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1 演習問題の解答例 ( 注 ) ( 注 ) 第章.5 dt 7 d ( 7 dl l ( ) l ) ( ) 7 ( mi) l l. 5596,. 865 mi 7 4 d t. 865 mi l. 8 mi.6.7 R b R b R a + ( b) R ( b) f x l x.8 f f f f ( x ) f + x + x + + x!!! f f ( x) R a + ( b) R ( b) d d( l( + x) ) dx + x f ( x) / dx + x f f + x x l( + x ) x + x.8 l x x l x x f x e x.54 e x x x x x !!!! x e x !!! 4! 5!! x x 5 p( q + px ) r C p q x r r r r r 4 演習問題の解答例

2 p( q + p) p r C p q r r r r 5 5 E x m p 4 x x r r r r r r p( q + px ) x r C p q x rb(, r ) x { } r p ( ) p( q + px ) x + ( q + px ) r b(, r ) x 6 r 6 x σ r σ r r ( r m) b(, r ) r b(, r ) m rb(, r ) + m b(, r ) r r r b(, r ) m + m ( m rb(, r ), b(, r ) ) r r b(, r ) ( p) ( m p) r { } p ( ) p + ( p) ( ) p( p) pq r r 7. σ pq x u x x, x dx x u x ( ) ( ) + x + dx u x + dx u x u x x dx u dx du dx x, y u x, y, v x, y y v C y dy y D C B D B x x dx x u x, y u x, y, v x, y x dx, y u x dx, y, v x dx, y B B 演習問題の解答例

3 u u( x, y ) + dx, v x, y + v x x, y x, y dx x dx, y dy u x dx, y dy, v x dx, y dy C C u u v v u( x, y ) + x + y, v( x, y ) + x + d d d dy x, y dy u x, y dy, v x, y dy D D u u( x, y ) + dy, v x, y + v dy y v C v D v B u u u S BCD S B C D S BCD dxdy uv uv ( v + v )( u u ) S B C D uv u v ( )( ) u + u v v u u u u dy, u dx, u dx + dy u + u v v v v dy, v dx, v dx + dy v + v ( + )( + ) S B C D u u v v uv uv v + v u u + u v uv + u v + u v + u v u v u v u v u v x y d d v dxdy J dxdy v J J u, v x, y Jaobia J u v (, ) ( x, y ). x r os θ y r si θ u, v x u, v, y u, v u r, v θ x, y u, v 演習問題の解答例

4 x y x y S( ) u v v B C D v d d S( B C D ) dxdy x y ds dxdy (, ) dudv ( u, v ) v x y u v (, ) d d dudv ( u, v ) v ds dxdy r θ osθ drdθ r θ siθ r siθ drdθ rdrdθ r osθ dr rdθ dθ r dr x, y, z / u, v, w u r v θ w f x r si θ os f y r si θ si f z r os θ d dr rdθ r si θ df r θ φ d dxdydz J drdθdφ r θ drdθdφ φ z z z r θ φ si θ os φ r os θ os φ r si θ si φ si θ si φ r os θ si φ r si θ os φ drdθdφ os θ r si θ 4 演習問題の解答例

5 J r os θ si θ os φ + r si θ si θ si φ + r os θ si θ si φ + r si θ si θ os φ r si θ si θ + r os θ si θ r si θ d r dr si θ dθ dφ z r si θ O θ dθ dr y d x. x i, i,,,, u i u i x, x, x,, x i,,,, ( u, u, u,, u ) ( x, x, x,, x ) u i j u i det j {u i } {y i } {x i } {u i }, {y i }, {x i } i j i j C B det C det B det det B. ( u, u, u,, u ) ( u, u, u,, u ) ( y, y, y,, y ) ( x, x, x,, x ) ( y, y, y,, y ) ( x, x, x,, x ) u x, y, z, u x, y, z, u u, u y, u z, x x, x y, x z, x, y, z, 演習問題の解答例 5

6 z ( u, y, z, ) ( x, y, z, ) x z u y, z, ( u, y, z, ) ( x, y, z, ) 第章.7 a x mol dm mmol dm ( m) mmol mol x m b 5.7 al J g g al. mol 4. 4 J mol g.6 m 6 g m g m. 6 4 g m.8.9 d Wh W 6 s.6 MJ J mol 5 C v/m s m a g g m / ( a / b) ( a / b) M M b mol mol... F mg h mh h h g ρ g g m (. 76 m) m s 5 a R ( 5 ) ( 4 79 m. a. dm mol ) dm g g m g ha m s g m m s 8. 5 J mol 6 dy bar mbar m ha bar..4 m N g m s s m. g g g F G m m ( N m g ) (. g) r (. m) N 6 演習問題の解答例

7 .5 Π mol dm R. J 8. 4 dm m mol ( 9. 5 ) a 47 ha. 47 bar. 4 atm.6 d F m v d d r /dt m dt dt N g m s dw Fdt J N m g m s w d dt W J s g m s dq Idt C s w E d dq J C g m s R E Ω g m s I R 5 atm (.5 5 a atm ) 4 dm ( m dm ) ( 8. 4 J mol ) ( ) ( 44 mol) ( 4 g mol ) 97 m M.. 6 g C e E F E J ( ) mol C 65 B R J 8. 4 mol.44 mol.9 x 4.84 J 6 g 5 7 al. t g al 6 s 9 9. J. W, x 5. 6 t s. v rms R v M N J g m s 8 4 mol. 98 ) J ( 8. g g mol 55 m s g v rms.5 発展. v v rms v v v rms R v γ γ.56 γ 7/5. M. vrms / v /( 7 / 5) v N 5 m s 46 m s ε ε.6 9 Q. 6 C E 4πrε m F m 7. 演習問題の解答例 7

