1.0 70 /,

08· 56 /\ 42 0 .. 6 [;J ! ' r:f.f{- ./ }

/ I 04 28 /' I

<",,"' \ ~#'V,-/t7

\ 14 " ... ",

0.2 ,,>P' ~ '"

\ (I " " 0.0

4.6 9.2 13.8 18.4 23.0 0.0 9.2 W 13.8 1804 23,0 0.0 \V

PIO·IO (a) Iso,ocrene +. Hydro gcn --? 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

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 P A .;. 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.) % elmr expo

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 of mechanism 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

PIO-IO (c)

0.2223 C~o (RTr {l-Xr / (l-O.SXY ··r A =.-.... ---.. --.--.--.-.--................ --.-~.-.--'J-

r 1 + 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!\ = ----. ~------.. --.--.------..

. r 1 + 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

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

:1 0..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

FIX P __ ...:1 .. _ ........... _ •. l-P

r -2· .. ·X

10-25

c..J 0.4 as cu. 0:: lUI

"