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物理化学电子教案 —第 5章
Chemical Equilibrium
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Chapter 5 Chemical equilibrium
5.1 The conditions of chemical equilibrium
and affinity of chemical reaction
5.2 The equilibrium constant of a reaction and
isothermal equation
5.3 Heterogeneous chemical equilibrium
5.4 Determination of equilibrium constants
5.5 The standard Gibbs function of formation
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Contents
5.8 Coupling reaction
5.7 Chemical equilibrium of simultaneous
reaction
5.6 The response of reactions to the conditions
Express mathematically how the equilibrium
constant depends on the temperature,and derive
and use the van’t Hoff equation.
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Chemical reactions
We have seen that the natural direction of all
change at constant temperature and pressure is
towards minimum Gibbs function.
The idea is entirely general,and in this
chapter we use it as a basis for the discussion of
chemical transformations.
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Consider the reaction A+B ? C+D
Is the natural tendency for the mixture A+B to go
to the mixture C+D,or the opposite? This can be
answered by calculating the Gibbs function of
each mixture.
If the sum of the Gibbs functions of A+B is
higher than that of C+D,then the reaction has a
tendency to roll from left to right.
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Chemical reaction system
Suppose a reaction：
D E F Gd e f g? ? ? ? ? ? ? ? ? ? ?
B
Bdd
?
?
n
? BBddn ???
Based on extent of reaction：
??
B
B B?0
Or:
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Fundamental equation
?????
B
BB dddd npVTSG ?
,B B B B
BB
d d dTpGn ? ? ? ?????（） BB
( d d )n ???
At const,T and P，
,B B
B
( ) ( a ) TpG ??
?
? ?
? ?
：1 m o l? ?
r m,B B
B
( b) TpG ???? ?（）
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,B r m,
B
( ),( )T p B T pG G???? ?? ? 或
r m,() 0TpG? ?
The reaction spontaneously
proceeds from left to right.
rm,() 0TpG? ?
The reaction spontaneously
proceeds from right to left.
rm,() 0TpG? ?
The reaction is at equilibrium.
Direction and limit of a chemical reaction
Use to determine:
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0)(,?
?
?
pT
G
?
From left to right
0)(,?
?
?
pT
G
?
From right to left
0)(,?
?
?
pT
G
?
At equilibrium
Direction and limit of a chemical reaction
PT
G
,
?????????
is the slope of G with recpect to the extent
of reaction ?.
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Direction and limit of a chemical reaction
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Van’t Hoff equilibrium box
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Affinity of chemical reaction
1922年，比利时热力学专家德唐德（ De donder）首
先引进了化学反应亲和势的概念。他定义化学亲和势 A为：
de f
,B B
B
( ) TpGA ????? ? ?? ?
mr- GA ??
或
A是状态函数，体系的强度性质。用 A判断化学反
应的方向具有, 势, 的性质，即：
A>0 反应正向进行
A<0 反应逆向进行
A=0 反应达平衡
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5.2 For pg reactions aA ﹦ bB
The simplest assumption is to suppose that the
species are perfect gases,in which case their
chemical potentials are determined by their partial
pressures:
ABmr abG ?? ???
a
A
A
b
B
B P
P
RTa
P
P
RTb ?
?
?
?
?
?
???
?
?
?
?
?
?? ???? ?? lnln
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Isothermal equation of chemical reaction
?? mr G
? ?
? ? ?
?
?
?
?
?
?
?
?? a
A
b
B
AB
PP
PP
RTab
?
?
?? ??
/
/
ln
? ?
? ? a
A
b
B
mr
PP
PP
RTG
?
?
?
/
/
ln??? 0?
＜ - Reaction proceeds
＝ - Reaction is at equilibrium
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The chemical potential of a real gases：
???
B BB,mr
)( ??pTG BB B B
BB
( ) l n fT R T p? ? ????? $ $
B
BB(,) ( ) l n
fT p T R T
p?? ??
$
$
r m B B
B
( ) ( )G T T???? ?$$
B
r m,r m B
B
( ) ( ) l nTp fG G T R T p?? ? ? ? ?$ $
is the standard molar Gibbs function of
the reaction
rm()GT? $
fB is the fugacity of B
Substituting this expression,gives
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gh
GH
rm de
D
r
E
m
( / ) ( / )( ) l n
( / ) ( / )
f p f pG T R T
f p f p
G? ? ? ?
$$
$
$$
rm ( ) l n fG T R T Q? ? ?$
D E G Hd e g h? ? ? ? ?
Reaction:
Isothermal equation of chemical reaction
Where Q is the reaction quotient.
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When the reaction is at equilibrium，
0mr ?? G
gh
GH
rm de
DE
( / ) ( / )ln
( / ) )) (/(
f p f pRT
f p fT pG? ??
$$
$
$
$
ln fR T K?? $
is the thermodynamic equilibrium constant.
fK
$
The thermodynamic equilibrium constant
It should be noticed that eq.provides a way of
measuring the standard Gibbs functions of reactions.
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Predict the direction of reaction
Use the van’t Hoff equation：
rm l n l nffG R T K R T Q? ? ? ?$
rm l n l nppG R T K R T Q? ? ? ?$
For pg reaction:
rm 0ppK Q G? ? ?$
from left to right
rm 0ppK Q G? ? ?$
from right to left
rm 0ppK Q G? ? ?$ at equilibrium.