8 . 9 E Q r Q r. 6 C / /. m. 5 4πrε 4. 4 ( F m ) m. 4 r U.59 ε ε ε r.59 U U Q Q. 6 4πrε m mol 9 ( C) 9 ( F m ). U m UN. J 6. mol / 9 J mol. J Na Cl ε ε ε r.58 /8 Na Cl. C NaCl. v rms.5 v v rms ( He) MN ( N ) M rms He 8. g mol 4. g mol M 問 mol M ρ M R 問 d ρgdh d M d g R h l Mg h d( l ) dh l R Mgh Mgh l( / ) exp R R 問問 ( ) 8. 8 ( g mol g g ) ( 9. 8 m s ) ( 8 m) ( atm) exp ( 8 4 J mol ) ( 7 ) 問 4 h Mgh ( h)dh exp R R Mg.. 7 atm Mgh Mgh R R R exp d Mg h M h h exp g h R d R Mg 問 5 問 d M d g R h exp h/h d Mg h exp dh R h l Mg h h Mgh d( l ) h/ h h exp dh l R h exp d( h h ) R h / Mgh h l( / ) exp R h h R Mg l( h / ) exp h exp{ exp h/h } h M 問 6 h exp exp exp gh exp R ( atm) exp exp ( ) ( 8 8. g mol g g ) ( 9. 8 m s ) ( 8 m) ( 8. 4 J mol ) ( 7 ). 8 atm 8 演習問題の解答例

9 E h λ E N h λ 4 8 ( J s).9979 m s 7 9 J ( 4. m) 6. e. e ( ) ( 4 7. m) mol J s m s.76 Δm E/ m E ( e ) (. 6 J e ) m e m 8 e.998 m s 9. 9 g ( ) 9 M w w t M EN 9 ( J s ) ( 5 g mol ) 6 9 ( e ) (. 6 ) ( 6. ) J e mol J 99 J. g s. mg s C C.8 e..4 e.79 mol N N liear radom E exp liear E R radom exp 5 J mol ( 8. 4 J mol ) ( ). 44 F v d F( v ). v dv d v v mv mv exp v d exp B B mα α B F v ( α v at d ( )) dv mv mv exp B B B R α m M 8. 4 Jmol α r g mol g g 5 m s 第章.7.8 a b d e f g b d d 演習問題の解答例 9

10 .9.4 r mi du 6 σ 6σ 4ε + dr 7 σ 6 r 6 mi r mi /6 σ r r mi mi.4 u mi ( rmi ) / 6 σ σ 4ε 6 / 6 σ σ 4 ε 4 ε. q q δqrev 5 rev rev d + d d + d qrev 5 qrev,. qrev 5 qrev δq rev δqrev Rδqrev 5R R ( qrev / ) ( q ) rev / d + d d + d ( q / ) rev 5R, ( q / ) rev R. qrev / qrev / δq rev / 7 atm.4 dm mol.5 atm.4 dm mol d ΔU ex ex w d. 5 atm. a atm 4 dm 4 dm m dm 5 (.. ) 4 J q ΔU w 4 J ΔH ΔU Δ ΔU Δ R ΔU d q w exd R R l ( mol) J. 5 atm l mol. atm 57 J ΔH ΔU Δ ΔU Δ R 演習問題の解答例

11 . d. U H vap vap vap 4. 6 J mol atm. 5 a 4 m mol atm m. 6 m J J 7. 7 J mol..4.5 C w ( H ) C M M M w H H C w w M 88 J mol (. 9 ) ( 8. 6 g mol ) (. 95 g) ( 6 J mol ) (. 746 g) (. 6 ) (. g mol ) w H.54 ω ele EIt C M w t H. 95 g 6 J mol. 9 M EI. 6. g mol 6 s. Δ sub H Δ fus H Δ vap H O g C s O g CO g CO g CO g C s / O g CO g / O g.6 Δ r H. CO g Δ f H CO g Δ r H Δ f H CO g Δ f H C s 9.5 J mol Δ r H Δ f H CO g Δ f H C s.5 J mol Δ r H Δ r H Δ r H J mol CO stadar molar ethaphy of ombustio Δ H CO g /O g CO g Δ r H Δ H 8.98 J mol Δ r H Δ f H C 6 H Δ f H C 6 H 6 Δ f H H. 8.9 J mol 6. J mol Δ r H Δ f H C 6 H Δ f H C 6 H 8 Δ f H H. 7. J mol 6. J mol Δ r H 48 J mol Δ r H Δ r H r H 4 J mol r H r H r H 演習問題の解答例

