Ert 316 reaction engineering chapter 3 rate laws stoichiometry
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ERT 316: REACTION ENGINEERING CHAPTER 3 RATE LAWS & STOICHIOMETRY. Lecturer: Miss Anis Atikah Ahmad Email: anisatikah@unimap.edu.my Tel: +604 976 3245. Outline. PART 1: Rate Laws Relative Rates of Reaction Reaction Order & Rate Law Reaction Rate Constant, k PART 2: Stoichiometry

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Ert 316 reaction engineering chapter 3 rate laws stoichiometry

ERT 316: REACTION ENGINEERINGCHAPTER 3RATE LAWS & STOICHIOMETRY

Lecturer: Miss Anis Atikah Ahmad

Email: anisatikah@unimap.edu.my

Tel: +604 976 3245


Outline
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
1. Relative Rates of Reaction

Reaction Stoichiometry

EXAMPLE

If NO2 formed at 4 mol/m3/s (r NO2= 4 mol/m3/s), what is the rate of formation of NO?


1 relative rates of reaction1
1. Relative Rates of Reaction

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

what is the rate of formation of NO?


1 relative rates of reaction2
1. Relative Rates of Reaction

  • 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?

EXERCISE


1 relative rates of reaction3
1. Relative Rates of Reaction

  • The relative rates are

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

  • Thus, solving the rates of B & C;

r A= -10 mol/dm3/s


2 reaction order rate law

Rate law is a kinetic expression that gives the relationship between reaction rate, -rA, and concentration.

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, kAand a function of concentrations (activities) of the reactants involved in the reaction:


2 reaction order rate law1

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


2 1 power law models elementary rate laws
2.1 Power Law Models & Elementary Rate Laws

  • Power Law Model:

    The rxn is 𝛂 order wrt reactant A

    AND

    The rxn is 𝛃 order wrt reactant B

    The overall order of the reaction, n;


2 1 power law models elementary rate laws1
2.1 Power Law Models & Elementary Rate Laws

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

    Products

Zero order (n=0)

First order (n=1)

Second order (n=2)

Third order (n=3)


2 1 power law models elementary rate laws2
2.1 Power Law Models & Elementary Rate Laws

  • 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.

Products

Unimolecular reaction

Products

Bimolecular reaction

Non-elementary rxn

But follows the elementary rate law!





2 2 non elementary rate laws
2.2 Non-Elementary 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.

Gas phase synthesis of phosgene


2 2 non elementary rate laws1
2.2 Non-Elementary Rate Laws

Gas-solid catalyzed rxn: Hydrodemethylation of toluene (T)

  • Example 2: Heterogeneous Rxn

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

    where KB & KT is the adsorption constants.

In terms of partial pressure rather than concentrations


2 3 reversible reactions
2.3 Reversible Reactions

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

Thermodynamic Equilibrium Relationship


2 3 reversible reactions1
2.3 Reversible Reactions

EXAMPLE: combination rxn of 2 mol of benzene to form 1 mol

H2 and 1 mol diphenyl.

kB

k-B

kB

symbolically;

k-B

The rate of disappearance of benzene;

OR

The reverse rxnbtweendiphenyl & hydrogen;

k-B

The rate of formation of benzene (in reverse direction);


2 3 reversible reactions2
2.3 Reversible Reactions

The net rate of formation of benzene is;

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


2 3 reversible reactions3
2.3 Reversible Reactions

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

where

Concentration equilibrium constant


3 the reaction rate constant
3. The Reaction Rate Constant

Arrhenius equation

A= preexponential factor or frequency factor

E= activation energy, J/mol or cal/mol

R=gas constant = 8.314 J/mol-K = 1.987 cal/mol-K

T= absolute temperature, K

-no of collision

-probability that

the collision will

result in a reaction


3 the reaction rate constant1
3. The Reaction Rate Constant

  • 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).

Transition state

- no of collision that

result in a rxn

-total no of collision

Energy barier

probability that

- the collision will

result in a rxn

Reactants

Products


3 the reaction rate constant2
3. The Reaction Rate Constant

Taking a natural logarithm;

The larger the activation energy, the more temperature sensitive k and thus the reaction rate.

  • E ⬆, k ⬆, -r = ⬆


4 batch systems stoichiometric table
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.


4 batch systems stoichiometric table1
4. Batch Systems Stoichiometric Table

refers to moles of species reacted or formed

  • Components of stoichiometric table:


4 batch systems stoichiometric table2

  • aA + bB cC + dD

4. Batch Systems Stoichiometric Table

  • Recall from Chapter 2:

  • Factorizing;

moles of A reacted

moles of A remaining

in the reactor at a conversion

of X


4 batch systems stoichiometric table3
4. Batch Systems Stoichiometric Table

Moles B

reacted, NB

Moles B reacted

Moles A reacted

Moles A reacted

Moles C

formed, NC

Moles D

formed, ND


4 batch systems stoichiometric table4
4. Batch Systems Stoichiometric Table

moles B remaining in the system, NB

moles of B

reacted

moles of B

initially in the system

NC

moles of C

formed

ND

moles of D

formed


4 batch systems stoichiometric table5
4. Batch Systems Stoichiometric Table


4 batch systems stoichiometric table6
4. Batch Systems Stoichiometric Table

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

    where

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


4 batch systems stoichiometric table7
4. Batch Systems Stoichiometric Table

Can we express concentration of each species??


