Side 1 av 4
Norges Teknisk Naturvitenskapelige Universitet
Institutt for kjemisk prosessteknologi
Faglig kontakt under eksamen:
Professor Anders Holmen, tlf.: 73 59 41 51 / 91897164
Førsteamanuensis Jens-Petter Andreassen, tlf.: 73 59 42 09 / 92032209
EKSAMEN I TKP 4110 Kjemisk reaksjonsteknikk
11. august 2008
Tid: 0900 - 1300
Hjelpemidler: D - Ingen trykte eller håndskrevne hjelpemidler tillatt. Bestemt, enkel kalkulator tillatt.
Problem 1
The methanation of CO is studied on a 10 wt% Ni/Al
2
O
3
catalyst at differential conditions:
CO + 3H
2
→ CH
4
+ H
2
O (1)
The reaction is studied in a PBR at 523 K and 1 bar total pressure. Using a H
2
/CO ratio of 8 in the feed and a conversion of 10 %, the rate of reaction is determined to be 4∙10
-7 mol CO/g cat, sec. a) What do we mean with differential conditions and calculate the space velocity at the given conditions.
The consentration of active sites on the catalyst surface is determined by chemisorption of H
2 in the usual way. It can be assumed that the dissociative chemisorption of H
2
on Ni follows the Langmuir-isotherm. The following experimental data for the chemisorption of H
2
at 298
K is found for the methanation catalyst:
p H
2
ads.
mm Hg cm 3 (STP)
9
14.5
36
74
121
196
0.849
0.979
1.268
1.459
1.579
1.702
The mass of the sample is 1 gram. b) Calculate the concentration of active sites on the surface of the catalyst.

Side 2 av 4
The mechanism for reaction (1) can be described by the following sequence of elementary reaction steps:
CO
(g)
+ 2∙S ↔ C∙S + O∙S
O∙S + H
2(g)
↔ H
2
O
(g)
+ S
C∙S + H
2(g)
↔ CH
2
∙S
CH
2
∙S + H
2(g)
↔ CH
4(g)
+ S
(2)
(3)
(4)
(5)
S represents an active site on the surface and index g refers to the gas phase. c) Derive the rate expression for the formation of methane provided that the hydrogenation of adsorbed carbon is the rate determining step (rds).
Given: 1 mol gas is 22400cm
3
and the mol weight for Ni = 58.69.
Problem 2
A continuous stirred tank reactor (CSTR) with constant liquid voulume of 1 m 3 is fed by a liquid stream of 2 m
3
/h. The liquid feed contains the component A in a concentration of 4 mol/l. Component A reacts irreversibly by 1. order kinetics to the product R by the following reaction rate:
r
A
= kC
A
The rate constant k is expressed by Arrhenius equation as: k = Ae й к
E
RT щ ъ
The activation energy (E) is 70 kJ/mol and the rate constant is determined to 0,8 h -1
At 40 ºC. The liquid can be assumed to have a constant density of 950 kg/m 3 heat capacity of 3 kJ/kg∙K, independent of conversion and temperature. The heat of reaction of -50 kJ/mol, is also assumed constant within the relevant temperature interval. The gas constant R = 8,314 J/K∙mol. a) Determine the degree of conversion in the reactor at a temperature of 40 ºC assuming ideal mixing conditions. b) Determine the feed temperature when the reactor in a) is working adiabatically.. c) Determine the degree of conversion and the corresponding feed temperature at adiabatic conditions when the reactor temperature is 80 ºC. d) How many possible steady states can be found at a feed temperature of 20 ºC?
Explain the answer.

Side 3 av 4
Problem 3 a)
Show how the Michaelis-Menten equation:
r s
=
V S max
( )
K m
+ can be derived for the decomposition of urea to NH
3
and O
2 by the enzyme urease:
NH
2
CONH
2
+ urease + H
2
O → 2 NH
3
+ CO
2
+ urease. b)
Give a definition of the effectiveness factor, η for a first order irreversible reaction A

B in porous spherical catalyst particles. Formulate (by a shell balance) a differential equation that describes the coupling between diffusion and reaction within the catalyst particles.
The Thiele Modulus, Φ
1
is defined by:
1
R k S / D
1 ўў r a c e
What do the different symbols represent and how can the experimental conditions be changed in order to make Φ
1
as small as possible? The effectiveness factor depends on the Thiele modulus by the following equation: h =
3
2
( F
1 coth 1 )
F
1
Show a (qualitative) plot of the effectiveness factor as a function of Φ
1
and indicate in which regions diffusion and reaction limits the reaction.

т x
0
Useful integrals for reactor design: т x
0
1 dx x
= ln
1 -
1 x dx
-
= x
2
(1 ) 1 x x т x
0 x a + x dx = a ln x
0 + x
0
x b x b т x
0
1 dx 1
=
+ e x e ln(1 + e x ) т
0 x т x
0 т x
0 т
0 x
1 + e x
(1 x ) dx = (1 + e ) ln
1 -
1 x
- e x
1 + e x
(1 x )
2 dx =
(1 + e x )
2 dx
(1 x ) 2
(1 - e ) x
1 x
- e ln
1 -
1 x
2 (1 ) ln(1 x ) + e
2 x + dx
-
=
(1 )( x ) a -
1
1 ln a a x
(1 x )
(1 + e )
2 x
1 x
Side 4 av 4