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Subscript m denoting the extent of reaction is
unity i.e,1 mol,
rm()GT? $ fK$
Relation of constant and equation
rm ( ) l n fG T R T K? ? ?$$
r m,2 r m,12GG? ? ?$$
2,2,1()ffKK?$$
Example：
H I ( g )2g)(Ig)(H 22 ??
H I ( g )g)(Ig)(H 221221 ??（ 1）
（ 2）
is referred to
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Empirical equilibrium constants
Distinguish the thermodynamic equilibrium
constant from pressure and composition
equilibrium constants,Example：
D E G Hd e g h? ? ? ? ?
BHG
Bd B
DE
g h
p e
ppKp
pp
??? ? ?
?
pK
1,Pressure equilibrium constant
when? ? 0B?
pK
(Dimension
is unity)
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BHG
BB
DE
g h
x de
xx
Kx
xx
??? ? ?
?
??
? B
B?
pKK px
xK
2.mole fraction equilibrium constant
A pg obeys Dolton partial pressure law，
BB pxp ?
Empirical equilibrium constants
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BHG
BB
DE
g h
c de
cc
Kc
cc
??? ? ?
?
??
? B
B
)(
?
RTKK pc
cK
3,Concentration equilibrium constant
pg，
c R Tp ?
Empirical equilibrium constants
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B
BB
?aK
a ??
，
BB
B
ca
c
??
$
B
B
()a c rK K K c ??? ? ? ? $
aK
4,Activity equilibrium constant
Empirical equilibrium constants
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Different Forms of Equilibrium Constants
? ?
? ? aA
b
B
mr PP
PP
RTKG ?
?
?
/
/
ln)298( ??? ?KRT ln??
? ?
? ? aA
b
B
PP
PP
K
?
?
?
/
/
? ? ? )( ab
a
A
b
B P
P
P ??
? ?
)()( ab
P PK
??? ?
)()(
)(
)( ab
a
A
b
B P
RTC
RTC ??
? ?
)()( ab
a
A
b
B
RT
P
C
C ??
?
?
)()( ab
C RT
PK ??? ? ? ?? ?
)(
/
/ ab
a
A
b
B
RTC
P
CC
CC ???
?
??
?
?
? ?
?
?
?
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Heterogeneous chemical reaction
32C a C O ( s ) C a O ( s ) C O ( g )?
2(C O ) /pK p p?$$
is dissociation pressure)CO(
2p )s(C a C O 3
Consider a reaction
Equilibrium between ideal gas and pure condensed
phases,If the substances taking part in the
chemical equilibrium is of more than one phase,
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dissociation pressure
S ( g )H)g(NHH S ( s )NH 234 ??
example：
S)H()NH( 23 ppp ??
3 2( N H ) ( H S)
p
p p
p
K
p
?? $$ $ 214 ( / )pp? $
It is said earlier that chemical potentials of
condensed phases are insensitive to the pressure
change,unless the pressure is very large.
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The standard Gibbs function of formation
△ G concentrates our attention on the system,
and lets us avoid having to think explicitly
about the entropy of the surroundings,In an
isothermal change △ G can be related to the
enthalpy and entropy changes of the system by
? ?BGG mfBmr ?? ? ??? ?
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rm ln aG R T K? ? ?
$$
rme x p ( / )aK G R T? ??
$$
1,Using △ rG?m,calculate the thermodynamic
equilibrium constant:
The standard Gibbs function of reaction
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2 2 r m( 1) C ( s) O ( g) C O ( g) ( 1 )G? ? ? $
1 2 2 r m2( 2 ) C O ( g ) O ( g ) C O ( g ) ( 2 )G? ? ? $
1 2 r m2( 3) C ( s) O ( g) C O ( g) ( 3 )G? ? ? $
r m r m r m( 3 ) ( 1 ) ( 2 )G G G? ? ? ? ?$ $ $
(1 )( 3 )
( 2)
p
p
p
KK
K?
$
$
$
(1) - (2) 得（ 3）
2,计算实验不易测定的平衡常数
例如，求 的 平衡常数1 2
2C ( s ) O ( g ) C O ( g )??
The standard Gibbs function of reaction
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The standard Gibbs function of reaction
3．近似估计反应的可能性
r m r m ln pG G R T Q? ? ? ?$
只能用 判断反应的方向。但是，当
的绝对值很大时，基本上决定了 的值，所以可
以用来近似地估计反应的可能性。
0,,mr f)( ?? wpTG rmG? $
mrG?
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fmG?
$
（ B,?,T）
The standard Gibbs function of formation
Define the Gibbs function of reaction and calculate
it from tables of Gibbs function of formation.
Calculate the equilibrium constants for reactions on
the basis of the Gibbs function information given in
Table X.X.
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is very important
fmG? $
r m B f m
B
( B )GG ?? ? ??$$
rmG?
$
At T(1)
??
mrmr STH ????
dTCKH mp
T
K
rmr,
2 98
)2 9 8( ? ???? ?
})198({
298
,? ????
T
K
mpr
mr T
dTC
KST ?
