第3回分(10/17)PDF

¤¢£¦¡£¢¡£©
7A7f7
ÿ)rø2014.10.17ù
wý^ÉHm
f7¬ö¬7HÈ
²fÉÖ¬ö
Q ('fù
™˜z
HgŒ
lLgŒ
ν A A + ν BB
ν CC + ν DD
− Q (pfù
£
¤¢£¦¡£¢¡£©
Hf
lLgŒ
Üçòßöóîò
ν CC + ν DD
Q ('fù
HgŒ
ν A A + ν BB
− Q (pfù
lLgŒ
ν CC + ν DD
Δ = øS}qÇhKālLzùöøSÉhKāHzù
Hf
:;uÉÄÉH
Q = ΔU
:;Hf Δ U ĂølLgŒÉ“ÜçòßöɁ(ù ¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬öøHgŒÉ“ÜçòßöɁ(ù
(
ΔU = ν CU m, C + ν DU m, D
)
product
(
− ν AU m, A + ν BU m, B
)
react
1 mol EÁÖɓÜçòßö
:,ÉÄÉH
Q = ΔH
:,Hf Δ H ĂølLgŒÉÜõâòéöɁ(ù ¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬öøHgŒÉÜõâòéöɁ(ù
(
ΔH = ν C H m, C + ν D H m, D
)
product
(
− ν A H m, A + ν B H m, B
pfH¬ā¬ΔU ÏÁÊΔHʋ
)
react
1 mol EÁÖÉÜõâòéö
'fH¬ā¬ΔU ÏÁÊΔHÊY
¤
¤¢£¦¡£¢¡£©
:;HfÅ:,Hfɚ
:;Hf ΔU
ΔH = ΔU + PΔV
:,Hf ΔH
HFÉ;u1
ν A A + ν BB
(
ΔV = ν CVm, C + ν DVm, D
ν CC + ν DD
)
product
(
− ν AVm, A + ν BVm, B
)
react
1 mol EÁÖÉ;u
HgŒûlLgŒÃµkJZŎĶ×ÉÇÕËû
RT
RT
ΔV = ⎡(ν C + ν D ) product − (ν A + ν B )react ⎤ ×
= Δν ×
⎣
⎦ P
P
ΔH = ΔU + PΔV = ΔU + Δν RT
HfɈy
(
Δ r H = ν C H m, C + ν D H m, D
)
product
(
− ν A H m, A + ν B H m, B
)
react
#gŒÉðòÜõâòéöµÙ´ØˈyĶ×
€<µQ÷
-chKډ:»Ãû¿ÉhKÄÉÜõâòéöÚüŽ×
Üõâòéö
|ø-chKā 1 bar, 25˚Cù
Δ f H (react)
!
Δ f H ( product)
!
WclLÜõâòéö
Hg
Δr H
!
