3章 問題・略解

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1 S S W R S O( l) O( ) c Jg g J Jg S R J 7. K.9 JK S W S R S JK S S R J 7. K.9JK 4 (a) -Tice 7.K T ice T N 77 K S R.9 JK 4. JK T T ice N.6JK S W S R S JK S S.6JK R (b) S R JK S.6 JK T T ice N 6

2 O( c) O( ) l 68J S c l 68J 7. K. JK g O( l) O( ) 488J -8 S l g 488 J 7. K 9.6 JK 7T 7.K q (J) w(j) ql (J) TL 7.K q T L S q T L q L T T q. 7q ( L ) (a) q J q ( T T ) q 7 J (b) w q q (c) ( w q ) 6. 8 L L L 68J (d) q L q TL T T C P C P /T 台形の面積 Entropy 6

3 .6 エントロピーの計算 CP/T T(K) S - 9.JK - C O N( c ) C O N ( c) O( ) 4 8 l ( ) kj S ( JK ) S 89.9 JK.JK JK.87 JK ( 746.kJ ) ( 8.4 kj ) ( 7.kJ ) 4.6kJ S熱環境 46 J 4.9JK 98. K S 世界 S S 熱環境 9.4 JK 6

4 4 C O() l II kj C () O l C () l ( g) O ( g) C O( l) II 74.8 kj S 6.4 JK.9 JK.69 JK..JK 44.6JK S 44.6JK 98. K T S kj ( 44.6 kjk ) 74.kJ II 4.atm ( ) (.atm) I G 7.9 kj ( ) G atm 8.6 kj ( ) ( atm) (.atm) 8.9kJ G G. 64

5 dg V VdP dp 8cc / 9atm 8 6 m VdP 8 6 m 4.6 Nm 9atm Nm.kJ atm ( atm ) G ( ) VdP G 7.9kJ.kJ 7.6kJ atm atm III 6 (.atm ) G () RTlnP P.atm G RTlnP 8.4JK 98.K kj/j ln(.) 8.94kJ 8.6kJ RT.479kJ 7 O (.atm O ) G (O ) RTlnP G G ( ) P.atm RTlnP.479kJ ln(.).87kj 8 CO m CO G (CO (g)) G (CO (aq) ) CO (aq) (CO (aq) ) G (CO (aq)) RTln G RTln G (CO (g)) G (CO (aq)) 6

6 94.8kJ ( 86. kj ) 8.6kJ ln 8.6 kj /.479kJ.96 ep( m.64 CO /.7/g.64 / CO 44 / 9 (O (aq)) G (O (aq)) RTln G (O (aq)) G (O (aq)) RTlnRTlnγ γ G RTlnγ RTlnγ.479kJ ln..6kj CaF (c) Ca (aq) F (aq) G (CaF (c)) G (Ca (aq)) G (F (aq)) (CaF (c)) G (CaF (c)) G (Ca (aq)) G (Ca (aq)) RTln[Ca G (F (aq)) G (F (aq)) RTln[F G G (CaF (c)) 6.9 G (Ca (aq)).4 G (F (aq)) kj RTln[Ca [F G (CaF (c)) G (Ca (aq)) G (F (aq)) ln[ca [F K SP [Ca [F.9kJ.9kJ.479 kj.. e.6 m SP: Solubility Product 66

7 N (g) N (aq) (a) m P.764 atm (b) G (N (g).764 atm) G (N (g)) RTln.764 (c) 6.64kJ.479kJ (4.8) 6.6kJ G (N (aq)m) G (N (aq)) G (N (g).764 atm) 6.6kJ I 6.7kJ N (Ca (aq)) G (Ca (aq)) RTlnγ Ca [Ca G.4kJ.479kJ ln(.8.9) 67.8kJ (CO (aq)) G (CO (aq)) RTlnγ CO [CO G 8.kJ.479kJ ln(..4 ) 8.4kJ Ca CO ( Ca CO ) G (Ca CO ) G (Ca (aq)) G (CO (aq)) 6.8kJ Ca CO (c) G (Ca CO (c)) 8.76kJ Ca (aq) CO (aq) Ca CO (c) 67

