1. Spontaneous Processes
Spontaneous: process that does occur under a specific set of conditions
Nonspontaneous: process that does not occur under a specific set of conditions

2. Spontaneous Physical and Chemical Processes
A waterfall runs downhill
A lump of sugar dissolves in a cup of coffee
At 1 atm, water freezes below 0 0C and ice melts above 0 0C
Heat flows from a hotter object to a colder object
A gas expands in an evacuated bulb
Iron exposed to oxygen and water forms rust
spontaneous
nonspontaneous

3. Spontaneous vs Nonspontaneous

4. Spontaneous expansion of a gas
stopcock closed
1 atm
evacuated
stopcock opened
0.5 atm

5. Spontaneous Processes
Often spontaneous processes are exothermic, but not always….
Methane gas burns spontaneously and is exothermic
Ice melts spontaneously but this is an endothermic process…
There is another quantity!

6. A spontaneous endothermic chemical reaction.
water
Ba(OH)2 8H2O(s) + 2NH4NO3(s) Ba2+(aq) + 2NO3-(aq) + 2NH3(aq) + 10H2O(l) .
DrH0 = kJ/mol

7. Entropy
Entropy (S): Can be thought of as a measure of the disorder of a system
In general, greater disorder means greater entropy

8. Probability- what is the chance that the order of the cards can be restored by reshuffling?

9. Microstates - How many different arrangements?

10. Microstates - Possible distributions

11. Microstates - More possible distributions

12. Microstates
Boltzmann - entropy of a system is related to the natural log of the number of microstates (W)
S = k ln W
k = Boltzmann constant (1.38 x 1023J/K)

13. Microstates Entropy is a state function just as enthalpy
S = Sfinal  Sinitial
Rewrite:
S = k ln Wfinal  k ln Winitial
Wf > Wi then S > 0 entropy increases

14. Standard Entropy
Standard entropy: absolute entropy of a substance at 1 atm (typically at 25C)
Complete list in Appendix 2 of text
What do you notice about entropy values for elements and compounds?
Units: J/K·mol

15. Entropies

16. Entropy (S) is a measure of the randomness or disorder of a system.
DS = Sf - Si
If the change from initial to final results in an increase in randomness
Sf > Si
DS > 0
For any substance, the solid state is more ordered than the liquid state and the liquid state is more ordered than gas state
Ssolid < Sliquid << Sgas
H2O (s) H2O (l)
DS > 0

17. Predicting Relative S0 Values of a System

18. 1. Temperature changes
The increase in entropy from solid to liquid to gas.
S0 increases as the temperature rises.

19. 2. Physical states and phase changes
The entropy change accompanying the dissolution of a salt.
pure solid
solution
MIX
pure liquid
S0 increases as a more ordered phase changes to a less ordered phase.

20. The small increase in entropy when ethanol dissolves in water.
3. Dissolution of a solid or liquid
The small increase in entropy when ethanol dissolves in water.
Ethanol
Solution of ethanol and water
Water
S0 of a dissolved solid or liquid is usually greater than the S0 of the pure solute. However, the extent depends upon the nature of the solute and solvent.

21. 4. Dissolution of a gas
The large decrease in entropy when a gas dissolves in a liquid.
O2 gas
O2 gas in H2O
A gas becomes more ordered when it dissolves in a liquid or solid.

22. 5. Atomic size or molecular complexity
Entropy and vibrational motion.
N2O4 NO
NO2
In similar substances, increases in mass relate directly to entropy.
In allotropic substances, increases in complexity (e.g. bond flexibility) relate directly to entropy.

23. Processes that lead to an increase in entropy (DS > 0)

24. The Second and Third Laws of Thermodynamics
System: the reaction
Surroundings: everything else
Both undergo changes in entropy during physical and chemical processes

25. Second Law of Thermodynamics
Entropy of the universe increases in a spontaneous process and remains unchanged in an equilibrium process.
Equilibrium process: caused to occur by adding or removing energy from a system that is at equilibrium

26. Second Law of Thermodynamics
Mathematically speaking:
Spontaneous process:
Suniverse = Ssystem + Ssurroundings > 0
Equilibrium process:
Suniverse = Ssystem + Ssurroundings = 0

27. Entropy Changes in the System
Entropy can be calculated from the table of standard values just as enthalpy change was calculated.
Srxn = nS products  mS reactants

28. Entropy Changes in the Surroundings
Change in entropy of surroundings is directly proportional to the enthalpy of the system.
Ssurroundings   Hsystem
Notice: exothermic process corresponds to positive entropy change in surroundings

