8 Thermo-Chemistry & Chemical Equilibrium Objective Thermo-effect in chemical reaction and...
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Transcript of 8 Thermo-Chemistry & Chemical Equilibrium Objective Thermo-effect in chemical reaction and...
8 Thermo-Chemistry & Chemical Equilibrium
Objective• Thermo-effect in chemical reaction and evaluation of
reaction heat
• Theoretical adiabatic combustion temperature
• Chemical equilibrium and equilibrium constant
• Judgment on direction and limitation of chemical reaction
• Evaluation on equilibrium constant and dissociation
8.1 1st Law Analysis of Chemical Reaction
8.1.1 Internal Energy and Enthalpy
InternalEnergy
Physical
Chemical
Potential
KineticphU
Depends on componentsIrreverent to temperature chU
ph chU U U
ph chH H H
8.1 1st Law Analysis of Chemical Reaction
8.1.2 Work of Chemical Reaction
Work
Volumetric Work
Non-volumetric Work
W
eW
Example: Electricity by Fuel Cell
tot eW W W
8.1 1st Law Analysis of Chemical Reaction
8.1.3 Heat of Chemical Reaction
Definition:
The heat transferred between system and surroundings
during chemical reaction.
Q > 0: heat transfer to the system
Q < 0: heat transfer from the system
Q = 0: adiabatic
8.1 1st Law Analysis of Chemical Reaction
8.1.4 1st Law of Chemical Reaction
tot P R eQ U W U U W W
δ d δ d d δ δtot P R eQ U W U U W W
Product React
8.2 Thermo-effect of Chemical Reaction
8.2.1 Thermo-effect of chemical reaction
Constant Volume VQ
d 0 0, 0tot
V P R
V W W
Q U U
Constant Pressure PQ
( ) P R tot
P P R P R
W p V V W W
Q U U W H H
定容热效应等于系统内能的变化
定压热效应等于系统焓的变化
0eW P RT TReaction Heat under and
8.2.1 Thermo-effect at Constant Volume and Pressure
Same react
Const. P & T
Const. V & T
Same Product
( ) P V V P RQ Q W Q p V V
For Ideal Gas
( )P V P R mQ Q n n R T
n - gas moles
8.2.2 Hess Law
Hess (Russian 1802-1852) Law
The thermo-effect of chemical reaction only depends
on the initial and ending state of reaction and is unrelated
with reaction path.
It is important that different reactions can be related
through Hess Law.
8.2.2 Hess Law
Example:
2
1C+ O =CO
2
2 2 1
2 2 2
C+O =CO 393520 kJ/kmol
1CO+ O =CO 282990 kJ/kmol
2
p
p
Q
Q
(1)
(2)
(1) - (2) 3 1 2 110530 kJ/kmolp p pQ Q Q
NOTICE:
Hess Law must be applied to the same reaction.
8.2.3 Temperature Effect
Standard Thermo-effect0pQ
The thermo-effect at 101325Pa and
25 .℃aA bB dD eE
aA bB
aA bB
dD eE
dD eE
2pQ
2T
1pQ
1T
RH PH
Two ways:
1. React - Product at T2
2. React T2—T1
React - Product at T1
Product T1—T2
8.2.3 Temperature Effect
aA bB
aA bB
dD eE
dD eE
2pQ
2T
1pQ
1T
RH PH
2 1PT PT R PQ Q H H
1
2
2
1
d
d
T
R i pmiTR
T
P i pmiTP
H nC T
H nC T
Kirchhoff Equation
化学反应的热效应随温度变化,是由于生成物和反应物的物理焓随温度变化而引起的。
Physical enthalpy
8.2.3 Temperature Effect
Generally, the standard thermo-effect is known
The thermo-effect at any temperature
2
2 2
0
298
0 ' ' ' '298 298
( )d
( ) ( )
T
p p i pmi i pmiP R
p T TP R
Q Q nC nC T
Q H H H H
2
12 1 ( )d
T
p p i pmi i pmiTP R
Q Q nC nC T
8.3 Combustion Heat & Production Heat
Fuel +combustion supporting gases = products + heat
Oxygen Air
Theoretical oxygen quantity: according to reaction equation
Theoretical air quantity=4.76× theoretical oxygen quantity
In practical combustions, the air is always excessive
actual air quantityexcess air coefficent=
theoretical air quantity
8.3 Combustion Heat & Production Heat
8.3.2 Combustion Heat & Thermo-effect of Reaction
Combustion Enthalpy:
The thermo-effect of 1 mole fuel during complete
combustion at standard condition. Its absolute value is heat
value.
