REACTOR DESIGN
Problem Sheet No.1: Reaction Kinetics and Batch Reactor
Instructor: Prof,
Dr.
Mohammad Fadhil Abid
Pl
Given the reaction 2NOz + 0.5 02
NzOs, what is the
relation between the rates of formation and disappearance of the three
-e
reaction components?
P2 For the complex reaction with stoichiometry A + 3B
2R + S
and with a second- order rate expression -r4 - k1 Ca Cs are the reaction
rates related as followS! 14: rs : rp? If the rates are not so related, then
P3 For a gas reaction at 400 K the rate is reported as
置
靱一
how are they related?
(a) What are the units of the rate constant?
(b) What is the value of the rate constant for this reaction
if the rate
equation is expressed as - rA :
-;#:
-
3.66 p2 a
k C2e (-ra in mol/m3.s)
P4 For each of the followilg reactions and rate laws at low temperatures,
suggest a rate law at high temperatures. The reactions are highly
exothermic and therefore reversible at high temperatures.
(a) The reaction A
B, is irreversible at low temperatures, and
the rate law is -r4 ---+'
keCo
(b) The reaction A+2 B--.)
2D, is irreversible at low temperatures
and the rate law is -ra: keCao'5 CB
P5 Calculate the equilibrium conversion and concentrations for each of
the following reactions:
:
mol/dm3 and Ke 10 dm3/mol.
The gas-phase reaction
3C is carried out in a reactor
with. Pure A enters at a temperature of 400 K and 10 atm. At this
temperature, Ke :0.25 [dm3/mol]2.
(b)
A:>
P6Between O° C and 100° C detelllline the equilibrium conversiott fOr the
elementary aqucous reaction A lヒ 〓
11ヽ
====〓
△G° 298= 14130J/mol;△ H° 298= 75300J/mol;CPA=CPR
Present the results in the f01111 0fa plot Oftemperature versus cOnversiOn.
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P7 the rate of reaction doubles for a 1OoC increase in temperature
occurs
only at a specific temperature for a given activation energy.
(a) Develop a relationship between the temperature and activation
energy.
Neglect any variation of concentration with temperature.
(b) Determine the activation energy and frequency factor from
the
following data:
kA mln
0.001
0.050
I ("C
0.00
100
■ ‘
P8 Uitt< is pasteurized if it is heated to 63oC for 30 min, but if it is heated
to 74"C it only needs l5 s for the same result. Find the activation energy
of this sterilization process.
P9 Experimental studies of a specific decomposition of A in a batch
reactor using
pressure units show exactly tlre same rate attwo different
temperatures:
at 400
-r4 - 2.3 po'
at 500K
-r4 - 2.3po'
where p.s: [atm] and -r4- [mol/m3.s]
(a) Evaluate the activation energy using these units
(b) Transform the rate expressions intoloncentration
units and then
evaluate the activation energy.
K
P10 rhe irreversible gas phase reaction 2A + B
D
c+
is an
elementary reaction. The constant pressure reaction is carried
out
rsothermally at 7270 C and at a pressure of 20 atm in a batch
reactor. The
feed consists of 4l% A and 41%B and I 8%D. The reaction
rate constant
is 0.01(dm3mol-')2. ,-'. calr.rlate the time necessary
to achiev e 7Syo
conversion of the limiting reactant.
-+
Pl1 A gas-phase
reaction d
B + C is to be conducted in a lO_Liter
(initially)^isothermal batch reactor
-; at 250 c .The reaction rate constant
is
0'023 dm3 mol-r s-'. Determine the time required
for Tsyo conversion of 5
moles
of A if:
(a) A constant - volume batch reactor is
used.
(b) A constant- pressure batch reactor is
used.
yl? A liquid-phase
reaction A + B-+C
is conducted in an
isothermal batch reactor. The reaction
is f,rrst-order with respect to each
reactant, with rate constant (k) : g.gz*f
O-, Am: mol-i;'fi ;;r, a:" "
2/5
Determine the reactor volume required to produce 175 mol C h-r,
xA:0.9 and the shutdown time between batches is 30 min.
if
P13 Ethyl acetate is to be produced from ethanol and acetic acid in a 500
dm3 batch reactor at 100d c according to the elementary liquid-phase
reaction
cH3cooH (A) + C:HsOH (B)
■
-->tr2o(c)
+ CH3COOC2H5(D)
The reaction is elementary and has an equilibrium constant of 2.93, and,
the rate constant for the forward reaction (k) is 4* 10-a dm3 mol-r s-,. The
feed contains 30 weight percent (wt%) acetic acid,,50yo ethanol, and the
balance is water. The density of fluid is essentially constant at 1.0 g cm-3.
