Chemical Reaction Engineering

1
Chemical Reaction Engineering
Lecture 2
Lecturer ???
2
This course focuses on how to obtain the rate of
reaction as a function of conversion

• Define the rate law, which relates the rate of
  reaction to the concentrations of the reacting
  species and to temperature
• Define concentrations for flow and batch systems
  and develop a stoichiometric table

3
Relative rates of reaction

• For reaction
• Rate law (rate equation)
• Algebraic equation accurately describes the
  reaction rate as a function of concentration and
  temperature.
• Why functions of concentrations and temperature?
• How do molecules react? By collision

Rate of formation of C c/a (rate of
disappearance of A)
4
Concentration and temperature

• Collision frequency ? concentration
• Rate of reaction ? concentration.
• At constant temperature r f(CA, CB, .)
• As temperature increases, collision frequency
  increases.
• Rate of reaction f ( CA, CB, ), (T)

Reaction rate constant of A
5
Questions about the rate of reaction, -rA

• At this point we need to develop means of
  expressing reaction kinetics because design
  equations allow batch, plug flow and CSTR
  reactors to be sized for a given throughput or
  conversion
• what does (-rA) depend on?
• How do reactions occur?
• Which parameters determine reaction rate?

6
Factors affecting reaction rate
rA f (T, C)
This has been observed empirically - but it will
now be examined quantitatively.
7
(Specific) rate constant, kA

• It is strongly dependent on temperature.
• In gas-phase reactions
• It depends on catalysts and may be a function of
  total pressure.
• In liquid system
• It can be a function of total pressure.
• It may depend on ionic strength and choice of
  solvent.
• Here, we consider the temperature only.
• Unit issue

8
Rate of reaction and temperature
Where A preexponential factor or frequency
factor (1/time) E Activation energy, J/mol or
cal/mol R Gas constant, 8.314 J/mol K (or 1.987
cal/mol K) T Absolute temperature, K
9
Arrhenius equation has been verified empirically
to give the temperature behaviour of most
reaction rate constants (within experimental
accuracy) over fairy large experimental ranges.
Activation energy determined experimentally by
carrying out the reaction at several
temperatures. After taking the natural logarithm
of the Arrhenius equation
Question Have these observations any
fundamental basis?
(1) Thermodynamics (2) Collision theory (3)
Absolute reaction rate theory
10
Activation energy

• Distort or stretch the bonds
• Overcome the steric and electron repulsion force
• Quantum effects can in some cases produce a
  barrier
• There usually isnt an active energy needed for
  free radical reactant reactions.

11
Example 3-1 Calculate the activation energy for
the first-order decomposition reaction of benzene
diazonium chloride to give chlorobenzene and
nitrogen
ln kA
Arrhenius Equation
1/T
Arrhenius Equation
12
Order of reaction

• This reaction has no simple overall order because
  it is a complex chain reaction (not elementary
  reaction).
• The overall order is not necessarily an integer,
  and this is particularly true for free radical
  and heterogeneous reactions.
• For simple homogeneous reactions, the order of
  reaction, n 0, 1, 2 or 3 (rare).

13
One of the most general forms
where k velocity constant or specific rate
constant. If CA, CB , . 1 then r k
a , b reaction order with respect to CA , CB .
a b ... overall order (this treatment is
only applicable to simple reactions).

• Reaction order
• Power to which concentration is raised to make
  rate proportional to it.
• It can only be determined experimentally.

14
Elementary reaction Elementary rate laws

• Elementary reaction is one that evolves a single
  step.The stoichiometric coefficients in an
  elementary reaction are identical to the powers
  in the rate law
• An elementary reaction has an elementary rate
  law.
• Some reaction follows an elementary rate law is
  not an elementary reaction.

2NO O2 ? 2NO2
15
Stoichiometric Equation

• This describes the overall reaction but the
  reaction order cannot be deduced from it.

Examples
rf kfCH2CI2
rb kbCHI2
and
Forward reaction is 1st order in CH2 and CI2 (
2nd order overall) Reverse reaction is 2nd order
in CHI
Compare the above reaction with the analogous
nonelementary reaction between H2 and Br2 .
k1
k2
16
Molecularity

• This is the number of atoms, ions, or molecules
  involved (colliding) in the rate-limiting step of
  a reaction.

Examples (i)
Bimolecular reaction, since two species are
involved in the reaction step.
(ii)
Unimolecular
urianium-238
helium
thorium
17
(iii)
This is not a bimolecular reaction. Why?
Because the reaction occurs as follows
Each step has a molecularity, which must be an
integer. Thus, order and molecularity are not
necessarily identical for a given reaction.
18
Back to reaction rate law

• The dependence of the reaction rate -rA on the
  concentrations of the species present, f (Cj), is
  almost without exception determined by
  experimental observations. Hence rate laws are
  determined by experimental observation and they
  are a function of the reaction chemistry and not
  the type of reactor.

