problema del libro de Ingeniería de la Cinética Química J. M. Smith Hidrogenacion de iso octano, numero del problema 10-10

1. 1.0 70
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08· 56
/420..6 [;J ! 'r:f.f{- ./ }
/ I
04 28
/' I<",,"'
~#'V,-/t7
14
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0.2 ,,>P' ~ '"
(I
""0.0
4.6 9.2 13.8 18.4 23.00.0 9.2
W
13.8 1804 23,0 0.0 V
PIO·IO (a)
Iso,ocrene +. Hydrogcn --? isCH)Ctanc
A -t. B
Discrirninarion of mcdds:
Assume 'fA ;: k C1 q q:
For runs 2 and J, 0 < a: < 1 ; 2 and 4, 0 < f) < 1 ; and 2 and 5 , ·1 < r < O. From
Perry's handbook, 5th cd". p. 4-8; the reaction is probably surface reaction rate con'Q'"olling.
Mechanism I (H. Alvord):
A+S+!A.S
B2+2S ~ 2B·S
A·S,2B·S;:! C·S+2S
C·S ;:! C+S
Hence.
Hence,
k fp;.. PB - PcfKuJ-rA, "'" _._.,..•,..._.'--,•..,_.,-""-,...._-,._..
[1 +'KAP;..+KfPft+ KcPcP
Mechanism II (S. L Mullick):
A+S +! A.S
B+S ~ B.S
A·S+B·S f:!: C·S+S
C·S ~ C+,S
, _ k[PA Ps - Pc/l<.,qJ"1;.. - ...."._..._,...•"...•_...,••.•.- ." •.._ ......_ ••..., ..,....•.
[1 ,. K... FA t· KB Ps -+- Kc PcP
10·22

2. From runs 2. 9 11. 12. P A:::: PB =Pc "" P. a plot of ~rA vs. P shows a parabollic
behavior. therefore we Mil drop the second term in the denominator for easy linearization.
Tne readers can calculate ~ value by Gibbs free energy change 4'1 this equation (up to 650
K. the reverse reaction is negligible)
Tne linearized regression model is:
Using given 12 data pointS to solve for these four unknowns:
y :::: 3.0 -+ 1.42 PA .;. 0.97 Pa -t. 1.42 Pc
The tinal results are:
0..1113 PA Fg-fA:: ...- ....".._._-,,--,,-,,_.- _ ..............._ ...._"
(1 + 0.475 PAt 0322 PB .;. 0..414 Pcr
The comparison of the pen:emage error between the model and the experimental data are:
r
(~A.!:lit .5
r
Run PA Pa Pc (exp.) (calc.) % elmrexpo
1 1 0 0..0362 :'5.26 0.0345 -4.8
2 1 1 1 0..0.239 647 0.0227 -4.7
3 1 :3 1 0..0390 8.77 0..0410 +5.0
4 3 1 1 o...Q351 9.25 0.0334 A.a
5 1 1 3 O.D114 9.37 0.0120 +5..7
6 I 10 0 0.0534 13,,69 0..0.505 -5.4
7 10 1 0 0..0310 17.96 0.0302 -2.6
8 1 1 10. 0.0033 lo.Al 0.00315 -4.5
9 2- 2 2 0..0380 10.26 0.0380 0
10. 0.2 0.2 0.2 0.0032 3.54 0.00288 ·9.8
11 0.1 0.1 0.1 0..0008 3.54 0.00089 +10.7
12 5 5 5 0.0566 21.02 0.0599 ....:.1:2 _
Isuml =59.2
avg. =4.9
PIO-IO (b)
Discussion: The readers may check the validity ofmechanism L To reduce the
accumulation of error in calculations, the readers should have used ail data points and
solved all unblowns simultaneously. To get the maximum informacion of complex kinetics
of a reaction from the least runs, it is advantageous to do planned experiments such as
factOrial design.. (W. G.. Humer. and A. C. Atkinson. Olem1cai Engin~~rin!!, p.. 159. June
6. 1966).
A paper discussing chemical reaction rare equations from experimental data is in:
C. n. Vare 11., Summer Compmer Simulation Conference. Proceedings. 1975, Pa.."t 1. p..
368.
10-23

3. PIO-IO (c)
0.2223 C~o (RTr {l-Xr / (l-O.SXY··rA =.-....- - -..--.--.--.-.--................--.-~.-.--'J-
r1 + CAOO ~T {(0.475 + 0..322 (I-X)} + OA14x}1-
l 1- .)x .
0..1 113 (RT CAot (l·.xF I {l-O.5Xr
-r! = ----.~------..--.--.------..
. r1 + c.:..o RT fO 797 • 0383 x'j2.. 1-0.SX . , . ' !
FAO::: 2.5 =:::i50 I~l
CSTR:
w;;;;;; 21.380 g ::::: 21.4 kg
x
w::; 1501
o 2:1l13J1.5J:i!·X(LL0.5 x)Z
~ 1 ..,..
11+' _...........,..2............ {O.797- 0..383 X)I~
l. 1 - 0...5 X 'j
10-24

4. w=...- ....J~Q 1x
G (X}dX
0.1113 x 2.25 0
where
[
. 1..5 (0..797'- 0..383 Xl]2
1 + -.-----------. (1 - 0.5 xjZ
G(X):= ...-.. L.:Q~.X___..__.._._....._..........._.....
(1- xf
x G{X)
0. 4.82 ~l
0..1 5.38 ~t
0.2 6.13
:10..3 7.16 COO
OA 8.66
05 11.00
0.6 IS.03 0
I) a.l 0':'
0.7 23.15
0..8 44..62
Using Simpson s rule.
area. under the curve ~ i 0
w:;: ..._____.J2!1_____.__ x. 10:;: 6000 g "" 6 kg
0.1113 x. 2.25
PIO-IO (d)
Consider the differential section between L and L +dL
In - Out + Generation"" Accumulation
r)C4 ,L)Ar Pc-H······ t/J)dL == -.dl{"1·Arv{L)CJL)]
But: A1
v(L)C4 (L):= N)L).:::: f~ll(I ... X)
:. FAD f·::TA pdl .. $) rA {Pd
Relating the expression fA to X and L :
;; lFo (l·X)
2
:;: }Fo (l-X)
Fc=FAOX == tFox
PA == PA ... 1:.:X.Pr Pc=-X-Pr
2·X 2-X
LetP=Pr,
1
R =-(2······ X), 2
FIXP __...:1.. _ ..........._•.
l-Pr
-2·..·X
10-25
c..J 0.4 as cu. 0:: lUI
"