ERT 316: REACTION ENGINEERING CHAPTER 3 RATE LAWS & STOICHIOMETRY Lecturer: Miss Anis Atikah Ahmad...

ERT 316: REACTION ENGINEERING

CHAPTER 3RATE LAWS & STOICHIOMETRY

Lecturer: Miss Anis Atikah Ahmad

Email: [email protected]

Tel: +604 976 3245

1

mailto:[email protected]

OUTLINE

PART 1: Rate Laws Relative Rates of Reaction Reaction Order & Rate Law Reaction Rate Constant, k

PART 2: Stoichiometry Batch System Stoichiometric Table Flow System Stoichiometric Table Calculation for Concentration in terms of

Conversion

1. RELATIVE RATES OF REACTION

d

r

c

r

b

r

a

r DCBA

dDcCbBaA

21222 NOONO

rrr

EXAMPLE

Reaction Stoichiometr

y

If NO2 formed at 4 mol/m3/s (r NO2

= 4

mol/m3/s), what is the rate of formation of NO?

22 22 NOONO


2

//4

2

3 smmolrNO

21222 NOONO

rrr

smmolsmmol

rNO //42

//42 3

3

222NONO

rr

If NO2 formed at 4 mol/m3/s (r NO2= 4

mol/m3/s), what is the rate of formation of NO?

22 22 NOONO


The Reaction:

is carried out in a reactor. If at a particular point, the rate of disappearance of A is 10 mol/dm3/s, what are the rates of B and C?

CBA 532

EXERCISE


The relative rates are

Given, the rate of disappearance of A, -rA, is 10mol/dm3/s

Thus, solving the rates of B & C;

532CBA rrr

CBA 532

r A= -10 mol/dm3/s

sdmmolrB //102

3 3

32

BA rr

52CA rr

sdmmolrC //102

5 3

sdmmol //15 3 sdmmol //25 3

2. REACTION ORDER & RATE LAW

The reaction rate (rate of disappearance) depends on temperature and composition.

It can be written as the product of reaction rate constant, kA and a function of concentrations (activities) of the reactants involved in the reaction:

..., BAAA CCfnTkr

Rate law is a kinetic expression that gives

the relationship between reaction rate, -rA, and concentration.

2. REACTION ORDER & RATE LAW

For reaction in which the stoichiometric coefficient is 1 for ALL species:

we shall delete the subscript on the specific reaction rate, (e.g.; A in kA) to let

OHNaClHClNaOH kkkkk2

Rate law is a kinetic expression that gives

the relationship between reaction rate, -rA, and concentration.

OHNaClHClNaOH 21111

2.1 POWER LAW MODELS & ELEMENTARY RATE LAWS

Power Law Model:

The rxn is order wrt reactant A𝛂AND

The rxn is order wrt reactant B𝛃The overall order of the reaction, n;

BAA CkCr

n


The unit of the specific reaction, k, will vary with the order of reaction.

ProductsA

Time

ionConcentratk

n

1

AA kr sdmmolk 3/Zero order (n=0)First order (n=1) AAA Ckr 1sk

Second order (n=2)

2AAA Ckr smoldmk /3

Third order (n=3)3AAA Ckr 123 / smoldmk


Elementary reaction: a chemical reaction in which one or more of the chemical species react directly to form products in a single reaction step and with a single transition state.

Elementary rate law: The rxn is said to follow the elementary rate law if the stoichiometic coefficients are IDENTICAL to the reaction order of each species.

A Products

BA Products

Unimolecular reaction

Bimolecular reaction

22 22 NOONO

2

2ONONONO CCkr

Non-elementary

rxn

But follows the elementary rate law!

EXAMPLES OF REACTION RATE LAWS



Non-elementary rate laws: reactions that do not follow simple rate laws (power rate laws).

Example 1: Homogeneous Rxn

The kinetic rate law is:

Rxn order: first order wrt to CO, three-halves order wrt Cl2, five-halves order overall.

