LECTURE 17.1 (Assignment)
Submitted by:
ALMES, ALLYANNA MARIE R
AMMOG-AO II, RUDYARD N
BALITE, TIMMY S
DOMILIES, ALISTER MARC B
GAMENG, YVETH
MADULID, GELLINNE MICAH
OMBI-ON, GLEENA RIO N
RAMOS, KATRHYNE L
RAZON, STEPHANIE NICOLE R
ROLDAN, JOHN PATRICK
17.1. Gaseous reactant A diffuses through a gas film and reacts on the surface
of a solid according to a reversible first-order rate,
-r”A=k”(CAS-CAe)
where CAe is the concentration of A in equilibrium with the solid surface. Develop
an expression for the rate of reaction of A accounting for both the mass transfer
and reaction steps.
Solution:
For the mass transfer step:
−r A =- {1} over {S} {{dN} rsub {A}} over {dt} = {k} rsub {g} ( {C} rsub {Ag} - {C} rsub {As}
--------(1)
For the reversible reaction step:
−r A = {k} rsub {S} ( {C} rsub {As} - {C} rsub {Ae}
--------(2)
Eliminating CAs gives:
−r A = {1} over {{1} over {{k} rsub {g}} + {1} over {{k} rsub {s}}} ( {C} rsub {Ag} - {C} rsub {Ae}
17.2. Example 17.4 gives the final rate expression for film mass transfer followed
by a second-order rate expression for reaction on a plane surface. Please derive
this expression and show that it is correct.
Solution:
r A 1 = {1} over {S} {{dN} rsub {A}} over {dt} =- {D} over {∆x} ( {C} rsub {Al} - {C} rsub {As} )= {k} r
r A 2 =k C A
2
Combining the reaction steps to eliminate C As gives
2
k l +4 k {k} rsub {l} {C} rsub {Al}}
2k } (2k C Al +k l −√ ¿
k
−r A =−r A 1 =-r A2= ¿l
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17.3 In slurry reactors, pure reactant gas is bubbled through liquid containing
suspended catalyst particles. Let us view these kinetics in terms of the film
theory, as shown in Fig. P17.3. Thus, to reach the surface of the solid, the
reactant which enters the liquid must diffuse through the liquid film into the main
body of the liquid, and then through the film surrounding the catalyst particle. At
the surface of the particle, reactant yields product according to first-order
kinetics. Derive an expression for the rate of reaction in terms of these
resistances.
Required: expression for rate of reaction
Solution:
For the interference between gas bubbles and liquid,
−r=−
1 dN
=k Al ai (C Ai−C Al )
V dt
… (i)
Where kAl = gas-liquid mass transfer coefficient
ai = area of gas-liquid interface per volume of reactor
For the interface between the solid catalyst particles & the surrounding liquid,
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−r=−
1 dN '
=k Al as (C Al −C As )
V dt
… (ii)
Where k’Al = liquid-solid mass transfer coefficient
as = area of liquid-solid interface per volume of reactor
For surface reaction,
−r=−
1 dN
=k C a
V dt 1 As s
…(iii)
Combining (i), (ii), and (iii), eliminating the intermediate concentrations C Al and
CAs gives, on manipulation
−r=−
1 dN
1
=
C
V dt
1
1
1 Ai
a+
+
k Al i k 'Al as k s
Where -r = rate based on unit volume of reactor
This expression is the special case of Eq. 22.2 for slurry reactors.
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