2011 /21

3

B

1

:

http://www.tagen.tohoku.ac.jp/labo/ueda/index-j.htmlWeb

12

1 dU(dQ)

(dW) dU = dQ dW

2

U:

F=U-TS:

H=U+pV:

G=H-TS:

: p, T, V, S

0 F F()

0 G G

dU = TdS pdV S, V)

dH = TdS + Vdp p, S )

dF = SdT pdV T, V)

dG = SdT + Vdp p, T ) pT TV

pS

=

VT Tp

VS

=

Sp pT

SV

=

SV VT

Sp

=

i

i

iii

nG

dnVdpSdTdG

=

++=

),,(),,( ii nTpGnTpG =

ii i

ii nn

nTpGnTpG

= )(

),,(),,(

(ni) iT, p, ni

ii

ii nnTpG = ),,(

G

(G/n)

+=

++=

+=

++=

iii

iii

iii

iii

dnpdVTdSdU

dnVdpTdSdH

dnpdVSdTdF

dnVdpSdTdG

ijijijij nVSinpSinVTinpTii n

UnH

nF

nG

=

=

=

=,,,,,,,,

dni = 0

ni

dndn

dnnGdn

nGnnTpdG

21

22

11

21

)(

),,,(

+=

+

=

122 G=G1 +G2 p, T dn

n1dn

p1 T1 p2 T2

1 =2 :

dn)( 12 =n2

= 0

p1 =p2 , T1 =T2

pRTV

pm

T

==

( ) ( )

===

1

212 ln,,

2

1 ppRT

pdpRTpTpT

p

p

p0(=1bar) 0

( ) ( ) ( )00 /ln, ppRTTpT +=

n1 ,T,p

V1 (T,p)

n2 ,T,p

V2 (T,p)

T,p1 ,p2 (p=p1 +p2 )

V(T,p)

( = G/n)

)lnln(lnln 22112211 xxxxnRTppRTn

ppRTnGmix +=

+

=

( ) ( )( ) ( ) ( )( )00220011 /ln/ln ppRTTnppRTTnGi +++= Gi

( ) ( )( ) ( ) ( )( )0202201011 /ln/ln ppRTTnppRTTnG f +++= G

p1 , p2

mix G

n=n1 +n2 xi =ni /n

p=p1 +p2 :

0= mixH

)lnln( 2211,, 1

xxxxnRTGS

nnp

mixmix +=

=

mix S

mix H

G=H-TS

Smix >0 :

mix V G p

0= mixV

( ) ( ) ( )221100110011 lnln)/ln()()/ln()( xnxnRTppRTTnppRTTnGGG mixif

+++++=+=

100

1

1

22

1

111

001

,,11

ln)/ln()(

lnlnln)/ln()(22

2

xRTppRTT

nxn

nxnRTxRTppRTT

nG

nn

npT

f

++=

+

+++=

=

)/ln()(),( 00* ppRTTpT ii +

Gf

iii xRTpT ln),(* +=

i* i

* asterisk

iii xRTpT ln),(* +=

)lnln( 2211 xxxxnRTGmix +=

)lnln( 2211 xxxxnRSmix +=

i*

0= mixH 0= mixV

(Raoult)

(Raoult)

`ln),( ln),(

)()*()(

)()*()(

li

li

li

gi

gi

gi

xRTpTxRTpT

+=+=

=

RTpTpTxx

gi

lil

ig

i),(),(exp

)*()*()()(

)(* liii xpp =

T, p(1,2) i

(g)=i(l)

pi pi =xi(g)p

xi(g)=xi(l)=1

p=pi*

exp[]=1

==

RTpTpTpxp

gi

lil

ii),(),(exp

)*()*()(

ii

1

1(g), 2(g)

1(l), 2(l)

p1 , p2 (p1 +p2 =p)

2

CS2

)(* liii xpp =

x11, x2 0: 1

p2 = k2 x2

(Henry)

CS2 (CH3 O)2 CH2

iaRTpT ln),(*11 +=

*1

01

*1 ln)( pRTT +=

*11

*11 /ln ppRT+=

ai

ai =xi

(x1 =1)x1

p1*, p1

p0=1bar

1011 ln)( pRTT +=

a1 =p1 /p1*

2*2

*2

*22

*22 ln/ln/ln xRTpKRTppRT ++=+=

*2

*2

02 /ln pKRT+

2022 ln xRT+=

a

: p2 =Kx2

2022 ln aRT+=

b

: x2 a2

a2 =p2 /K

p

)(1

*11

lxpp =

*11

*121

*1 )1( pxpxppp ===

x1 a1

p-T

2TH

TG

T p=

pTGTGH

=

( ) 221 1lnln xxx =

),(ln),( )*(11)*(

1 pTxRTpTgl =+

RTGGx

lmgm )(1

)(1

1ln

=

1(l)1*(g)

22

)(1

)(11ln

RTH

RTHH

Tx mvaplmgm

p

=

=

2*20 2211'

*

2

b

bm

vap

bb

mvap

T

T

mvapx

TT

RH

TTRH

RTH

xxb

b

=

=

x2 +x1 =1, x2 ~0 x1 ~1

Tb =Tb -Tb *

:mvap H

Tb ~T*b

1(l)1*(s)

),(ln),( )*(11)*(

1 pTxRTpTsl =+

22

)(1

)(11ln

RTH

RTHH

Tx mfuslmsm

p

=

=

:mfus H

2*20 2211'

*

2

m

mm

fus

mm

mfus

T

mfusx

TT

RH

TTRH

RTH

xxmT

m

=

=

-Tm =Tm *-Tm

Tm ~T*m

1000100012

21

2

11

22

Mm

mM

mnn

nx +

=+

=

221

2

1000mKmM

HRTT bpmvap

bb =

=

m2 1kgM1 (g/mol)x2

221

2

1000mKmM

HRTT fpmfus

mm =

=

m2

Kbp :

Kfp :

1.

2.

3. 1

4. 1

5. 22

6. 2

7.

8.

9.

10.

11.

12.

13.

14.

15.

1.

25, 1atm 2.00mol 3.00mol Gmix =RT(n1 ln(x1 )+n2 ln(x2 ))

2.

1000.05 KNO3

99.95kPa 1atm=101.325kPa

3.

100g2.8g 2.00K kg/mol Kfp20.0 K kg/mol

m2

1kg

2mKT fpm =

ln2=0.69315, ln3=1.0986, ln5=1.6094

1

Gmix =8.314(J/molK)298.15(K) {2ln(2/5)+3ln(3/5)}(mol)=-8.341 kJ

Smix =-8.314(J/molK) {2ln(2/5)+3ln(3/5)}(mol)=28.0(J/K)

2 a = 99.95 (kPa)/101.325 (kPa)=0.9864

3 m m = 2.00/20.0=0.100 (mol/kg)

M

)/(2801.0

8.2)(1.0

1)/(

)(8.2

molgm

M

kgmolgMgm

=

=

=

M = 0.28 (kg/mol)

12(Raoult)