12 .7 NH CH CONHCH COOH s O g NH CONH s CO g H O l. H H ( H + H + H H f H O ) f urea f CO f H O f GG g [.5 + ( 9. 5) + ( 85. 8) ( ) ] J mol. J. g mol.8 a C s O g CO g b H g / O g H O l C H 5 OH l O g CO g H O l d C s / O g H g C H 5 OH l d a b Δ f H C H 5 OH l Δ H C s Δ H H Δ H C H 5 OH l J mol d Δ r ν gas / 7/ ru r H r gas R J mol ν 7 J mol 69. J mol Δ r ν gas Δ r H.9. Δ r U Δ r ν gas R H g O g H O l Δ r ν gas δq ΔS IEΔt ΔS surr q surr / IEΔt/ I RΔt/ Ω s / 98.6 J du d S δqrev du δwrev wrev ex d δ d d d d d d d d d d d d R d d. d S d ds R R d S R l R l q q rev. ΔS q surr q. ΔS surr ΔS total ΔS total ΔS ΔS surr ΔS ΔS ΔS d du qrev δq δw..6 S R l > q surr q. ΔS surr ΔS total ΔS ΔS surr.4 演習問題の解答例

13 . δq total δq δq surr δw total δw δw surr. du total. qtotal dstotal( ds + dssurr ) > δ δq total ds total.4 δq surr δq δq surr δqsurr δq.6 ds surr δq dstotal ds + dssurr ds > δq ds.8. δq ds dh ds dg, δq ds du ds d dg dg.7 q w.. du.5 ΔH ΔU Δ ΔS ΔS du d..6 δq S rev R l d. G H S R l.5 w ex Δ Δ r Δ r ν gas R r 8.4 J mol 98.5 / r U 4.96 J mol r H r r G q Δ r H Δ f H C H 5 OH l Δ f H CO g Δ f H C 6 H O aq 6 78 J mol 9 J mol 6 J mol 79 J mol Δ r U Δ r H Δ r 79 J mol 4.96 J mol 84 J mol r S 演習問題の解答例

14 Δ r S surr q / Δ r H/ 79 J mol / J mol Δ r S {Δ S C H 5 OH l Δ S CO g } Δ S C 6 H O aq 6 6 J mol 4 J mol 64 J mol 486 J mol Δ r G Δ r H Δ r S 79 J mol J mol / 4 J mol Δ r H.6 5. U E R.49.5 H U + R + R R U H.4 C R.8 C 5 R C C + R.7.8 C H O l 99.6 C 99.6 C 99.6 C H O g C H H + H + ( C, H ) + O( l ) C, HO( g ) vap H vap C C C H O( l ) vap C C HO( g ) J mol 99.6 /( J J ) J mol 44. J mol H U d H U + + H U / R U R R H U + + C U C U R du,.9. U U U C.9.4 H C d ( C + R ) (. 5 mol) (. 8 J mol J mol ) ( 9 98 )/( J J ).8 J.9 q.8 J 4.4 U C d (. 5 mol) (. 8 J mol ) ( 9 98 )/( J J ). 99 J. w ΔU q.99 J.8 J.9 J C.9 Δ f H Δ f H C. Δ r H Δ r H Δ r C r C νc ( ) νc ( ) キルヒホッフの法則 irhhoff s law Δ r H 4 演習問題の解答例

15 . H g O g H O g..4 S S C d l 7 l S H + C H d l 7 S O C, l + l 98 l 98 l 7 7 H O +, H O l 98 ( S HO S H S O ) + ( C, HO C, H C, O ) l J 9. J mol ( ) J mol l 98 mol, O d( l ). f...44 C S l C C 7 d dl l l 7. C ΔS surr, rev ΔS C C ( ) C S surr surr surr surr qsurr q C C C.. C. 76C. 6C C 5 C. C / 4 C S d C S C C S C l d C d( l ) l( / ) l S/C.4.58 / γ γ C.5,, U ( U, ) ( U, ) (, ) U (, ) (, ) (, ) U U 演習問題の解答例 5

16 第 4 章 q q H w H ΔS H q w L ΔS H. 4.9 w rev w w ΔS H H L rev H ε max w q H H L 4.7 ql,rev qh,rev S + L H q H,rev q L,rev H L ΔU q L,rev q L,rev w rev w H L rev H ql,rev ε q max w L L H L L,rev rev q L,rev q L,rev H L 4.8 C H 5 OH l O g CO g H O l Δ r S S CO S H O S C H 5 OH S O J mol 8.9 J mol 4.9 H O l H aq OH aq Δ r S S H S OH S H O J mol.66 J mol q S surr 4. S M log M/g mol S S log M/ g mol q r H r H rs total rs + S surr rs Δ r S total Δ r S total Δ r S total Δ r G Δ r S total 5. Δ r G Δ r H Δ r S 4. Δ mix S R.79 l.79. l.. l. 4.6 J mol Δ mix G Δ mix S mol /.7 J mol 4. C H W S J mol M/g mol S B l W 4. S J mol log M/g mol 6 演習問題の解答例

17 h.86 ε 8ma m a S Q lq S B Q + l N, 5.8. 発展 5. πmb Q N! h N / lq N N, N S mol R B N / S πm B BN + BN l h + πmb BN l B l N! R + R l h.55 l N! N l N N M N m / m S 5 π R + R R h N 5 B l + π MB R l h N / N S l M/g mol / B l N! S C C S Δ diss S Δ diss S hydrophobi iteratio Δ diss G Δ diss H Δ diss S Δ diss G Δ diss H Δ diss S 6 Δ diss S 演習問題の解答例 7

