IUPAC Quantities, Units and Symbols in Physical Chemistry 3th Ed 2012

8/9/2019 IUPAC Quantities, Units and Symbols in Physical Chemistry 3th Ed 2012

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ISBN: 978-0-85404-433-7

A catalogue record for this book is available from the British Library

International Union of Pure and Applied Chemistry2007

Reprinted 2008

All rights reserved

Apart from fair dealing for the purposes of research

for non-commercial purposes or for private study, criticism or review,as permitted under the Copyright, Designs and Patents Act 1988 and the Copyright and Related Rights Regulations 2003,

this publication may not be reproduced, stored or transmitted, in any form or by any means, without the prior permission in

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be sent to The Royal Society of Chemistry at the address printed on this page.

Published by The Royal Society of Chemistry,

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Cambridge CB4 0WF, UK

Registered Charity Number 207890

For further information see our web site at www.rsc.org

Please cite this document as follows:

E.R. Cohen, T. Cvitas, J.G. Frey, B. Holmstrm, K. Kuchitsu,

R. Marquardt, I. Mills, F. Pavese, M. Quack, J. Stohner,

H.L. Strauss, M. Takami, and A.J. Thor, "Quantities, Units and

Symbols in Physical Chemistry", IUPAC Green Book, 3rd Edition,

2nd Printing, IUPAC & RSC Publishing, Cambridge (2008)


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1

2

1

2


11/251


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18/251

Q

{Q}

Q

Q= {Q} [Q]

1

7

9

9

9

/ 7

/

ln(p/MPa) = a + b/T =

a + b(103 K/T)

T /

3

/T p/

ln(p/

)

3.0 3.5 4.0 4.5 5.01.0

0.5

0.0

0.5

1.0

1.5

2.0

2.5

103K/T

ln(p/MPa)

3

/T

/T

3T /

1


19/251

v

2

2

1

dim(E) = dim(m l2 t2) = 2 2

2 2

Q=

t2t1

I t

1

Q

Q

Q

2


20/251

1

Cp

pi C

E

H

Vm A10

S 2,

154.3

1

1

i= (G/ni)T,p,...,nj ,...;j=i i= (G/ni)T,p,nj=i

AAA, aaa

S,T

1


21/251

2

v

V /m

/

p

p p/

V

Vm= V /n

H

Hm= H/n

a/c

/c

2


22/251


23/251

2

. . . 1

2 2

2 1

1 1

1

X 3 1 . . . 1

2 2

2 1

2a 1

1

. . .

2u 2

1g 4

X 1 1g

H

Hm

Cp CV

p

V

p

V

Ar

i

i

i

. . .

. . .

log

10

e 2

e

H=H(final) H(initial)

p

t

x

x

F

t

F = F0exp(t)sin(t)

x

x

t

t

t


24/251

Eh

c0 me h

NA L e a0

e 19

O

N

S

P

H

4

N

O

H

H


25/251


26/251


27/251


28/251

i

x y z

2

(v)

3

s

r

A

r2

/

1

1

1

| |

1

1

.

1

| | 1

2

n

n

N

t

vvv= rrr


29/251

= m1m2/ (m1+ m2)

= m/V

3

d d= /

A S A= m/A

2

v v= V /m= 1/

3

1

=m

1

=

I, J I =

i

miri2

2

t= m

(

)

=

E

E

V

E

=

E

T

K E

= (1/2)mv2

W

A

w W =

P P =

W t

q

p

L L(q, q) =T(q, q) V(q)

H H(q, p) =

ipiqi L(q, q)

S S= L t

p, (P) p= F /A

2

, =

W

A

1

2

G, (W, P) G= mg

G F =Gm1m2/r

2

2

2

=

2

I =

i mi

2i +

2i

I =i miii =

x

y

z

Ep(r1, r2) = r2r1

Ep(r) = r

L

p

q H t


30/251

= F /A

=F /A

, e = l/l

E E= /

= x/d

G G= /

= V /V0

K K= V0( p V)

, () xz = ( vx z)

= 1/

1

= /

2

1

, (f) F

=F

P, P

P =

E

t

= P

/P0

, ()

= 1

=P

/P0

=

d

x

P0 P P


31/251

I, i

, I= n 2

Q Q=

I t

= Q/V

3

= Q/A

2

V, V =

W/

Q

1

U

V, U=V2 V1

E, E=

(

/Q)

(Emf, EMK)

= /Q=

V

1

= eeen

=

2

C C= Q/U

1

=

1

0 0= 0

1c02

1

=/0

= 0 2

= 1

(2)