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How equilibrium responds to temperature.
If the equilibrium constant is known at a
temperature T*,its value at another temperature T
can be found as follows,In each case
?
?
? ???
RT
TG
TK mr
)(
)(ln
?
RT
TG
TK mr
)(
)(ln
??
??
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How equilibrium responds to temperature
Subtracting these relates the two equilibrium
constants:
?
?
?
?
?
?
?
? ?
?
?
?? ?
?
? RT
TG
RT
TG
TK
TK mrmr )()(
)(
)(
ln
??
Now write △ G = △ H - T △ S,and make the
approximation that neither △ H nor △ S changes
significantly over the temperature range of interest:
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The isobaric equation of chemical reaction.
?
?
?
?
?
? ?
?
?
?
?
?
?
??
?
?
?
? R
TS
RT
TH
R
TS
RT
TH
TK
TK mrmrmrmr )()()()(
)(
)(
ln
????
?
?
?
?
?
?
?
?
?? ?
?
TTR
TH mr 11)(?
)(
)(
ln ?
TK
TK
The last equation is very remarkable because it
predicts the shift in equilibrium when the temperature
is changed; all we need to known is the standard molar
enthalpy of reaction.
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Deduce the isobaric equation
2
)
)(
(
T
H
T
T
G
mr
p
mr
?
?
?
??
?
?
?
??
fmr KRTG ln???
?
?
f
mr KR
T
G ln???
p
f
T
K
R )
ln
(
?
?
??
?
2
ln
RT
H
dT
Kd
mrf
?? ?
?
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The T affects the chemical equilibrium
The infinitesimal expression of van’t Hoff relation
rm
2
d l n
d
pK H
T RT
?
?
$ $
对吸热反应，,升高温度,增加，
对正反应有利。
rm 0H??$ pK$
对放热反应，,升高温度,降低，
对正反应不利。 p
K$rm 0H??$
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The T affects the chemical equilibrium
If we assure that does not depend on the
temperature this equation integrates to
rmH? $
2 rm
121
() 11
l n ( )
()
p
p
KT H
R T TKT
???$ $
$
C
RT
H
K mrf ?
?
??
?
?ln
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The T affects the chemical equilibrium
当理想气体用浓度表示时，因为,可以得到p cR T?
rm
2
d l n
d
cK U
T RT
??$ $
2 rm
121
() 11l n ( )
()
c
c
KT U
R T TKT
???$ $
$
这个公式在气体反应动力学中有用处。
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The van’t Hoff equation
Provides a way of measuring the enthalpy of a
reaction without using a calorimeter,but in practice
it is inaccurate.
Equilibrium compositions are measured over a
range of temperatures (at constant pressure),and
lnK is plotted against 1/T,It follows from eq.that
the slope is -△ Hm?/R.
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The P affects the chemical equilibrium
Le chatelier原理,增加压力，反应向体积减小的
方向进行 。这里可以用压力对平衡常数的影响从本
质上对原理加以说明。
BB
B
()p pK p ???$ $
B
p
py B ?
???
B
)( ?
? B
p
pk
y
?
? )(
)l n (lnlnln ?? ?? ppkK BBy ?? ???
Tp
K
)
ln
(
?
? ?
T
y
p
k
)
ln
(
?
?
? p
B?? ? = 0
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The P affects the chemical equilibrium
T
y
p
k
)
ln
(
?
?
p
B??? ? 0?
? 0?B? aA=bB
0?ab ?
ab ?
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The inert gas affects the chemical equi.
对于分子数增加的反应，加入水气或氮气，会使
反应物转化率提高，使产物的含量增加。
)l n (lnlnln ?? ?? ppkK BBy ?? ???
? ???
B B
B
By B
B
B
n
n
yk ?
?
? ?? ? Bnk
n
?
pT
n
pT n
k
n
K
,,)
ln()ln(
?
??
?
? ?
0?? ?
n
B?
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5.9 simultaneous equilibrium
在一个反应体系中，如果 同时发生 几个反应，
当到达平衡态时，这种情况称为同时平衡。
在处理同时平衡的问题时，要考虑每个物质的
数量在各个反应中的变化，并在各个平衡方程式中
同一物质的数量应保持一致 。
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simultaneous equilibrium
例题, 600 K时,与 发生反应生成,
继而又生成,同时存在两个平衡：
3C H C l(g) 2H O(g) 3CH OH
32(C H ) O
3 2 3
3 3 2 2
( 1 ) C H C l ( g ) H O ( g ) C H O H ( g ) H C l ( g )
( 2 ) 2 C H O H ( g ) ( C H ) O ( g ) H O ( g )
??
?
已知在该温度下,。今以等量
的 和 开始，求 的平衡转化率。
,1,20, 0 0 1 5 4,1 0, 6ppKK??$$
3CH Cl 2HO 3CH Cl
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simultaneous equilibrium
解,设开始时 和 的量为 1.0，到达平衡时，
生成 HCl的量为 x,生成 的量为
y，则在平衡时各物的量为：
3CH Cl 2HO
32(C H ) O
3 2 3( 1 ) C H C l ( g ) H O ( g ) C H O H ( g ) H C l ( g )
1 1 2xy x xyx
??
