KINETIC DESCRIPTION OF THE HYDROGENATION
213
COMPUTATIONAL PROCEDURE
determined at the
ith point in time in the
jth experiꢀ
ment, and is the average value over all experiments.
ni
The rate constants for hydrogen adsorption on the
nickel catalyst surface and for propanꢀ2ꢀol dehydrogeꢀ
nation were found from the experimental data, and the
adsorption equilibrium constant was determined from
an aniline adsorption isotherm [3]. The adsorption
constants of phenylhydroxylamine and azoxyꢀ, azoꢀ,
and hydrazobenzenes as well as the constants of the
reactions of these compounds with hydrogen in the
surface layer were obtained by simulation [4]. Thus,
when developing the model, some constants were calꢀ
culated from our experimental data and others were
determined using published data.
The adequacy of the proposed model to experiꢀ
mental data was checked in terms of three indepenꢀ
dent parameters: changes in the amounts of the startꢀ
ing compound and the reaction product in the soluꢀ
tion bulk and the amount of hydrogen absorbed from
the gas phase as functions of time. The goodness of fit
between the calculated and experimental values was
estimated using Fischer’s criterion, whose values were
calculated on the basis of the averaged reproducibility
2
variance and residual variance (
)
Sres
q
exp
ij
calc
ij
2
Sr2es j
=
(n − n
)
q − r ,
(
)
The changes in the concentrations of the starting
compounds, intermediates, and reaction products in
time were calculated earlier using UV and IR spectrosꢀ
copy, liquid chromatography, and GLC data [10].
Azoxybenzene concentrations were determined on a
CARY 50 scan UVꢀVisible Spectrophotometers specꢀ
trophotometer (Varian, Australia) in a wavelength range
of 240–500 nm using quartz cells with an optical path of
1 cm and the pure solvent as the reference sample. The
concentrations of nitrobenzene and aniline were calcuꢀ
lated from GLC data obtained on an LKhMꢀ80.6 chroꢀ
matograph (Russia) with a flameꢀionization detector
and a 1.5ꢀmꢀlong packed column (solid phase Chromꢀ
∑
i=1
where
q is the number of measurements, and r is the
number of constants estimated in the model.
The checking of the hypothesis about the equality
of the variances using the indicated criterion showed
that the difference between the residual variance and
the reproducibility variance was statistically insignifiꢀ
cant at a confidence probability of p = 1 – α = 0.95.
The following assumptions were accepted for the
development of the kinetic schemes:
(a) the conversions proceed via the Langmuir–
Hinshelwood adsorption mechanism;
(b) the reversible adsorption of the hydrogenated
compound, reaction product, and intermediate comꢀ
aton NꢀAW (400–600
µm fraction) with supported
Lukopren Gꢀ1000 (7 wt %), oven temperature of 451 K,
injection port temperature of 593 K, detector temperaꢀ
ture of 513 K, He as the carrier gas (2.50 atm)). The
concentrations of nitrobenzene, nitrosobenzene, and
phenylhydroxylamine were measured on an LCꢀ6A liqꢀ
uid chromatograph (Shimadzu, Japan) equipped with a
spectrophotometric detector with deuterium and tungꢀ
sten lamps (220–500 nm) and a stainless steel packed
column (25 cm, oven temperature of 303.5 K, solid
pounds occurs on the active sites
adsorbed on the sites
Z, and hydrogen is
Y;
(c) hydrogen adsorption involves one active site of
the catalyst surface, and the possibility of hydrogen
migration in the surface layer is excluded;
(d) the starting compounds react irreversibly with
hydrogen;
(e) the activated adsorption of the starting and
intermediate compounds on the active sites of the catꢀ
alyst surface can be accompanied by the oxidation of
the latter;
phase Lichrosorb RPꢀ18 (5 µm fraction)) using aqueous
solutions of acetonitrile as the eluent (30 wt %, eluent
glow rate 0.9 cm3/min) and a sample injector.
The reproducibility of experimental data was deterꢀ
mined from the results of a series of experiments on
the liquidꢀphase hydrogenation of each of the comꢀ
pounds. Each experiment was repeated 3–5 times in
such a way that the initial amounts of the hydrogeꢀ
nated compound differed by no more than 0.5% and
the difference between the sampling times in repeated
injections did not exceed 2–3 s.
(f) there can be both the reversible and irreversible
oxidation of the active sites of the catalyst surface;
(g) the solvent can undergo reversible dehydrogeꢀ
nation, and the resulting hydrogen can participate in
the reduction of reactive groups.
The following conditions were fulfilled at each
stage of the calculations:
(a) no more than 30% of the constants were varied
in the model calculations;
(b) the constants determined from experimental or
earlier published data and those calculated for simpler
schemes were varied within one order of magnitude;
(c) the constants of the steps that were not rateꢀ
determining were related to other constants by certain
equations;
(d) the rate constants of the reversible steps
included in the kinetic schemes were calculated from
adsorption equilibrium constants;
The average value of the measured parameter was
calculated for each time interval, and then the averꢀ
aged reproducibility variance ( 2) was determined via
Sy
the equation
mi
Sy2i
=
(nij − ni)2 (mi −1),
∑
j=1
where mi is the number of replica experiments at the
th point in time, nij is the amount of the compound
i
KINETICS AND CATALYSIS Vol. 57
No. 2 2016