(2) =01 (2P/ E2)

1

1

(3)

(3) =01 (3P/E3)

2

2

2

2

2

I

eeen A

c0

P

PPP

EEE

i

Pi= 0[ (1)Ei+ (1/2)

(2)E2i + (1/6) (3)E3i + ]

Ei i

(1)

1

(1)

(2)

(3)

(2)


32/251

,

=

i

Qi i

=Q

=

n

=

1

2

1

0 0 = 4 107 1 1

=/0

= /0 1

,, (

) =

1

=V

3

1

, E=

2

1

R R= U/I

G G= 1/R

= U I

X X= (U/I)sin

Z Z

R

X

Y Y =

Z

B Y

G

B

=

,,

=

1

L E= L( I/ t) 1

M, L12 E1= L12( I2/ t) 1

=

1

=

2

()

(, )

Vm m = 0 Vm

m = NA

Q

Q

r

R= (U/I)

G= R/(R2 + X2).

I U


33/251

= i

1

T T = (2/2m)2

H H=T+V

, , H = E

3/2

nlm(r,,) nlm= Rnl(r)Ylm(, )

3/2

Ylm(, ) Ylm = Nl|m|Pl|m|(cos )eim

P P =

3

= eP

3

= (i/2m) 2 1

( )

= e 2

=

ij | | Aij = iAj

A

A A A = A

A

(x, t)

(x)

(x, t) =(x)

( Et/)

r/a0,E/Eh

Pl|m|

l

|m| Nl|m|

n

(r1, , rn)

2

n

2 n

e


34/251

A Aij

= (Aji)

A

[A,B] [A,B] [A,B] =AB BA

A

B

[A,B]+ [A,B]+=AB+BA

A

B

r

3/2

i i=

rrcri

3/2

Hrr r Hrr = rHr

Hrs rs Hrs =

rHs

x x= ( E) /

Srs S Srs =

r

s

qr qr =

ni=1

bicri2

prs prs =

ni=1

bicricsi

z sz |sz| = +(1/2),|sz| =(1/2),|sz| = |sz| = 0 .

ms

H

i

j

r

s

Hrs

r

s

Srs r =s

r

r

s

x

eqr r qr n

r

qr = n

bi i

bi

prs r s


35/251

a0

Eh me e

i()

i() () i() ()

= (n!)1/2 i()

H H = (1/2)2 A

ZA/rA

Hii Hii=

i

(1)

H1

i(1) 1

Jij Jij =

i

(1)j(2) 1r12

i(1)j(2) 1 2

Kij Kij =

i

(1)j(2) 1r12 j

(1)i(2) 1 2

i i= Hii+

j

(2Jij Kij)

E E= 2i

Hii+i

j

(2Jij Kij) =

i

(i+ Hii)

Ji Jij(2) = i(1) 1r12 i(1)j(2)

Ki Kij(2) = i(1) 1r12 j(1)i(2)

F F =H +i

2Ji Ki

i

j

i i i i

n

1/2

n

ZA rA

Hii

i

Jij = ij|ij

Jij = (i

i|jj)

Kij = ij|ji

Kij = (i

j|ji)

j

j = i

Jii= Kii,

2Jii Kii= Jii


36/251

r

i i=r

rcri

Srs Srs =

r

sd,r,s

criSrscsj = ij

Prs Prs = 2

i

cricsi

Hrs Hrs =

r

(1)H1 s(1)d1

(rs|tu) (rs|tu) = r (1) s(1) 1r12 t (2) u(2) d1d2

E E=

r sPrsHrs

+(1/2)r

s

t

u

PrsPtu[(rs|tu) (1/2) (ru|ts)]

Frs Frs = Hrs+

t

u

Ptu[(rs|tu) (1/2) (ru|ts)]

(F j)j = 0

i Ji Ki

r

s

(r,,) =N rn1

(

nlr) Ylm(, )

nl

n

l

(x,y ,z) =N xaybzc expr2

N

Prs r s

(rs|tu)

Hii Jij Kij

Hii=r

s

cricsiHrs

Jij = (ii|jj) =

r

s

t

u

cricsictj

cuj(rs|tu)

Kij = (ij|ji) =

r

s

t

u

cricsictj

cuj(ru|ts)

Frs Srs

s(Frs iSrs) csi= 0


37/251

A

Z

N N=A Z

m

m

, m

m

m

=m

(12

)/12

=m

Am

e

h

= h/2

a0 a0 = 4 0

2/m

e2

E Eh= 2/m a20

R R= E

/2hc

1

= e2/4

0c

E

, I

E

, A

= (1/2) (E

+ E

)