8 4 µ [.( ).8( ).46( ).( ).( ). 68 Cl SO 4 Na Mg Ca

9 A G ( A ) ( A ) ( A ) ( A ) G p G ( O l) G( O g p) G( O l) G ( O l) G( O g p) G ( O g) RT ln p RT p G ( O l) G ( O g) ( O l) ( O g) ln RT 8.4 JK 98.K.479 kj I ( O l) ( O g) 7.9 kj 8.6 kj 8.9 kj ln p.46 p e.46 p.7 atm 76mmgatm.7 atm.76mmg G ( AgCl c) G( Ag aq) G( Cl aq) G( Ag aq) G ( Ag aq) RT ln[ag G( Cl aq) G ( Cl aq) RT ln[cl RT ln[ Ag [Cl G ( Ag aq) G ( Cl aq) G ( AgCl c) ( Ag aq) ( Cl aq) ( AgCl c).64kj Solubility Product 69

10 K SP ep(.64 /.479).788 m glucose lactic acid G L G G aq G G aq RT ln a ( ) ( ) G G L aq G L aq RT ln a ( ) ( ) L a X G ( aq) G( L aq) G G aq ( ) G L aq X 94.4 kj 8.77 kj ( ) II G K ( a ) 8 a L G equilibrium.96 4 (a) CO ( g) O ( g) CO( g) CO (b) CO g P CO g RT ln P ( CO ) ( ) CO O g P O g RT ln P ( O ) ( ) O CO g P CO g RT ln P ( CO ) ( ) CO I ( CO g) 94.8 kj ( O g) G CO g 7.7 kj ( ) G 7

11 O ( g) ( CO g) ( CO g) 4. kj ( g P ) ( CO g P ) ( CO g P ) O O CO CO ln 4. kj.479 kj 7. 4 K P K P P e O P CO PCO equilibrium atm (c) P.atm P.atm P C? atm O C O O P CO K P P P O CO atm P CO atm -- glucose -phosphate -6- glucose 6-phosphate gp g6p g p eqbu gp eqbu RT ln a ( ) ( ) g p g6 p eqbu g6 p eq bu RT ln a 6 ( ) ( ) g p ( gp eqbu ) ( g6 p eqbu ) 6 ag p [ kj ln g p ln. agp [ gp.479kj [ g6 p. e. [ gp 7

12 6 ATP O ADP Pi RT ln K kj K [ADP[P i [ATP equilibrium (a) J ln K. RT 8.4 JK. K K (b).6669 M.7 M kj 8.4 JK 48.8kJ [ADP[P i RT ln [ATP. K kj J 4 ln (c) ATP (b) 48.8kJ ATP ADP Pi.kJ.kJ 7 (d) (b) [ [ [ 7 ln K ln K T R T T RT T 4 kj T. K T 7.7 K K.66 K K 4J. ln K 8.4 JK. K 7. K.78K d( ) VdP V ( P P ) P atm kj V ml P 4atm V P P V cm 6 m cm. 9atm 9atm Nm ( P P ) 79J atm m 7

13 79 J 9 C C(O)COO C 6O( aq) C O ( aq) ( aq) G C O aq G C O aq RT ln ( 6 ) ( 6 ) C6O G C O aq G C O aq RT ln a ( ) ( ) G aq ( ) ( ) G aq RT ln a II C O aq 8.77 kj a CO ( ) ( ) 6 G G C O ( C O aq) G( aq) G( C 6O aq) ( C O aq) G ( aq) G ( C O aq) RT ln a CO RT ln a RT ln a RT ln K C6O aq 6.7 kj 6 K ac a O a C6O equilibrium G ( C O aq) G ( aq) G ( C 6O aq) ( C O aq) ( C O aq).kj 6 K.kJ ep.479kj.7 4 7

14 O( l) ( aq) O ( aq) G ( O l) G ( O l) G( aq) G ( aq) RT ln[ G( O aq) G ( O aq) RT ln[o I ( O l) 7.9 kj ( aq) G ( O aq) 7. kj RT ln[ [O ( O aq) ( O l) 79.89kJ K w 79.89kJ.479kJ 4 [ [O ep. m O( l) O( ) g P RT P ( O g P) ( O l) ln T 98.K P.7 atm K P T ( K) K P (atm) ln K ln K R T T ln K T RT.479kJ ln P (.46) T 4.kJ. 87 T 7.6 K

15 C O N( aq) C O N ( aq) O( l) 4 8 I II 9.8kJ ( O N aq) ( O l) ( C O N aq) C 4 8.9kJ ( O N aq) ( O l) ( C O N aq) C 4 8 K ep RT 9.8kJ ep.479 kj K ln K ln K T 98. K T.K R T T K K K ep RT T T ep O( l) ( aq) O ( aq) I O aq ( ) ( ) O l.9kj ln K ln K T 98. K T.K R T T 7