18 第 5 章 5.8 a 4.7 b q ex w ΔU ΔU Δ RΔ ΔH ΔU Δ ΔS ΔG ΔH Δ S ΔH ΔS ΔH q q : ΔU ΔH Δ ΔH R b ΔU H G H ΔG S > d H OH H O ΔH q q ΔU ΔH Δ ΔH ΔG ΔS r S S H O S H + S OH ( + ) [ { + (. 75)}] J mol J mol b b t w G M G w Mt ( ) 8 g mol ( 5 J s ) ( 6 s) G 88 J mol dg ( G N t N ) 6 / / ( J mol ) ( s ) / ( 6. mol ). W m 4πr / 6 4 π / m ( R / ) R g S S R S ds S S d R R d l l d l R l 5. あ U S.8 い S + う d Sd え + d d おか S きくけ + こ R 5.4 あ U + d U d い U + d U d う + d d え U お U + U か U + U きあ H S い d Sd う G + d G d えおか 8 演習問題の解答例

19 5.6 あ H + H d d い H + H d d う + d d え H お H + H か U + H き ΔH ΔS ΔG ΔH ΔS ΔG.8.9 ΔH ΔS 5.6 G G/ G S G/ H 5. a I/m / b I/m / I/m / 4 d I/m / e b / i zi / ε ε / r B Ne I ε ε r B 9 ( ) ( F m ) (. 8 J ) ( ) 9 m (.4 Å ) 6. mol. 6 C. mol dm dm m. 4 b) a b m m Å b NaCl CuCl CuSO / + I. mol g 5 C log. 59 g γ ± / / ( mol ) / / / mol g γ I 演習問題の解答例 9

20 5. S, S, S S ( S, ) ( S, ) (, ) (, ) (, ) (, ) S S S / S S S / / S < C C NH 4 H O H Δ r G Gl N ( mol ) G N N r G ( r ) Gl 5.67 q N / tras B B B mol m M π π h N h 4. J mol J mol ( B ) / 5/ (. 4) (. 995 g mol ) ( 6 4 ). mol 6.66 J s ( 6. mol ). 8 /. 86 J / 5. a q l ( 8. 4 J mol µ tras B R ) 7 4 J mol l < > (l q ) B l ε tras tras B.5 B 第 6 章 pt S pt H 9 J mol. 95 J mol pt, phase trasitio fus < d fus H d m fus 演習問題の解答例

21 fus H m fus ( 6. 8 J mol ) ( ) m mol. 5 J m a /. a atm. 9 atm 5 g.5 m 5 g 9.8 m s / 5 5 m 98 5 a 97 atm.7 C 6.9 vap H l, R R l / / b vaph b b R l / H vap ( 8. 4 J mol ) l ( 6 / ) / J mol 6 C 6. a, p f b, p f, 5.47 p f 問 a, a x bezee.8 問 l ΔH vap /R J mol J mol.4 J mol J mol l /a H vap 5.4 J mol H vap.4 J mol / 問問 4 演習問題の解答例

22 浸透圧ショック法 6. Π Π μ μ μ x NaCl 6 7 C m solute m 5. 9 mol g.855 g mol m a w m solute M solute W solvet 5.9 mol g.4 g mol 5. g 864 g b w m solute M solute W solvet 5.9 mol g 6.68 g mol 5. g 67 g x w/v NaCl. 9 (w/v) x (w/v) g mol 8. g mol x C g dm. 9 dm m J 5 Π R a 794 ha 7.8 atm g mol mol 6.55 Π R R/M M R (. g dm ) ( dm m ) 8. 4 J mol Π 5.44 atm.5 a atm. 4 g mol 演習問題の解答例

23 6.8 μ, S μ L m m x, S, L µ µ + ( R l x ) d d, x, d x,s,l S d S d + Rd( l x ) ( ) Rd( l x ) fus S fus H d d ( ) m l X fus H d d( l x ) R m l fus H R / d(/ ) 6 / 99 J mol 8 4 J mol log X m X. 98 X.96, x x x m Δ m m m fus H fus H m fus H R m m R m Rm m M l( x ) x 8 g g B B α B α B B α i i α ファントホッフ係数 Π i R i α i α 第 7 章 7.6 ΔG ΔG, ΔG 4 ΔG 5 ΔG 6 ΔG 7 ΔG NDH ND aq H O l hν NDH aq O g H aq ν ΔG 演習問題の解答例

24 μ Δ f G Δ r G / Δ f G H g / Δ f G N g Δ f G NH g 6.45 J mol 6.45 J mol 7.9 G r exp R exp 645 J mol 8.45 J. mol 98.5 NH g H g N g Δ r G Δ r G.9 J mol NH N mol G G, exp exp ex R r r R p rg ( ). 7 R Δ r S Δ r H Δ r G Δ r H Δ r G NH 4 NO G r exp R 6 7 J mol exp 5 (8.45 J mol ) (98.5 ). f G6 F6 + F6 F6 G6 + + F6. 5 ( +. 5). G6 F6 G Δ r G Δ r G 7.4 Δ r G / Δ r H 7.5 Δ r H Δ r G v Δ r G v 7.4 l / Δ r H 7.4 l / Δ r U 98 l p vs. / / / / / Δ l p l r H R 8. 4 J mol / ( ) 8 / 46. J mol. Δ r H Δ f H NH g / Δ f H N g / Δ f H H g Δ f H NH g 46. J mol 98 l Δ r G R l 8.4 J mol J mol 5. Δ r G Δ f G NH g 6.45 J mol 4 演習問題の解答例