29. Entropy Changes in the Surroundings
Change in entropy of surroundings is inversely proportional to temperature
Ssurroundings  1 / T
Combining the two expressions:

30. Entropy Changes
If the entropy change for a system is known to be 187.5 J/Kmol and the enthalpy change for a system is known to be 35.8 kJ/mol, is the reaction spontaneous?
Spontaneous if: Suniv= Ssys + Ssurr > 0

31. Entropy Changes Is the reaction spontaneous?
Suniv= < 0 so the reaction is non-spontaneous

32. Third Law of Thermodynamics
Entropy of a perfect crystalline substance is zero at absolute zero.
Importance of this law: it allows us to calculate absolute entropies for substances

33. Gibbs Free Energy G = H – T S
The Gibbs free energy, expressed in terms of enthalpy and entropy, refers only to the system, yet can be used to predict spontaneity.

34. Gibbs Free Energy
If G < 0,negative, the forward reaction is spontaneous.
If G = 0, the reaction is at equilibrium.
If G > 0, positive, the forward reaction is nonspontaneous

35. Predicting Sign of G

36. Predicting Temperature from Gibbs Equation
Set G = 0 (equilibrium condition)
0 = H – T S
Rearrange equation to solve for T- watch for units!
This equation will also be useful to calculate temperature of a phase change.

37. Gibbs Free Energy (G)
G, the change in the free energy of a system, is a measure of the spontaneity of the process and of the useful energy available from it.
DG0system = DH0system - TDS0system
G < 0 for a spontaneous process
G > 0 for a nonspontaneous process
G = 0 for a process at equilibrium
DrG0 = S mDG0products - S nDG0reactants

38. DG0 of any element in its stable form is zero.
The standard free-energy of reaction (DrxnG0 ) is the free-energy change for a reaction when it occurs under standard-state conditions.
aA + bB cC + dD
D G0
rxn
dD G0 (D) f
cD G0 (C) = [ + ] -
bD G0 (B)
aD G0 (A)
D G0
nD G0 (products) S
mD G0 (reactants)
Standard free energy of formation (D G0) is the free-energy change that occurs when 1 mole of the compound is formed from its elements in their standard states. f m
DG0 of any element in its stable form is zero. f m

39. 2C6H6 (l) + 15O2 (g) 12CO2 (g) + 6H2O (l)
What is the standard free-energy change for the following reaction at 25 0C?
2C6H6 (l) + 15O2 (g) CO2 (g) + 6H2O (l)
DG0
rxn
nDG0 (products) f = S
mDG0 (reactants) -
DG0
rxn
6DG0 (H2O) f
12DG0 (CO2) = [ + ] -
2DG0 (C6H6)
DG0
rxn =
[ 12x– x–237.2 ] – [ 2x124.5 ] = kJ
Is the reaction spontaneous at 25 0C?
DG0 = kJ
< 0
spontaneous

40. Sample Problem 2.5:
Determining the Effect of Temperature on DG0
PROBLEM:
An important reaction in the production of sulfuric acid is the oxidation of SO2(g) to SO3(g):
2SO2(g) + O2(g) SO3(g)
At 298K, DG0 = kJ; DH0 = kJ; and DS0 = J/K
(a) Use the data to decide if this reaction is spontaneous at 250C, and predict how DG0 will change with increasing T.
(b) Assuming DH0 and DS0 are constant with increasing T, is the reaction spontaneous at 900.0C?
PLAN:
The sign of DG0 tells us whether the reaction is spontaneous and the signs of DH0 and DS0 will be indicative of the T effect. Use the Gibbs free energy equation for part (b).
SOLUTION:
(a) The reaction is spontaneous at 250C because DG0 is (-). Since DH0 is (-) but DS0 is also (-), DG0 will become less spontaneous as the temperature increases.

41. Sample Problem 2.5:
Determining the Effect of Temperature on DG0
continued
(b) DG0rxn = DH0rxn - T DS0rxn
DG0rxn = kJ - (1173K)(-187.9J/mol*K)(kJ/103J)
DG0rxn = 22.0 kJ; the reaction will be nonspontaneous at 900.0C

42. DG and the Work a System Can Do
For a spontaneous process, DG is the maximum work obtainable from the system as the process takes place: DG = workmax
For a nonspontaneous process, DG is the minimum work that must be done to the system as the process takes place: DG = workmax
An example

43. Reaction Spontaneity and the Signs of DH0, DS0, and DG0
-TDS0
DG0
Description - +
Spontaneous at all T + -
Nonspontaneous at all T + -
+ or -
Spontaneous at higher T;
nonspontaneous at lower T - +
+ or -
Spontaneous at lower T;
nonspontaneous at higher T