8/17/2019 TOPIC 2_PART 1

1/19

• Constant-volume of batch reactor1. Differential method of analysis of data

2. Integral method of analysis of data

3. Method of Initial Rates

4. Method of Half-Lives

• Varying-volume batch reactor

TOPIC 2

Determination of Rate Law

8/17/2019 TOPIC 2_PART 1

2/19

• Constant-volume of batch reactor1. Differential method of analysis of data

- Graphical Differentiation

- Numerical Differentiation

- Polynomial-fit Differentiation

1. Integral method of analysis of data

TOPIC 2 (PART 1)

Determination of Rate Law

8/17/2019 TOPIC 2_PART 1

3/19

Constant volume of batch reactor refer to volume of

reaction mixture, not the volume of the reactor.

It also known as constant-density reaction system.

The measure of reaction rate of component ibecomes

For ideal gas

therefore,

*This means the rate of

reaction of a

component can be

given by the rate of

change of concentration

or partial pressure

[1]

[2]

8/17/2019 TOPIC 2_PART 1

4/19

• Say A, converted to something else, or the fraction of Areacted away. We call this, simply, the conversion of A,with symbol X  A .

• Suppose that N A0 is the initial amount of A in the reactorat time t = 0, and that N A is the amount present at timet. Then the conversion of A in the constant volumesystem is given by

The Conversion

8/17/2019 TOPIC 2_PART 1

5/19

• and

• We will develop the equations in this chapter in terms of

concentration of reaction components and also in terms

of conversions.• Later we will relate X  A and C  A for the more general case

where the volume of the system does not stay constant.

[7]

[8]

8/17/2019 TOPIC 2_PART 1

6/19

8/17/2019 TOPIC 2_PART 1

7/19

For irreversible reaction, the reaction order   α   andspecific rate constant can be determined by

.

It is applicable when the rate is essentially a functionof the concentration of only .

Consider a reaction carried out isothermally in a

constant volume batch reactor and the concentration

is as a function of time.

 

 A A  kC r 

 P  A

8/17/2019 TOPIC 2_PART 1

8/19

 – Combine mole balance and rate law:

 – The reaction order can be found by taking the natural

logarithm of both side

 

 A A

 AC k 

dt 

dC 

 A A

 AC k 

dt 

dC lnlnln    

 

  

 

8/17/2019 TOPIC 2_PART 1

9/19

• Three Ways to Determine (-dCA/dt) from

Concentration-Time Data: – Graphical differentiation

 – Numerical differentiation

 – Differentiation of a polynomial fit to the data

FAKULTI OF CHEMICALENGINEERING, UiTM CHE584/594

  9

8/17/2019 TOPIC 2_PART 1

10/19

Graphical Method

• This method accentuates measurement error!

time (s) 0 t1 t2 t3

concentration(mol/dm3)

CAo CA1 CA2 CA3

8/17/2019 TOPIC 2_PART 1

11/19

Numerical Method• Can be used when the data points in the independent

variable are equally spaced.

• dCA/dt can be calculated by

 – Initial point

 – Interior points

 – Last point

time (s) 0 t1 t2 t3 t4 t5

concentration

(mol/dm3)CAo CA1 CA2 CA3 CA4 CA5

t t t t t      1201

t 

C C C 

dt 

dC  A A A

t 

 A

 

  

 

2

43210

0

112

1  

 

  

 i Ai A

t 

 AC C 

t dt 

dC 

i

543

5

34

2

1

 A A A

 AC C C 

t dt 

dC 

 

 

 

 

8/17/2019 TOPIC 2_PART 1

12/19

8/17/2019 TOPIC 2_PART 1

13/19

8/17/2019 TOPIC 2_PART 1

14/19

• The integral method of analysis always puts a particularrate equation to the test bythe with the

.

• If the fit is unsatisfactory, another rate equation is. This procedure is shown and used

in the cases next treated.

• It should be noted that the integral method is

especially useful for fitting simple reaction typescorresponding to .

8/17/2019 TOPIC 2_PART 1

15/19

• Consider the reaction

Irreversible Unimolecular-Type

First-Order Reactions

[9]

• For this reaction. Separating and integrating we obtain

[11]

8/17/2019 TOPIC 2_PART 1

16/19

• In terms of conversion (see Eqs. 7 and 8), the rate

equation, Eq. 10, becomes

•

which on rearranging and integrating gives

[12]

Or

8/17/2019 TOPIC 2_PART 1

17/19

• A plot of , as shown in Fig.

below.

• If the experimental data seems to be better fitted by a

curve than by a straight line,

because the first-order reaction

.

8/17/2019 TOPIC 2_PART 1

18/19

• Integral Method Rate Analysis

•

We could integrate the combined mole balanceand rate law to plot reaction rate data in terms of

concentration vs. time for 0, 1st, and 2nd order

reactions.

8/17/2019 TOPIC 2_PART 1

19/19

• Zero order

• First order