? ???
3 3 2 2( 2 ) 2 C H O H ( g ) ( C H ) O ( g ) H O ( g )
-2 1- xyx yy
?
?
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simultaneous equilibrium
因为两个反应的 都等于零，所以
pxKK?$B
B
??
,1
,2 2
( 2 )
0,0 0 1 5 4
( 1 ) ( 1 )
( 1 )
1 0,6
( 2 )
p
p
x y x
K
x x y
y x y
K
xy
?
??
? ? ?
??
??
?
$
$
将两个方程联立，解得 。
的转化率为 0.048或 4.8? 。
0, 0 4 8,0, 0 0 9xy??
3CH Cl
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5.10 Coupled Reactions
It can be seen quite often that certain reactions are
not spontaneous i.e,△ G ＞ 0,But if the same
reactions are coupled to other reactions,which are
spontaneous,the original reactions become feasible,
This can only be possible if the total free energy
change I.e.,sum of the free energies of the second
and the original reaction is negative.
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Application of Coupled Reactions
例如：在 298.15 K时：
-12 2 4 2 r m,1 ( 1 ) T i O ( s ) 2 C l ( g ) T i C l ( l ) O ( g ) 1 6 1, 9 4 k J m o l G? ? ? ? ? ?$
反应 (1),(2)耦合，使反应 (3)得以顺利进行。
-12 2 r m,2(2 ) C ( s ) O ( g ) C O ( g ) 3 9 4, 3 8 k J m o lG? ? ? ? ? ?$
-1
r m
2 2 4 2
,3
( 3 ) T i O ( s ) C ( s ) 2 C l ( g ) T i C l ( l ) C O ( g )
2 3 2, 4 4 k J m o l G ??
?
?
??
?
?则
$
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Thermodynamic data from K
The standard Gibbs free energy for the forward
reaction is related to the equilibrium constant by
the expression,
The ?H can be obtained from the variation of
lnK with temperature:
The ?S is then calculable as …
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5.11 Approximately Calculation
1,的估算
rm()GT? $
r( 2 9 8, 1 5 K )T ?
r
r
r m r m r m
r m r m r
r m r m r
( ) ( ) ( )
( ) ( ) d
( ) ( ) d
T
p
T
T
p
T
G T H T T S T
H T H T C T
C
S T S T T
T
? ? ? ? ?
? ? ? ? ?
?
? ? ? ?
?
?
$ $ $
$$
$$
当 不大，或不要作精确计算时，设,则：pC? 0pC??
r m r m r r m r( ) ( ) ( ) G T H T T S T a b T? ? ? ? ? ??$ $ $
这里实际上设焓和熵变化值与温度无关，从
298.15 K的表值求出任意温度时的 值。
rmG? $
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Physical transitions
For an equilibrium between a liquid A and a gas
A (the vaporization and condensation of A):
)()( gl AA ?
At P?,T;
??
l
??
g
??? ??
lgmr G ???
)}l n ({ ??? ??
P
PRT A
gg
?
???
??? p
lg ??
? ??? P
gg ??
?
)ln ( ?
P
PRT A???
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Approximately Calculation
2．估计反应的有利温度
r m r m r m( ) ( ) ( )G T H T T S T? ? ? ? ?$ $ $
通常焓变与熵变在化学反应中的符号是相同的。
要使反应顺利进行，则 越小越好。
rm()GT? $
r m r m( 1 ) ( ) 0,( ) 0H T S T? ? ? ?$$
提高温度对反应有利。
r m r m( 2 ) ( ) 0,( ) 0H T S T? ? ? ?$$
降低温度对反应有利。
The end
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JACOBUS HENRICUS VAN’T HOFF
JACOBUS HENRICUS VAN’T HOFF (1852-1911)
Dutch physical chemist,received the first Nobel
Prize in chemistry in 1901 for,the discovery of the laws
of chemical dynamics and of osmotic pressure.” Van’t
Hoff was one of the early developers of the laws of
chemical kinetics,developing mehtods for determining
the order of a reaction;he deduced the relation between
temperature and the equilbrium constant of a chemical
reaction,
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JACOBUS HENRICUS VAN’T HOFF
In 1874,van’t Hoff (and also J.A,Le Bel,independently)
proposed what must be considered one of the most
important ideas in the history of chemistry,namely the
tetrahedral carbon bond,Van’t Hoff carried Pasteur’s
ideas on asymmetry to the molecular level,and
asymmetry required bonds tetrahedrally distributed
about a central carbon atom,Structural organic
chemistry was born.
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JOHN DALTON
JOHN DALTON (1766-1844)
English chemist,physicist,and meteorologist,is
considered by many to be the,father of the atomic
theory of matter,although grandfather is perhaps a more
he suffered,In 1803,he published his paper
“Absorption of Gases by Water and Other Liquids,” in
which he presented what is now known as Dalton’s law
of partial pressures,
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JOHN DALTON
He was led to his theory of atomism by his studies of
gases,In one of his papers published in 1805,he said,
“Why does not water admit its bulk of every kind of gas
alike?…The circumstance depends on the weight and
number of the ultimate particles of the several gases.”
John Dalton was led to the atom by reflecting that
different gases had different values of the Henry’s law
constant.
