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GT0, S


-


1 2

1 2 D

d

m r2 2

r2 2


ht

h

r2 2


H cS

H p .u

H dch

H dS

H cch


C

Q T2

T1

Q T

T = 110-50 = 60째C (60K) : 233 x 103 mol

(55,8g/mol) = 13,0.106 g (13,000 kg)

= = 0,45 J g-1 K-1

T 13,0 x 106 g

60K

= 351.106 J

S

Entropy

Q T


S

QTN T

QTN T

dS

S

S

QBTN T

QTN T


-

QTN T CdT

ds

QTN

T2

S

CP T1

dT T

T2

S

C T1

dT T


T2

S

CV T1

dT T

QT T

Q

HT T

ST

QT

S

ST

1 T

Q T

ST

V2 V1 V nR ln 2 V1

nRT ln

QT T

nR ln

P1 P2

0

0

T

S

ST

ST

ST

0

dT T

nCT T 0

R S

S1

R

ST

ST

S2

0

L ST

S3

S1

L S2

S4

H S3

S5

S4

H S5


0 S 298

S T0

S S

S SP

0 S 298

S PU

0 S 298 ( sp )

0 S 298 (tg )

S S

SO2 (k )

0 S 298

0 S 298 ( SO 3 )

1 O2 ( k ) 2

1 0 S 298 (O2 ) 2

0 S 298 ( SO2 )

S

S

S

S S S

S S

SO3 (k )

94,81JK

1

0

0


S

H mt T

S mt

S

H

T S

H T

0

0

H T

H

T S

0

S


GT0, S

0 G298

0 G298

G T

0 G298 ( sp )

S ( G) T

S P

0 G298 (tg )


G

H ( G T

T

T

( G) T T2

T

0 G298

G P

( G) T

T

G

P

H

P

G P

G T

P

T

G T

H T0

P

H T2

H T2

GT0

f (T )

V T

2

P2

dG 1

VdP P1 P2

GTp2

GTp1

VdP P1

GTp2

GTp1

V

V ( P2

RT P

P1 )

f (T )


P2 P1

GTp2

GTp1

RT ln

GT

GT0

RT ln P

( Hf0) ( S0)

C2H5OH(k) + 3O2(k)

2CO2(k) + 3H2O(k)

Hf0 (kJ/mol) C2H5OH(g)

-234

283

CO2(g)

-394

214

H2O(g)

-242

189

O2(g)

0

( H0)

a) H0 =

p

Hf0(

H0 = ((2 (-394)+(3

)-

r

Hf0(

(-242)) - ((1 (-234)+(3 0)) kJ /mol

H0 = (-1,514) - (-234) kJ/mol H0 = -1,280 kJ/mol –1,28 x

kJ /mol ( S0)

b) S0 =

S0 (J/mol K)

0 pS (

)-

0 rS (

)


S0 = ((2 214)+(3

189)) - ((1 283)+(3 205)) J/mol K

S0 = (995) - (898) J/mol K S0 = 97 J/mol K

0.097 kJ/mol K G0

c)

298K

G0 = H0 – T. S0 G0 = (-1,280 kJ/mol) - (298K)(0,097 kJ/mol K) G0 = (-1,280 kJ/mol) - (28,9 kJ/mol) G0 = -1,309 kJ/mol

-1.31 x 103 kJ/mol

d)

298K

( G0 <0 )

dG G n3

G T

dT P, N

dn3 T , P , nj 3

...

G P G ni

G n1

dP T ,N

dn1 T , P , nJ 1

dn j T , P , nj i

Gi

i

G ni

T , P , nj i

G n2

dn2 T , P , nJ 2


dG

VdP SdT

i

i

i

dni

W'

dni

dni

G P

T

0 T

P

T

V T

RT ln P

0 T

iT

Pi

Ni P

0 iT

RT ln( N i P)

i

i

(tg )

i i

(tg )

( sp ) i

( sp )

dni

0


KP KC

2 PNH 3

PN 2 PH32

2 C NH 3

C N 2 C H3 2

i

0 i

(T ) RT ln Pi


GT

GT0

RT ln

PDd PAa PBb

p

GT0

0 D

d

a

0 A

b

p

0 B

GT0

RT ln(

)

P cb

ln(

P ) cb

GT0 RT (

KP

(

P ) cb

PDd PAa PBb

cb

GT0 GT0

4,575 lg K P

GT GT

P

KP

RT ln

RT ln K P P

KP

RT ln

P

)

