1. 1 Thermodynamics Chapter 18

2. Thermaldynamics: 熱力學三大定律 : (1) 熱力學第一定律 : 能量以不同形式轉變，能量守恆， Enthalpy( 焓 ) 是一種用來度量系統中能量變化的參數 (  H) (2) 熱力學第二定律：孤立系統熵 ( 亂度 ) 不會減少 ── 簡言之，熱不 能自發的從冷處轉到熱處，而不引起其他變化。任何高溫的物體 在不受熱的情況下，都會逐漸冷卻。 (  S ≧ 0 ) ( 預測化學程序發生的趨勢 ~ 特定濃度、壓力、溫度下的反應 是否會發生 ? ) (3) 熱力學第三定律：所有完美結晶物質於絕對溫度零度時 ( 即攝 氏 -273.15 度 ) ，熵皆為零。

3. 3 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 o C and ice melts above 0 o C 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

4. 4 spontaneous nonspontaneous

5. 5 Does a decrease in enthalpy mean a reaction proceeds spontaneously? H + (aq) + OH - (aq) H 2 O (l)  H ° = -56.2 kJ/mol H 2 O (s) H 2 O (l)  H ° = 6.01 kJ/mol NH 4 NO 3 (s) NH 4 + (aq) + NO 3 - (aq)  H ° = 25 kJ/mol H2OH2O Spontaneous reactions CH 4 (g) + 2O 2 (g) CO 2 (g) + 2H 2 O (l)  H ° = -890.4 kJ/mol 放熱反應多是自發性反應，但不是全部的自發性的反應 都是放熱反應

6. 6 Entropy (S) is a measure of the randomness or disorder of a system. orderS disorder S  S = S f - S i If the change from initial to final results in an increase in randomness S f > S i  S > 0 For any substance, the solid state is more ordered than the liquid state and the liquid state is more ordered than gas state S solid < S liquid << S gas H 2 O (s) H 2 O (l)  S > 0 度量系統內質量與能量散布的方式，散布方式越多， S 越大 ~

7. 7 After the value was opened, the S increased….

8. 8 W = number of microstates S = k ln W  S = S f - S i  S = k ln WfWf WiWi W f > W i then  S > 0 W f < W i then  S < 0 Entropy 微觀狀態 分布 (1 microstates) (4 microstates) (6- microstates) 1868 年波茲曼提出系統熵與微觀態數之關係 : 熵的變化

9. 9 Processes that lead to an increase in entropy (  S > 0) 所以系統自有序變成無序 的相變化，因為微態數增 加，而使熵增加 ! Ex: NaCl( 溶解 + 解離 ) 但水合會減熵 溫度造成分子 動量以及震動

10. 10  S > 0 Example: Br 2 (l) Br 2 (g)  S > 0 Example: I 2 (s) I 2 (g) Standard entropy, ( 標準熵 ): 1 atm 及 25 度下的絕對熵值。 Other example: diamond and graphite,….

11. 11 How does the entropy of a system change for each of the following processes? (a) Condensing water vapor Randomness decreases Entropy decreases (  S < 0) (b) Forming sucrose crystals from a supersaturated solution Randomness decreases Entropy decreases (  S < 0) (c) Heating hydrogen gas from 60 ° C to 80 ° C Randomness increases Entropy increases (  S > 0) (d) Subliming dry ice Randomness increases Entropy increases (  S > 0)

12. 12 Entropy State functions are properties that are determined by the state of the system, regardless of how that condition was achieved. Potential energy of hiker 1 and hiker 2 is the same even though they took different paths. energy, enthalpy, pressure, volume, temperature, entropy Review Examples:

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14. 14 First Law of Thermodynamics Energy can be converted from one form to another but energy cannot be created or destroyed. Second Law of Thermodynamics The entropy of the universe increases in a spontaneous process and remains unchanged in an equilibrium process.  S univ =  S sys +  S surr > 0 Spontaneous process:  S univ =  S sys +  S surr = 0 Equilibrium process: 如果有個反應  S univ <0, 代表此程序非自發性，其逆反應才是自發性 系統熵與外界熵的變化

15. 15 Entropy Changes in the System (  S sys ) aA + bB cC + dD S°S° rxn dS ° (D) cS ° (C) = [+] - bS ° (B) aS ° (A) [+] S°S° rxn nS ° (products) =  mS ° (reactants)  - The standard entropy of reaction (  S 0 ) is the entropy change for a reaction carried out at 1 atm and 25 0 C. rxn What is the standard entropy change for the following reaction at 25 ° C? 2CO (g) + O 2 (g) 2CO 2 (g) S ° (CO) = 197.9 J/K mol S ° (O 2 ) = 205.0 J/K mol S ° (CO 2 ) = 213.6 J/K mol S°S° rxn = 2 x S ° (CO 2 ) – [2 x S ° (CO) + S ° (O 2 )] S°S° rxn = 427.2 – [395.8 + 205.0] = -173.6 J/K mol 標準反應熵 = 生成物與反應物的標準熵之差

16. 16 Ex 17.2

17. 17 Entropy Changes in the System (  S sys ) When gases are produced (or consumed) If a reaction produces more gas molecules than it consumes,  S ° > 0. If the total number of gas molecules diminishes,  S ° < 0. If there is no net change in the total number of gas molecules, then  S ° may be positive or negative BUT  S ° will be a small number. What is the sign of the entropy change for the following reaction? 2Zn (s) + O 2 (g) 2ZnO (s) The total number of gas molecules goes down,  S is negative.

