Chapter 19

1. Chapter 19 Chemical Thermodynamics Entropy, Free Energy andEquilibrium

2. 19.1 Thermodynamics • Thermo: heat Dynamics: power • State Functions: considers only initial and final states • Does not consider pathways or rate

3. 19.1 Thermodynamics • Study of energy flow and its transformations (heat and energy flow) • Determines direction of reactions (spontaneous or nonspontaneous under given conditions) • Considers only initial and final states • Organized into three laws: • 1st Law • 2nd Law • 3rd Law

4. 19.1 Basic Definitions • System • Surrounding • Open system • Closed system • Isolated system • State of system: defined by values of composition, pressure, T, V. • State Function: defined only by initial and final condition of the system (Enthalpy, Entropy, Gibbs Free Energy). • Energy change signaled by: accomplishment of work and/or appearance or disappearance of heat.

5. 19.1 Reversible and Irreversible Processes • Reversible process: the system can be restored to its original state by exactly reversing the original change. • Example: melting ice at its melting point • Irreversible process: we cannot restore the system to its original state by simple reversing the process. Different path has to be used. • Example: expansion a gas into vacuum.

6. 19.1 First Law of Thermodynamics • 1st Law: • Energy can be neither created nor destroyed • Energy of the universe is constant • Important concepts from thermochemistry • Enthalpy • Hess’s law • Purpose of 1st Law • Energy bookkeeping • How much energy? • Exothermic or endothermic? • What type of energy? • Δu = q + w • q = heat; w = work system does on the surroundings (-PΔV)

7. 19.2 Spontaneous vs Nonspontaneous • Spontaneous process • Occurs without outside assistance in the form of energy (occurs naturally) • Product-favored at equilibrium • May be fast or slow • May be influenced by temperature Spontaneous versus nonspontaneous processes. Expansion of gas: spontaneous. Reverse: not.

8. 19.2 Spontaneous vs. Nonspontaneous Spontaneous Processes: (exothermic or endothermic?) • Gases expand into larger volumes at constant temperature ________________ • H2O(s) melts above 0C ____________ • H2O(l) freezes below 0C ____________ • NH4NO3 dissolves spontaneously in H2O ____________ • Steel (iron) rusts in presence of O2 and H2O ________ • Wood burns to form CO2 and H2O __________ • CH4 gas burns to form CO2 and H2O __________ • Evolution of Heat (Exothermicity) : not enough to predict spontaneity

9. 19.2 Spontaneous vs Nonspontaneous • Nonspontaneous process • Does not occur unless there is outside assistance (energy?) • Reactants-favored at equilibrium • All processes which are spontaneous in one direction cannot be spontaneous in the reverse direction • Spontaneous processes have a definite direction • Spontaneous processes are irreversible. Can be reversed with considerable input of energy.

10. 19.2 Factors That Favor Spontaneity • Spontaneous Processes driven by • Enthalpy, H (Joules) • Many, but not all, spontaneous processes tend to be exothermic. • Entropy, S (Joules/K) • Measure of the disorder of a system • Many, but not all, spontaneous processes tend to increase disorder of the system • Exothermicity favors spontaneity, but does not guarantee it.

11. 19.2 Factors That Favor Spontaneity: Enthalpy • Examples of spontaneous reaction that is not exothermic: NH4NO3(s) → NH4+ (aq) + NO3-(aq) ΔH = 25 kJ/mol • Expansion of gas: energy neutral • Phase changes: endothermic processes that occurs spontaneously. • Chemical system: H2(g) + I2(g) ↔ 2HI(g)Equilibrium can be approached from both sides (spontaneous both ways) even though the forward reaction is endothermic and the reverse is exothermic.

12. 19.2 Spontaneity: Examples 1. Based on your experience, predict whether the following processes are spontaneous, are spontaneous in reverse direction, or are in equilibrium: • When a piece of metal heated to 150 ºC is added to water at 40 ºC, the water gets hotter. • Water at room temperature decomposes into hydrogen and oxygen gases • Benzene vapor, C6H6(g), at a pressure of 1 atm condenses to liquid benzene at the normal boiling point of benzene, 80.1 ºC.

