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Lecture 2

Stoichiometry and Chemical

Reaction Equilibria

Departemen Teknik Kimia

Universitas Indonesia

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Stoichimetry, Extent of Reaction and

ConversionStiochiometry coefficients

a A+ b B c C + d DA + b/a Bc/a C + d/a D

= c/a + d/ab/a -1

A A + B B + CC + D D =0A = -1,B = - b/a,C = c/a,D = d/aI: coeff. stoichiometry 0iiAv

Extent ofreaction,

dn1/v1 = dn2/v2= dn3/v3= = dni/vi= d= (ni-ni0)/vi

Conversion, X

X = (ni0-ni)/ni0 = - (vi/nio)

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Examples:2HI22

IH rf=

kfCH2CI

2

rb=kbCHI

2and

Forward reaction is 1st order in CH2and CI

2( 2nd order overall)

Reverse reaction is 2nd order in CHI

Stoichiometric Equation

This describes theoverall reaction

but the reaction ordercannot

be deduced from it.

Compare the above reaction with the analogous nonelementaryreaction between H2and Br2 .

2HBr22

BrH 2

22

2

211

BrHBr

BrH

f CCk

CCk

r

k1

k2

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Chemical Reaction Equilibrium

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Kinetics vs. Themodynamics

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Chemical Reaction Equilibria

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Equilibrium state for given T and PCriteria :

(G)T,P = (G/)T, P= 0iiv

(G) : Gibbs free energy change, i: the chemical potential

0)ln()( , ii

oiiPT aRTGvG

- RT ln Ka= Go

aaaa

ab

BA

ad

D

ac

CRTG/

//

ln0

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Consider the general reversible reaction:

DcC dbBaA At equilibrium rA=0

Therefore:

Therefore:b

B

a

A

d

D

c

CC

bB

fA

CC

CCK

k

k

Thermodynamic equilibrium relationship

b

B

a

AfAfA CCkr

d

D

c

CbAbA CCkr 0 bAfAA rrr

rfA= rbAdD

c

CbA

b

B

a

AfA CCkCCk

Thermodynamic equilibrium constant

TTR

HTKTK RXCC

11exp)()(

1

1

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TTR

HTKTK RXCC

11exp)()(

1

1

KC

T

KC

T

Endothermic Exothermic

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All reactions are reversible in principle. The extent of reversibility depends on -G, the Gibbs

Free Energy change.

pRTInKG Where Kpis the equilibrium constant interms of partial pressures.

Chemical equilibrium

If Kp is large, reaction is essentially irreversible, whichmeans that the equilibrium position lies very far to the

product side.

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Equilibrium Constants

Pa KKK ai= fi/fi,o= iPi

CCCC

ab

BA

ad

D

ac

CCK /

//

CCCC

ab

BA

ad

D

ac

CCK /

//

Pa KKK

)(RTKK CP

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Impact of T, P, Inert changes

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Total pressure changePi=yi P

KP=KyP

d ln K/dT = Ho(T) /RT2

Temperature change

dTCHTH opoo

)(

plot log K vs 1/T , slope = -(Ho/R), (see Fig EC-1.1)Exo. Reaction (Honegative), K decreases with increasing TEndo. Reaction (Hopositive), K increases with increasing T

Ka=Kf/P [P/nA+ nB+nC+nD+ nI]c+d-a-b)(

dD

cC

bB

aA

nn

nnInert change

Impact of T, P, Inert changes

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Calculation ProcedureDetermine (Go) or (Ho).

a A + b B c C + d D maka:Xo= c. Xof,C+ d. X

of,D a. X

of,A b. X

of,B , X : G, H

Calculate KPat T

with Ho(T) = Ho(25oC) +CpdT2

)(ln

RT

TH

dT

Kd oP

)()(ln TGTKRT o

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Calculation ProcedureCombine equilibrium composition and Equilibrium

constant

b

B

a

A

d

D

c

C

aa

aaK

.

.iiaK

Express in Extent of reaction, composition or conversion

0 iiAv

oi

i

oi

ioiin

v

n

nnX

Solve analytically/graph or numerically

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Example 3-6 The reversible gas-phase decomposition of nitrogentetroxide, N2O4, to nitrogen dioxide, NO2, is to be carried out atconstant temperature. The feed consists of pure N2O4at 340 K and202.6 kPa (2 atm). The concentration equilibrium constant, Kc, at 340

K is 0.1 mol/dm3. BA 2

concentration equilibrium constant:at

equilibrium !!

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(a) Calculate the equilibrium conversion of N2O4in a constant-volume batch reactor.

atequilibrium !!

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(b) Calculate the equilibrium conversion of N2O4in a flowreactor.

atequilibrium !!

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for batch system

for flow system

(c) Assuming the reaction is elementary, express the rate ofreaction solely as a function of conversion for a flow systemand for a batch system.

Elementary reaction:

BA 2

(d) Determine the CSTR volume necessary to achieve 80% of

the equilibrium conversion.

CSTR design equation

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HW2

Scott Fogler P3-11A

P3-15B

P3-16B