物理化学电子教案 —第 5章
Chemical Equilibrium
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Chapter 5 Chemical equilibrium
5.1 The conditions of chemical equilibrium
and affinity of chemical reaction
5.2 The equilibrium constant of a reaction and
isothermal equation
5.3 Heterogeneous chemical equilibrium
5.4 Determination of equilibrium constants
5.5 The standard Gibbs function of formation
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Contents
5.8 Coupling reaction
5.7 Chemical equilibrium of simultaneous
reaction
5.6 The response of reactions to the conditions
Express mathematically how the equilibrium
constant depends on the temperature,and derive
and use the van’t Hoff equation.
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Chemical reactions
We have seen that the natural direction of all
change at constant temperature and pressure is
towards minimum Gibbs function.
The idea is entirely general,and in this
chapter we use it as a basis for the discussion of
chemical transformations.
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Consider the reaction A+B ? C+D
Is the natural tendency for the mixture A+B to go
to the mixture C+D,or the opposite? This can be
answered by calculating the Gibbs function of
each mixture.
If the sum of the Gibbs functions of A+B is
higher than that of C+D,then the reaction has a
tendency to roll from left to right.
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Chemical reaction system
Suppose a reaction：
D E F Gd e f g? ? ? ? ? ? ? ? ? ? ?
B
Bdd
?
?
n
? BBddn ???
Based on extent of reaction：
??
B
B B?0
Or:
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Fundamental equation
?????
B
BB dddd npVTSG ?
,B B B B
BB
d d dTpGn ? ? ? ?????（） BB
( d d )n ???
At const,T and P，
,B B
B
( ) ( a ) TpG ??
?
? ?
? ?
：1 m o l? ?
r m,B B
B
( b) TpG ???? ?（）
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,B r m,
B
( ),( )T p B T pG G???? ?? ? 或
r m,() 0TpG? ?
The reaction spontaneously
proceeds from left to right.
rm,() 0TpG? ?
The reaction spontaneously
proceeds from right to left.
rm,() 0TpG? ?
The reaction is at equilibrium.
Direction and limit of a chemical reaction
Use to determine:
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0)(,?
?
?
pT
G
?
From left to right
0)(,?
?
?
pT
G
?
From right to left
0)(,?
?
?
pT
G
?
At equilibrium
Direction and limit of a chemical reaction
PT
G
,
?????????
is the slope of G with recpect to the extent
of reaction ?.
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Direction and limit of a chemical reaction
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Van’t Hoff equilibrium box
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Affinity of chemical reaction
1922年，比利时热力学专家德唐德（ De donder）首
先引进了化学反应亲和势的概念。他定义化学亲和势 A为：
de f
,B B
B
( ) TpGA ????? ? ?? ?
mr- GA ??
或
A是状态函数，体系的强度性质。用 A判断化学反
应的方向具有, 势, 的性质，即：
A>0 反应正向进行
A<0 反应逆向进行
A=0 反应达平衡
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5.2 For pg reactions aA ﹦ bB
The simplest assumption is to suppose that the
species are perfect gases,in which case their
chemical potentials are determined by their partial
pressures:
ABmr abG ?? ???
a
A
A
b
B
B P
P
RTa
P
P
RTb ?
?
?
?
?
?
???
?
?
?
?
?
?? ???? ?? lnln
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Isothermal equation of chemical reaction
?? mr G
? ?
? ? ?
?
?
?
?
?
?
?
?? a
A
b
B
AB
PP
PP
RTab
?
?
?? ??
/
/
ln
? ?
? ? a
A
b
B
mr
PP
PP
RTG
?
?
?
/
/
ln??? 0?
＜ - Reaction proceeds
＝ - Reaction is at equilibrium
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The chemical potential of a real gases：
???
B BB,mr
)( ??pTG BB B B
BB
( ) l n fT R T p? ? ????? $ $
B
BB(,) ( ) l n
fT p T R T
p?? ??
$
$
r m B B
B
( ) ( )G T T???? ?$$
B
r m,r m B
B
( ) ( ) l nTp fG G T R T p?? ? ? ? ?$ $
is the standard molar Gibbs function of
the reaction
rm()GT? $
fB is the fugacity of B
Substituting this expression,gives
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gh
GH
rm de
D
r
E
m
( / ) ( / )( ) l n
( / ) ( / )
f p f pG T R T
f p f p
G? ? ? ?
$$
$
$$
rm ( ) l n fG T R T Q? ? ?$
D E G Hd e g h? ? ? ? ?
Reaction:
Isothermal equation of chemical reaction
Where Q is the reaction quotient.
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When the reaction is at equilibrium，
0mr ?? G
gh
GH
rm de
DE
( / ) ( / )ln
( / ) )) (/(
f p f pRT
f p fT pG? ??
$$
$
$
$
ln fR T K?? $
is the thermodynamic equilibrium constant.
fK
$
The thermodynamic equilibrium constant
It should be noticed that eq.provides a way of
measuring the standard Gibbs functions of reactions.
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Predict the direction of reaction
Use the van’t Hoff equation：
rm l n l nffG R T K R T Q? ? ? ?$
rm l n l nppG R T K R T Q? ? ? ?$
For pg reaction:
rm 0ppK Q G? ? ?$
from left to right
rm 0ppK Q G? ? ?$
from right to left
rm 0ppK Q G? ? ?$ at equilibrium.