13. 19.2 Entropy • Direct measure of the randomness or disorder of the system. • Related to probability • describes # of ways the particles in a system can be arranged in a given state (position and/or energy levels) • The most likely state – the most random • More possible arrangements, the higher disorder, higher entropy • Ordered state – low probability of occurring • Disordered state: high probability of occurring

14. 19.2 Entropy versus Probability • Systems tend to move spontaneously towards increased entropy. Why? • Entropy is related to probability (positional) • Disordered states are more probable than ordered states • S = k (lnW) • k (Boltzman’s constant) = 1.38 x 10-23 J/K • W = # possible arrangements in system

15. 19.2 Spontaneous Processes: Dispersal of Matter • Isothermal (constant temperature) expansion of gas Two molecules present: 25% probability 25% probability After opening stopcock the molecules could be in any arrangement shown (4 arrangements) Probability for each arrangement = (1/2)2

16. 19.2 Spontaneous Process: Isothermal Gas Expansion Consider why gases tend to isothermally expand into larger volumes. Gas Container = two bulbed flask Ordered State Gas Molecules

17. 19.2 Spontaneous Process: Isothermal Gas Expansion Gas Container Ordered State S = k ln (W) = k (ln 1) = (1.38 x 10-23 J/K)(0) = 0 J/K For 3 particles, probability = (1/2)3 For N particles, probability = (1/2)N

18. Disordered States

19. Disordered States

20. Disordered States

21. Disordered States

22. Disordered States

23. Disordered States

24. Disordered States

25. Disordered States More probable that the gas molecules will disperse between two halves than remain on one side

26. Disordered States Driving force for expansion is entropy (probability); gas molecules have a tendency to spread out

27. Disordered States S = k(ln 7) = (1.38 x 10-23 J/K)(1.95) = 2.7 x 10-23 J/K

28. Total Arrangements Stotal = k(ln 23) = k(ln 8) = (1.38 x 10-23 J/K)(1.79) = 2.9 x 10-23 J/K

29. 19.2 Spontaneous Processes With 1 mole of molecules, the number of possible arrangements increases dramatically. The probability that the gas molecules will be distributed between the two flasks increases greatly. Spontaneous processes are those in which the disorder of the system increases The isothermal expansion of a gas is spontaneous because of the increase in randomness or “disorder” of the system.

30. 19.2 Entropy • Entropy, S (J/K) • State Function • S= (heat change)/T = q/T • S = Sfinal – Sinitial •  S > 0 represents increased randomness or disorder • Note: The magnitude of change in entropy depends on temperature.

31. 19.2 Entropy: example 1. ΔS = q/T The element mercury, Hg, is a silvery liquid at room temperature. The normal freezing point of mercury is -38.9 ºC, and its molar enthalpy of fusion is ΔHfusion = 2.331 kJ/mol. What is the entropy change when 50.0 g of Hg(l) freezes at the normal freezing point? (-2.48 J/K)

32. 19.2 Patterns of Entropy Change • For the same or similar substances: Ssolid < Sliquid < < Sgas solid vapor liquid

33. 19.2 Patterns of Entropy Change Particles farther apart, occupy larger volume of space; even more positions available to particles Particles free to flow; more positions available for particles Rigidly held particles; few positions available to particles solid vapor liquid

34. 19.2 Patterns of Entropy Change least ordered less ordered most ordered solid vapor liquid

35. 19.2 Patterns of Entropy Change 19.2 Patterns of Entropy Change • Solution formation usually leads to increased entropy for the system. Is it true for the surroundings (solvent)? particles more disordered solvent solute solution

36. 19.2 Patterns of Entropy Change Describe in words the entropy of the system

37. 19.2 Patterns of Entropy Change Dissolution of NaCl in water: • The crystal breaks up • The Na+ and Cl- ions are surrounded by hydrating water molecules. NaCl(s) → Na+(aq) + Cl-(aq) • Each ion is surrounded by several water molecules. 4. NaCl becomes disordered (entropy increases) 5. The water molecules become more ordered! (entropy decreases) 6. NaCl dissolves – net entropy increases.