18. 18 Entropy Changes in the Surroundings (  S surr ) Exothermic Process  S surr > 0 Endothermic Process  S surr < 0

19. 19 # 對定壓的程序來說, 外界熵的變化  s surr 正比於 -  H sys: Ex : 放熱反應則  H sys 為負值；這時外界熵是增加的  S surr > 0 # 溫度與熵變化的關係 :  s surr = -  H sys / T Ex: 當外界溫度高，分子運動劇烈，收放熱所造成分子運動 的變化量小。反之，當外界溫度低，分子運動緩，熱能傳遞 就會使其變化量大。

20. 20 氨的合成反應 ( 判斷 25 度室溫下, 其反應是否為自發性反應 ? )

21. 21 Third Law of Thermodynamics The entropy of a perfect crystalline substance is zero at the absolute zero of temperature. S = k ln W W = 1 S = 0

22. 22 熱機效率 (The efficiency of Heat Engines)

23. 23 熱機效率 (The efficiency of Heat Engines)

24. 24  S univ =  S sys +  S surr > 0 Spontaneous process:  S univ =  S sys +  S surr = 0 Equilibrium process: Gibbs Free Energy  s surr = -  H sys / T 改以系統的變化來看, 會簡易很多 將此定義為 Gibbs Free Energy

25. 25 For a constant temperature and constant pressure process:  G =  H sys -T  S sys Gibbs free energy (G)  G < 0 The reaction is spontaneous in the forward direction.  G > 0 The reaction is nonspontaneous as written. The reaction is spontaneous in the reverse direction.  G = 0 The reaction is at equilibrium. Gibbs Free Energy

26. 26 aA + bB cC + dD G°G° rxn d  G ° (D) f c  G ° (C) f = [+] - b  G ° (B) f a  G ° (A) f [+] G°G° rxn n  G ° (products) f =  m  G ° (reactants) f  - The standard free-energy of reaction (  G ° ) is the free- energy change for a reaction when it occurs under standard- state conditions. rxn Standard free energy of formation (  G ° ) is the free-energy change that occurs when 1 mole of the compound is formed from its elements in their standard states. f  G ° of any element in its stable form is zero. f 標準反應自由能 = 標準狀態下生成物與反應物自由能變化 Ex: 石墨燃燒反應

27. 27 EX 17.4

28. 28

29. 29 2C 6 H 6 (l) + 15O 2 (g) 12CO 2 (g) + 6H 2 O (l) G°G° rxn n  G ° (products) f =  m  G ° (reactants) f  - What is the standard free-energy change for the following reaction at 25 0 C? G°G° rxn 6  G ° (H 2 O) f 12  G ° (CO 2 ) f = [+] - 2  G ° (C 6 H 6 ) f [] G°G° rxn = [ 12x–394.4 + 6x–237.2 ] – [ 2x124.5 ] = -6405 kJ/mol Is the reaction spontaneous at 25 ° C?  G ° = -6405 kJ/mol < 0 spontaneous

30. 30  G =  H - T  S

31. 31 CaCO 3 (s) CaO (s) + CO 2 (g)  H ° = 177.8 kJ/mol  S ° = 160.5 J/K·mol  G ° =  H ° – T  S ° At 25°C,  G ° = 130.0 kJ/mol  G ° = 0 at 835 o C Temperature and Spontaneity of Chemical Reactions Equilibrium Pressure of CO 2

32. 32 Gibbs Free Energy and Phase Transitions H 2 O (l) H 2 O (g)  G ° = 0=  H ° – T  S °  S = T HH = 109 J/K·mol = 40.79 kJ/mol 373 K = 1.09 x 10 -1 kJ/K·mol

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34. 34 Gibbs Free Energy and Chemical Equilibrium  G =  G ° + RT lnQ R is the gas constant (8.314 J/K mol) T is the absolute temperature (K) Q is the reaction quotient At Equilibrium  G = 0 Q = K 0 =  G ° + RT lnK  G ° =  RT lnK 平衡常數與標準自由能關係

35. 35 Free Energy Versus Extent of Reaction  G ° < 0  G ° > 0 記住 :  G 的正負號決定反應的自發方向  G ° 的正負號說明系統平衡時，反應物與生成物的相對量

36. 36  G ° =  RT lnK K 值越大，  G ° 負值越大，  G <0 ( 淨反應由左向右 )

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38. 38

39. 39 Thermal Dynamatics in Living System

40. 40 Mechanical Analog of Couple Reactions Make the smaller weight move upward (a nonspontaneous process) by coupling it with the falling of a larger weight. 耦合反應 : 利用另一系統的釋能反應來驅動非 自發性的程序

41. 41 EX: 工業上獲取 Zn 的方法 (Couple Reactions)

42. 42 ATP + H 2 O + Alanine + Glycine ADP + H 3 PO 4 + Alanylglycine Alanine + Glycine Alanylglycine  G ° = +29 kJ  G ° = -2 kJ K < 1 K > 1 Coupled Reactions Example:

43. 43 The Structure of ATP and ADP in Ionized Forms

44. 44 18.17 Calculate ΔG° for the following reactions at 25°C: N 2 (g) + O 2 (g) → 2NO(g) H 2 O(l) → H 2 O(g) 2C 2 H 2 (g) + 5O 2 (g) → 4CO 2 (g) + 2H 2 O(l) 18.19 From the values of ΔH and ΔS, predict which of the following reactions would be spontaneous at 25°C: Reaction A: ΔH = 10.5 kJ/mol, ΔS = 30 J/K · mol; reaction B: ΔH = 1.8 kJ/mol, ΔS = −113 J/K · mol. If either of the reactions is nonspontaneous at 25°C, at what temperature might it become spontaneous? 18.42 Predict the signs of ΔH, ΔS, and ΔG of the system for the following processes at 1 atm: (a) ammonia melts at −60°C, (b) ammonia melts at −77.7°C, (c) ammonia melts at −100°C. (The normal melting point of ammonia is −77.7°C.) HW