25 7. Δ r G Δ r H r H rg [ 46. ( 6. 4)] J mol rs J mol rs S NH ( g) ( / ) S N ( g) + ( / ) S H ( g) ( )) J mol. C C [( / ) C + ( / ) C ] ( / ( / )) J mol r NH N H. 75 J mol r H 5 r H 97 + [( 5 97) ] rc 46. J mol.. /. / J mol J mol / J mol Δ r H 5 5 J mol ( ) rg r H rs J mol J mol J / J J mol exp R l 695 J mol ( 8.4 J mol ) ( 98 ). 5 Δ r H 7.4 l H r R H exp r R.4 ( J mol ) exp ( 8. 4 J mol. ) 8 98 Δ r S S Δ r S 7.5 ( ) rg r H rs J mol 8 46 J mol J / J 68. J mol R l 68 J mol exp (. ) ( 8 4 J mol 8 ) m Δ r G Δ r G 6.mR 9.5 J mol J mol 98.5 / J/J.5 J mol 演習問題の解答例 5

26 ph ph 7 H Δ r G J mol Δ r G 高エネルギーリン酸結合 high-eergy phosphate bod 7.6 ν ν B B ν ν Q Q ν X X X, ξ, ν ξ B B, ν B ξ, ν ξ Q Q, ν Q ξ d ν dξ d B ν B dξ d ν dξ d Q ν Q dξ dg, ν μ ν Q μ Q ν μ ν B μ B dξ µ G X 7.8 dg rg ν µ ν Qµ Q ν µ ν Bµ B dξ +, X,, ( i X ) ξ G d rg ( + ξ dξ ξ ν µ ν Q µ Q ν µ ν Bµ B ) >,, ξ i, rg Δ r G ξ ( ξ, rg ) ( ξ, rg ) ( ξ, ) ( G, ξ ) ξ, G (, rg ) ( ξ, ) (, ) (, ξ ) (, r ) rg (, ) rg rg, rg ξ ξ, r G G H S Δ r G rg r H H ξ, ξ, ξ H ξ, G, r rg ξ, r G > H/ ξ > ξ, ξ >, rg H/ ξ ξ <, rg ξ, rg Δ r G 6 演習問題の解答例

27 ξ ( ξ, rg ) ( ξ, rg ) ( ξ, ) ( G, ξ ) ξ, G (, rg ) ( ξ, ) (, ) (, ξ ) (, r ) rg (, ) rg rg, rg ξ ξ, r G rg r ξ ξ rg ξ r, G, r, ξ, r G > Δ r ξ, ξ <, rg Δ r ξ >, rg 第 8 章 p HClO a 4 p HCl a p H a O HCl H O Cl H O HClO 4 H O ClO 4 H O H O OH H O H OH H O + q r H H f ( HO( l )) H f ( H ( aq )) H f ( OH ( aq )) [ J mol ( 9. 99)] J mol J mol H O /H O H O/OH ph CH COOH/CH COO H O/OH ph Δ r S Δ r H Δ r G / J mol J J / J mol q Δ r H Δ r H ΔH f H O l ΔH f H aq ΔH f OH aq J mol J mol H aq OH aq Δ r H J mol 7.4 ph CH COOH 4 HCl, HClO BOH, / H, 演習問題の解答例 7

28 log w ( ) H. R 5584 J mol w 5 C J mol 98 ( 5 ) + ( 96. ) p p C w w C p W C p W.5 ph p W / C ph α H α H α a a + a + H H ( α ) a ( α ) H H ( / ) α 5 α a /. 75 /.. ph log H / log..9 α α x a 8. x x x ± x x mol dm. mol dm H,. mol dm B,.5 mol dm B, ph p a + log log H, 8.8 γ B, ph pa + p a + + log logγ log H, 5. I z z ( B ) B ( ) (. 5 mol dm + ( ). 5 mol dm ). 5 mol dm 5.4 log γ / / B, H, ( z ) I (. mol dm ) mol + I / m +. 5 / dm. 9 ph.9 第 9 章 C C CH CH OH COOH C,, CH COCOOH C,, H 8 演習問題の解答例

29 9.8 Δ r G O Δ f G H O Δ f G O 4Δ f G H + Δ f G H O 7. J mol J mol E O rg O J mol F C mol. H /H Δ f G H E ell E O E H.. O /H O H /H ph 9.9 ph Ce I aq Fe II aq Ce III aq Fe III aq E Fe III / II 5 m E Fe R Fe(III) R Fe(III) E Fe + l EFe +. log F Fe(II) F Fe(II) (. mol dm ) (.5 dm ) (. 59 ) log mol dm. dm. mol dm m E Fe.77 E Fe (. ).5 dm. 74. m Fe II Ce I, Fe III Ce III E E Fe Ce III / I E Ce Ce E + R F l Ce(I) Ce(III) Fe Ce Fe Ce E E + E E + E + R F l Ce(III) Ce(I) Fe(II) Ce(III) Fe E + E Ce E E Fe + E Ce ( ). 9 E. m Ce I / III Ce Ce E + R F l Ce(I) Ce(III).6 + (. 59 ) log (. mol dm ) (. dm ) (. mol dm ) (. dm ) (. mol dm ) (. dm ). 59 Fe III / II Ce I / III.8.6 E Ce E/ vs. SHE.4..8 E Fe E Fe E Fe / /m 演習問題の解答例 9