lLg
Δ r H ! = (ν C Δ f H !C + ν D Δ f H ! D ) product − (ν A Δ f H ! A + ν B Δ f H ! B )react
¥
¤¢£¦¡£¢¡£©
HfɈy
íáÉ^
f7PtDÉNˆy
CH4 + 2O2 → CO2 + 2H2O
C + 2H2
CH4
CO2 + 2H2O
ÞòèïäêÉ^
HÜõâòéöÉbC5I
f7wþ^
wý^āÜçòßö1MɆÙØ×ÃɒtÄÜçòßöÊ5ºØ× ¬¬¬¬¬¬6vzɓÜçòßöÊ1»Ç± ¬¬¬¬¬¬øÜçòßöɕȚ½×^ù
6vz
Of0
„pq
×
„pq
–@ýā100˚C
–@þā20˚C
–@ýā60˚C
–@þā60˚C
„ejŠÉP&Ú]Ñ×Ô²Ç^µ°×
¦
¤¢£¦¡£¢¡£©
Üõåôéö
wý^ÈÔØËû6vzɓÜçòßöÊ:
6vzÉzÅ2nÍÉÜçòßöɔP^ÊdNÈ°×
d›É”É~Ð$Ù¾ÉÄûÆص„pqÇ1
Ä°×´Ú:½×ÁÑÉhKšN
Üõåôéö¬Ą
f7wþ^
6vzč¹×½ÎÃɄpqÇ1Êû6vzÉÜõåôéöµ/3½×
P&øΔS > 0ùÈÉБ†»ûÜõåôéöU3øΔS = 0ùÄB‡hKÅÇ×­
¹¹ÄûΔS = ΔSzúΔS2nûÄ°×­
Üõåôéö S ÊûXDÄ:ƒºØ×hK•Ä°×­
dS =
dQrev
T
"qÈÖ½×f•
ΔS = ΔSzúΔS2n = 0
"’tÏÁÊB‡
ΔS = ΔSzúΔS2n > 0
"’tÏÁʄp1
ÜõåôéöÊÏÁzɜºÉ?C
SøZùăSø_ùăSø+ù
SøžbùăSøbù
§
¤¢£¦¡£¢¡£©
Üõåôéö/3
z2É2nø20˚Cù
z2É2nø20˚Cù
6vzā89
Q
„pq
zāÝäìÈÂÁàöèöø20˚Cù
zāÝäìÈÂÁàöèöø90˚Cù
ΔS = ΔSzúΔS2n > 0
bCµ½×¬ΔSz < 0
fÚ!¸
׬ΔS2n > 0
B‡É-c
wý^Åwþ^É$D
wþ^
wý^
dU = dQ + dW
dW = −PdV
dQ = TdS
dQ < TdS
dU = TdS − PdV
dU < TdS − PdV
"’tÏÁÊB‡
"’tÏÁʄp1
"’tÏÁÊB‡
"’tÏÁʄp1
¨
¤¢£¦¡£¢¡£©
:bû:,TÉB‡É-c øGibbs Üçòßöù
dU − TdS + PdV = 0
"’tÏÁÊB‡
dU − TdS + PdV < 0
"’tÏÁʄp1
:bû:,TÄÊûTdS = d (TS ) ,
PdV = d ( PV )
dU − TdS + PdV = dU − d (TS ) + d ( PV ) = d (U − TS + PV ) = 0
dU − TdS + PdV = dU − d (TS ) + d ( PV ) = d (U − TS + PV ) < 0
H = U + PV ÔÖ
d ( H − TS ) = 0
T, Pā:ûB‡
d ( H − TS ) < 0
T, Pā:û„p1
Gibbs Üçòßö G = H − TS
( dG )T , P = 0
( dG )T , P < 0
"’tÏÁÊB‡
"’tÏÁʄp1
:bû:,TÉB‡É-c øGibbs Üçòßöù
:bû:,TÄÉhK1Ê Gibbs Üçòßöµa>
½×P&ȍ¹ÖûGibbs ÜçòßöU=ÉŶB‡ÅÇ×
Gøzù
„pq
„pq
Zs
_s
Gøzù = GøZsùú Gø_sù
Z_B‡hK …pɑ†C$±
©
¤¢£¦¡£¢¡£©
{gŒÉZ_B‡
Zs
_s
Gm, g [ J mol]
…ZÉðò Gibbs Üçòßö
ng [ mol]
…ZÉðòN
Gm, l [ J mol]
nl [ mol]
