Mole. Objectives: Define mole. Convert mole to number of particles.
1. Mole Balances - CHERIC · 1. Mole Balances oThe Rate of ... - Advantages • high conversion -...
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1. Mole Balances
oThe Rate of Reaction, -rA
oThe General Mole Balance Equation
oContinuous Flow Reactors
- CSTR (Continuous-Stirred Tank Reactor)
- PFR (Tubular Reactor)
- PBR (Packed-Bed Reactor)
o Industrial Reactors
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0. Chemical Identity
o Reaction
- When a chemical species has lost its chemical
identity
o Identity of a chemical species
- The kind, number, and configuration of that species’
atoms
• decomposition CH3CH3 → H2 + CH2=CH2
• combination N2 + O2 → 2NO
• isomerization C2H5CH=CH2 → CH2=C(CH3)2
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1. Reaction Rate I (p.2)
o Reaction Rate
- The rate at which a species looses its chemical identity per unit volume
A → B
rA = the rate of formation of species A per unit volume
-rA = the rate of a disappearance of species A per unit volume
rB = the rate of formation of species B per unit volume
☞ For a catalytic reaction, we refer to -rA', which is the
rate of disappearance of species A on a per mass of catalyst basis
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1. Reaction Rate II
o Reaction Rate [Example]
A → B
- If B is being created at a rate of 0.2 moles per liter
per second, ie, the rate of formation of B is,
rB = 0.2 mole/l/s
then A is disappearing at the same rate:
-rA = 0.2 mole/l/s
the rate of formation of A is
rA = -0.2 mole/l/s
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1. Reaction Rate III
o Is sodium hydroxide reacting?
- Reaction rate definition, rA = dCA/dt
• only holds for constant volume batch system
carried out to obtain chemical reaction rate data
- Sodium hydroxide and ethyl acetate are
continuously fed to a rapidly stirred tank in which
they react to form sodium acetate and ethanol:
NaOH + CH3COOC2H5 → CH3COONa + C2H5OH
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1. Reaction Rate IV
o Consider species j
- rj is the rate of formation of species j per unit volume
[e.g. mol/dm3*s]
- rj is a function of concentration, temperature,
pressure, and the type of catalyst (if any)
- rj is independent of the type of reaction system
(batch, plug flow, etc.)
- rj is an algebraic equation, not a differential equation
o Examples of other rate laws
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A
AA
Ck
Ckr
2
1
1 krA AA Ckr 1
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1. Reaction Rate V
o Self test
- The convention for rates of reaction
A + 2B → 3C
in which the rate of disappearance of A is 5 moles of
A per dm3 per second at the start of the reaction.
- At the start of the reaction
(a) What is -rA?
(b) What is the rate of formation of B?
(c) What is the rate of formation of C?
(d) What is the rate of disappearance of C?
(e) What is the rate of formation of A, rA?
(f) What is -rB?
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2. General Mole Balance Equation (p.8) I
o In a given boundary system
- FA0= Entering molar flow rate of A (mol/time)
FA= Exiting molar flow rate of A (mol/time)
GA= Rate of generation(formation) of A (mol/time)
V = Volume (vol e.g. m3)
rA= rate of generation(formation) of A (mole/time•vol)
NA= number of moles of A inside the system Volume
V (mols)
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2. General Mole Balance Equation II
o Self Test
1. The rate law
(a) is a differential equation T F
(b) relates reaction rate and concentration of
reacting species T F
(c) is a function of temperature; T F
2. The rate of formation of species A is per unit volume
(a) rA T F
(b) -rA T F
(c) the rate of generation of species A per unit
volume T F
(d) r'A T F
(e) none of the above T F2/21/2011 2011 Spring 9
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2. General Mole Balance Equation III
3. At a particular time t, the rate of formation of B in
the reaction, rB, is 10 mole/dm3*min. Which of the
following are true? A → B
a. The rate of disappearance of B is -10 moles/dm3*min.
b. The rate of formation of A is -10 mole/dm3*min.
c. The rate of disappearance of A is 10 moles/dm3*min.
