Transcript 3-Interpretation The Use of Rate Law.pptx

ITK-329 Kinetika & Katalisis
Chapter 3
Interpretation & The Use of Rate
Law
Dicky Dermawan
www.dickydermawan.net78.net
[email protected]
49
Conversion
Batch Systems
Conversion of A 
Number of A reacted ( consumed)
Number of A fed
Moles of A consumed = Moles of A fed – Moles of A IN the reactor
XA 
N A0  N A
N A0
 N A  N A 0  (1  X)
Flow Systems
Conversion of A 
XA 
Number of A reacted ( consumed) per unit time
Number of A fed per unit time
FA 0  FA
FA 0
 FA  FA 0  (1  X)
50
Typical Questions:
3.9
A first-order polymerization reaction is being run in a batch
reactor. A concentration of 0.007 mol/liter of monomer is
loaded into the reactor, and then a catalyst is added to
initiate the reaction. Experiments show that the reaction is
30% complete in 10 minutes.
a. Calculate the rate constant
b. Calculate the half-life
c. How long will it take for the reaction to be 90% complete?
d. How would the time in (c) change if you increased the
concentration in the reactor to 0.16 mol/liter?
e. Repeat for a second order reaction.
51
Typical Questions (2):
3.10
N2O5 can be made via oxidation of ammonia over a platinum gauze.
You do an experiment and find that you get 50% conversion of the
ammonia with a 0.1 second residence time in the reactor at 1000 K.
a. Calculate the rate constant for the reaction assuming that the
reaction is first-order in the ammonia pressure and zero-order in
oxygen pressure.
b. How long of a residence time will you need to get 90% conversion at
1000 K?
c. Now assume that the reaction is instead secondorder in the ammonia
pressure.
d. Estimate the rate constant for the reaction assuming 50% conversion
in 0.1 second.
Assume a stoichiometric feed at 1 atm pressure
52
Kinetics from Minimal Number of Data
L3.5
In a homogeneous isothermal liquid polymerization, 20% of the
monomer disappears in 34 min for initial monomer
concentration of 0.04 mol/L and also for 0.8 mol/L. What is the
rate of disappearance of the monomer?
L3.10
In units of moles, liters, and seconds, find the rate expression for
the decomposition of ethane at 620oC from the following
information obtained at atmospheric pressure. The
decomposition rate of pure ethane is 7.7%/sec, but with
85.26% inerts present the decomposition rate drops to
2.9%/sec.
53
Kinetics from Minimal Number of Data
L3.21
Find the first-order rate constant for the disappearance of A in
the gas reaction 2 A > R if, on holding the pressure constant,
the volume of the reaction mixture, starting with 80% A,
decreases by 20% in 3 min.
L3.22
Find the first-order rate constant for the disappearance of A in
the gas reaction A > 1.6 R if the volume of the reaction
mixture, starting with pure A, increases by 50% in 4 min. The
total pressure within the system stays constant at 1.2 atm,
and the temperature is 25oC
54
Kinetics from Minimal Number of Data:
Reversible Reaction
L3.9
The first-order reversible liquid reaction
A  R, CA0 = 0,5 mol/L, CR0 = 0
Takes place in a batch reactor. After 8 minutes,
conversion of A is 33.3% while equilibrium
conversion is 66.7%. Find the rate equation for
this reaction
55
Integration of a Rate Equation:
Interpretation of Reaction Order
L3.2
Liquid A decomposes by first order kinetics, and in a
batch reactor 50% of A is converted in a 5-minute
run. How much longer would it take to reach 75%
conversion?
L3.3
Repeat the previous problem for second-order kinetics
56
Integration of a Rate Equation
For homogeneous reaction taking place in a batch reactor:
For a constant volume batch reactor:
 rA  
 rA  
1 dN A

V dt
d(N A / V )
dC A
1 dN A


  rA  
V
dt
dt
dt
Assume that you are running a reaction A  B that follows:
  20 kcal/mol 
r A  1  10 13  exp
 CA

RT


Where rA is the rate of reaction in mol/(L.sec), T is temperature in Kelvin, R =
1.987 cal./(mol.K)
The temperatur varies during the course of the reaction according to:
 t 
T  300  10  sin

 10 
where t is time in second
How long will it take to reduce the A concentration from 1 mol/L to 0,1 mol/L?
57
Integration of a Rate Equation:
Interpretation of Reaction Order
L3.4
A 10-minute experimental run shows that 75%
of liquid reactant is converted to product by a
½ order rate. What would be the amount
converted in a half-hour run?
58
Integration of a Rate Equation:
Constant Volume vs Constant Pressure Batch
Reactor
L3.23
A zero-order homogeneous gas reaction
ArR
Proceeds in a constant-volume bomb, 20% inerts, and the
pressure rises from 1 to 1.3 atm in 2 min.
If the same reaction takes place in a constant-pressure
batch reactor, what is the fractional volume change in 4
min if the feed is at 3 atm and consist of 40% inerts?
59
Integration of a Rate Equation:
Constant Volume vs Constant Pressure Batch
Reactor
L3.24
A zero-order homogeneous gas reaction
ArR
Proceeds in a constant-volume bomb, P = 1 at t =
0, and P = 1.5 when t = 1.
If the same reaction, same feed composition, and
initial pressure proceeds in a constant-pressure
setup, find V at t = 1 if V = 1 at t = 0
60
Integration of a Rate Equation:
Constant Volume vs Constant Pressure Batch
Reactor
L3.25
The first-order homogeneous gaseous decomposition
A  2.5 R
Is carried out in an isothermal batch reactor at 2 atm with
20% inerts present, and the volume increases by 60%
in 20 min.
In a constant-volume reactor, find the time required for the
pressure to reach 8 atm if the initial pressure is 5 atm, 2
atm of which consist of inerts.
61
Integration of a Rate Equation:
Constant Volume vs Constant Pressure Batch
Reactor
L3.26
The gas reaction
2AR+2S
Is approximately second order with respect to A. When
pure A is introduced at 1 atm into a constant-volume
batch reactor, the pressure rises 40% in 3 min.
For a constant-pressure batch reactor, find:
a. the time required for the same conversion
b. The fractional increase in volume at that time.
62
Multiple Reactions
L3.16
Nitrogen pentoxide decomposes as follows:
N2O5  ½ O2 + N2O4
–rN2O5 = (2.2x10-3 min-1).CN2O5
N2O4  2 NO2
Kp = 45 mmHg
Find the partial pressures of the contents of a constantvolume bomb after 6.5 hours if we start with pure at
atmospheric pressure
63
Multiple Reactions:
L3.18
For the reactions in series:
k
k
1
2 S
A 

R 

Find the maximum concentration of R and when it is
reached if:
a. k1 = 2 k2
b. k1 = k2
64