23

2ClCOCO CkCr

2.2 NON-ELEMENTARY RATE LAWS

22 COClClCO Gas phase

synthesis of phosgene

Example 2: Heterogeneous Rxn

The rate of disappearance of toluene per mass of catalyst is:

where KB & KT is the adsorption constants.

TTBB

THT PKPK

PkPr

1

2'

2.2 NON-ELEMENTARY RATE LAWS

4662356 CHHCHCHHCcat

Gas-solid catalyzed rxn:

Hydrodemethylation of toluene (T)

In terms of partial pressure rather

than concentrations

MBHTcat

2

2.3 REVERSIBLE REACTIONS

For reversible rxn, all rate laws must reduce to the thermodynamic relationship relating the reacting species concentrations at equilibrium.

dDcCbBaA ⇌

beB

aeA

deD

cCe

C CC

CCK

Thermodynamic Equilibrium Relationship


21012662 HHCHC ⇌

2, BBforwardB Ckr

EXAMPLE: combination rxn of 2 mol of benzene to form 1 mol H2 and 1 mol diphenyl.kB

k-B

22 HDB ⇌kB

k-B

symbolically;

The rate of disappearance of benzene;2

, BBforwardB Ckr

The reverse rxn btween diphenyl & hydrogen;

6621012 2 HCHHC ⇌k-B

OR

2, HDBreverseB CCkr The rate of formation of benzene (in reverse direction);


The net rate of formation of benzene is;

Multiplying both sides by -1, we obtain the rate law of disappearance of benzene, -rB

reverseBforwardBnetBB rrrr ,,,

2

2HDBBB CCkCk

2

2HDBBBB CCkCkr

2

2HD

B

BBB CC

k

kCk


Replacing the ratio of the reverse & forward rate law constant by equilibrium constants;

where

CB

B Kk

k

2

2HD

B

BBBB CC

k

kCkr

C

HDBBB K

CCCkr 22

Concentration equilibrium constant

3. THE REACTION RATE CONSTANT

RTEA AeTk /

A= preexponential factor or frequency factorE= activation energy, J/mol or cal/molR=gas constant = 8.314 J/mol-K = 1.987 cal/mol-KT= absolute temperature, K

Arrhenius equation

-no of collision

RTEe /

A

-probability thatthe collision willresult in a reaction


RTEA AeTk /

Activation energy is a measure of the minimum energy that the reacting molecules must have in order for the reaction to occur (energy required to reach transition state).

Reactants Products

Transition state

Energy barier -total no of collision

RTEe /

A

probability that- the collision will result in a rxn

k - no of collision that result in a rxn


RTEA AeTk /

Taking a natural logarithm;

E ⬆, k ⬆, -r = ⬆The larger the

activation energy, the more

temperature sensitive k and

thus the reaction rate.

TR

EAkA

1lnln

4. BATCH SYSTEMS STOICHIOMETRIC TABLE

Purpose of developing stoichiometric table:

To determine the no of moles of each species remaining at a conversion of X.


Species Initially (mol)

Change (mol)

Remaining (mol)

ABCDI

Totals

Components of stoichiometric table:refers to moles of species reacted or

formed

Recall from Chapter 2:

Factorizing;


0

0

A

AA

N

NNX

XNNN AAA 00

XNN AA 10

moles of A reacted

aA + bB cC + dD

moles of A remaining in the reactor at a

conversion of X


Moles B reacted, NB

XNa

dA0

XNa

cA0Moles C

formed, NC

Moles Dformed, ND

XNa

bA0

Moles B reacted

Moles A reactedMoles A reacted


moles B remaining in the

system, NB

XNa

bN AB 00

NC

moles of Binitially in the

system

moles of Cformed

XNa

cN AC 00

NDXN

a

dN AD 00

moles of Breacted

moles of Dformed


Species

Initially (mol)

Change (mol)

Remaining (mol)

A

B

C

D

I -

Totals

0AN

0BN

0CN

0DN

0IN

XNa

bA0

XNa

cA0

XNa

dA0

XN A0

XNa

cNN ACC 00

XNa

dNN ADD 00

XNa

bNN ABB 00

XNNN AAA 00

0II NN

XNa

b

a

c

a

dNN ATT 00 1

0TN


XNa

b

a

c

a

dNN ATT 00 1

Total no of moles per mole of A reacted can be calculated as:

where

XNN AT 00

1a

b

a

c

a

d

Change in the total number of moles per mole of A reacted


Species Initially Change Remaining

Concentration

ABCDI

Totals

Can we express concentration of each species??