means:
2
2
2
2
C CO
H H O
S SO
N N
Metal Dissociative State
Gas: Low Heat Value
Liquid: High Heat Value
0ch
0 0 0 0 0 0p P R i i i i
P R
Q H H H n h n h
Total enthalpy of
react and product
Molar enthalpy at
standard condition
at standard
condition 0 0ch h
at any temperature, the molar enthalpy:
0
298d
T
c pmh h C T thermo-effect of chemical reaction:
p i i i iP R
Q n h n h
0 0 0p i ci i ci
R P
Q n h n h
8.3.2 Combustion Heat & Thermo-effect of Reaction
Example: Propane Decomposition0
3 8 2 2 2 1
02 4 2 2 2 2
04 2 2 2 3
C H +5O ==3CO +4H O 2220 kJ/kmol
C H +3O ==2CO +2H O 1411 kJ/kmol
CH +2O ==CO +2H O 890 kJ/kmol
c
c
c
h
h
h
(1)
(2)
(3)(1) - (2) - (3)
3 8 2 4 4C H C H CH
0 0 0 01 2 3
2220 1411 890
81kJ/kmol
c c ch h h h
8.3.3 Production Heat & Thermo-effect of Reaction
0 0 0 0 0 0p P R i i i i
P R
Q H H H n h n h
Total enthalpy of
react and product
Molar enthalpy at
standard condition
The enthalpy of simple substance at standard condition is ze
ro.
Standard Production Enthalpy of Compound
The thermo-effect of 1mol compound produced by stable sim
ple substance at standard condition.
0fh
8.3.3 Production Heat & Thermo-effect of Reaction
at standard
condition 0 0fh h
at any temperature, the molar enthalpy:
0
298d
T
f pmh h C T at any temperature, thermo-effect of chemical reaction:
p i i i iP R
Q n h n h NOTICE: phase change
0 0( ) ( )f g f l evh h h
8.4 Flame Temperature
Adiabatic Combustion:
The heat generated by combustion reaction is totally
used to raise the temperature of products.
Theoretical Flame Temperature:
The highest temperature of adiabatic combustion.
• at constant pressure
• at constant volume
8.4.1 Theoretical Flame Temperature at Constant Pressure
012 iR
iiP
iRTPTp hnhnHHQ
2 10 0
298 298( d ) ( d ) 0
i i
T T
p i f pmi i f pmiP R
Q n h C T n h C T
1st Law
2
2 2
0
298
0 ' ' ' '298 298
( )d 0
( ) ( ) 0
T
p p i pmi i pmiP R
p p T TP R
Q Q nC nC T
Q Q H H H H
8.4.2 Theoretical Flame Temperature at Constant Volume
0VQ
2 1
2 1
2 1
0
( ) ( ) 0
( ) ( ) 0
V PT RT i i i iP R
i i i iP R
i i p m i i R mP R
Q U U nu n u
n h p V n h pV
n h n R T n h n R T
V
TRnp mp 2
2
8.5 Chemical Equilibrium
2nd Law of Thermodynamics:
(d ) 0isoS
Chemical Reaction at Constant Pressure & and Temperature
,( ) 0T pG
8.5.1 Request of Chemical Equilibrium
Chemical Equilibrium:
The state that the concentrations of reactants and
products is not changed with time.