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Subscript m denoting the extent of reaction is
unity i.e,1 mol,
rm()GT? $ fK$
Relation of constant and equation
rm ( ) l n fG T R T K? ? ?$$
r m,2 r m,12GG? ? ?$$
2,2,1()ffKK?$$
Example：
H I ( g )2g)(Ig)(H 22 ??
H I ( g )g)(Ig)(H 221221 ??（ 1）
（ 2）
is referred to
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Empirical equilibrium constants
Distinguish the thermodynamic equilibrium
constant from pressure and composition
equilibrium constants,Example：
D E G Hd e g h? ? ? ? ?
BHG
Bd B
DE
g h
p e
ppKp
pp
??? ? ?
?
pK
1,Pressure equilibrium constant
when? ? 0B?
pK
(Dimension
is unity)
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BHG
BB
DE
g h
x de
xx
Kx
xx
??? ? ?
?
??
? B
B?
pKK px
xK
2.mole fraction equilibrium constant
A pg obeys Dolton partial pressure law，
BB pxp ?
Empirical equilibrium constants
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BHG
BB
DE
g h
c de
cc
Kc
cc
??? ? ?
?
??
? B
B
)(
?
RTKK pc
cK
3,Concentration equilibrium constant
pg，
c R Tp ?
Empirical equilibrium constants
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B
BB
?aK
a ??
，
BB
B
ca
c
??
$
B
B
()a c rK K K c ??? ? ? ? $
aK
4,Activity equilibrium constant
Empirical equilibrium constants
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Different Forms of Equilibrium Constants
? ?
? ? aA
b
B
mr PP
PP
RTKG ?
?
?
/
/
ln)298( ??? ?KRT ln??
? ?
? ? aA
b
B
PP
PP
K
?
?
?
/
/
? ? ? )( ab
a
A
b
B P
P
P ??
? ?
)()( ab
P PK
??? ?
)()(
)(
)( ab
a
A
b
B P
RTC
RTC ??
? ?
)()( ab
a
A
b
B
RT
P
C
C ??
?
?
)()( ab
C RT
PK ??? ? ? ?? ?
)(
/
/ ab
a
A
b
B
RTC
P
CC
CC ???
?
??
?
?
? ?
?
?
?
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Heterogeneous chemical reaction
32C a C O ( s ) C a O ( s ) C O ( g )?
2(C O ) /pK p p?$$
is dissociation pressure)CO(
2p )s(C a C O 3
Consider a reaction
Equilibrium between ideal gas and pure condensed
phases,If the substances taking part in the
chemical equilibrium is of more than one phase,
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dissociation pressure
S ( g )H)g(NHH S ( s )NH 234 ??
example：
S)H()NH( 23 ppp ??
3 2( N H ) ( H S)
p
p p
p
K
p
?? $$ $ 214 ( / )pp? $
It is said earlier that chemical potentials of
condensed phases are insensitive to the pressure
change,unless the pressure is very large.
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The standard Gibbs function of formation
△ G concentrates our attention on the system,
and lets us avoid having to think explicitly
about the entropy of the surroundings,In an
isothermal change △ G can be related to the
enthalpy and entropy changes of the system by
? ?BGG mfBmr ?? ? ??? ?
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rm ln aG R T K? ? ?
$$
rme x p ( / )aK G R T? ??
$$
1,Using △ rG?m,calculate the thermodynamic
equilibrium constant:
The standard Gibbs function of reaction
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2 2 r m( 1) C ( s) O ( g) C O ( g) ( 1 )G? ? ? $
1 2 2 r m2( 2 ) C O ( g ) O ( g ) C O ( g ) ( 2 )G? ? ? $
1 2 r m2( 3) C ( s) O ( g) C O ( g) ( 3 )G? ? ? $
r m r m r m( 3 ) ( 1 ) ( 2 )G G G? ? ? ? ?$ $ $
(1 )( 3 )
( 2)
p
p
p
KK
K?
$
$
$
(1) - (2) 得（ 3）
2,计算实验不易测定的平衡常数
例如，求 的 平衡常数1 2
2C ( s ) O ( g ) C O ( g )??
The standard Gibbs function of reaction
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The standard Gibbs function of reaction
3．近似估计反应的可能性
r m r m ln pG G R T Q? ? ? ?$
只能用 判断反应的方向。但是，当
的绝对值很大时，基本上决定了 的值，所以可
以用来近似地估计反应的可能性。
0,,mr f)( ?? wpTG rmG? $
mrG?
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fmG?
$
（ B,?,T）
The standard Gibbs function of formation
Define the Gibbs function of reaction and calculate
it from tables of Gibbs function of formation.
Calculate the equilibrium constants for reactions on
the basis of the Gibbs function information given in
Table X.X.
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is very important
fmG? $
r m B f m
B
( B )GG ?? ? ??$$
rmG?
$
At T(1)
??
mrmr STH ????
dTCKH mp
T
K
rmr,
2 98
)2 9 8( ? ???? ?
})198({
298
,? ????
T
K
mpr
mr T
dTC
KST ?