AA kCr 2AA kCr 3

AAA Ckr

Concentration of each species in terms of conversion can be expressed as:


V

XN

V

NC AA

A

10

V

XNabN

V

NC ABB

B00 /

Remaining (mol)

A

B

C

D

XNa

cNN ACC 00

XNa

dNN ADD 00

XNa

bNN ABB 00

XNNN AAA 00

V

XNacN

V

NC ACC

C00 /

V

XNadN

V

NC ADD

D00 /

Recall from stoichiometric

table

V

XabNNN ABA // 000


V

XNabNC AB

B00 /

V

XNacNC AC

C00 /

V

XacNNN ACA // 000

V

XabN BA /0

V

XacN CA /0

V

XadNNN ADA // 000


V

XNadNC AD

D00 /

V

XadN DA /0

0

0

0

0

0

0

A

i

A

i

A

ii y

y

C

C

N

N


Species

Initially Change Remaining Concentration

A

B

C

D

I -

0AN

0BN

0CN

0DN

0IN

XNa

bA0

XNa

cA0

XNa

dA0

XN A0

XNa

cNN ACC 00

XNa

dNN ADD 00

XNa

bNN ABB 00

XNNN AAA 00

0II NN

V

XNC A

A

10

V

XabNC BA

B

/0

V

XacNC CA

C

/0

V

XadNC DA

D

/0

IOC

X

a

b

N

NNXN

a

bNN

A

BAABB

0

0000

X

a

bN BA0

0

0

0

0

0

0

A

i

A

i

A

ii y

y

C

C

N

N


Species


A

B

C

D

I -

0AN

0BN

0CN

0DN

0IN

XNa

bA0

XNa

cA0

XNa

dA0

XN A0

X

a

bNN BAB 0

XNNN AAA 00

0II NN

V

XNC A

A

10

V

XabNC BA

B

/0

V

XacNC CA

C

/0

V

XadNC DA

D

/0

IOC

X

a

cNN CAC 0

X

a

dNN DAD 0

Given the saponification for the formation of soap from aqueous caustic soda & glyceryl stearate is:

Letting X the conversion of sodium hydroxide, set up astoichiometric table expressing the concentration of each species in terms of its initial concentration and

the conversion.


3533517533517 33 OHHCCOONaHCHCOOHCaqNaOH

EXAMPLE


3533517533517 33 OHHCCOONaHCHCOOHCaqNaOH

We know that this is a liquid-phase reaction.Therefore, V=V0

XCV

XN

V

XNC A

AAA

1

110

0

00

DCBA 33

XC

V

XabNC BA

BAB 3

1/0

0

0

1313 dcba

EXAMPLE


Species


A

B

C

D

I -

Total 0

0AN

0BN

0CN

0DN

0IN

XN A03

1

XN A0

XN A03

1

XN A0

XNN BAB 3

10

XNN AA 10

0II NN

XCC AA 10

XCC BAB 3

10

XCC CAC 0

XCC DAD 3

10

IOC

XNN CAC 0

XNN DAD 3

10

EXAMPLE

0TN 0TT NN

5. FLOW SYSTEMS STOICHIOMETRIC TABLE

Purpose of developing stoichiometric table:

To determine the effluent flow rate of each species at a conversion of X.