d. rA = -10 moles/dm3*min
e. -rA = 10 moles/dm3*min
f. -rB = -10 moles/dm3*min
g. Some of the above
h. All of the above
i. None of the above
j. A will disappear faster if a magician is present
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3. Batch Reactors I
o Batch Reactors
- Used for a small-scale operation,
• testing a new process not fully developed
• manufacturing expensive products
• processes difficult to convert to
continuous operation
- Advantages
• high conversion
- Disadvantages
• high labor cost per batch
• variability of product quality
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3. Batch Reactors II
o Reaction rate
- Neither inflow not outflow
- Rxn rate is uniform throughout the reactor volume
- For isomerization of species A
A → B
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dt
dNdVrFF
jV
jjj 0
dt
dNdVr A
V
A
Vrdt
dNA
A
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3. Batch Reactors III
o Reaction time
- Time t1 to change NA0 → NA1, (Generally NA0 > NA1)
- Rearranging
- Integrating
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0
11
A
A
N
NA
A
Vr
dNt
Vrdt
dNA
A
Vr
dNdt
A
A
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4. Continuous Flow Reactors I
o Continuous-Stirred tank Reactor 1
- CSTR, vat, or Backmix reactor
- Primarily for liquid phase reactions
- Operated at steady state (perfectly mixed)
• T, Cj, rj inside CSTR is uniform
☜ residence-time distribution study for
highly non-ideal mixing system
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4. Continuous Flow Reactors II
o Continuous-Stirred tank Reactor 2
- General mole balance
- Operated at st-st
- Design equation for CSTR
or
- With volumetric flow rate v, FA = CA • v
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dt
dNdVrFF
jV
jjj 0
0dt
dNA
A
V
A VrdVr
dt
dNdVrFF A
V
AAA 0
A
AA
r
FFV
0
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4. Continuous Flow Reactors III
o Tubular Reactor 1
- A cylindrical pipe normally operated at st-st
- Used most often for gas-phase rxn
- Reactants are continually consumed as they flow
down the length of the reactor
- Plug flow along pipe
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4. Continuous Flow Reactors IV
o Tubular Reactor 2
- General mole balance
- Operated at st-st
- Design equation for PFR
- Differential w.r.t V
- Or
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dt
dNdVrFF
jV
jjj 0
0dt
dNA
00 V
AAA dVrFF
AA r
dV
dF0
AA r
dV
dF
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4. Continuous Flow Reactors V
o Tubular Reactor 3
- Rearranging and integrating between
V = 0, FA = FA0
V = V1, FA = FA1
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0
1
1
01
A
A
A
A
F
FA
AF
FA
A
r
dF
r
dFV
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4. Continuous Flow Reactors VI
o Pack-Bed Reactor 1
- Involving fluid-solid heterogeneous rxns
• the rxn takes place on the surface of the catalysts
• rxn rat is based on mass of solid catalyst W (rather
than on volume V
-r’A = mol A reacted/s • g cat.
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4. Continuous Flow Reactors VII
o Pack-Bed Reactor 2
- General mole balance
- Operated at st-st
- Design equation for PBR
- Differential w.r.t W
- Or
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dt
dNdVrFF
jV
jjj 0
0dt
dNA
0'
0 V
AAA dWrFF
'0 AA r
dW
dF
'
AA r
dW
dF
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4. Continuous Flow Reactors VIII
o Pack-Bed Reactor 3
- Rearranging and integrating between
W = 0, FA = FA0
W = W1, FA = FA1
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0
1
1
0''1
A
A
A
A
F
FA
AF
FA
A
r
dF
r
dFW
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5. Industrial Reactors I
o Liquid-Phase Reactions 1
- Semibatch reactors
• T control by regulation of
feed rate
• minimizing side rxns to
maintain conc of one of the
reactants
• 2-phase rxns where gas
bubbled out
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5. Industrial Reactors II
o Liquid-Phase Reactions 2
- CSTRs
• intense agitation required
• stand alone or in series
• relatively good T control
• the smallest conversion ⇒ large size necessary
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5. Industrial Reactors III
o Gas-Phase Reactions 1
- PFRs
• easy to maintain (no moving parts)
• the highest conversion
• difficult T control ⇒
hot spot if exothermic rxn
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5. Industrial Reactors IV
o Gas-Phase Reactions 2
- PBRs
• basically the same to PFRs with solid catalyst
particles
• the catalyst is troublesome to replace
• channeling of the gas flow ⇒ dead zone
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5. Industrial Reactors V
o Gas-Phase Reactions 3
- Fluidized-Bed Reactors
• analogous to CSTR – well mixed, even T
distribution
• approximately modeled as a CSTR [for exact
design, it need customizing]
• often high cost of reactor and
catalyst regeneration
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