280a0f63-2da2-4b6b-90cb-eda6b6eb0311 30 Javier Ochoa 4 5 false false 0 0 decimal

&[DATE] &[TIME] - &[FILENAME]

Directly determine reaction order. Author: Sarab R. Vatcha. Chemical Engineering, February 16, 1987. A method is presented to directly determine the order of the kinetics of a reaction from the kinetic data, without trial and error. The method replaces the conventional on of integral analysis that generally requires trial and error, and data analysis by graphical or linear-regression methods.The principle underlying the methos is that the ratio of the times at which two specific conversions occur depends solely on the order of the reaction. The method is applicable so single irreversible reactions of any order - positive or negative, integral or fractional - as well as to reversible first order reactions.

Derivation: The power law kinetic model for a single reaction is:

3 appVersion 1.0.8348

Rate A t diff - ≡ (k A n^* ≡

where the order and the rate constant are unknown. The initial condition is:

A A.o ≡

U Reaction order, n t(3/4)/t(1/2) t(2/3)/t(1/3) 1 - 1.25 1.60 0 1.50 2 0.5 1.71 2.30 12 2.71 23435 6.40 73 mat :

U U

U
Reaction order, n	t(3/4)/t(1/2)	t(2/3)/t(1/3)
-1	1.25	1.6
0	1.5	2
0.5	1.71	2.3
1	2	2.71
2	3	4
3	5	6.4
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The solution of the rate equation for the residence time and n = 1 or n not equal 1 are the following:

t2 1 X.A - (1 n - (^1 - (n 1 - (k * A.0 n 1 -^* / ≡

t1 1 X.A - ln (k / - ≡

n 1 ≡

n 1 ≠

The ratio of the times at whicho two distinct conversions occur is given by:

t.XA1 t.XA2 / 1 X.A1 - (1 n - (^1 - 1 X.A2 - (1 n - (^1 - / ≡

t.XA1 t.XA2 / 1 X.A1 - ln 1 X.A2 - ln / ≡

n 1 ≡

n 1 ≠

V Time, m Conc. DBC, mlo/m3 Conversion, XDBC 0 69.7 06 46.7 0.330 9 38.7 0.445 12 30.8 0.558 14 26.7 0.617 18 20.4 0.707 20 18.01 0.742 22 15.98 0.771 24 14.18 0.797 26 11.92 0.829 30 9.59 0.862 10001133 mat :

W Time, min Conc. PTA, mol/m3 Conversion XPTA 0100015 86.3 0.137 30 75.2 0.248 45 64.0 0.360 60 56.8 0.432 120 38.7 0.613 180 29.7 0.703 300 19.6 0.804 93 mat :

V W V U

V
Time, m	Conc. DBC, mlo/m3	Conversion, XDBC
0	69.7	0
6	46.7	0.33
9	38.7	0.44
12	30.8	0.56
14	26.7	0.62
18	20.4	0.71
20	18.01	0.74
22	15.98	0.77
24	14.18	0.8
26	11.92	0.83
30	9.59	0.86
100	0	1
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xx V 213 range 1 el :

yy V 213 range 3 el :

W yy xx W V U

W
Time, min	Conc. PTA, mol/m3	Conversion XPTA
0	100	0
15	86.3	0.14
30	75.2	0.25
45	64	0.36
60	56.8	0.43
120	38.7	0.61
180	29.7	0.7
300	19.6	0.8
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ww W 29 range 1 el :

vv W 29 range 3 el :

x y char size color plotG n x length : plot x 1 el y 1 el char size color augment : i 2 n range plot plot x i el y i el char size color augment stack : for plot 41 line :

plot1 xx yy . 20 Dark Blue plotG :

plot2 ww vv o 10 Green plotG :

plot1 plot2 2 1 sys

The method proposed by the author requires to evaluate the time for the following conversion points by interpolation: 0.5 0.75 0.33 and 0.66

t12 yy xx 0.5 cinterp :

t34 yy xx 0.75 cinterp :

t13 yy xx 0.33 cinterp :

t23 yy xx 0.66 cinterp :

res1 t34 t12 / : 1.9732

res2 t23 t13 / : 2.6236

Then, from the Table 1 we found that n = 1.

In the same way we evaluate the results for the experimental data from Table 3.

t12 vv ww 0.5 cinterp :

t34 vv ww 0.75 cinterp :

t13 vv ww 0.33 cinterp :

t23 vv ww 0.66 cinterp :

res1 t34 t12 / : 2.9585

res2 t23 t13 / : 3.644

From Table 2 we found that n = 2.

Now, the problem to find the other kinetic parameter, k, could be solved because it is a linear equation.