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How equilibrium responds to temperature.
If the equilibrium constant is known at a
temperature T*,its value at another temperature T
can be found as follows,In each case
?
?
? ???
RT
TG
TK mr
)(
)(ln
?
RT
TG
TK mr
)(
)(ln
??
??
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How equilibrium responds to temperature
Subtracting these relates the two equilibrium
constants:
?
?
?
?
?
?
?
? ?
?
?
?? ?
?
? RT
TG
RT
TG
TK
TK mrmr )()(
)(
)(
ln
??
Now write △ G = △ H - T △ S,and make the
approximation that neither △ H nor △ S changes
significantly over the temperature range of interest:
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The isobaric equation of chemical reaction.
?
?
?
?
?
? ?
?
?
?
?
?
?
??
?
?
?
? R
TS
RT
TH
R
TS
RT
TH
TK
TK mrmrmrmr )()()()(
)(
)(
ln
????
?
?
?
?
?
?
?
?
?? ?
?
TTR
TH mr 11)(?
)(
)(
ln ?
TK
TK
The last equation is very remarkable because it
predicts the shift in equilibrium when the temperature
is changed; all we need to known is the standard molar
enthalpy of reaction.
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Deduce the isobaric equation
2
)
)(
(
T
H
T
T
G
mr
p
mr
?
?
?
??
?
?
?
??
fmr KRTG ln???
?
?
f
mr KR
T
G ln???
p
f
T
K
R )
ln
(
?
?
??
?
2
ln
RT
H
dT
Kd
mrf
?? ?
?
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The T affects the chemical equilibrium
The infinitesimal expression of van’t Hoff relation
rm
2
d l n
d
pK H
T RT
?
?
$ $
对吸热反应，,升高温度,增加，
对正反应有利。
rm 0H??$ pK$
对放热反应，,升高温度,降低，
对正反应不利。 p
K$rm 0H??$
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The T affects the chemical equilibrium
If we assure that does not depend on the
temperature this equation integrates to
rmH? $
2 rm
121
() 11
l n ( )
()
p
p
KT H
R T TKT
???$ $
$
C
RT
H
K mrf ?
?
??
?
?ln
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The T affects the chemical equilibrium
当理想气体用浓度表示时，因为,可以得到p cR T?
rm
2
d l n
d
cK U
T RT
??$ $
2 rm
121
() 11l n ( )
()
c
c
KT U
R T TKT
???$ $
$
这个公式在气体反应动力学中有用处。
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The van’t Hoff equation
Provides a way of measuring the enthalpy of a
reaction without using a calorimeter,but in practice
it is inaccurate.
Equilibrium compositions are measured over a
range of temperatures (at constant pressure),and
lnK is plotted against 1/T,It follows from eq.that
the slope is -△ Hm?/R.
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The P affects the chemical equilibrium
Le chatelier原理,增加压力，反应向体积减小的
方向进行 。这里可以用压力对平衡常数的影响从本
质上对原理加以说明。
BB
B
()p pK p ???$ $
B
p
py B ?
???
B
)( ?
? B
p
pk
y
?
? )(
)l n (lnlnln ?? ?? ppkK BBy ?? ???
Tp
K
)
ln
(
?
? ?
T
y
p
k
)
ln
(
?
?
? p
B?? ? = 0
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The P affects the chemical equilibrium
T
y
p
k
)
ln
(
?
?
p
B??? ? 0?
? 0?B? aA=bB
0?ab ?
ab ?
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The inert gas affects the chemical equi.
对于分子数增加的反应，加入水气或氮气，会使
反应物转化率提高，使产物的含量增加。
)l n (lnlnln ?? ?? ppkK BBy ?? ???
? ???
B B
B
By B
B
B
n
n
yk ?
?
? ?? ? Bnk
n
?
pT
n
pT n
k
n
K
,,)
ln()ln(
?
??
?
? ?
0?? ?
n
B?
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5.9 simultaneous equilibrium
在一个反应体系中，如果 同时发生 几个反应，
当到达平衡态时，这种情况称为同时平衡。
在处理同时平衡的问题时，要考虑每个物质的
数量在各个反应中的变化，并在各个平衡方程式中
同一物质的数量应保持一致 。
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simultaneous equilibrium
例题, 600 K时,与 发生反应生成,
继而又生成,同时存在两个平衡：
3C H C l(g) 2H O(g) 3CH OH
32(C H ) O
3 2 3
3 3 2 2
( 1 ) C H C l ( g ) H O ( g ) C H O H ( g ) H C l ( g )
( 2 ) 2 C H O H ( g ) ( C H ) O ( g ) H O ( g )
??
?
已知在该温度下,。今以等量
的 和 开始，求 的平衡转化率。
,1,20, 0 0 1 5 4,1 0, 6ppKK??$$
3CH Cl 2HO 3CH Cl
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simultaneous equilibrium
解,设开始时 和 的量为 1.0，到达平衡时，
生成 HCl的量为 x,生成 的量为
y，则在平衡时各物的量为：
3CH Cl 2HO
32(C H ) O
3 2 3( 1 ) C H C l ( g ) H O ( g ) C H O H ( g ) H C l ( g )
1 1 2xy x xyx
??
? ???