16 K K K ep RT.98.9 T T ep C COCOO (a) cathode reaction Fe (cyt c)( aq) e Fe (cyt c)( aq) anode reaction C COCOO ( aq) C COCOO ( aq) ( aq) e (b) (c). p 7 cathode reaction anode reaction.4v.9v.4v.9v.444v.44v (d) ε.444 V Fε 9648C (e) [.444 V 8679 J 8.68kJ 7 ( ) ( ) ( ) 7 G aq G aq RT ln [ G 7 ( aq) G ( aq) RT ln (a) G( Fe (cyt c) aq) G ( Fe (cyt c) aq) RT ln[fe (cyt c) G( Fe (cyt c) aq) G ( Fe (cyt c) aq) RT ln[fe (cyt c) G( COCOO aq) G ( C COCOO aq) RT ln[c COCOO C G( COCOO aq) G ( C COCOO aq) RT ln[c COCOO C 76

17 ( ) ( ) ( ) ( ) G Fe (cyt c) aq G C COCOO aq G( G Fe (cyt c) aq G C COCOO aq RT ln K K [Fe (cyt c) aq [C COCOO RT ln 7 4 ( / ) [ aq) [ 7 [Fe (cyt c) aq [C COCOO equilibrium K 8.68kJ ep ep.4 RT.479kJ () K [C COCOO [C COCOO.4 cathode reaction Fe (cyt c)( aq) e Fe (cyt c)( aq) anode reaction C O( aq) C CO( aq) ( aq. ε ( V ) RT ln K Fε ε.44 V ) e.4.8 K Fε 9648C.44 V ep ep 4.7 RT 479CV 4 4 K [Fe (a) (cyt c) aq [C [Fe CO [ (cyt c) aq [C 4 ( / ) O equilibrium 77

18 [Fe (cyt c) aq ( m) [Fe (cyt c) aq. ( m) [C O. ( m) [C CO ( m) 4 ( ) ( ) [.. δ δ : very small δ ( ) ( ) 4δ. 9 δ 4.6 [Fe (cyt c) aq.m [C O.m [C (b) [ 4 [Fe (cyt c) aq 4.6 CO.m 9 m [ ( ) ( ) ( ) ( ) X. X ( X ) ( X ) ( ).86 (.7). 86 (.8) X.7 ε.7 ε.7 ε ε ( ) ( ) ( ).86.87ε.86.87ε 7 7 m ( m) X ε [Fe (cyt c) aq.74 m [Fe (cyt c) aq..6m [C O..6m [C CO.7 m 78

19 6 C6 N ( aq) C6 N ( aq) ( aq).. K a M [.4 4 [O M.4.8 M 4 CO ( aq) CO ( aq) ( aq) acid conjugate base ( aq) O CO ( aq) O ( aq) CO [CO [ K a pk. a [CO [CO [O K b K [CO w [ [O 4 K K K pk pk p K b w a b w a K b pkb C COCOO( aq) C COCOO ( aq) ( aq) M

20 α.9( M ).( M ) ( aq) O N ( aq) O ( aq) N 4 [N 4 [O K b K a.6 6. [N [ 4 N. [N [O M..79 ( K K ).4 M [N 4.4 M.. [N.M w a..m 9 Na CO Na ( aq) ( aq) CO ( aq) O CO ( aq) O ( aq) CO K b 4 [ CO [O K w 4. [CO 4.7 K a [ CO. [CO [O M 8

21 6. p p p log[o K w B aq O B aq O aq B : C NO ( ) ( ) ( ) 7 9 [B [O K b pk b 6. [B B ( aq) K a B( aq) [B[ [B ( aq) p K pk pk 7. 9 a w b [B. [B [O [. p [O.8 ( ) N( aq) O ( C ) N ( aq) O ( aq) C.. ml.m ( ) N( aq) O ( C ) N ( aq) O( aq) C pk b 4 pk a 4.8. K b ( C ) N. [( C ) N [O [ [.6 p

22 p p [( C ) N ( C ) N pka log [ ( C ) N [.M Cl ml ( C ) N [ ( C ) N [( C ) N [ p pka. 8.M Cl ml ml ( C ) N. [( C ) N [ O [ p p log 7 log X ml Y p X Y ( aq) O B ( aq) O ( aq) B [B [O K b pk b 4 or 8 [B B ( aq) K a B( aq) [B[ [B ( aq) 8

