IUPAC Quantities, Units and Symbols in Physical Chemistry 3th Ed 2012
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Transcript of 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
writing of The Royal Society of Chemistry, or in the case of reproduction in accordance with the terms of licences issued by
the Copyright Licensing Agency in the UK, or in accordance with the terms of the licences issued by the appropriate
Reproduction Rights Organization outside the UK. Enquiries concerning reproduction outside the terms stated here should
be sent to The Royal Society of Chemistry at the address printed on this page.
Published by The Royal Society of Chemistry,
Thomas Graham House, Science Park, Milton Road,
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
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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
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v
2
2
1
dim(E) = dim(m l2 t2) = 2 2
2 2
Q=
t2t1
I t
1
Q
Q
Q
2
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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
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2
v
V /m
/
p
p p/
V
Vm= V /n
H
Hm= H/n
a/c
/c
2
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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
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Eh
c0 me h
NA L e a0
e 19
O
N
S
P
H
4
N
O
H
H
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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
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= 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
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= 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
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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)
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,
=
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
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= 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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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)
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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
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(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
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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
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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
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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
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=/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
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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
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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
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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
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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
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,
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.
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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
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(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
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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
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, 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
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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
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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
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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
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VII II 0
+
+
+
p
+
3
2+
4
2+
n
e
e
+
0
,
14
17
59
60
23
20
31
29
147N + 178O + p
e
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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
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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
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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
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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
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CV Vm U
2
2
fH
2
Vm
l
Vms
Sm
Sm
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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
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, () = 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
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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
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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
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=
,
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 =
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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
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(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
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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
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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)
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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)
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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
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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
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=
=
3 3 2 6
2 3 2 6
vC= 12
CCH3
t
=k CCH32
Lh
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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)
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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