3 3 2 2( 2 ) 2 C H O H ( g ) ( C H ) O ( g ) H O ( g )
-2 1- xyx yy
?
?
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simultaneous equilibrium
因为两个反应的 都等于零，所以
pxKK?$B
B
??
,1
,2 2
( 2 )
0,0 0 1 5 4
( 1 ) ( 1 )
( 1 )
1 0,6
( 2 )
p
p
x y x
K
x x y
y x y
K
xy
?
??
? ? ?
??
??
?
$
$
将两个方程联立，解得 。
的转化率为 0.048或 4.8? 。
0, 0 4 8,0, 0 0 9xy??
3CH Cl
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5.10 Coupled Reactions
It can be seen quite often that certain reactions are
not spontaneous i.e,△ G ＞ 0,But if the same
reactions are coupled to other reactions,which are
spontaneous,the original reactions become feasible,
This can only be possible if the total free energy
change I.e.,sum of the free energies of the second
and the original reaction is negative.
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Application of Coupled Reactions
例如：在 298.15 K时：
-12 2 4 2 r m,1 ( 1 ) T i O ( s ) 2 C l ( g ) T i C l ( l ) O ( g ) 1 6 1, 9 4 k J m o l G? ? ? ? ? ?$
反应 (1),(2)耦合，使反应 (3)得以顺利进行。
-12 2 r m,2(2 ) C ( s ) O ( g ) C O ( g ) 3 9 4, 3 8 k J m o lG? ? ? ? ? ?$
-1
r m
2 2 4 2
,3
( 3 ) T i O ( s ) C ( s ) 2 C l ( g ) T i C l ( l ) C O ( g )
2 3 2, 4 4 k J m o l G ??
?
?
??
?
?则
$
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Thermodynamic data from K
The standard Gibbs free energy for the forward
reaction is related to the equilibrium constant by
the expression,
The ?H can be obtained from the variation of
lnK with temperature:
The ?S is then calculable as …
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5.11 Approximately Calculation
1,的估算
rm()GT? $
r( 2 9 8, 1 5 K )T ?
r
r
r m r m r m
r m r m r
r m r m r
( ) ( ) ( )
( ) ( ) d
( ) ( ) d
T
p
T
T
p
T
G T H T T S T
H T H T C T
C
S T S T T
T
? ? ? ? ?
? ? ? ? ?
?
? ? ? ?
?
?
$ $ $
$$
$$
当 不大，或不要作精确计算时，设,则：pC? 0pC??
r m r m r r m r( ) ( ) ( ) G T H T T S T a b T? ? ? ? ? ??$ $ $
这里实际上设焓和熵变化值与温度无关，从
298.15 K的表值求出任意温度时的 值。
rmG? $
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Physical transitions
For an equilibrium between a liquid A and a gas
A (the vaporization and condensation of A):
)()( gl AA ?
At P?,T;
??
l
??
g
??? ??
lgmr G ???
)}l n ({ ??? ??
P
PRT A
gg
?
???
??? p
lg ??
? ??? P
gg ??
?
)ln ( ?
P
PRT A???
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Approximately Calculation
2．估计反应的有利温度
r m r m r m( ) ( ) ( )G T H T T S T? ? ? ? ?$ $ $
通常焓变与熵变在化学反应中的符号是相同的。
要使反应顺利进行，则 越小越好。
rm()GT? $
r m r m( 1 ) ( ) 0,( ) 0H T S T? ? ? ?$$
提高温度对反应有利。
r m r m( 2 ) ( ) 0,( ) 0H T S T? ? ? ?$$
降低温度对反应有利。
The end
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JACOBUS HENRICUS VAN’T HOFF
JACOBUS HENRICUS VAN’T HOFF (1852-1911)
Dutch physical chemist,received the first Nobel
Prize in chemistry in 1901 for,the discovery of the laws
of chemical dynamics and of osmotic pressure.” Van’t
Hoff was one of the early developers of the laws of
chemical kinetics,developing mehtods for determining
the order of a reaction;he deduced the relation between
temperature and the equilbrium constant of a chemical
reaction,
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JACOBUS HENRICUS VAN’T HOFF
In 1874,van’t Hoff (and also J.A,Le Bel,independently)
proposed what must be considered one of the most
important ideas in the history of chemistry,namely the
tetrahedral carbon bond,Van’t Hoff carried Pasteur’s
ideas on asymmetry to the molecular level,and
asymmetry required bonds tetrahedrally distributed
about a central carbon atom,Structural organic
chemistry was born.
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JOHN DALTON
JOHN DALTON (1766-1844)
English chemist,physicist,and meteorologist,is
considered by many to be the,father of the atomic
theory of matter,although grandfather is perhaps a more
he suffered,In 1803,he published his paper
“Absorption of Gases by Water and Other Liquids,” in
which he presented what is now known as Dalton’s law
of partial pressures,
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JOHN DALTON
He was led to his theory of atomism by his studies of
gases,In one of his papers published in 1805,he said,
“Why does not water admit its bulk of every kind of gas
alike?…The circumstance depends on the weight and
number of the ultimate particles of the several gases.”
John Dalton was led to the atom by reflecting that
different gases had different values of the Henry’s law
constant.
