontaneous at low temps
Process not spontaneous at any temp

30. 18.7 Free Energy and Chemical Reactions
Standard free energy change can be calculated (free energy under standard conditions)
ΔGo = ΔHo – TΔSo

31. Standard Free Energy
The standard free energy of formation of a compound is the free energy change when forming one mole of the compound from the component elements. (element in standard state is zero)
ΔGrxno = ΣΔGfo(products) – ΣΔGfo(reactants)

32. Practice Problem
Using values of ΔHfo and So to find ΔHrxno and ΔSrxno respectively, calculate the free energy change, ΔGo, for the formation of 2 mol of NH3(g) from the elements at standard conditions.
N2(g) + 3H2(g)  2NH3(g)

33. Practice Problem
Calculate the standard free energy change for the oxidation of 1.00 mol of SO2(g) to form SO3(g).

34. Homework
After reading sections , you should be able to do the following…
P. 711b (15-16,21-24,29-32)