30 9. L a Cu 5.9 E L R E L + l F Cu + / a Cu log(.). 78 R E R E + l ( F / ) og (./.) l + + R R Fe Fe L R Fe Cu Fe Cu r r,r r,l ( R L ) ( C ) [( ) ] G G G F E E mol / J mol L R L R E ell E ell E L E R Δ r G FΔE F E R E L C mol J mol exp G R r exp 8748 J mol ( 8. 4 J mol ) ( 98 ) aode aio athode atio Fe CN 6 Fe CN 4 6 Ru NH 6 Ru NH 6 al J al h al al J 問 6 6 W h mi s 6 6 mi s 4 問問 6 W. 6 mol s. C mol J s J s d mol J g x J g. 4 g 8 mol x. 64 g d 9. Δ r G FE Cell d rg d d ell rs F E E ell d F Δ r S E ell Δ r G d ell r H rg + rs FE ell + F E Δ r H d 演習問題の解答例

31 ND aq H aq e NDH E ND. r G ND FE ND ( C mol ) (. ) / 6. 7 J mol aq H aq e aq E S. r G S FE S ( C mol ) (. )/ 8. 6 J mol rg r G ND r G S J mol ( ). J mol, H ph m r G ND,pH r G ND R l( a + H / 7 ) r G ND +. R( ph 7) m G G R a + 7 l( / ) G +. R( ph 7) r ND,pH r ND H r ph G G G G r r ND,pH r S,pH r ND ND r G S +. R( m m )( ph 7). J mol. 8.4 J mol 98.5 ph 7 ph. ph 問 b r G FE J J rg r G a + r G b F E a E b ) mol (. +. J 5 J mol Δ r G 問 4 G /( G + G (( J mol )/(( ) J mol )). 6 問 5.. Δ r G J mol 8 J mol Δ r H J mol 9 J mol Δ r G 8 J mol Δ r H 問 4 uoupler protei, UC φ R F a l a + H,out + H, i a H,i R a + H,pH4 R φ φph4 φph7 l. a + H,pH4 l F a + H, ph7 F a + H, ph7 ( 8. 4 J mol ) ( 9. 5 ). ( ) C mol 演習問題の解答例

32 第章.4.5 r N S w surfae. 6 ( ) γ wsurfae NS r N m. m m dm γ γ γ 4π ( 4π ) / r r 6. 5 m ρ w w h mg ρg. g m J surfae surfae J ( g g ) (. m ) ( 9. 8 m s ) m. S S B S S, B θ θ B, B, B μ μ R l / μ B μ B R l B / μ S μ S R l θ θ B μ S μ S R l θ μ BS μ BS R l θ B μ μ S μ S μ S μ μ S R l B R [l θ l / l θ θ B B B θ ( θ θ B )( / ) B B B B B θ B ( θ θ B )( B / 4 ) 4 θ θ B B BBB 5 5 θ B B / θ + + B B B / B / BBB / θ B + + B B B / B /.6 問 S U S S U / 問 / / / / / / / 演習問題の解答例

33 ( / ) ( / ) + + U U 問 ( / ) U it / U it / it U it E it 問 4 µ it it θ it N N N θ znsωθ zn ωθ N i,, j i,,, { i } i. + S, i i,, i j i + G µ ii µ ii µ G i i i i,, i j i,, j i µ i i,, i + µ ii i j i 第章.7.8.7, B, v, B, v B. s τ τ / l τ s.69 s. s log v /mol dm s.5. B,. mmol dm..9,. mmol dm log, /mmol dm log B, /mmol dm heo.9.6 log(, / ) log 4 t τ/ ( 57 a) 46 a log log t ( a) τ / / (8.79 a) β 9 4 Zr 9 8 Sr N. dn N N N exp( t ) dt 演習問題の解答例

34 N.4 τ / N τ ( 65 4 / dn N dt dn l dt (.7 moleule s ). a 6 6) s a moleule mol τ.999. τ.999 l /. τ / l τ.999 l /. τ / /l l τ / /l 9.97τ /.9 log N/N t/g log g t log /log N/N 8 6 mi log /log 8 / 4 6. mi di/dl I di / I dl l I/I l log I /I ε /. I I l, B, v,. B, B, H O aq Br aq BrO aq H O l H O aq BrO aq H O l O g Br aq l t. 9.9 d τ / 4 d 5. 9 d t/d l H + B + BH + + H d + dt H B + H B BH H + BH + H.9 d H B v H dt + + BH H DN D D / τ / τ / 4 演習問題の解答例