4 batch systems stoichiometric table8
4. Batch Systems Stoichiometric Table

  • Concentrationof each species in terms of conversion can be expressed as:

Recall from stoichiometric table




4 batch systems stoichiometric table11
4. Batch Systems Stoichiometric Table


4 batch systems stoichiometric table12
4. Batch Systems Stoichiometric Table


4 batch systems stoichiometric table13
4. Batch Systems Stoichiometric Table

EXAMPLE

Given the saponification for the formation of soap

from aqueous caustic soda & glycerylstearate is:

Letting X the conversion of sodium hydroxide, set up a

stoichiometric table expressing the concentration of

each species in terms of its initial concentration and the

conversion.


4 batch systems stoichiometric table14
4. Batch Systems Stoichiometric Table

EXAMPLE

We know that this is a liquid-phase reaction.

Therefore, V=V0


4 batch systems stoichiometric table15
4. Batch Systems Stoichiometric Table

EXAMPLE


5 flow systems stoichiometric table
5. Flow Systems Stoichiometric Table

  • Purpose of developing stoichiometric table:

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


5 flow systems stoichiometric table1
5. Flow Systems Stoichiometric Table

  • Components of stoichiometric table:


5 flow systems stoichiometric table2
5. Flow Systems Stoichiometric Table


Quiz 5
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
Answer For Quiz 5

A+ 2B  C + D

Given:

From stoichiometry, we know that,

Since C & D are

products.



Answer for quiz 52
Answer for quiz 5

Substituting the numerical values;


6 concentration in terms of conversion
6. Concentration in terms of conversion

1. For liquid phase:

  • Batch System:


6 concentration in terms of conversion1
6. Concentration in terms of conversion

1. For liquid phase:

  • Flow System -


6 concentration in terms of conversion2
6. Concentration in terms of conversion

2. For gas phase:

  • Batch System

Need to substitute V from gas law equation

From equation of state;

At any time t,

At initial condition (t=0)

T= temperature, K

P= total pressure, atm (1 atm= 101.3 kPa)

Z= compressibility factor

R= gas constant = 0.08206 dm3-atm/mol-K

(1)

(2)


6 concentration in terms of conversion3
6. Concentration in terms of conversion

2. For gas phase:

  • Batch System

    Dividing (1) by (2);

(1)

(2)

Recall from stoichiometric table

(4)

(3)

Dividing (4) by NT0 ;


6 concentration in terms of conversion4
6. Concentration in terms of conversion

Applies for both batch and flow systems

2. For gas phase:

  • Batch System

Will be substitute

in (3)

Rearranging;

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


6 concentration in terms of conversion5
6. Concentration in terms of conversion

2. For gas phase:

  • Batch System

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

(3)

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

(5)


6 concentration in terms of conversion6
6. Concentration in terms of conversion

2. For gas phase:

  • Flow System

Need to substitute υ from gas law equation

From gas law, at any point in the reactor,

At the entrance of reactor;

(1)

(2)

Dividing (1) by (2)

(3)


6 concentration in terms of conversion7
6. Concentration in terms of conversion

Recall from stoichiometric table

2. For gas phase:

  • Flow System

    Substituting for FT;

(4)


6 concentration in terms of conversion8
6. Concentration in terms of conversion

2. For gas phase:

  • Flow System

    Substitutingυ & Fj;

Need to substitute υ from gas law equation

(5)

(4)

Stoichiometric coefficient

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


6 concentration in terms of conversion9

  • aA + bB cC + dD

6. Concentration in terms of conversion

2. For gas phase:

  • Flow System

    Concentration for each species:


Summary
Summary

  • Relative rate of reaction:

  • Power Law Model:


Summary1
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 NOTIDENTICAL 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:


Summary2
Summary

  • Reaction Rate Constant, k

  • E ⬆, k ⬆, -r ⬆

The larger the activation energy, the more sensitive k is, (towards the change in temperature)


Summary3
Summary

  • Stoichiometric Table for Batch Systems


Summary4
Summary

  • Stoichiometric Table for Flow Systems


Ert 316 reaction engineering chapter 3 rate laws stoichiometry

Summary

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

    • Batch systems

      • Liquid phase:

      • Gas phase:

    • Flow systems

      • Liquid phase:

      • Gas phase:


Quiz 6
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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