Chemical-Reaction Equilibra ERT 206: Thermodynamics Miss Anis Atikah Ahmad Tel: 04-9763245 Email: anis [email protected].

Chemical-Reaction Equilibra

ERT 206: ThermodynamicsMiss Anis Atikah Ahmad

Tel: 04-9763245 Email: anis [email protected]

OUTLINE

1. The Reaction Coordinate2. Application of Equilibrium Criteria to Chemical

Reactions3. The Standard Gibbs-Energy Change & the

Equilibrium Constant4. Effect of Temperature on the Equilibrium Constant5. Relation of Equilibrium Constants to Composition6. Multireaction Equilibria

1. The Reaction Coordinate

• The general chemical reaction is written as:

is the stoichiometric coefficient * positive (+) for product

* negative (-) for reactant stands for chemical formula

..... 44332211 AvAvAvAv

iv

iA

1. The Reaction Coordinate• For reaction:

the stoichiometric numbers are:

If 0.5 mol of CH4 and 0.5 mol of H2O dissappear in reaction;

Thus;0.5 mol of CO and 1.5 mol of H2 are formed.

224 3HCOOHCH

14

CHv 12

OHv 1COv 32Hv

dv

dn

v

dn

v

dn

v

dn ...

4

4

3

3

2

2

1

1Reaction coordinate (the extent

or degree to which a reaction has taken place)

The general relation connecting the differential change dni with dε:

Integrating;

Summation over all species;

where


dvdn ii

0

0

dvdn i

n

n

i

i

i

iii vnn 0

vnn 0 i

inn i

inn00

iivv

The mole fraction yi of the species:


vn

vn

n

ny iiii

0

0

Example 1

For a system in which the following reaction occurs:

Assume there are present initially 2 mol CH4, 1 mol H2O, 1 mol

CO and 4 mol H2. Determine expressions for the mole fractions yi

as a function of ε


224 3HCOOHCH

Recall:Example 1-SOLUTION


vn

vn

n

ny iiii

0

0

224 3HCOOHCH

23111 i

ivv

8411200

iinn

28

24

CHy

28

1

COy28

12

OHy

28

342

Hy

14

CHv 12

OHv 1COv 32Hv

204CHn 1

02OHn 1

0COn 4

02Hn

Multireaction Stoichiometry:

When two or more independent reactions process simultaneously,

Where j serves as the reaction indexanda separate reaction coordinate εj applies to each reaction.


j jj

j jjii

i vn

vny

0

,0

Example 2: Multireaction

Consider a system in which the following reaction occur:

If there are present initially 2 mol of CH4, and 3 mol H2O,

determine expressions for the mole fractions yi as a function of

ε1 and ε2.


13 224 HCOOHCH

242 2224 HCOOHCH

Recall:

j jj

j jjii

i vn

vny

0

,0

Example 2: Multireaction- Solution


13 224 HCOOHCH 242 2224 HCOOHCH

i CH4 H2O CO CO2 H2

j vj

1 -1 -1 1 0 3 2

2 -1 -2 0 1 4 2

j 204CHn 3

02OHn

Given:

21

21

225

24

CHy21

1

225

COy

21

21

225

232

OHy21

21

225

432

Hy

231111,1 i

ivv

53200

iinn

Recall:

j jj

j jjii

i vn

vny

0

,0

241212,2 i

ivv

21

2

2252

COy

• Criterion of equilibrium at constant T & P:– The total Gibbs

energy Gt is a minimum

– Its differential is zero

2. Application of Equilibrium Criteria to Chemical Reactions

Total Gibbs Energy vs Reaction Coordinate

0, PTtnGd

Any reaction that occurs at constant T & P must lead to decrease in the total Gibbs

energy of the system

From previous chapter,

Since ,

At constant T and P,

At equilibrium state,

Thus,

3. The Standard Gibbs-Energy Change & The Equilibrium Constant

ii

idndTnSdPnVnGd

dvdn ii

dvdTnSdPnVnGdi

ii

PT

t

PTiii

GnGv

,,

0

,

PT

tG

0i

iiv

Recall fugacity of a species in solution;

The fugacity of pure species in its standard state;

The difference between these two equations;


iii fRTT ˆln

iii fRTTG ln

(1)

(2)

i

iii f

fRTG

ˆln

i

iii f

fRTG

ˆln (3)

Substituting into ;

OR

OR

In exponential form;

where ,


i

iii f

fRTG

ˆln 0

iiiv

0ˆln

iiiii ffRTGv

0ˆln

i

v

iiii

i

ffRTGv

RT

Gvff i

ii

i

v

ii

i

ˆln

Kffi

v

ii

i ˆ

RT

GK exp

iiiGvG

Equilibrium constant

Standard Gibbs energy change of

reaction

Depends only on T

4. Effect of Temperature on the Equilibrium Constant

The relation between standard heat of reaction and the standardGibbs energy change of reaction;

Integrating;

dT

RTGdRTH

2

2RT

H

dT

RTGd

2

ln

RT

H

dT

Kd

RT

GK exp

TTR

H

K

K 11ln

For exothermic (-ΔH°): As T increases, K decreases.For endothermic (+ΔH°): As T increases, K increases.

Equilibrium constant as a function of temperature

5. Relation of Equilibrium Constants to Composition

• For Gas Phase Reaction:– The standard state for a gas is the ideal gas state of the

pure gas at the standard-state pressure P° of 1 bar.