_Éðò Gibbs Üçòßö
_ÉðòN
zÉ Gibbs ÜçòßöÚ G Ž×Å
G = nl Gm, l + ngGm, g
™˜zÄ°×´Õ
nl + ng = nT ( const )
G½×Å
dG = Gm, l dnl + Gm, g dng
:b:,ÇÕ Gibbs ÜçòßöÊ:
dnl + dng = 0 ∴dnl = −dng
{gŒÉZ_B‡
B‡ÄÊûdG = 0 Ä°×´Õû
(
)
(
)
dG = Gm, l dnl + Gm, g dng = Gm, l −dng + Gm, g dng = Gm, g − Gm, l dng = 0
dng ≠ 0 Ä°×´ÕûB‡Ä°×ÁÑÈÊû
Gm, g = Gm, l
{gŒÉþsµB‡hKÄ5½×ÁÑÈÊû¿ØÀØÉsÉ
ðò Gibbs Üçòßöµx»·Ç¸ØËÇÕDZ
ª
¤¢£¦¡£¢¡£©
:bû:;TÉB‡É-c øHelmholtz Üçòßöù
:bû:;TÄÊû TdS = d (TS ) ,
PdV = 0
dU − TdS + PdV = dU − d (TS ) = d (U − TS ) = 0
dU − TdS + PdV = dU − d (TS ) = d (U − TS ) < 0
d (U − TS ) = 0
T, Vā:ûB‡
d (U − TS ) < 0
T, Vā:û„p1
Helmholtz Üçòßö
A = U − TS
( dA )T , V = 0
( dA )T , V < 0
"’tÏÁÊB‡
"’tÏÁʄp1
:bû:;TÄÉhK1Ê Helmholtz Üçòßöµa>
½×P&ȍ¹ÖûHelmholtz ÜçòßöU=ÉŶB‡ÅÇ×
Gibbs ÜçòßöÚ]Ñ×*4
ýùgŒÉ7~LÅV
VL|µ%¼ÄÒû¿ÉRVÓ4VµoÇ×Å Gibbs ÜçòßöÊoÇ×
GøãÛñðõæù ≠ GøŸ—ù
Gøn – ëâõù ≠ Gøi – ëâõù
þùgŒÉhKøZû+û_û`$gù
Gø[…Zù ≠ Gø[ù ≠ Gø\ù
A
B
Gøzù = GA + GB
z
A + B
Gøzù ≠ GA + GB
ÿùbC
Āù,
«
¤¢£¦¡£¢¡£©
Gibbs ÜçòßöÉbC³ÔÌ,5I
G = H − TS
∴ dG = dH − TdS − SdT
H = U + PV
dH = dU + PdV + VdP
dU = dQ + dW = TdS − PdV
∴ dH = TdS + VdP
∴ dG = VdP − SdT
Gibbs ÜçòßöÉ,5I
bC:É.$ dT = 0 ÔÖ
dG = VdP
⎛ ∂G ⎞
∴⎜
=V
⎝ ∂P ⎟⎠ T
,1È<½×Gibbs Üçòßö1iÊ®u¯ÅÇ×
G
G
T ā:
V
V
P2
P2
P1
P1
ΔG = ∫ V dP = ∫
ΔG = V ( P2 − P1 )
RT
P
dP = RT ln 2
P1
P
,µ1½ØËuÒ1
P
P
,‚Iø+û_ùÉ.$
,‚IøZùÉ.$
£¢
¤¢£¦¡£¢¡£©
Gibbs ÜçòßöÉbC5I
,:É.$ dP = 0 ÔÖ dG = −SdT
⎛ ∂G ⎞
∴⎜
= −S
⎝ ∂T ⎟⎠ P
bC1È<½× Gibbs Üçòßö1iÊ®Üõåôéö¯ÅÇ×
G
-­‐S
ΔG = −S (T2 − T1 )
Üõåôéö:É.$
T
Gibbs ÜçòßöÉbC5I
⎛ ∂G ⎞
∴⎜
= −S
⎝ ∂T ⎟⎠ P
bC1È<½× Gibbs Üçòßö1iÊ®Üõåôéö¯ÅÇ×
G [ J/mol ]
Gm, g
P : 101.3 kPa
Gm, l
Gm, l
{gŒÉZ_B‡
Gm, g = Gm, l
Gm, g
B‡bCāTb
T [ K ]
££