CRE TUTORIAL 0
1. An isothermal reactor is to convert reactant A to products. The reaction
is first order in A, occurs in the liquid phase, and the rate constant, k1 , is
0.1 min−1 .
(a) Tabulate CA , −rA , and −r1A for the following values of CA : 0.01, 0.02,
0.03, 0.04, 0.05 kmol m−3 .
(b) Plot −r1A vs. CA on graph paper.
(c) From the graph or otherwise, estimate the residence times required in (i)
a CSTR and (ii) a PFR with inlet concentration of 0.05 kmol m−3 and outlet
concentration of 0.01 kmol m−3 . [Ans: 40min, 16.1min resp.]
(d) Sketch roughly a graph of −r1A vs. CA for a zero order reaction with
kzero = 0.1 kmol m−3 min−1 . Discuss the residence times required in a PFR
and a CSTR respectively with inlet concentration of 0.05 kmol m−3 and outlet
concentration of 0.01 kmol m−3 .
2. An irreversible reaction A → P is studied in an isothermal batch reactor
at 300K. The initial concentration of A is 1 mol cm−3 , and after 1 hr the
concentration of A is 0.1 mol cm−3 . Calculate what the concentration of A
was after 30 minutes using first order kinetics. The reaction occurs in the
liquid phase. [Ans: 0.316mol/cc] Optional: Repeat using second order
kinetics. [Ans: 0.18mol/cc]
3. System A has a PFR (residence time of 1 hr) followed by a CSTR (mean
residence time 1 hr) in series. For an initial concentration, CA0 = 1 kmol/m3 ,
and a first order irreversible reaction with rate constant of 1 hr−1 , calculate
the final concentration, CA2 . System B has the above reactors in the reverse
order. Using the same reaction data, show by calculating CA2 that the con-
version is the same for system B as for system A. Note: This result does
not necessarily hold for reactions of other orders.
Optional: Repeat the above using second order kinetics (k2 = 1 m3 kmol−1 hr−1 )
to show that CA2 is different for systems A and B.
⇀ P + Q is
4. Show that the overall reaction rate for the reaction A + B ↽
given by
CP CQ
−rA = kf CA CB −
Kc
where Kc is the equilibrium constant and kf is the rate constant of the
forward reaction.
5. If the rate of a reaction increases tenfold from 500K to 600K, calculate
the activation energy of the reaction. [Ans: 57.435MJ/kmol]
1
6. A liquid effluent containing A is to be treated by converting it to harmless
product P . A → P is first order with a rate constant k1 = 1 hr−1 . If a
catalyst is added, the reaction kinetics are zero order with rate constant
kzero = 0.1 kmol m−3 hr−1 . Two CSTRs are to be used in series with catalyst
added only to the second CSTR. If the feed rate is 15 m3 /hr, the initial
concentration of A is 3.5 kmol m−3 , and the volume of the first CSTR is
60 m3 , calculate the volume of the second reactor required for all A to be
consumed. [Ans: 105m3 ]
7. An isothermal reactor is to convert 50% of reactant A to products. The
reaction is first order in A and occurs in the liquid phase. A continuous
stirred tank reactor (CSTR) of volume V and feed rate F (in which A is
present at a concentration CA0 ), the outlet concentration CA1 is to be used.
(a) Using the Arrhenius law, k = k0 e−E/(RT ) , and the following data, calculate
the volume of the CSTR required for 50% conversion of A at TC = 373K [Ans:
50m3 ], where the feed rate is 10 m3 hr−1 .
k0 = 5 hr−1
E = 10000 kJ kmol−1
R = 8.314 kJ kmol−1 K−1
(b) For a first order reaction taking place in a plug flow reactor (PFR), the
relationship between inlet and outlet concentrations is
CA1 k1 V
ln =− .
CA0 F
Determine the temperature TP at which a PFR of the same volume as the
CSTR in (a) must be operated to obtain the same conversion. [Ans: 335K]
(c)(i) Comment on the residence times in the above CSTR and PFR.
(c)(ii) If the CSTR were replaced by 2 CSTRs (each of volume V /2) in series,
indicate relative to TC and TP how you expect the temperature required for
50% conversion would change. What value would the temperature approach
as more reactors (each of size V /n for n CSTRs) are used in series?