E

, D

D0

D

m

m

= 1

I

Ed

=

E

(

)

12

[E

(

) + E

(

)]

= 2.1

D0 D


38/251

n E= hcZ2R/n

2

, Ep = 1

=

2

=e/2m

1

=e/2m

= (m

/m

)

1

e = geB/ 1 1

g, ge ge= e(2m /e)

g

g

=N(2m /e)

= BBB

1

=

/2

T1

T2

, E

=

; E

= (1/2)

:

= (1/3) :

2

Z

N= gNN/

ge > 0 e e < 0

N gN g

L

Q= rr V

x y

z

= (1/2)

3rr r2

V

(1/2)[3Q (Qxx+ Qyy + Qzz)]

V = q=2V /

Ep = (1/2) : = (1/2)

QV


39/251

eQ eQ= 2 zz 2

q= 2V / 2

=eQq

ab = pa/Eb

2

2

1

abc=

2pa/EbEc 3

3

2

abcd=

3pa/EbEcEd 4

4

3

A A=

N

/ t

, k A= N

1

t1/2, T1/2 N (t1/2) =N (0) /2

=

= /

Q

2

QW QW Z(1 4sin2 W) N

eQq/h

, ,

a

pa= p(0)a +

b

abEb+ (1/2)bc

abcEbEc+ (1/6)bcd

abcdEbEcEd+

ab abc abcd

0 3

a0

3

/(4 0)

2

a05e1

/(4 0)

3

a0

7e2

N

1

t1/2=

N

Z

W


40/251

T T =Etot/hc

1

=T T 1

= (E E) /h

Te Te= Ee/hc

1

G G= Evib/hc

1

F F =Erot/hc

1

A Tso= A 1

IA; IB; IC IA IB IC

2

A;B;C A= h/8

2cIA 1

A; B; C A= h/8

2IA

=IC IA IB 2

=2B A C

A C

DJ; DJK; DK; d1; d2

1

J; JK; K; J; K

1

e; r

1

exe; xrs; gtt 1

1

c

E/hc

1

T =E/hc

T =E/h

,

T ,

A,

B,

C

bp = (C B) / (2A B C) bo = (A B) / (2C A B)

G(v) =e

v+ 12

exe v+ 122 +

3N 6

3N 5

r,s,t,

i,j,k,

r


41/251

vr; lt

r, 0r , r r = T(vr = 1) T(vr = 0) 1

rs

g ,d,

, Ep =

,

t

G (v) =r r(vr+ dr/2) +rsxrs(vr+ dr/2) (vs+ ds/2) +tt gttltlt+

T(v) =i

vii +rs

xrsvrvs+

tt

gttltlt+

vv

1

= x, y, z

r

s rs

vr = 1 vs = 1

vv

=B rss/r+ r/s

B B vv

d

Ep

30

(

)

ea0

lp = p/e

p/

p/

p/ea0 lp/ 30 1.08 22.5 2 30 1.87 38.9

29 9.00

187


42/251

re

rz

r0

rs

Ri, ri, j,

Sj

Qr

1/2

qr

f, (k) f=2V /r2

2

1

fij fij =

2V /rirj

Fij Fij =2V /SiSj

rst, krst,

1

Crst

= /

S(S+ 1)

1

1

g

g h=gBB

a, A Hhfs/h= a

Hhfs/h=

10

re

r0

1 =

2

1

V/hc=rstqrqsqt

r,s,t,

SSS

L= 0

III

g

S= 1/2

Hhfs

S

a

gB/h geB/h 28.025 1

=

1

ge g


43/251

0

1, 2

CA

DAB DAB=

0

8

2

ABr 3AB

F1, F2 f1, f2

A,

A

IA

A

nJ

n

KAB KAB=

JABh

2

A

2

B

2

1

2

3

Az mA

0 1

3

eQ

2

a

g

g

g

g

1 2

1 2 1, 2 1 2

1= 1 2 = 2

1

1

A, A IAx,IAy,IAz SAx,SAy,SAz

J(13C, 1H)

J

JCH

M

m

m

0


44/251

q= 2V / 2

= eqzzQ/h

t1, t2

T

A

1

T A2

;

= /

I(I+ 1)

1

1

A A= (A ref)/ref

N N= (me/mp)B

1

ref

1

2

A

A BA= (1 A)B0

c

2

= eqzzQ/h e = e2qzzQ/h qXX, qY Y, qZZ

1

1

T1

A

1 +

I

S

I

me mp B

A

A ref BA


45/251

1

L ML

l ml

S MS

s ms

+

= +

R KR, kR I MI

l (l) Kl

,

l (l)

R+ L (+j)

N K, k

N+ S

J MJ K, k

J+ I

F MF

2

= J(J+ 1) , JZ = MJ, Jz = K ,

MJ K J MJ +J, J K +J.

