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