23 [B ν [B [B [B [B pk w [ B Ka K w p pkb 4 pkb p [B [ K b[ p K 4 or 8 ν 4 or ν 8 b p p6 ν ( ) ν ( ) 4 8 プロトン化の程度 p 4 4 PO ( aq) PO ( aq) ( aq) pka 7. K a [PO [ 4 PO [ 4 p p [PO 4 log [ PO pk a 4 p Ka 7. p 7 [PO 4 [PO 4. log..6 [ PO [ PO Na PO 4 O Na PO 4 O.6 8

24 7 CO CO K 4. CO CO K 4.7 K [ [CO K [ CO [ [CO [CO [ p p p [ CO K [ CO [ CO K [CO ν [ CO [CO [ CO [CO [CO p7 4. p7 4.. p7. プロトン化の程度 p 6 6.(a) (b) NaB 84

25 B B K B B K [B [ [B [B[ [ B [ B [ B B K [ B [ p K p K i i i [B ν [ [ B B [ [ B B [B [B [B ppk ppk pk () ppk ppkpk ppkpk pk [ B 6.(b) ν [ [ B B [ [ B B [B [B [B ppk ppk pk pk ppk ppkpk ppkpk pk. p K i i (a). p pk pk. p pk pk. p pk pk (b) プロトン化の程度 P 8

26 . プロトン化の程度 p 7 G G6P 6 [G[P i K Σ [G6P [G6P [P i [ [G OPO [G OPO [G OPO 9. [ [ PO 4 [PO 4 [PO (a) K [G[PO [G OPO 4 K Σ (b)[ [ K 4.89K [ (c) (a) [ K Σ 7 7 [ [ K K.77K

27 7 Trouton s rule 7p v T b v 9JK v: vaporization T b G Gg l dgl SldT VldP dgg S g dt V g dp G l Gg dg l dgg ( S S ) dt ( V V )dp g l g l v ( S g Sl ) S v Vg Vl V Vg T dp v v Clausius-Clapeyron dt T V V T g PV RT P RT V dp P dp P dt v v v ln dt RT P RT P R T T P atm T T b 7.8..K T 98.K 9Tb 9 Tb ln P. 4 R T T R T b g g P.4 e.atm 87

28 ln(p/) /T 88

29 P ln 8.4 T P 76 mmg T 7. K b v R 8 v 8R 896 J 9J S v v Tb 69.7 J K.66atm P v ln P R T T P atm T 7. K P.66atm 4.67 kj 76. v 88. g g/8.g/. A B (a) m n A. A. 98 n n. A B P A.8mmg P A APA.6mmg PA. mmg ob PA ob PA PA ob.8..6 mmg. P P P mmg A cal A A 89

30 (b) m A na n n A.96 B.. P A APA.7mmg PA. mmg ob p A A PA ob PA PA ob.8.. mmg. 9 P P P.8.7.mmg A cal A A 9 A 6 O N 4 NO l 98.4g l 98.4 g n - 8.g. Raoult P 76 mmg.8 mmg P 76 mmg. 986 n n n n.7n.9 ( n n )

31 7 lim c Π c 67.4atm ml g (6) RT M 67.4atm ml g RT M 67.4atm ml g 8.6 ml atm K 8. K 67.4atm ml g Π/c(atm ml/g) y c(g/ml) 4g 8 Π Π n RT V T. K 7.6atm n Π 7.6 atm V RT.86l atm K.986 l. l R.86l atm K. K 9 NaCl g NaCl.4 c.8 l Π crt 7.84 atm T. K.8 l R.86l atm K.86l atm K. K kg kg/l kg kg. kg l. 946l 9

32 c Π.9. l.976l crt 7.4 atm. l.86 atml K 98. K (a) M M n n nm nm M M M n n M w nm M nm nm nm M M M M M.667 (b) M M m m m/m m/m M n m M M m M m M m M M M M M M. mm mm M M M w m m amu amu C / 9

2

2 th 37 ICh Theoretical Examination - - - - 5 - - : - ( ): ( ) - : 279 - - - - - - - G D L U C K 1 2 1 amu = 1.6605 10-27 kg N = 6.02 10 23 mol -1 k = 1.3806503 10-23 J K -1 e = 1.6022 10-19 C F = 9.6485

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