2 = J(J+ 1) 2,JZ = MJ Jz = K.) l

ml

, , l

K

k

K

K= |k|

j, , p

G

j

l

l

v l +v

l

l

J

N

S= 0

Ka, Kc, K= |k| a c

JKa,Kc = 52,3


46/251

E

P

p

E

P

P (=P E)

p

P

3 P= (123)

E

P

P

p

E.

l

K

l

+

J

J

(A)

(A) (

(A)

(A)

)

A

J

+

Sn Sn

P(Sn)

S4

+1

+

1

+

2

+

2

+1

2

+

1

2

E

2

/n Cn

, v, d, h

i

Sn(=Cnh)


47/251

Cn

Cn

(2 s/n) s

i

h

L

L

L

(2S+ 1)

J

L

S

J

(1

)2 (2

)2

1

2

1/2

(1

)2 (2

)2 (

)2, 3

0

(

)2 (

)2

)3, 4

o

e

+

+

4 3/2 3

+0

(2S+ 1)

(= + )

J

)

X

(1

)2 (2

)2 (3

)2 (1

)1

X 2r,

21/2

23/2


48/251

(1

)2 (2

)2 (3

)2 (1

)3

2i 23/2

21/2

2 (2 1)2 (1 2)2 (3 1)2 , 1 1, (2

1)2 (1

2)2 (3

1)1 (1

1)1 ,

3 1.

6 6 ( 2u)2 ( 1g)4,X 1 1g.

(0, 0, 0)

(1, 0, 0) 1 v1= 1,

(1, 2, 0) 1+ 2 2 v1= 1, v2= 2

h=E E

;

;

;

(0, 2, 1) (0, 0, 1) 2 2+ 3 3

r

vr v

r

vr =v

r = 0

110 220 3

11

20

20

v2= 0 v2= 2

J = J J

J =2, 1, 0, 1,

2

K

Ka Kc

p

K= 1, J= 0

K

p K

p 2

K = 2

K = 1

J


49/251

c

c

= 299 792 458

1

1

c c= c

/n

1

= /c

= 1/

1

= 1/

1

= c/

= 2

1

1

n n= c0/c

h

= h/2

Q, W

, w =

Q/

V

3

, w = /

3

1

e, we e= / 2

, w = /

4

P, P =

Q/

t

Ie Ie= P/

1

M M=

P/

A

2

n

1

(

)

I

, I

= P/

1

I

,

I

,

1

1

I

I

Asource


50/251

L I

=

L cos

A

1

2

I, E I =

P/

A

2

Ie, Ee Ie= I/ 1

F, (H) F =

I

t=

P

A)

t

2

Aij Nj/ t=

iAijNj

1

Bij Nj/ t=

i

e(ij)BijNj 1

Bji Ni/ t= j

e(ij)BjiNi 1

= M/Mbb

Mbb= T4

2

4

E, (e) E= A =P /L

2

I

E

,

i

j

Ej > Ei, Ej Ei = hcij, Bji = Bij

B

e

B

1

B = c0Be B Be

A

Be A= 8 hc0

3Be.

B

i

j

Be,ij = 8

3

3h2c0(4 0)

|i||j|2

B

Be B

Mbb


51/251

1

R R=/

= 1/2l

1

f f =

/

Q Q= 2

W

W/

t

c1 c1= 2 hc02 2

c2 c2= hc0/k

, T =P

/P0

= P

/P0

, R = P

/P0

A10, A A10= lg(1 )

A

, B A

= ln(1

)

a, K a= A10/l 1

= A

/l

1

= a/c = A10/cl

2

1

= /c = A

/cl

2

1

A

l

2l

W

dW/dt Q

Q= / =/

Q

k

+ + = 1

+

= 1

P

/P0= I /I0= = 1 = exp(cl) .