35 第章.9.49 J J Ea, Ea, R l 8.4 mol 76 mol J J mol J ( ) l E R a l / 8. 4 J mol ( 77 ) ( 98 ) l J J J mol.5 a E exp R J J mol J exp 4 J mol / exp E a, /R / exp E a, /R / exp E a, /R ( ) ( ) + ( ) l / l / l / l / E E + E l exp R a, a, a, E a E a, E a, E a, B I E a,, B, I B, ( ) I / ( ) / B, I E a, C M / S.6 exp 8. 4 J mol 6 J mol J J mi. t t 9. mi l ( / ) G (, ) R R E a, E a, E a, Ea, Ea, I Ea, B C Ea, Ea, I I 演習問題の解答例 5

36 l ( ) R J mol R l / ( 8. 4 ) 98 l atm 5 a atm [ ] 6 ( m m ) m mol.5 log B / C.8 log a C.8 log w.8 log b NH NO B NH NO BH N O H O OH N H N O O.6 log / C.46 log a CH CH OH OH H CH CH O H OH H O CH C H O log / I / mol g z z B. z zb I (. g mol ).4 / /. mol g 4.8 κ α H κ Λ Λ α λ H λ α λ H α λ H H Λ Λ λ. 4.6, λ H λ α H H H.59a Δ H E a R 5 J mol 8.4 J mol 67.5 / 9 J mol.5 Ea / / exp R. 4dm mol s dm mol s 5. 5 J mol exp ( 8. 4 J mol ) ( ) 演習問題の解答例

37 S h R B l ( 8. 4 J mol ) l J mol Δ S.6 E a 4 (. s ) ( J s) (.8 J ) ( ) R J mol l (. ) mi 8 4 l 6. 7 mi J mol 7. J mol. s.5 ( 6 ) 5. 7 J mol exp ( 8. 4 J mol ) ( 4. 5 ) E ( ) R. 7 mi / 6 mi s a / exp s λ /ν m s / 9.8 s. 5 m.4.5 Δ H E a R 7. J mol 8.4 J mol 4.5 / 4.5 J mol E a Δ H.54 κ.54 S h R J mol B l J mol l Δ S l v / v Ea R θ l v/m h / ( 9. 8 s ) ( J s) (. 8 J ) ( 4. 5 ) 6.6 E a /R E a E a J mol 5.4 J mol l v/m h / 演習問題の解答例 7

38 . H ρ,, ρ,, log log σ σ log, j ρ, σ j C log j / log, j ρ, σ j C biliear model σ j + + log j ρ, σ j C log ρ, ρ, σj C C.4 σ j log C Bσ j D 4 ρ, B ρ, ρ, C C C D C 4 ρ, ρ, 7 問 i D E ell E E D Δ r G FE ell C mol.6 /.59 J mol.9 obs DD DD rg exp R J mol ( dm mol s ) ( 4. 6 dm mol s ) exp 8. 4 J mol dm mol s Δ r G.59 J mol obs 5. 4 dm mol s ii i E ell Δ r G FE ell C mol.5 / 8.68 J mol obs DD rg exp R. 5 dm mol s ( dm mol s ) exp 4. 8 dm mol s J mol ( 8. 4 J mol ) ( ) ii 55 Δ r G obs obs 5.46 dm mol s 問.9 8 演習問題の解答例

39 DD obs obs rg exp R obs (. 6 dm mol s ) ( C mol ) dm mol s exp (. 5 ) dm mol s FE exp R ell [(.6. 4) ] 8. 4 J mol 第章.7 / M E,. 5 6 l. mol dm. mol dm 4 8 ( ). mol dm. s / M.6 6 dm mol s s. 4 mol dm M / s M.5 4 mol dm v d S t max d + / M d S M / S max dt S M S S max S S d d / dt S, S, ( S, S ) + M l S, S S max t t S t t.6 S ES / E, t t 44 s S M ES / E, /mol dm M t/s CES/C E, 4 4. s +. 4 s M 7 5. dm mol s mol dm / exp E a, /R / exp E a, /R / exp E a, /R ES S E ES E M / S v / M S E, E, S E ES ES E 演習問題の解答例 9

40 M / S ES / E S / M ES B ES E E a, B E a, E a, E a, E a, E a,, E a, ES E a, S E ES S E E E...7 v max /s.48. M /mol dm.58.7 v I max /s.8.9 M / mol dm.5.6 M max.4 問.7 v 5 s. mol dm E, + / mol dm / 5. mol dm. 7 6 mol dm s M, ( ) 8 ( ) 問.6 v or v I /s v v I S /mmol dm v,i / v I + I I E, I + + M, / + v I,I I M, / v / + v 5.,I M, / v E, + / M, M, ( / ) / / M, + M, / I + + M, / ( mol dm ) (. mol dm ) / ( 5. mol dm ) / I 6 ( mol dm ) ( mol dm ). 4 mol dm 問 M v / M E, S 4 演習問題の解答例

41 v v B /, M, E, /,B M,B E, B (, / M, ) / ( ) ( s ) 6 /. mol d (,B M,B ) 5 m 6 s /. mol dm substrate ihibitio S. I S E,t v M + + S S SI..4 + E E + F B + F FB 4 Q + E 4 4 E ae 4 E, e ea f fb 4 dea/dt e ea df/dt ea fb B f dfb/dt B f 4 fb v 4 fb 5 4 f { 4 / }/ B fb ea 4 fb ea 4 / f b 7 e { / }/ f b { / }/ 4 / f b 6, 7, E, + / f b B M 4 + M B,, B M, + M B 参考. 演習問題の解答例 4