– Since the fugacity of an ideal gas is equal to its pressure,

, thus becomes: Kff

i

v

ii

i ˆ

KPfi

v

i

i ˆ

Pfi


• Since , becomes;

where

• For pressures sufficiently low or temperature sufficiently high, the equilibrium mixture behaves essentially as an ideal gas. Thus,

KP

Py

v

i

v

ii

i

Pyf iii ˆ

KP

Py

v

i

vi

i

1ˆ i

KPfi

v

i

i ˆ

i

ivv


• For liquid phase reactions:

From previous chapter, . Thus,

Kffi

v

ii

i ˆ

iiii fxf ˆ

i

iii

i

iii

i

i

f

fx

f

fx

f

f ˆ

Can be substituted by Gibbs energy

expression


• For liquid phase reactions:

Integration of at constant T:

Thus, OR

or

i

iii f

fRTGG ln

PPVdPVGG i

P

P

iii

RT

PPV

f

f i

i

i

ln

iii fRTTG ln

iii fRTTG ln

i

iii f

fRTGG ln

SdTVdPdG

PPVf

fRT i

i

iln

RT

PPV

f

f i

i

i exp


Substituting into

Since

Thus,

iii

v

iii Vv

RT

PPKx i exp

i

iii

i

i

f

fx

f

f ˆ

RT

PPVx

f

f iii

i

i

exp

ˆ

RT

PPV

f

f i

i

i exp

Kffi

v

ii

i ˆ

K

RT

PPVx

i

v

iii

i

exp


For low to moderate pressure, the exponential term is close to unity and may be omitted. Thus

If the mixture is an ideal solution, is unity. Therefore,

Kx iv

iii

i

Kx iv

ii Law of mass action


Example 3The water-gas-shift-reaction,

is carried out under the different sets of conditions described below. Calculate the fraction of steam reacted in each case. Assume the mixture behaves as an ideal gas.

(a) The reactants consist of 1 mol of H2O vapor & 1 mol of CO. The temperature is 1,100 K and the pressure is 1 bar.

(b) Same as (a) except the pressure is 10 bar.(c) Same as (a) except that 2 mol of N2 is included in the reactants.

(d) The reactants are 2 mol of H2O & 1 mol of CO. Other conditions are the same as in part (a)

(e) Same as (a) except that the temperature is 1,650 K.

gHgCOgOHgCO 222


Example 3-Solution(a) The reactants consist of 1 mol of H2O vapor & 1 mol of CO. The temperature is

1,100 K and the pressure is 1 bar.

At T=1100 K, 104/T=9.05.From the ln K vs 1/T graph,At 1/T=9.05, ln K =0Thus, K= 1

gHgCOgOHgCO 222

KP

Py

v

i

vi

i

01111 i

ivv

111

10

2

22

OHCO

COH

yy

yy


Example 3-Solution(a) The reactants consist of 1 mol of H2O vapor & 1 mol of CO. The temperature is

1,100 K and the pressure is 1 bar.

Thus, fraction of steam reacted = 0.5

gHgCOgOHgCO 222

2

1 eCOy

vn

vny iii

0

0

2110 n

2

12

eOHy

22

eCOy

22

eHy

12

22 OHCO

COH

yy

yy

Substitute into

1

1 2

2

e

e

5.0e


Example 3-Solution(b) Same as (a) except the pressure is 10 bar.

Because v=0, the increase in pressure has no effect on the ideal-gas reaction and εe is still 0.5.

gHgCOgOHgCO 222

KP

Py

i

vi

i

0


Example 3-Solution(c) Same as (a) except that 2 mol of N2 is included in the reactants.

N2 does not take part in the reaction, and serves only as diluent.

Thus, remain unchanged. Therefore, εe is still 0.5

gHgCOgOHgCO 222

12

22 OHCO

COH

yy

yy


Example 3-Solution(d) The reactants are 2 mol of H2O & 1 mol of CO. Other conditions are the same as

in part (a)

gHgCOgOHgCO 222

Thus,

Thus, fraction of steam reacted 0.667/2= 0.333

3

1 eCOy

3

22

eOHy

32

eCOy

32

eHy

12

22 OHCO

COH

yy

yy

Substitute into

3120 n

121

2

ee

e

667.0e


Example 3-Solution(e) Same as (a) except that the temperature is 1,650 K.

At T=1650 K, 104/T=6.06.From the ln K vs 1/T graph,At 1/T=6.06, ln K =-1.15Thus, K= 0.317

gHgCOgOHgCO 222

317.0

1 2

2

e

e

36.0e

Thus, fraction of steam reacted 0.36.Increasing the temperature reduce the conversion.

6. Multireaction Equilibra

• For liquid-phase reaction;

• For gas-phase reaction;

• If equilibrium mixture is an ideal gas;

ji

v

ii Kffji ,ˆ rj ,...,2,1

ji

v

i KPfji ,ˆ rj ,...,2,1

j

v

i

vi K

P

Py

j

ji

,

Chemical-Reaction Equilibra ERT 206: Thermodynamics Miss Anis Atikah Ahmad Tel: 04-9763245 Email: anis [email protected].

Documents

following reaction

reaction coordinate

reaction coordinate

standard heat of reaction

gas phase reaction

equilibrium state

criterion of equilibrium

mol h2o