Ae = ln(i) A10= lg(i)

Ie()

()

T()

I(

)

Ie(

)

A10 Ae


52/251

=/NA 2

A, A A=

(

)

1

S S= A/NA S S= (1/pl) ln (I0/I) 1 2

ln = ()1

2

1

G

G

=

()1

2

k k= /4

n n= n + ik

R R=

n2 1n2 + 2

Vm

3

1

[]

[] =/l

2

1

m m= /cl

2

1

A

B

l

c

1

3

1

A,S, S, ,

G

G(1, 2)

A, S,

G

= /N

S = A/NA

A

A

Aij

f

Aij

1.

Aij

f

fij = [(4 0) mec0/8 2e2]2Aij or fij

1.4992 1014 (Aij/ 1) (/ )2

i

j

f


53/251

m

n

n

m

hc0 kT

>1000

1

ji()

i

j

i

j i

Gji =

ji()1 = ji() 1

i m j

n

pi

G

(n m) =i,j

piGji

S

A

p c. pi ciRT

S

A

S A/RT. S

I

I

ln(I

/I) = ln(I/I

) = ln(1 P

/P

) =A

(589.3

3 2 = +0.6647

/l

/cl

c

l

[]

[].

[]

[] =/l

3

1

1

3

1

1


54/251

G

(n m) =i,j

(pi pj) Gji =

pmdm

pndn

i,j

Gji

pi pj i j pi= exp{Ei/kT}/q

q

pm pn

dm dn (pi= pm/dm, ) .

Gji Aij Bji

i

j

Gji = hBe,ji = (h/c0) B,ji= Aij/(8 c03)

Gji = hBe,ji = Aij/(8 c0

3) =

8

3

3hc0(4 0)|Mji |2

Mji

|Mji |2 =

|i ||j|2

Gji

Mji Gji/

2 |Mji/ |2

30

A,S,S, , G

G

= /NA A/(0NA) S/0 S(kT /0)

A, S

S

0 A, S S

G

.

S

G

S

A, S

S

Gji , Be,ji, Aij,

|Mji |

A

Aij

A

A


55/251

A, S, S,

G

A, S, S,

G

.

A, A

1

1

G/

2

=

A/(

1)0/ 1S

1

2

1

2

G/

2

= 102

S/

1

2

(T / )0/ 1

S

G/

2

= 1020 (S/

)0/ 1

2

1

2

1

G/

2

=

104 /

2

1

G

2

2

A

n

k

n

k

n

k

n

k

n

k

r=r + r = Rer+ Imr n r = Rer

r = Imr r r=n2

r= n

2 k2 r = 2nk

loc

loc = + /30


56/251

r() 1r() + 2 = 130Vmm()

Vm m

m

m

Cj = 1

4 0

bandj

m()

j i

0 Cj =

NA

3hc0(4

0)0g(|Mji |2)

0g(|Mji |2)

g

j

Aliq=(n2 + 2)2

9n Agas

n

n

2nk+ k2 n2

g

g

0|Mji |2

Agas= 8

2Cj

Aliq= 8

2

Cj(n2 + 2)2

9n

n

Cj A

1

Cj Cj =

bandj m(

)

1


57/251

,

0

1; 2; 3, =n1 1+ n2 2+ n3 3

; ;

1; 2; 3, i k = 2 ik 1

;

;

=h1 1+ h2 2+ h3 3 =

1

h1

+ h2 + h3

= 2

m= 2

i

nihi

a; b; c

; ;

a; b; c

1

; ;

x; y; z x= X/a

f f=Ea/Ee

F(h,k,l) F =

Nn=1

fne2 i(hxn+kyn+lzn)

h,k,l

d

n= 2d sin

n

s

j , j 0

=

0

B, D D= e2

n1, n2 n3 a, b c

i k = ik.

m

m= n1h + n2k+ n3l

X

Ea Ee

N

j

j.


58/251

qD, kD kD= (Ci6

2)1/3

1

D D= kD c0

1

D D= D/2 1

D

D= D/c0

1

D D= hD/kB

= V/CV

, M Ecoul = NAz+ze

2

4 0R0

NE NE= N(E)/ E

1

3

N, g N = N()/

3

, (ik) =

, (ik) = 1

R

ik q = T 1 1

=l/vF

L L= /T

2

2

AH, RH = + RH( ) 3 1

E

E=

T

T

, () = /T

1

C,n,p

3

E

Ed

Ea

EF, F F= lim

T0

=E EF

,

k= 2

/

1

uk( ) ( ) =uk( )exp(i ) 3/2

(

) = e( )( ) 3

m

drift= 2

1

1

b b= n/p

D

= DC

2

1

L L=

D

, W

TC

TN

Ci c0 qd 2

V

CV

Ecoul z+e ze


59/251

(hkl)

(h1h2h3)

(hkl) hkl

h1h2h3

{hkl}

{h1h2h3}

[uvw]

< uvw >

(110)

h= 1, k= 1

l= 0.

n

n

n

n

n

nk 1 1 2

m

a; b; c; n; d

N(E)

E,

N()

,

q

l

vF

nn, n, (n); np,

n+, (p) nd na ni(ni2 =n+n).