P cb


P

KP

P

KP

C Dd C Aa .C Bb

KC

cb

xi Kx

Kn

x Dd x Aa .x Bb

n Dd n Aa .n Bb

ni ni

ni

cb

cb

n

KP

K c .( RT )

n

K x .P

n

Kn

P ni

n

i

0 i

RT ln Pi

i

* i

RT ln xi

K P,x

(

)

P , x cb

cb


KP

( PCO2 ) cb

H

G0

T

lg K P T

G0 T

RT ln K P

P

H0 T2

H (0Cal ) P

4,576.T 2

H H

0

H d ln K P dT

H RT 2

0)


H

H

KP

K n Pcbn

KC

CO CO2

n

n

n

2


a) b)

25°C.

Keq

c) d) G0 = -R.T. ln(Keq ) -32,300 J mol-1 = -(8,31 J mol-1 K-1)

(25+273K)

ln(Keq)

13,0 = ln(Keq) Keq = 442 x 103 b) G0 = H0 – T. S0 G0 = -92,200 J mol-1 - (273 + 475)K

(-201 J mol-1 K-1)

G0 = 58,1 x 103 J mol-1 c) G0 = -R.T.ln(Keq ) 58,1 x 103 J mol-1 = -(8,31 J mol-1 K-1) -9,35 = ln(Keq) Keq = 8,70 x 10-5 d) Keq Keq

25°C: 442 x 103

475°C: 8,70 x 10-5

(475+273K)

ln(Keq)


A Qh

max

1

Tc Th


q

E

a(Ti T0 ) R

aT 4


max

( m)

2898 T ( 0K )


m

v


V

ma

A

(r

mb

(r

A

(r

A

v

t

v

t)a

A v * t )b

v )a

(r

r A V

A

v )b


-


Cm

Cm

CS QS

CW QW

CS

Qm

(20 10 40 5)mg / l m3 / s (10 5)m3 / s

QS CW QW QS QW

26,7mg / l

dC dt

KC

C

dC C0 C ln(C ) ln(C0 )

ln

( K )dt C0

C C0

Kt


C

C0 e

Kt


C

1,0 105 28,6 103

3,5mg / l


V

dC dt

S QC

KCV

dC dt

C( x )

S Q KV

0


dC dt

Q

y

c

KV C V S Q KV

dy dt

dy dt

C( t )

Q y V

y0e

y0

C( t )

dC dt

K

y

S Q KV

C0

S Q KV

S Q KV

(k

Q / V )t

S Q KV

C0

C0

S e Q KV

S e Q KV

K

K

Q V

Q V

t

t

C


K

C( t )

C(

C(

C( t )

C0

C(

C0

)

C(

)

e

Q V

t

140mg / h 100m / h 0,4 / h 500m 3

)

3

)

e

K Q /V

t

0,117mg / m 3


(

C A1 C A2

1kg / l


3 100

C%

CM

30000 1000000

30000 ppm

14mgN 18mgNH 4

148mgNH 4

14mgN 62mgNO3

214mgNO3

m2 100% m1 m2

m , mol / lit M .V

N /l

N /l


N1

n1 n1

n2

Cm

; N2

n2 n1

n2

; N1

m2 .1000 , molan M .m1

CN

V1 V2

m N .V

CN2 C N1

N2

1


V NaCl

V AgNO3 .C N , AgNO3 C N , NaCl

150 0,16 0,3

80ml

50 103 mgCaCO3 eqCaCO3

100 g / mol 2eq / mol

92mg / l 20mg.meq

50 g / eq

4,6meq / l

50

mg meq 4,6 meq l


G

S

* i

i

H

0

V

0

H

G T

(T ) RT ln xi

0

0


P' P

t' t

P' P

i

1


Nq

N N

N

q 1

(q 1) 1

i 1 q 1

HA H 2O

Ka

[ A ][ H 3 O ] [ HA]

A

H 3O


Kb

[ BH ][OH ] [ B]

Ka

[ NH 3 ][ H 3O ] [ NH 4 ]

[ NH 4 ][OH ] [ NH 3 ] K a .K b

[ H 3O ][OH ] K H 2 O 10

14


H 3O A [ HA][ H 2 O]

Ka

Ka

pK a

[ H ][ A ] [ HA]

pH

lg

Kb

pK b

lg

[A ] [ HA]

