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: [email protected] 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

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ERT 316: REACTION ENGINEERINGCHAPTER 3RATE LAWS & STOICHIOMETRY

Lecturer: Miss Anis Atikah Ahmad

Email: [email protected]

Tel: +604 976 3245


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

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 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 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 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


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:


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

  • 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 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 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!


Examples of Reaction Rate Laws


Examples of Reaction Rate Laws


Examples of Reaction 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 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

  • 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 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 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 Reactions

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

where

Concentration equilibrium 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 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 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

  • Purpose of developing stoichiometric table:

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


4. Batch Systems Stoichiometric Table

refers to moles of species reacted or formed

  • Components of stoichiometric table:


  • 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 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 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 Table


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 Table

Can we express concentration of each species??


4. Batch Systems Stoichiometric Table

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

Recall from stoichiometric table


4. Batch Systems Stoichiometric Table


4. Batch Systems Stoichiometric Table


4. Batch Systems Stoichiometric Table


4. Batch Systems Stoichiometric Table


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 Table

EXAMPLE

We know that this is a liquid-phase reaction.

Therefore, V=V0


4. Batch Systems Stoichiometric Table

EXAMPLE


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 Table

  • Components of stoichiometric table:


5. Flow Systems Stoichiometric Table


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 + D

Given:

From stoichiometry, we know that,

Since C & D are

products.


Answer for quiz 5


Answer for quiz 5

Substituting the numerical values;


6. Concentration in terms of conversion

1. For liquid phase:

  • Batch System:


6. Concentration in terms of conversion

1. For liquid phase:

  • Flow System -


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 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 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 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 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 conversion

Recall from stoichiometric table

2. For gas phase:

  • Flow System

    Substituting for FT;

(4)


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)


  • aA + bB cC + dD

6. Concentration in terms of conversion

2. For gas phase:

  • Flow System

    Concentration for each species:


Summary

  • Relative rate of reaction:

  • Power Law Model:


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:


Summary

  • Reaction Rate Constant, k

  • E ⬆, k ⬆, -r ⬆

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


Summary

  • Stoichiometric Table for Batch Systems


Summary

  • Stoichiometric Table for Flow Systems


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

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

    A + B  C


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