Species Feed rate to reactor

(mol/time)

Change within the reactor (mol/time)

Effluent rate from reactor (mol/time)

ABCDI

Totals

Components of stoichiometric table:



(mol/time)

Change within the

reactor (mol/time)


Concentration(mol/L)

A

B

C

D

I -

Totals

0AF

00 ABB FF

00 ACC FF

00 ADD FF

00 AiI FF

XFa

bA0

XFa

cA0

XFa

dA0

XFA0

X

a

bFF BAB 0

XFFF AAA 00

IAI FF 0

X

a

cFF CAC 0

X

a

dFF DAD 0

0TF XFFF ATT 00

XFC A

A

10

XabFC BA

B

/0

XacFC CA

C

/0

XadFC DA

D

/0

IA

I

FC

0

QUIZ 5

Given a liquid phase reaction:A+ 2B C + D

The initial concentration of A and B are 1.8 kmol/m3 and 6.6 kmol/m3 respectively. Construct a stoichiometric table for a flow system considering A as the basis of calculation.

ANSWER FOR QUIZ 5

A+ 2B C + DGiven:

From stoichiometry, we know that,

3

30

/6.6

/8.1

mkmolC

mkmolC

BO

A

0

0

0

0

0

0

A

i

A

i

A

ii y

y

C

C

F

F

67.38.1

6.6B

1121 dcba

0

0

A

ii C

C

08.1

0C

3

30

/0

/0

mkmolC

mkmolC

DO

C

Since C & D areproducts.

08.1

0D

11 a

b

a

c

a

d

ANSWER FOR QUIZ 5


(mol/time)

Change within the

reactor (mol/time)


A

B

C

D

Totals

0AF

BAB FF 00

CAC FF 00

DAD FF 00

XFA02

XFA0

XFA0

XFA0

XFF BAB 20

XFF AA 10

XFF AC 0

XFF AD 0

0TF XFFF ATT 00

ANSWER FOR QUIZ 5


(mol/time)

Change within the

reactor (mol/time)


A

B

C

D

Totals

0AF

00 67.3 AB FF

00 CF

00 DF

XFA02

XFA0

XFA0

XFA0

XFF AB 267.30

XFF AA 10

XFF AC 0

XFF AD 0

0TF XFFF ATT 00

Substituting the numerical values;

1. For liquid phase: Batch System:

6. CONCENTRATION IN TERMS OF CONVERSION

0VV

V

XN

V

NC AA

A

10

V

NC B

B

V

NC C

C

V

NC D

D

V

XabN BA /0

V

XacN CA /0

V

XadN DA /0

0

0 /

V

XabN BA

0

0 /

V

XacN CA

0

0 /

V

XadN DA

XabC BA /0

XacC CA /0

XadC DA /0

1. For liquid phase: Flow System -


0

XFFC AA

A

10

B

B

FC

C

C

FC

D

D

FC

XabF BA /0

XacF CA /0

XadF DA /0

0

0 /

XabF BA

0

0 /

XacF CA

XabC BA /0

XacC CA /0

XadC DA /0 0

0 /

XadF DA

2. For gas phase: Batch System

From equation of state;

At any time t,

At initial condition (t=0)


V

NC A

A Need to substitute V from gas law equation

RTZNPV T

T= temperature, KP= total pressure, atm (1 atm= 101.3 kPa)Z= compressibility factorR= gas constant = 0.08206 dm3-atm/mol-K

00000 RTNZVP T

(1)

(2)


Dividing (1) by (2);


RTZNPV T

00000 RTNZVP T

(1)

(2)

000

00

T

T

N

N

Z

Z

T

T

P

PVV

Recall from stoichiometric table

XNNN ATT 00 (4)

Dividing (4) by NT0 ;

XN

N

N

N

T

A

T

T 0

0

0

1

XyA01

(3)


Applies for both batch and flow

systems


XyN

NA

T

T0

0

1

XN

N

T

T 10

0

1T

T

N

N

a

b

a

c

a

d

0Ay

At complete conversion (for irreversible rxn): X=1, NT=NTf

XN

NN

T

TT

0

0

Rearranging;

0

0

T

TTf

N

NN

Will be substitute in (3)


Substituting the expression for NT/NT0 in (3),


000

00

T

T

N

N

Z

Z

T

T

P

PVV

(3)

