105
Four rate expressions were derived by assuming each step as the
rate-determining step (RDS), except the adsorption of hydrogen (cf.
step 5 in Eq. (17)), as follows:
for the estimation at 555 and 575 K), compared to the other mod-
els. All kinetic parameters in the RDS 1 model are summarized in
Table 2.
kPBB
RDS1 :
− r =
(18)
2
(1 + K2−1K3−1K4−1K5−3/2PH
P
+ K−1K5−1/2PH
P
BuOH
+ K1/2PH1/2
)
2
−3/2
−1/2
BuOH
4
5
2
2
kK1K4K5PH PBBPB−u1OH
2
RDS2 :
− r =
(19)
2
(1 + K1K4K1/2PH1/2
P
PBB + K−1K5−1/2PH
P
BuOH
+ K1/2PH1/2
)
2
−1/2
−1
5
BuOH
4
5
2
2
kK1K2K4K3/2PH3/2
P
BB
P
−1
5
BuOH
2
RDS3 :
RDS4 :
− r =
− r =
(20)
(21)
1 + K1K4K1/2PH1/2
P
PBB + K−1K5−1/2PH
P
+ K1/2PH1/2
−1/2
−1
BuOH
5
BuOH
4
5
2
2
kK11/2K21/2K31/2K5PH
P
BB
1/2
2
2
−1/2
(1 + K11/2K2−1/2K3−1/2K5−1/2PH
P
1/2 + K11/2K21/2K31/2K51/2PH1/2PB1B/2 + K51/2PH1/2
)
2
BB
2
2
where the RDS1 denotes the reaction rate with step 1 (Eq. (13))
that is assumed to be the RDS, while the assumption of the rapid
equilibrium is made to the other steps. The equilibrium constant Kn
is defined as the ratio of the rate constant of the forward reaction to
that of the backward reaction, and Pi denotes the partial pressure
of species i.
After deriving the rate expressions, we determined the kinetic
parameters (k and Kn) to fit the data obtained at the tempera-
tures of 555, 564, and 575 K, using the nonlinear regression analysis
with the POLYMATH 5.1 (Polymath Software). Since experiments at
each temperature produced 8 data points (cf. Fig. 2), a total of 24
points were used in the nonlinear data-fitting procedure. The aim
of the data-fitting procedure is to minimize the mean-square dif-
ferences between calculated values of the rate and the rate values
obtained directly from the experimental data using the differen-
tial method. Mathematically this can be expressed by the following
equation:
It is very meaningful to compare the hydrogenolysis reaction
mechanism of ethyl acetate with that of butyl butyrate inves-
tigated in this study. In the proposed reaction scheme for the
reduction of ethyl acetate on silica-supported Cu catalyst [10], both
the dissociative adsorption of ethyl acetate and the hydrogenation
of acyl species are important in controlling the overall reduction
rate of esters. In partial accordance with the previous report, the
hydrogenolysis reaction of butyl butyrate proceeds via its disso-
ciative adsorption, which is considered to be the rate-determining
step in this study, to form surface C3H7CO and C4H9O fragments.
Furthermore, the former fragment is hydrogenated via butyralde-
hyde to butanol and the latter is directly hydrogenated, where both
reaction rates are relatively faster than those reported previously
for the hydrogenolysis reaction of ethyl acetate.
It should be noted that the temperature dependence of the equi-
librium constants, K2 and K4 in Table2, maybepoor, since thevalues
at 565 and 575 K are close. This feature may come from the quality
of data or from the estimation performance. The values of R2 for the
estimation at 555 and 575 K are higher than 95%, while the value at
565 K is relatively low although the average error at the tempera-
ture is still within the allowable limits. However, since the average
error for RDS1 model is still lowest at 575 K and the purpose of
the present study is to find the best fit model and to determine
the detailed mechanism for the hydrogenolysis reaction, relatively
poor performance of estimation at higher temperature exerts no
effect on our conclusion. It is recommended for readers to be careful
when the developed model with the estimated kinetic parame-
ters is used for quantitative analysis, especially when the correct
temperature dependence of equilibrium constants is required.
ꢀ
2
minꢁ =
(rcalc − rexp
)
(22)
p
all data samples
To find the best fit model and thus, the rate-determining step
which describes the kinetics of the hydrogenolysis reaction,
the value of R2 (the coefficient of determination) is calculated
ꢁ
ꢁ
as [1 −
(rexp − rcalc)2/ (rexp − rexp,avg)2]. The calculated rates
obtained at each RDS were compared with the experimental data,
as shown in Fig. 6. As a result, the rate expression model, whose RDS
was specified with the dissociative adsorption of butyl butyrate, i.e.,
Eq. (13), showed the most precise and reasonable results (R2 = 0.96
4. Conclusions
The kinetic study for the vapor-phase hydrogenolysis of butyl
butyrate to butanol over a commercial Cu/ZnO/Al2O3 catalyst was
carried out. The catalytic experiment was conducted far from equi-
librium, and several experimental conditions, such as the partial
pressures of two reactants, BB and H2, and the reaction tempera-
ture, were varied. In the empirical power law equation, the rate
of hydrogenolysis had a positive effect with respect to both BB
and hydrogen, and was dependent more on the BB concentra-
tion due to inhibited adsorption of ester on the Cu/ZnO-based
catalysts. In order to investigate the hydrogenolysis mechanism,
we conducted D2 isotopic labeling experiments. The analyses of
the resulting D-labeled liquid samples by GC–MS and 1H NMR
confirmed that the hydrogenolysis of butyl butyrate proceeds via
dissociative adsorption of ester, producing C3H7CO and C4H9O frag-
ments. The kinetics for the BB hydrogenolysis was interpreted on
Fig. 6. Comparison of the calculated rates using four different rate-determining
steps (Eqs. (13)–(16)) based upon the Langmuir-Hinshelwood model with the
observed rate for hydrogenolysis of butyl butyrate over Cu/ZnO/Al2O3 catalyst.