E

(

)

+

D


60/251

N

C C=N/V

3

L, NA L= N/n

1

k, kB

1

R R= Lk

1

1

(x,y ,z)

(cx, cy, cz) = t 1

(ux, uy, uz)

(vx, vy, vz)

(px, py, pz) =m 1

f(cx) f=

m2

kT

1/2 exp mc 2x2kT

1

F(c) F = 4

c2

m

2 kT

3/2exp

mc

2

2kT

1

c, u, v, c=

cF(c)

c

1

c, u, v

q

p p= L/q

= (1/h)

p

q

P, p

g,d,W,,

W, N W (E) =

i

H(E Ei)

(E) (E) =

W(E)/

E

1

q, z q =

i

giexp(Ei/kT)

Q, Z Q=i

giexp(Ei/kT)

n

NA

L

m

q

p

p

L

(x)

W

W(E)

E

Ei i

gi


61/251

, z, Z Z =

Zi=1

1

s

= 1/kT

1

B = exp(B/RT)

=

k

pk| k k|

PPP

= {Pmn}

Pmn mn Pmn= m|

|n

S S= k

ipilnpi

1

r= hc B/k

v =hc/k D =hcD/k, E =hcE/k

B

| k k pk

pk = 1 k

Pmn m

Pmn =

kpk cm

(k) cn(k)

cm

(k)

m | k {i}

k

pi

S = k ln Z


62/251

N

n nB = NB/L

L, NA

1

ma, m

m, mf

mu mu = ma(

12C)/12

M MB= m/nB

1

Mu Mu= muNA

1

Mr Mr= mf/mu

Ar Ar= ma/mu

Vm Vm,B = V /nB

3

1

w wB= mB/

i

mi

2

2 n( 2) = 3 (1/2)

2 n((1/2) 2) = 6 n((1/2) 2) = 2n( 2)

nB n( )

n(O2)

NA L

mu mu = 1

m

V

m/n

V /n

n=

i ni.

Mr Mr

Ar Mr

Mr,B = MB/Mu Mu = 1

1


63/251

B= VB/

i

Vi

x, y xB= nB/

i

ni

p, (P)

pB pB = yB p

, B = mB/V 3

C, n C B= NB/V

3

c

cB = nB/V 3

s sB = cB

3

m, b mB = nB/mA 1

B = nB/A

2

= (nB nB,0)/B

= /max

VB Vi

x

y

5

p

5

3

V

m

mB

mA

1

b

1

1

C

n

c

1

3

1

1


64/251

14

12

14

n

n

35

n

37

14

14

146

147

+

79

3+

+3

2

2

3+

+3

2

+++

=

1

A

nB,0 nB

= 0

max


65/251

VII II 0

+

+

+

p

+

3

2+

4

2+

n

e

e

+

0

,

14

17

59

60

23

20

31

29

147N + 178O + p

e


66/251

2 6 6 +

24

3 3

2

2

4

4

2

3 1

v= 2

J= 6

v= 2

J= 6

2 +

2 1

+ 0.91 6

2 4

2 4

2

3 6 3

3

CC

H

H

H

H

OH

C

O

OH

H3C O

OHHHO

OH

COOH

CH3

H

2 2 17

2


67/251

2 2 2 2

2 2 2 2 2 2 2 2 2 2 2 2

(1/2) 2 (1/2) 2

2 2 2

1

(1/5)

VII

4

(8/5)

(1/5)

II

2

(1/2)

2

(1/5)

(4/5)

2

4 8 2 (5/2) 2 4 2

4 5

8

+

2+

(5/2) 2 4 2

(1/5) 4

(8/5)

+

(1/5)

2+

(1/2) 2 (4/5) 2

z

(1/3)

0

(1/2)

I2 4 (1/6)

III2 4 3

0

3

3

6 6


68/251

0 =j

j Bj

j j

(1/2)