42 .4. + E E B + E EB EB( EQ) 4 EQ E + Q EQ E, e ea eab eq de/dt ea 4 eq e deab/dt B ea eab deq/dt eab 4 eq 4 v 4 eq eab 4 / eq 6 6 ea / B eab 4 / B eq 7 7 e / ea 4 / eq { 4 }/ }/ B eq 4 / eq 8 6, 7, 8 E, + / eq B B B M + ( 4 ) M B B 9 + ( + ) 4 ( + 4 ) I 問 ES 問 log max ph 問 p a 問 4 ES His His9 問 5 ES His9 His guplot. /v / / v/mmol dm s / /mmol dm B /s 6 7 B/dm mmol s 4 B max /B δmax δb δb / B d(/ ) B.5 mmol d 4.7 max 7..5 mmol dm s M /B B δm δ y δ y B ( / ) + B B δ + δb B B 4.7 M mmol dm.75 mmol dm 4 演習問題の解答例

43 .7 v v/mmol dm s C /mmol dm / D /mmol dm C/s 8..5 D/mmol dm 6 max C 8..5 s M D 6 mmol dm S v /v δ( / v ) δv δv / v d(/ ) v d δv/mmol dm s.4 /s 7 8 B/dm mmol s.4.7 max 8..5 s M mmol dm / v/mmol dm s / S /mmol dm v/mmol dm s S /mmol dm 第 4 章 J 9.5 B ξ D. m s 4. r ξ. 9 g s 6πη m ( a s) 9 g s m r 4. J 4.47 D Ru 8. ( ) 8. 9 mol z F C mol m s. 6 9 λ z Fu C m. mol s. C m 599. m 599 s mol mol. 6 m S mol m s J g m s C C z F B r mol 6πηD 6πηuN g m m s s... m. Å mol 演習問題の解答例 4

44 κ κ κ Λ Λ λ + λ g Cl S m ( ) S m mol 6 m dm 9. mol dm κ ell κcl RCl (. 69 s m ) ( 4. 6 Ω) ( m m ) Λ R R. mol dm dm m 98 Ω S m mol a Λ ( / ) ( S m mol Λ ( Λ Λ ) 4. ).,, ( 9. 7 S m mol ) ( ) S m mol CO CO H HCO κ H λ H HCO λ HCO κ H λ H λ HCO ( ) H HCO / H / / H H κ λ λ CO CO CO ( ) H ( ) CO [ 7. 9 S m / S m mol m dm mol dm atm orr/76 orr atm 4. mol dm 4.47 D D + Cl Rλ ( J mol ) ( ) 7. 5 z F C mol. 958 m s m s 4 ( S m mol ) ( mol ) 4 Rλ Cl J mol.. S m z F C mol 9. m s. 5 m s D Cl D + D Cl m s. 995 D + + D Cl 5 5 m s a ω x πν x 4π 6 mi / 6 s mi.65 m.56 6 m s.56 6 m s g/ 9.8 m s.6 5 g 4.79 M Rs Rs Dφ D vρ 8. 4 J mol ( 9.5 ) ( 8.6 s) s (.5 m s ) (. 6 m g ) (. g m ) 6. 4 g mol. 4 g mol 4.79 M rm r Rs Rs DN Dφ D vρ 4. 6 g mol. 5 s ( ) 8. 4 J mol s 6. m s m (. 69 g ) (. g m ) 44 演習問題の解答例

45 4.8 m E q v v ph ph pi 4.8 v/µm s.6.4 pi ph 4. 問 l x / t d l x / dt 8. 4 mi ( x ) 4 d l 8. mi 6 s mi / s ( πν ) dt. 4 5 mi. 95 s 9. 5 S l x / /m t/mi ( W ) mφ m vρ 問 s ξ 6πη r W s,w (,W ) m vρ 6πη r,w 4. s,w η s η W,W ( vρ,w ) vρ ( W ) (. m g ) (. 998 g m ). 4 ma s 556 問 s,w ( 9. 5 S). ma s (. 556 m g ). 4 g m. 4 S DEE ph CM ph 演習問題の解答例 45

46 ph ph ph ph ph ph 46 演習問題の解答例

D = [a, b] [c, d] D ij P ij (ξ ij, η ij ) f S(f,, {P ij }) S(f,, {P ij }) = = k m i=1 j=1 m n f(ξ ij, η ij )(x i x i 1 )(y j y j 1 ) = i=1 j

D = [a, b] [c, d] D ij P ij (ξ ij, η ij ) f S(f,, {P ij }) S(f,, {P ij }) = = k m i=1 j=1 m n f(ξ ij, η ij )(x i x i 1 )(y j y j 1 ) = i=1 j 6 6.. [, b] [, d] ij P ij ξ ij, η ij f Sf,, {P ij } Sf,, {P ij } k m i j m fξ ij, η ij i i j j i j i m i j k i i j j m i i j j k i i j j kb d {P ij } lim Sf,, {P ij} kb d f, k [, b] [, d] f, d kb d 6..