8.5.1 Request for Chemical Equilibrium
aA bB dD eE
d ( ),d ( ),d ( ),d ( )A B D En a dn n b dn n d dn n e dn
At constant pressure and temperature, system is still balanced, so…
d 0 d d 0i iG G n d d d d d
( )d 0
d 0
0
A A B B D D E E
D E A B
D E A B
G n n n n
d e a b n
n
d e a b
即 , 0i i
Stoichiometric Coefficient
Chemical Potential
,, , ,A B D Ep p p pPartial pressure
8.5.2 Chemical Equilibrium Constant
00
00
00
00
ln( / )
ln( / )
ln( / )
ln( / )
D D m D
E E m E
A A m A
B B m B
R T p p
R T p p
R T p p
R T p p
The chemical potential equation is applied to react (A,B) and product
(D,E). Their pressure is
0 0 0 00
0 0 0
[ ln( / )
ln( / ) ln( / ) ln( / )] 0D E A B m D
E A B
d e a b R T d p p
e p p a p p b p p
0 0 0 0 0 0 0 0 0T D E A B D E A BG d e a b dG eG aG bG
8.5.2 Chemical Equilibrium Constant
Standard-state Free Enthalpy Change
0
0
1ln
d eD E
Ta bA B m
p pG
p p p R T
( ) ( )d e a b
f(T)
0
0
Constant
Constant
T
d eD E
p a bA B
G
p pK
p p p
For given reaction at constant temperature
Chemical Equilibrium Constant
化学平衡常数
8.5.2 Chemical Equilibrium Constant
pK indicates the numerical relationship between react
and product in system when equilibrium.
Concentration of ProductpK
In handbook 0 101325Pap
0 lnT m pG R T K
1.Single phase2.All the components are gas.
8.5.2 Chemical Equilibrium Constant
If multi-phases and solid or liquid exists:
Because the saturated vapor pressure of solid or liquid is not change and has no relation with its quantity. So…
2
2
2CO
C CO
C(s)+CO 2CO
'p
pK
p p
Constant2
2CO
COp
pK
p
有多聚相的多相反应的平衡常数由参加反应的气态物质的分压确定。
8.5.2 Chemical Equilibrium Constant
• Chemical Equilibrium Constant - Concentration
TnRpV m
V
nC
TR
pC
m
( )( ) ( )d e d e d e
a b d eD E D E D Ec m ma b a b a b
A B A B A B
C C p p p pK R T R T
C C p p p p
)( 0
TR
pKK
mPc 0 c PK K
• Chemical Equilibrium Constant - Relative Molar Number
8.5.2 Chemical Equilibrium Constant
bB
aA
eE
dD
y yy
yyK
i ii
n py
n p
01( ) ( )
d eD E
y pa bA B
pp pK K
p p p p
0 0
( ) ( )d eD E
p y a bA B
n np pK K
p n n n p
0( ) ( )y p c
p VK K K
p n
0 y P CK K K f(T,p)
8.5.2 Chemical Equilibrium Constant
Remarks on Chemical Equilibrium Constant
① The pK of a reaction depends on the temperature only.
Example: at specific temperature the following four reactions have
same valuepK
2 2 2
2 2 2
2 2 2 2 2
2 2 2 2 2 2
1H + O H O at 1 atm
21
H + O H O at 5 atm21
H + O +3N H O+3N at 5 atm2
H +2O +5N H O+1.5O +5N at 2 atm
8.5.2 Chemical Equilibrium Constant
② pK is independent of the pressure of the equilibrium mixture.
00 101325PaTG p
③ Kp is relevant to the form of reaction equation, when the stoichio
metric coefficients are doubled, the value of Kp is squared. 2
2
2
2
2
2
CO2 2 1 1 2
CO O
2CO
2 2 2 2CO O
1 2CO O
2 2 3CO 3
1CO+ O CO
2
2CO+O 2CO
1 1CO CO+ O
2
p
p
pp
pK
p p
pK
p p
p pK
p K
8.5.2 Chemical Equilibrium Constant
⑤ Evaluation of complex reaction through simple ones.