38. 19.3 Entropy and Temperature (a) A substance at a higher temperature has greater molecular motion, more disorder, and greater entropy than (b) the same substance at a lower temperature.

39. What kind of changes are represented here? 50 40 30 Standard entropy,S°(J/K) 20 10 0 50 100 150 200 250 300 Temperature (K)

40. What is the effect of temperature on entropy? 50 Gas Liquid 40 Standard entropy,S°(J/K) 30 Solid 20 10 0 50 100 150 200 250 300 Temperature (K)

41. 19.3 Entropy in Temperature

42. 19.2 Standard Molar Entropies of Selected Substances at 298 K

43. 19.2 Patterns of Entropy Change • Chemical Reactions • #n gas molecules in product > #n molecules in reactants (Srxn > 0) • Physical Changes: cases where entropy increases • Expansion of gas • Formation of solutions • Temperature changes. • If only solids, ions and/or liquids involved, S increases if total # particles increases. • If ΔS > 0, , randomness increases and entropy increases

44. 19.2 Entropy: Examples 2. Predict if ΔS increases, decreases or does not change • Freezing liquid mercury • Condensing H2O(vapor) • Precipitating AgCl • Heating H2(g) from 60.0 ºC to 80 ºC • Subliming iodine crystals • Rusting iron nail

45. 19.3 Entropy - Examples 3. Predict which substance has the higher entropy: a) NO2(g) or N2O4(g) b) I2(g) or l2(s) 4. Predict whether each of the following leads to increase or decrease in entropy of a system If in doubt, explain why. a) The synthesis of ammonia: N2(g) + 3H2(g) ↔ 2NH3(g) b) C12H22O11(s) C12H22O11(aq) c) Evaporation to dryness of a solution of urea, CO(NH2)2 in vapor. CO(NH2)2(aq) → CO(NH2)2(s) H2O (l)

46. 19.3 Second Law of Thermodynamics: System 6. Predict the sign of ΔS0 for each of the following reactions: a) Ca+2(aq) + 2OH-(aq) → Ca(OH)2(s) b) MgCO3(s) → MgO(s) + CO2(g) d) H2(g) + Br2(g) → 2HBr

47. 19.3 Second Law of Thermodynamics • Expresses the connection between entropy and spontaneity. • In any spontaneous process there is always an increase in the entropy of the Universe. The entropy remains unchanged at equilibrium. SPONTANEOUS PROCESS: ΔSuniv = Δ Ssys + Δ Ssurr > 0 • NONSPONTANEOUS PROCESS: • ΔS universe= ΔS syst. + ΔS surr. <0 • Reversible process is spontaneous

48. 19.3 Second Law: Entropy Changes EQUILIBRIUM PROCESSES (reversible) • ΔS universe= ΔS syst. + ΔS surr. =0 • ΔS syst = ΔS surr • ΔS syst = ΔSº final - ΔS0initial

49. 19.3 Entropy Changes in a System (Reactions) • Entropy changes in a system aA + bB → cC + dD • Standard entropy change ΔSº (25 ºC, 1atm). • Only changes in entropy can be measured. • Each element has an entropy value (compare to enthalpy). • Absolute value for each substance can be determined. • For a chemical system: ΔSº rxn = ΔSº products - ΔS0reactants • Standard Molar entropy, S0, is the entropy of one mole of a substance in its standard state (298 K)

50. 19.3 Second Law: Example 5. Using standard molar entropies, calculate S°rxn for the following reaction at 25°C: 2SO2(g) + O2(g) → 2SO3(g) S° = 248.1 205.1 256.6 (J · K-1mol-1) (Ans.: -187.9 J/K)