[ BH ] [ B][ H ]

[ BH ] [ B]

pH


g

g g

ng g

ng

nW

g


K

K1

H 2CO3 CO2 (aq)

[ H ][ HCO3 ] * [ H 2CO3 ]

1,6 10

3

4.47 10 7 mol / l


2

K2

[ H ][CO3 ] [ HCO3 ]

4,8 10 11mol / l


K1

[ H ][ HCO3 ] * [ H 2CO3 ]

K1

[ H ][ H ] * [ H 2CO3 ]

4,47 10 7 mol / l


2

K2

260 1000 61

[ HCO3 ]

2

[CO3 ]

[H ]

30 1000 60

K2

[ HCO3 ] 2

[CO3 ]

[ H ][CO3 ] 2 [ HCO3 ]

4,26 10 3 mol / l

5,0 10 4 mol / l

3,72 10

11

4,26 10 3 5,0 10 4


[ HCO3 ] 61

[Ca 2 ] KLDL

[ Mg 2 ] 12,2

40 20

4meq / l

anion

6

5

x 23

cation

[ Mg 2 ] KLDL

4meq / l


S

TAgCl


TCaF 2

S (2S ) 2

4S 3

S

3

T 4


A

S

S0

A

S

GS

GS GS S

S


-

-


a

d dC d dC d dC

C d RT dC

0 0

d dC

0

C

0

A ln(1 BC )


a

am

K .P 1 KP

ai

am

K i pi n

1

K i pi i 1


v

vm cp / p0 1 p / p0 1 cp / p0 v

e

p0

p / p0

vmcp p 1 c 1 p / p0

( q n q1) / RT

x

p p0 v

vmcx 1 x 1 cx x

p p0 v p0 p

p0 vmc

c 1 p vm c


x v(1 x)

p 1 v p0 p

vm

1 cvm

(c 1) x cvm

f ( p ) hay

22400S 0 NA

x v(1 x)

f ( x)


-

-

Pi

k

R

. x il


Pi 0

kR kR Pi

Pi 0 . x ií

P

P1

P10 x1

P

P10

P10 (1

P10

P10 P P10

P P10

P10 x

x

x)


PV

nRT m M

m RT M


g

g

g


Pg

0,21 1amt

0,21atm

Pg g

g

Kh

0,21 3,27 104

6,42 10

ng g

6,42 10

ng

nW ng

6

ng

55,6

6


g

ng

0,79 8,04 104 ng ng

9,8 10

6

55,6

ng

5,46 10 4 mol / l

CS

5,46 10

4

28 103

15,29mg / l

g

0,00033 0,142 104

0,233 10

6


ng

ng ng

0,233 10

nW ng

6

ng

55,6

ng

0,13 10 4 mol / l

CS

0,13 10

4

44 103

0,57mg / l

dC A, h dt


dC A, h dt

C CS C0 C S

dC dt

r h

exp

kt h

rAs

k (C CS ) h

kt h

C0 / 2 CS C0 C S

t1 / 2

0,69

exp

h k

kt1 / 2 h


t1 / 2

0,69

h k

t1 / 2

t1 / 2

0,69 2 0,144 0,69 2 9,34 10 3

9,5h

147h


C t

v

v

v

-

dnA dt

dC dt

dnB dt

dnC dt


dC dt

v

v

dC dt

kC An1 CBn2

kC An1 CBn 2


v2

(T2 T1 )10

v1


Ni


W

dC A dt

v

kC A1 CB 2 C D3

kC 0

k


H 2O2

2 HI

v

W

dC A dt

2 H 2O

kCH 2 OC HI

k1C A


ln

C0 A CA

k1t

CA

ln

C0 A C0 A / e

1 k1

k1

W

dC A dt

CA

t1 / 2

ln 2 k1

0.693 k1

C0 A e


dC A dt

W

k2C A2

CA

dC A / C A2 C0 A

1 CA

1 C0 A

k 2t

k2

1 1 t CA

t1 / 2

1 k 2 C0 A

dC A dt dC A dt

1 C0 A

k3C AAÛ k 3C A2CB

k 2t


dC A dt

k3C AC BCC

1 C A2

1 C02

2k3t

CA

3 2k3C02A

t1 / 2

dC B dt

dC B dt

k1 C A

dC C dt

k '1 C A

dC C dt

dC A dt

( k1

k '1 )C A

C0 A 2


dC C dC B

CC

( k1

CB

CA

CC

k '1 k1

1 C0 A ln t CA

k '1 )