22 COO2
1CO
21
OCO
CO1
2
2
.pp
pK p
OHO2
1H 222
21
O.H
OH2
22
2
pp
pK p
222 HCOOHCO 2
1
OHCO
HCO3
2
22
.
.
p
pp K
K
pp
ppK
④ The larger the Kp, the more complete the reaction.A reaction with 1000 is assumed to preceed to completion.
A reaction with 0.001 is assumed not to occur at all.
p
p
K
K
8.5.3 Evaluation of Equilibrium Composition
Reaction Equation
Composition of Product
Equilibrium Constant
Equilibrium Composition
Following Steps:
① Reaction Equation
② Mass Equilibrium Equation
③ Equilibrium Constant
④ Solution to Equilibrium Composition
8.5.3 Evaluation of Equilibrium Composition
Example 8-3:
2 2 3
1 3N + H NH
2 2
400 , 30.4MPa℃
0.0138pK
2 2N :H 1: 3Init. Mol
React Mol
Equi. Mol
1 3 0
x 3x 2x1-x 3(1-x) 2x
Tot. Mol 1 3(1 ) 2 4 2n x x x x
3
2 2
NH
1 2 3/ 2N H 0
( ) 0.0138p
n pK
n n n p
,x n
2
2
3
N
H
NH
1
3(1 )
2
xy
nx
ynx
yn
8.6 Direction & Limits of Chemical Reaction
aA bB dD eE any pressure ' ' ' ', , ,A B D Ep p p p
at constant temperature and pressure
( )D E A BG d e a b for ideal gas
0
0
ln( )ii i m
pR T
p
' '0 0 0 0
' '0
' '0
' '0
ln
ln
d eD E
D E A B m a bA B
d eD E
T m a bA B
p pG d e a b R T
p p p
p pG R T
p p p
压力商
' '0 0
' '0
ln lnd e
D ET m T m pa b
A B
p pG G R T G R T J
p p p
8.6 Direction & Limits of Chemical Reaction
ln lnm p m pG R T K R T J
0,
0,
0,
p p
p p
p p
J K G
J K G
J K G
Spontaneously positive reaction
Spontaneously reverse reaction
Equilibrium State
8.7 Variation of Chemical Equilibrium
8.7.1 Temperature0
ln Tp
m
GK
R T
G H TS
G H T S
for reactant and product
( )i idG SdT Vdp dn
11
22
( )
( )
p
p
GS
TG
ST
( ) pG
ST
( ) pG
G H TT
at 101325MPa and constant temperature
0 0 0
( )T Tp
G G H
T T
2
0
)ln
(TR
H
T
K
mp
p
Vant’Hoff Equation
Enthalpy only depends on temperature for ideal-gas:
222
ln
TR
Q
TR
HH
TR
H
dT
Kd
m
p
m
Rp
m
p
8.7 Variation of Chemical Equilibrium
222
ln
TR
Q
TR
HH
TR
H
dT
Kd
m
p
m
Rp
m
p
• for endothermic reaction
d( ln )0 0
dp
p
KQ
T
product reactantpT K or T reaction more complete
• for exothermic reaction
d( ln )0 0
dp
p
KQ
T
product reactpT K or T reaction more uncomplete
8.7 Variation of Chemical Equilibrium
p
pvK
p Ty0)(ln
0( ) vy p
pK K
p
0 (ln ) 0 product , reacty TL R
Kp
压力增大,可以使摩尔数减少的反应进行得更完全一些。
0 (ln ) 0 product , reacty TL R
Kp
压力增大,可以使摩尔数增加的反应进行得更不完全一些。
8.7 Variation of Chemical Equilibrium
8.7.2 pressure
惰性气体的影响可以这样理解:在总压不变的条件下,增加惰性气体的量实际上起到了稀释的作用,因此它和减少反应系统总压的效应是一样的。
8.7 Variation of Chemical Equilibrium
8.7.3 Inert gases
0 0
( ) ( )d eD E
p y a bA B
n np pK K
p n n n p
if 0, then unchange product( , )
if 0, then unchange product( , )
p D E
p D E
n K n n
n K n n
如果把决定化学平衡的因素加以改变,则化学反应重新开始,新的化学平衡向着抵消或削弱这种因素的改变的方向移动。这个定律称为平衡移动定律,或吕 · 查德里原理。
•增高(或降低)温度,则反应向吸热(或放热)的方向进行;•增加(或减小)压力,则反应向摩尔数减小(或增大)的方向进
行;•增加(或减小)反应物的浓度,则反应正向(或逆向)进行;•增加(或减小)生成物的浓度,则反应逆向(或正向)进行;•增加(或减小)惰性气体的量,则反应向体积增大(或减小)的
方向进行。
8.7 Variation of Chemical Equilibrium
summary
The enthalpy of simple substance at standard condition is zero.