2 (3/2) 2 3 2 2 3 + 2 3 2 2 3 2 2 3 +

nj = nj nj,0 j

nj =nj,0+ j

n

2

n 2 n 3 + n 2

= 0

Aij

i

j

jk j

k

Ns Ne

Ne Ns N( ) =Ns

Nr Ns Nr

Ne Nr

(1/2)

2 (1/5) 4


69/251

nCl n n

2 2

n 2 4 2 4

n (1/5)

4 (1/5) 4M

4 4

cCl, c

2 4

4 4

(1/2)

4 (1/2) 4

2+

2+

(1/2)

2+

(1/2)

2+

n (1/5)

4 n 4

(1/2)

2+

2+

[(1/2) H2SO4] = 2 [H2SO4]

n

n

8

n 2

n

2

n

n

pV =nRT

n


70/251

CV Vm U

2

2

fH

2

Vm

l

Vms

Sm

Sm


71/251

Q, q

W, w

U

U

Q

W

H H=U+ pV

T

( )

T

t

T

S

S

Q

/T

1

A

F A= U T S

G G= H T S

J J= A/T 1

Y Y = G/T

1

, = (G/A

)T,p,ni 2

1

X X

X

X

= X/n

X

X x x= X/m

X

= (p/T)V

1

p p= (1/p)(p/T)V

1

T T = (1/V)(V /p)T 1

S S= (1/V)(V /p)S 1

l l= (1/l)(l/T)

1

, V, = (1/V)(V /T)p

1

Cp Cp= (H/T)p

1

CV CV = (U/T)V

1

U=Q + W

Q >0

W >0

th

F

n


72/251

, () = Cp/CV

,

= (T /p)H 1

, P = dQ/dt

B pV

=RT(1 + B/V

+

3

1

C C/V

2

+

6

2

a (p + a/V

2)(V

b) =RT

3

2

b

3

1

Z Z=pV

/RT

X

, (X

) X

= (X/n

)T,p,nj= X

X

= (G/n

)T,p,nj= 1

,

1

= exp(

/RT)

a a

= exp

RT

H

H

=

+ T S

1

S

S

= (

/T)p 1

1

X

X

V

=V

V /n

pVm = RT(1 + Bpp + Cpp2 + )

a

b

B = b a/RT

X

X

2 4

V 2 4

V

2 4

U

H A


73/251

G

G =

1

A

A A= (G/)p,T 1 =

H

H

=

H

1

S

S =

S

1

1

Q Q=

a

K, K K = exp(

G/RT)

Kp Kp=

p

B

B

Kc Kc=

c

B

3

B

Km Km=

m B 1 B

f, p f

=

limp0

(p

/

)T

=f

/p

k

k , = lim

x

0(f

/x

)

= (f

/x

)x

=0

K

a

=

/

= exp(

/RT)

H

r r

def= /

1

1

Q

K

K

Kf Kp

K

K Kp/(p)B Kc

K

K Kc/(c)B


74/251

f f

=a

/x

m am, =m, m /m

c ac, =c, c /c

x ax,

=x,

x

Im, I Im= (1/2)

i

mizi2

1

Ic, I Ic= (1/2)

i

cizi2

3

m m=

RT M m

x x=

RTln x

= (RT/VA) ln aA

K

K

K

K

K

K

K

1

3

1


75/251

=

,

H= lgH=H(g) H(l)

H=

1

H

,

H

H=

H

= (H/)T,p

2 3 2 2 3

H(298.15 ) = 92.4 1

S

= 199 1 1

1

H =

H

S =

S

G =


76/251

A=

G=

G + RTln

a

G =

RTln K

Q

1

H 4 1

4 2 2 2 2 2

+

S 2 1 1

2 2

,

U 2

1

2 2

T,

(T)

p= p

(T) = limp0

[

(T , p , y

,...)

RTln(y

p/p)]

p = p

(T) =

(T, p)

m

p


77/251

(T) = [

(T, p, m

,...) RTln(m

/m)]

m

p= p

(m

) =

+ RTln(m

m /m)

m

x

m

x

m

x = 1

m

c

x

p

m

c

p =

p = 0.1

= 100

=

m = 1

1

c = 1

3

m

c

p =

p

p

p

p

+

7

3

3 4 2

4 2

4 3

4


78/251

X

.X

.X X t

.

