Chemical Reaction Equilibria

Chapter 13-Part I

Definition of reaction coordinate

A A + B B C C + D D

Stoichiometric coefficients: by convention are <0 for reactants and >0 for products

As the rxn progresses, there is a change in the number of moles of each species, proportional to the stoichiometric numbers

ddndndndn

D

D

C

C

B

B

A

A .......

Reaction coordinate (e)• We defined:

dni = i dIntegrating between ni

o and ni and between 0 and :ni = ni

o + i

Summing over all species:

Mole fractions:

example4NH3 (g)+ 5O2(g)4NO(g)+6H2O(g)

Initially there are 2 mol NH3 and 5 mol O2

• Find mole fractions of reacting species as functions of the reaction coordinate,

• nNH3 = 2 -4

Two or more simultaneous reactions

• One reaction coordinate j for each reaction

jj

jjj i

jiji j

ji

jj

jiioi

jj

jii

nnnn

nn

ddn

0,0,0

,

,

(i) components allover Summing

gintegratin

exampleC2H4(g) + ½ O2(g) ((CH2)2)O(g)

C2H4(g) + 3 O2(g)2CO2(g) +2H2O(g)

• Initially there are 2 mol of C2H4(g) and 3 mol of O2(g). Find expressions for the mole fractions of the reacting species as functions of the reaction coordinates for the two reactions.

j i C2H4 O2 ((CH2)2)O CO2 H2O j

1

2

no =

jjjo

jj

jiio

i n

n

y

,

C2H4(g) + ½ O2(g) ((CH2)2)O(g)C2H4(g) + 3 O2(g)2CO2(g) +2H2O(g)

no(C2H4) =2; no (O2)=3

Equilibrium criteria for chemical reactions

• We showed that the total Gibbs energy of a closed system at constant T and P must decrease during an irreversible process.

• At equilibrium: (dG)T,P =0

• For a reacting system, G must be a minimum at equilibrium

Given G=G minimize and get the value of at equilibrium. Then you can calculate the equilibrium mole fractions y()

how to introduce in the dG expression

0

therefore

)()()(

since

)()()(

,,

TP

t

TPi

ii

ii

i

ii

ii

i

GnGν

dενdTnSdPnVnGd

dενdn

dndTnSdPnVnGd

Criterion of chemical equilibrium0 i

ii

Now we need to express the chemical potentials as functions of fugacities

iii fRTT ˆln)(

Solve for i and substitutein the equilibrium criterion

00 ln)( iii fRTTG

00

ˆln

_____________________

i

iii

f

fRTG

0ˆ

ln0

0

i

ii

ii

f

fRTG

Definition of equilibrium constant K

0ˆ

ln0

0 i

i

iii

ii

f

fRTG

0ˆ

ln0

0

i i

ii

ii

i

f

fRTG

i

ii

i

i

i

RT

G

f

fi

0

0

ˆln

Equilibrium constant K

00

0

0

ln

exp

ii

iGG

RT

GK

RT

GK

where

K is a function of temperature

Example: Water-gas shift reactionH2(g)+CO2(g)H2O(g)+CO(g)

Data for G0 is given. For a temperature of 1000 K and for a feed of 1 mol H2 and1 mol CO2, Determine the equilibrium value of

=no =yH2= yCO2=yH2O= yCO=

Go data (J/mol)T(K) H2O CO CO2

1,000 -192,420 -200,240 -395,790

1,100 -187,000 -209,110 -395,960

1,200 -181,380 -217,830 -396,020

1,300 -175,720 -226,530 -396,080

1,400 -170,020 -235,130 -396,130

1,500 -164,310 -243,740 -396,160

2

ln2

22

)1(ln

2

)1(2)240,200420,192(

2)790,395(

2

1)(

RTG

ii

iii

i yyRTGyG ln0

dG/d = 0 =0.453