CB

k '1 k1

C 0 B .e

k1 k1

k '1

( k1 k '1 ) t

C0 A 1 e

k '1 C0 A 1 e k1 k '1

( k1 k '1 ) t

( k1 k '1 ) t


dC D dt

dC E dt

dC D dt

k 2C AC B

dC E dt

k '2 C AC B

dC A dt

dC B dt

CE CD

k2

k '2

k '2 k2

1 t (C 0 A

k2

C0 B )

ln

C0 B C A C B C0 A

k

A A B

dC B dt

k2

ki

k1

C D

k 2 C AC B

k ' 2 )C A C B


dC A dt

dC A

CA

dC B dt

k1C A

k1 1 . dC B k2 CB

1

C0 A

C0 B

k 2C B C0 A

A

k 2 C AC B

k1 C ln B k 2 C0B

C0 B

k1

CB

B

k '1

k1 C B ln k 2 C0 B

C


dC A k1C A dt dC B k1C A k '1 C B dt dC C k '1 C B dt

CA

CB

CC

k1 k '1 k1

C0 A

k1t

C 0 A .e

C0 A e

k1t

k '1 .e k1t 1 k '1 k1

[A]

e

k '1 t

k1 .e k '1 t k '1 k1

[B] M s-1

1

3,28 x 10-2 M

8,77 x 10-3M

2,85 x 10-2

2

4,92 x 10-2 M

8,77 x 10-3M

4,28 x 10-2

3

4,92 x 10-2 M

1,32 x 10-2M

6,42 x 10-2

4

3,28 x 10-2 M

1,32 x 10-2M

4,28 x 10-2


= k x [A]m x [B]n, : ( (k x [A2]m x [B2]n) / (k x [A1]m x [B1]n) (4,28 x 10-2 / 2,85 x 10-2) = (4,92 x 10-2M)n / (3,28 x 10-2M)n 1,50 = (1,50)n

, n = 1. : m

n

m

n

( )/( 2) = (k x [A3] x [B3] ) / (k x [A2] x [B2] ) -2 (6,42 x 10 / 4,28 x 10-2) = (1,32 x 10-2M)m / (8,77 x 10-3M)m 1,50 = (1,50)m , m = 1.

B

(gi창y) 0 1 2 3 4 5 6 7 8 9 10

[M] 2,50.100 1,88.100 1,52.100 1,29.100 1,12.100 9,98.10-1 8,98.10-1 8,18.10-1 7,51.10-1 6,95.10-1 6,46.10-1

ln[A]

1/[A]

9,16.10-1 6,29.10-1 4,21.10-1 2,56.10-1 1,17.10-1 -1,88.10-3 -1,07.10-1 -2,01.10-1 -2,86.10-1 -3,65.10-1 -4,37.10-1

4,00.10-1 5,33.10-1 6,56.10-1 7,74.10-1 8,89.10-1 1,00.100 1,11.100 1,22.100 1,33.100 1,44.100 1,55.100


1/[A] = = (1,55-0.400)/(10-0) = 0,115 = 0,115M-1s-1

.


a. b. c. d.

(C) ( C) ( B) ( D)

H2(k) + Br2(k)

2HBr(k)


QC Ai

QC A0

rA

rAV

dC A dt

V

dC A dt


dC A dt

k0

C A0

t

k0 dt

dC A C Ai

0

C Ai

C A0

rA

k 0t

k1C A

dC A dt

k1C A

C A0

t

dC A CA

k1 dt C Ai

0

k1t

V

QC Ai

rA

ln

C A0 C Ai

dC A dt

0

QC A0

rAV

Q (C Ai V

C A0 )

rA

k0

0


C Ai

C A0

k0

V Q

V Q

C Ai

rA

C A0

k0

k1C A0 C Ai

C A0

C A0

k1

rA

k[ A] K S [ A]

k

kmaxC KS C


kmax C KS

k

k

kmax

-

k1

kmaxC KS C k1M

k1M K1

2,5

k maxC KS

kmax MC KS

0,05 5000 C 100

2,5C


k1

C1 C C

2,5

200 C C

C1

dC dt QC1 QC

QC1 QC V

Q (C1 C ) V

0 rV

0

Mkmax C KS C MkmaxC KS C

5000 0,05 C 100 C C1 C

250C 100 C

200 C 5

250C 100 C

0


2,5 2,5 5

C1 C

C1 C C 400 C C

250C 100 C

19,8h

k1t

K1M

ln

C C1

50000 0,05 C 100

MkmaxC KS

25 0,1

r

ln

dC dt

C 2000

25C


dC dt

50000 0,05 C 100 C

MkmaxC KC C

C A0

t

100 C dC C C Ai

2500 dt 0

C A0

2500t

100 C Ai

2500t

100 ln

dC C

C Ai C A0

C A0

dC C Ai

(C Ai

C A0 )