Standard Production Free Enthalpy of Compound
The free Enthalpy difference of 1mol compound produced by st
able simple substance at standard condition.
8.8 Evaluation of Equilibrium Constant pK
aA bB dD eE 0 0 0 0 0
0 0 0 0
T D E A B
D E A B
G d e a b
dg eg ag g
0 0 0 0 0298 ( ) ( ) ( ) ( ) f D f E f A f BG d g ed g ad g b g
0 fg
For ideal gas reactions
8.8.1 Based on Standard Production Free Enthalpy
Example:
试用标准生成自由焓的数据,求出 25℃ 时的平衡常数 pK
已知反应
8.8 Evaluation of Equilibrium Constant
8.8 Evaluation of Equilibrium Constant
8.8.1 Based on the third law of thermodynamics
The third law of thermodynamics
The entropy of any perfect crystal is zero. 00lim 0T
S
0( )0
0( ) ( )0
0( ) ( ) ( )0
dfor solid:
d dfor liquid:
d d dfor gas:
f
f
f b
f b
T
T pm s
T TfT pm s pm lT
f
T T Tf vT pm s pm l pm gT T
f b
Ts C
THT T
s C CT T T
H HT T Ts C C C
T T T T T
Standard entropy:
8.8 Evaluation of Equilibrium Constant
aA bB dD eE 0 0 0 0 0 0 0
T T T T D T E T A T BP R
S S S ds es as bs
0 0 0T T T
G H TS
G H T S
0T
pm
GK
R T
8.8 Evaluation of Equilibrium Constant
8.9 Reversible process of chemical reaction
8.9.1 Reversible process and reversible reaction
Reversible process: the reverse process could be
performed so that the system and surroundings can be
restored to their initial states with no change in the
system or surroundings.
Ex. storage battery
Reversible reaction: the reverse reaction could be
performed.
2 2 3N +3H 2NH
8.9.2 Max. Non-expansion Work
At constant temperature & volume
( ), 0Q T S TS W
, ,max ( )
( )e v
R P
W U TS
U TS A A A
,R PA A Free Energy of Reactant and Product
8.9 Reversible process of chemical reaction
At constant temperature & pressure
)( pVVpW
, ,max P
0 ' ' 0298
0 ' ' 0298
( )
[ ( ) ( 298 ) ]
[ ( ) ( 298 ) ]
i
i
e p R
i f i iR
i f i ip
W H TS G G G
n g h h Ts s
n g h h Ts s
,R PG G Free Enthalpy of React and Product
8.9 Reversible process of chemical reaction
8.10 Dissociation & Its Degree
•离解 (Dissociation) 是指化合物(或反应生成物)分解成为 一些较为简单的物质与元素。•离解度 (Degree of Dissociation, ) 是指达到化学平衡时 ,
物质离解了的百分数。•离解度随着温度和压力的变化符合平衡移动原理。
T p