.

t

1

rB, vB rB cB t

3

1

v, vc v B

1

cB t 3

1

. /V

v, vC vC=B

1

CB t 3

1

m

B, n

B v= k cBmB

m, n m=

mB

k, k(T) v= k

cBmB

3

1

m1

1

p

p

t

1

S

t

1

1

rB

v

vp = B

1pB t

V

cB

(dcB/dt)total = (dcB/dt)reaction+ (dcB/dt)transport

m n

m

k

A

3

1

m1

1

3

m1

1

3

1

m1

1

k(T)

k= 108.2

3

1

1

k

3

1

1

k= 1012.6

3

1

k

3

1


79/251

kuni, kuni(T, cM) v= kunicB

1

k kuni(cM ) 1

k0 v= k0cMcB

3

1

1

k, kB

1

t1/2 c(t1/2) =c(0)/2

c() = c(0)/e

EA, Ea EA= RT

2

ln k

T

1

A A= k exp(EA/RT)

3

1

m1

1

r

dAB dAB= rA+ rB

=

dAB

2

2

cAB cAB= (8kT / )

1/2

1

zA(A) zA(A) =

2CAc

1

zA(B) zA(B) =CBcAB

1

cM

kuni(T, cM)

cM( ) cM( 0)

cM k0

c

c(0)

t

EA = Rd(ln k)/d(1/T)

k(T) =A Tn exp(Ea/RT)

A

n

Ea

E0

Ea E0

EA EA(T)

A

A(T)

C

= mAmB/(mA+ mB)


80/251

ZAA ZAA= CAzA(A)

1

3

ZAB ZAB= CAzA(B)

1

3

zAB zAB= ZAB/LcAcB

3

1

1

= c/zA

b

Iji Iji = ji/

2

1

ji ji =

Iji

2

Pji Pji = |Sji |2

H, H k(T) =

kT

h exp

SR

exp

HRT

1

V, V V = RT((ln k)/p)T 3 1

U, U

1

S

S

1

1

ZAA ZAB

b

= 0

i

j

ji/

i= j

Iji ji

Iji(E) ji(E)

kji(T) =8kBT

1/2 0

EkBT

ji(E) exp(E/kBT)

dEkBT

E

ji

1 Pji = |Sji |2 i

j

H

U

S

G

k

k= (kBT /h) exp(G/RT)


81/251

G

G G = H TS

1

q, q(T) k=

kBT

h

q

qAexp(E0/kBT)

= kh

kBTqAq

exp(E0/kBT)

q q= q/V

3

kuni(E, J) kuni(E, J) = d(ln cA(E, J))

dt

1

E, J

kbi(Et) kbi(Et) =(Et)

2Et/

3

1

Et

(E,J, ) (E,J, ) = dN(E,J, )/dE 1

N(E) W(E) N(E) =

E0

(E) dE

(E) (E) = dN(E)/dE

1

N(E)

W(E) N(E) =

EE0

(E) dE

W(E) W(E) =

aH(E Vamax)

KM v=

V [S]

KM+ [S]

3

Kfi d

dt =

1

kf

d[h]fdt

=kfc

1

0 0= 1/kf

f = kf

p diss p = kp

k

n

c)1n

V = (c)1 = (kT/p)

G =H T S

H U

S

G

p

c

H

S

G

k

= 1


82/251

kbi = kBT

h

qqAqB exp(E0/kBT)

q

q,

qA,

qB

E0

E

J

cA(E,J, )

k(E) =N(E)

h(E)

(E)

N(E)

E

N(E) =i

H(E Ei) =E0

(E) dE

N(E)

k(E, J) = W(E, J)

h(E, J)

Vmaxa a (x)

J

J

k1 k2

k1 k2

V

= (c1, c2, , cn)T Kfi

= / t

n/ t

c

d[h]

dt = dc

dt =kfc

p kp


83/251

=

=

3 3 2 6

2 3 2 6

vC= 12

CCH3

t

=k CCH32

Lh


84/251

3 (1/2) 2 6

vC= CCH3

t =k CCH3

2

k = 2k

2

2 2

vc= 1

2

[H]

t =k [H]3

2

X + A X + B

A = B

vc =d[A]/dt = k[A][X] (= d[X]/dt = 0)


85/251

e

F F =eNA

1

z zB = QB/e

Im, I Im= (1/2)

i

mizi2

1

Ic, I Ic= (1/2)

i

cizi2

3

m m

(++) =m++m

1

(++) =+

+

a a= m/m

a(A+B) a(A+B) =a

(++)

lg(aH+

= +

=

I

I

I

+ +

2 4 3, += 2 = 3

m+ m + + m m+ =+m m =m

c

m = 1

1

a+, a +,

Q

Q

r

Documents

IUPAC Quantities, Units and Symbols in Physical Chemistry 3th Ed 2012