0,1h

t C A1

2500C 100 C

200mg / l

C A0 C A0

64mg / l

16,4mg / l ,

0,174h

25 0,2 C A0

4000t

C A0

27mg / l

t

1,12h

ln

C A0

4000

27mg / l

100 ln

4000 C A0

C A0

3220mg / l

(4000 C A0 )


ox

ne

kh


E

E0

RT aox ln nF akh RT F

E0

E

E

0,059 a ox lg n a kh

E

E0

0,059 lg[Cu 2 ] 2

E

E0

0,059 lg

E0

[ Fe 3 ] [ Fe 2 ]

0,059 MnO4 H lg 5 Mn 2

8


E

E1

E pin

E 20

E10

E0

0,059 lg PO2 H 2

0,059 [ox1 ] lg n1 [kh1 ]

E10

0,059

1 [ox 2 ] lg n2 [kh2 ]

E

E

E2

E 20

2

0,059 [ox 2 ] lg n2 [kh2 ]

1 [ox1 ] lg n1 [kh1 ]

0,77 0,059 lg

[ Fe 3 ] [ Fe 2 ]

0,059 [ MnO4 ][ H ]8 1,51 lg 5 [ Mn 2 ]


0,77 0,06 lg

K

[ Fe3 ] [ Fe 2 ]

1,51

0,06 [ MnO4 ][ H ]8 lg 5 [ Mn 2 ]

[ Mn2 ][ Fe3 ]5 [ MnO4 ][ Fe 2 ]5 [ H ]8 0,56 lg K 5


Eh

E0

RT Ox ln nF Re d


Eh

E0

1,23

RT [O2 ][ H ]4 ln 4F [ H 2O]2

8,314 298 ln [O2 ][ H ]4 4 96487


K

Mn 2 4 H [e]2

p

43 lg[Mn2 ] 4 pH 2

lg K

lg[Mn2 ] 4 lg[ H ] 2 lg[e]

43 8 4 6 2


K

1 [ H ] .[O2 (aq)].[e]4 4


E

E0

0,059 [ PU ] lg n [ SP]


pE

pE

E 0,0591

pE 0

1 [ PU ] lg n [ SP]


k

MgCO3 Ca 2 CaCO3 Mg 2


FI

FD

CD

(

S

W

CD AS

W

)Vol

VS2 2

24 Vs d

F1

FD

(

S

W

VS

VS

)

6

g 18

g ( 18

d

24 d2 VS d 4

3

SP 1 d 2

S

W

)d 2

W

VS2 2


H VS

L V

V

Q WH

t

WHL Q Vol Q

VS

Q LW

Q AP

Vol Q H VS


X1

b c a c

(V1 / V ) L (VS / V ) L

V1 VS

XS

Xr

(1 X S ) 0

XS

0

V dx VS

Xr

(1 X S )

1 VS

V X

V dx VS


AP

WOR

Q W

36400 12

3033m 2


VS

g ( 18

S

W

)d 2

9,81 (1,15 1,0)d 2 3 18 1,002 10

VS

H tX


36400 50 x 24 60

1264m3 1264 25

50,5 5

10,1m

50,5m 2


VS

g ( 18

P

V1

Q AP

VS

Q AP

W

)d 2


dN dt

ln

Nt N0

Nt

kN t

kt

N 0e

kt


[ HCO3 ]

K1

K2

CT

[ H ][ HCO3 ] H 2CO3*

H CO32 H 2CO3*

[ HCO3 1

200

61 10 50

3

1 61


1 1 [ H ] / K1 K 2 /[ H ] 1 7,5 7 1 10 /(4,47 10 ) (4,8 10 11 ) / 10 1

CT

4 10 3 0,93

4,29 10 3 mol / l

7,5

0,93


0

A

9 5 5 9



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