ChE 471
Fall 2008
Homework 7
Due Friday, October 24
1.
The liquid-phase hydrolysis of dilute aqueous acetic anhydride solution is second order
and irreversible, as indicated by the reaction
(CH3CO)2O + H2O  2CH3COOH
A batch reactor for carrying out the hydrolysis is charged with 200 liters of anhydride
solution at 15˚C at anhydride initial concentration of 2.16 x 10-4 mol/cm3. The specific heat and
density of the reaction mixture are essentially constant and equal to 0.9 cal/(g)(˚C) and
1.05 g/cm3, respectively. The heat of reaction may be assumed constant at
-50,000 cal/mol. The rate has been investigated over a range of temperatures, of which
the following results are typical ( Note, r is the equivalent rate of reaction):
T(˚C)
r(mol/cm3 min)
10
0.0567C
15
0.0806C
25
0.1580C
40____
0.380C
where C is the acetic anhydride concentration, in moles per cubic centimeter.
(a)
Explain why the rate expression can be written as shown in the table even though the
reaction is second order.
(b)
If the reactor is cooled so that operation is isothermal at 15˚C, what time would be required
to obtain a conversion of 70% of the anhydride? How much heat would need to be added
(removed) during this period?
(c)
Determine an analytical expression for the rate of reaction in terms of temperature and
concentration.
(d)
What time is required for a conversion of 70% if the reactor is operated adiabatically?
2.
A tubular flow reactor is to be designed for the production of butadiene from butene by the
gas phase reaction:
C4H8  C4H6 + H2
The composition of the feed is 10 moles of steam per mole of butene and no butadiene or
hydrogen. The reactor operates at 2 atmospheres pressure with an inlet (feed) temperature
of 1200˚F. The reaction rate follows a first-order, irreversible equation for which the
rate constant k (mol butene reacted/h L atm) as a function of temperature is:
T.K
k
922(1200˚F)
11.0
900
4.90
877
2.04
855
0.85
832
0.32
The heat of reaction may be taken as constant and equal to  HR = 26,360 cal/mol.
1
Similarly the specific heat of the feed stream may be regarded as constant and equal
to 0.5 Btu/lb ˚R.
(a)
What would be the volume required for a conversion (of butenes) of 20% if the reactor
were operated isothermally at 1200˚F with a butene-plus-steam feed rate of 22 lb mol/h?
What is the heat addition ( removal) requirement?
(b)
It is desired to determine the conversion as a function of reactor volume (ft3) for
adiabatic operation if the feed rate is 2.0 lb mol of butene per hour and 20 lb mol of
steam per hour. Demonstrate your ability to solve this type of problem by calculating
the reactor volume for conversions (of butenes) of 10 and 20%. What changes in operating
conditions could be employed to reduce the volume required for a given conversion?
3.
A first-order irreversible (liquid-phase) reaction is carried out in a continuous flow stirred-tank
reactor (CSTR). The density is 1.2 g/cm3 and the specific heat is 0.9 cal/(g)(˚C). The volumetric
flow rate is 200 cm3/s and the reactor volume is 10 liters. The rate constant is:
k = 1.8 x 105e-12,000/RgT
s-1;
Rg = universal gas constant in (cal/mol K)
where T is in degrees Kelvin. If the heat of reaction is  HR = -46,000 cal/mol
and the feed temperature is 20˚C, what is the steady state temperature and conversion
in stable, adiabatic operation at a feed concentration of 4.0 mol/liter?
4.
The reaction between sodium thiosulfate and hydrogen peroxide in dilute aqueous solution
is irreversible and second order in thiosulfate. The rate constant for the thiosulfate is the
following function of temperature:
 18300 
 (cm3/mol s) ;
k = 6.85 x 1014 exp 
 Rg T 
Rg= gas constant (cal/mol K)
Reaction stoichiometry indicates that 2 moles of H2O2 react with one mole of Na2S2O3.
The heat of reaction at 25˚C is  HR = -131,000 cal/mol.
Kearns and Manning (AIChE J., 15, 660 (1969)) experimental studies in a continuous
flow stirred tank reactor included the following conditions:
Reactor volume
Feed temperature
Feed rate
= 2790 cm3
= 25˚C
= 14.2 cm3/s
Consider adiabatic operation and feed concentration of 2.04 x 10-4 (mol/cm3) and
4.08 x 10-4 g (mol/cm3) of thiosulfate and hydrogen peroxide, respectively. What would
be the thiosulfate conversion and temperature in the reactor effluent?
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