19
Reversible reaction

• The rate law must satisfy thermodynamic
  relationships at equilibrium.
• The rate law must reduce to the irreversible rate
  law when the concentration of one or more of the
  reaction products is zero.
• The form of the irreversible rate law provides a
  big clue as to the form of the reversible
  reaction rate expression.

20
Consider the general reversible reaction
At equilibrium rA0
rfA rbA
Therefore
Therefore
Thermodynamic equilibrium relationship
Thermodynamic equilibrium constant
21
Endothermic
Exothermic
KC
KC
T
T
22
Chemical equilibrium

• All reactions are reversible in principle.
• The extent of reversibility depends on -?G, the
  Gibbs Free Energy change.

Where Kp is the equilibrium constant in terms of
partial pressures.
If Kp is large, reaction is essentially
irreversible, which means that the equilibrium
position lies very far to the product side.
23
Stoichiometric table

• Stoichiometric relationships between reacting
  molecules for a single reaction.

t t
NA NB NC ND NI
t 0
NA0 NB0 NC0 ND0 NI0
Batch reactor
24
The change in the total number of moles per mole
of A reacted.
25

• Major objective
• Rate law -rA as a function of conversion
• Our experience

e.g.
26
Example 3-2 Soap consists of the sodium and
potassium salts of various fatty acids such as
oleic, stearic, palmitic, lauric, and myristic
acids. The saponification for the formation of
soap from aqueous caustic soda and glyceryl
stearate is Letting X represent 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 X.
liquid phase reaction
27
Example 3-3 Having set up the stoichiometric
table in Example 3-2, one can now readily use it
to calculate the concentrations at a given
conversion. If the initial mixture consists
solely of sodium hydroxide at a concentration of
10 mol/dm3 (i.e., 10 mol/L or 10 kmol/m3) and of
glyceryl stearate at a concentration of 2
mol/dm3, what is the concentration of glycerine
when the conversion of sodium hydroxide is (a)
20 and (b) 90 ?
Only the reactants NaOH and (C17H35COO)3C3H5 are
initially present ?C?D0.
X 20
X 90
28
Stoichiometric table (flow system)
entering
Leaving
FA FB FC FD FI
FA0 FB0 FC0 FD0 FI0
Continuous-flow reactor
29
(No Transcript)
30

• Major objective
• Rate law -rA as a function of conversion
• Our experience e.g.
• Liquid phase
• Volume change with reaction is negligible when no
  phase changes are taking place.

31

• Gas-phase
• The reaction volume (V) or volumetric flow rate
  (v) most often changes during the course of the
  reaction because of a change in the total number
  of moles or in temperature or pressure
• e.g.

4 mol
2 mol
32

• Variable volume
• Equation of state

t 0
from stoichiometri table
1
33

• Variable volumetric flow rate

1
entering
From stoichiometri table
Stoichiometric coefficient
For species j
34
(No Transcript)
35
Example 3-5 A mixture of 28 SO2 and 72 air is
charged to a flow reactor in which SO2 is
oxidized First, set up a stoichiometric table
using only the symbols (i.e., Ti, Fi) and then
prepare a second stoichiometric table evaluating
numerically as many symbols as possible for the
case when the total pressure is 1485 kPa (14.7
atm) and the temperature is constant at 227 ?C.
Taking SO2 as the basis of calculation
36

37
Change concentration!!
38
If the rate law for this reaction were first
order in SO2 (i.e., A) and in O2 (i.e., B) with
k200 dm3/mol.s
39
Example 3-6 The reversible gas-phase
decomposition of nitrogen tetroxide, N2O4, to
nitrogen dioxide, NO2, is to be carried out at
constant temperature. The feed consists of pure
N2O4 at 340 K and 202.6 kPa (2 tam). The
concentration equilibrium constant, Kc, at 340 K
is 0.1 mol/dm3.
concentration equilibrium constant
at equilibrium !!
40
(a) Calculate the equilibrium conversion of N2O4
in a constant-volume batch reactor.
at equilibrium !!
41
(b) Calculate the equilibrium conversion of N2O4
in a flow reactor.
at equilibrium !!
42
(c) Assuming the reaction is elementary, express
the rate of reaction solely as a function of
conversion for a flow system and for a batch
system.
Elementary reaction
for flow system
for batch system
(d) Determine the CSTR volume necessary to
achieve 80 of the equilibrium conversion.
CSTR design equation