(a) What is the maximum conversion of acid that can be obtained?
(b) Determine the time required to achieve 25%o of the acetic acid.
P14 A gas-phase reaction A +R+S is carried out in a batch reactor
with initial conditions (T0):300K, total pressure :5 atm, and a constant
volume of 0.5 m'. The reaction rate constant is:
k:10r4 exp (-10000/T) h-r. The heat of reaction is 1500 kcal/kmol and
the heat capacity (kcal/kmol .K ) of A, R and S are 30,25, and 20,
respectively .
(a) compute the time requiied for isothermal conditions if the conversion
is 80%.
(b) compute the time required for adiabatic conditions if the conversion
is 80%.
Pl5 An endothermic
elementary liquid-phase reaction 34 ___*B is
carried out in a batch reactor .The reaction mixture is heated up till 400
c
and the reaction then proceeds adiabaticaly .During the heating
period
up
, 10 mol %o of A is converted . From this instant on, what is thelim;
required to reach a conversion of 70 o/o of A. Specific heat
and mass of
reaction mixture are 0.59 kcal / kg. K and 950 Lg, respectively.
The
volume of the reaction mixture is constant (1 m3j and the
number of
moles of A initially is 10.9 kmol . The heat of reaction
being 25000 kcal /
kmol .The variation of the rate constant with temperature
is
Ln k = (-10000/RT + 5) [k in {m3/mol.;2 /s]
Pl6
20 moles of A decomposes isorhermally
at 300 K in a l0 dm3
constant volume batch reactor supplied
with a cooling jacket. The
reaction rate constant at 300 K is'd.65
_Id
min-,.
Aff_:
UA6:25.0 W K-'.
3/5
I _"i
i .ra
(a)
(b)
Estimate the time required for 80% conversion of A.
Determine the rate of heat transferred (e ) ,as function of time,
required to maintain isothermal conditions in the reactor.
(c) Estimate the temperature of the cooling fluid (Tc).
P17 Consider the reaction A
B in a l0-dm3 batch reactor with initial
->temperature (To) : 350 K. The reaction rate
concentration Cas: 2 molfl and
:
constant (at 300 K) 0.65 Llmol.s, (-AHx) : 300 kcal/mol. The activation
energy is 600 call mol. Determine the heat transfer rate required to maintain
the reaction temperature at 350 K with 95yo conversion of A.
P18Theelementarygas-phasereactionA_2Bistobe
carried out adiabatically in a constant volume batch ieactor. The
initial temperature Ts:300 K, and the reaction mixture consists of
80% A and2jYo inert. The volume of reactor is 50 dm3 and
containing 1000 gmoles of reaction mixture. What time is required
to achieve l|Yo conversion of A?
Additional data:
. Specific heats ( callmol.K): A:12 ;p:6 ; Inert : l5
o Heat of reaction( AHp) at 300K: -20000 callmole A
o I! is a function of temperature and its value at 300K is 100000
.
mol/lit.
Ln( ktl}.2l7):3.4[ (T-300yT] , k1 in min-r
,Ine
P19
liquid- phase hydrolysis of dilute aqueous acetic anhydride
solution is second order and irreversible, as indicated by the reaction:
(cH3coo)zco + HzO
-2CH3COOH
「I:11::litilhydr°
lySis is charged with 200 dln3
fllililble::￨:lillf』
肌ぶ 靭l=質寧
叩
1お
investigated Over a range gitettЪ
are typical.
cal.
°
T c
10
( rA)gmO1/c拓 両面ln
0.0567CA
:
°
eiltur」 JI(尋 11《 Jl・ lhLキ:l:;￨11:・
le:[i:
15
25
0.0806CA
The heat OfreactiOn(△ HR)=‐
500oo cal gmol‐
4/5
0。
1
1580cA
40
0。
380CA
｀ 三
ぞ
暉
嘔
ロ
￨
ロ
"軒
(a) Explain why the rate of reaction can be written as shown in table,
although the reaction is second order'
(b) If the reactor is cooled so that the operation is isothermal at 15o C,
what time would be required to obtain a conversion of 70o/o of the
anhydride?
terms
(c) Determine an analyical expression for the rate of reaction in
temperature and concentration.
of
(d)What time is required for a conversion of 70%,ifthe reactor is being
operated adiabatically?
薔
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