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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 š order wrt reactant A

AND

The rxn is š 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: aĀ chemical reactionĀ in which one or more of theĀ chemical speciesĀ react directly to form products in a singleĀ reaction stepĀ and with a singleĀ 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

- 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

ā

- 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

ā

k-B

kB

ā

symbolically;

k-B

The rate of disappearance of benzene;

OR

The reverse rxnbtweendiphenyl & hydrogen;

k-B

ā

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 ā¬, k ā¬, -r = ā¬

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 + bBļ cC + dD4. 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

- 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

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

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:

QUIZ 5

- Given a liquid phase reaction:

A+ 2B ļ 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

Substituting the numerical values;

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, Z0ā©³Z

(5)

6. Concentration in terms of conversion

2. For gas phase:

- Flow System

Need to substitute Ļ 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

SubstitutingĻ & Fj;

Need to substitute Ļ from gas law equation

(5)

(4)

Stoichiometric coefficient

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

aA + bBļ cC + dD6. 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 ā¬, k ā¬, -r ā¬

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 Ļ 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 ļ C

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