XZ

Z

T

T

P

PVV

1

00

00

If the compressibility factor are not change significantly during rxn, Z0 Z⩳

0

00 1

T

TX

P

PVV

(5)

2. For gas phase: Flow System

From gas law, at any point in the reactor,

At the entrance of reactor;


ZRT

PFC T

T

0

0

00 T

T

P

P

F

F

T

T (3)

00

0

0

00 RTZ

PFC T

T

(1)

(2)

Dividing (1) by (2)

j

j

FC

Need to substitute υ from gas law equation

0

0

00 T

T

P

P

F

F

T

T


Substituting for FT;


Recall from stoichiometric table XFFF ATT 00

0

0

0

000 T

T

P

P

F

XFF

T

AT

0

0

0

00 1 T

T

P

PX

F

F

T

A

0

000 1 T

T

P

PXyA

0

00 1 T

T

P

PX (4)


Substituting υ & Fj;

0

00 1 T

T

P

PX


(4)

j

j

FC

Need to substitute υ from gas law equation

0

00

0

1TT

PP

x

XvFC jjA

j

XvFF jjjj 0(5)

T

T

P

P

x

XvC jj

A0

00 1

Stoichiometric coefficient

(d/a, c/a, -b/a, -a)

0

00 1 T

T

P

PX

2. For gas phase: Flow System Concentration for each species:


aA + bB cC + dD

XFFC AA

A

10

B

B

FC

C

C

FC

D

D

FC

XabF BA /0

XacF CA /0

XadF DA /0

0

00 1

/

P

P

T

T

x

XabC B

A

0

00 1

/

P

P

T

T

x

XacC C

A

0

00 1

/

P

P

T

T

x

XadC D

A

0

00 1

1

P

P

T

T

x

XCA

I

I

FC

IIF 0

0

00

1 P

P

T

T

x

C IA

SUMMARY

Relative rate of reaction:

Power Law Model:

d

r

c

r

b

r

a

r DCBA

dDcCbBaA

BAA CkCr

SUMMARY Elementary rate law:

The rxn that in which its stoichiometic coefficients are IDENTICAL to the reaction order of each species.

Non-elementary rate laws:

The reactions that do not follow simple rate laws (power rate laws) in which its stoichiometic coefficients are NOT IDENTICAL to the reaction order of each species.

Reversible reaction:

All rate laws must reduce to the thermodynamic relationship relating the reacting species concentrations at equilibrium.

Power Law Model:

SUMMARY Reaction Rate Constant, k

RTEA AeTk /

E ⬆, k ⬆, -r ⬆The larger the activation

energy, the more sensitive k is, (towards the change in

temperature)

SUMMARY

Stoichiometric Table for Batch Systems

Species

Initially Change Remaining

A

B

C

D

I -

0AN

0BN

0CN

0DN

0IN

XNa

bA0

XNa

cA0

XNa

dA0

XN A0

XNa

cNN ACC 00

XNa

dNN ADD 00

XNa

bNN ABB 00

XNNN AAA 00

0II NN

Species

Feed rate to reactor

(mol/time)

Change within the reactor (mol/time)


A

B

C

D

I -

Totals

SUMMARY Stoichiometric Table for Flow Systems

0AF

00 ABB FF

00 ACC FF

00 ADD FF

00 AiI FF

XFa

bA0

XFa

cA0

XFa

dA0

XFA0

X

a

bFF BAB 0

XFFF AAA 00

IAI FF 0

X

a

cFF CAC 0

X

a

dFF DAD 0

0TF XFFF ATT 00

Expression of V and υ in calculating the concentration of each species: Batch systems

Liquid phase:

Gas phase:

Flow systems Liquid phase:

Gas phase:

SUMMARY

0VV

0

P

P

T

TXVV 0

00 1

P

P

T

TX 0

00 1

QUIZ 6

Derive a concentration for each species for the isothermal gas phase reaction below, neglecting the pressure drop:

A + B C

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ERT 316: REACTION ENGINEERING CHAPTER 3 RATE LAWS & STOICHIOMETRY Lecturer: Miss Anis Atikah Ahmad...

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