Kinetics of alcoholysis of valeric anhydride by cyclohexanol in the presence of formic acid

Article abstract of DOI:10.1134/S1070427209030227

Kinetics of the reaction proceeding at the industrial process of cyclohexane oxidation are studied by the model reaction of the alcoholysis of valeric anhydride by cyclohexanol in the presence of formic acid.

Full text of DOI:10.1134/S1070427209030227

ISSN 1070-4272, Russian Journal of Applied Chemistry, 2009, Vol. 82, No. 3, pp. 466−472. © Pleiades Publishing, Ltd., 2009.
Original Russian Text © T.S. Kotel’nikova, O.A. Revkov, S.G. Voronina, A.L. Perkel, 2009, published in Zhurnal Prikladnoi Khimii, 2009, Vol. 82, No. 3,
pp. 472−478.
ORGANIC SYNTHESIS
AND INDUSTRIAL ORGANIC CHEMISTRY
Kinetics of Alcoholysis of Valeric Anhydride
by Cyclohexanol in the Presence of Formic Acid
T. S. Kotel’nikova, O. A. Revkov, S. G. Voronina, and A. L. Perkel
Kuzbass State Technical University, Kemerovo, Russia
Received July 30, 2008
Abstract—Kinetics of the reaction proceeding at the industrial process of cyclohexane oxidation are studied by
the model reaction of the alcoholysis of valeric anhydride by cyclohexanol in the presence of formic acid.
DOI: 10.1134/S1070427209030227
EXPERIMENTAL
The reactions of the alcoholysis of mixed anhydrides
of carboxylic acids by cyclohexanol are a main way of
formation of cyclohexyl esters of mono- and dicarboxylic
acids in the industrial process of cyclohexane oxidation
[1–4]. It was assumed that the mixed anhydrides
are produced as a result of transacylation of adipic
anhydride by free acids and they contain the residues of
all the carboxylic acids present in the reaction medium
[2, 3] including the formic acid. High relative yield of
cyclohexyl formate in the course of oxidation of the
cyclohexane was understood through the features of
the alcoholysis reaction of the mixed anhydrides with
formyl group [5].
Formic acid (85%, pure for analysis) was maintained
over anhydrous MgSO4 for dehydration and then
it was sublimated in a water-jet pump vacuum. For
additional drying a working solution of formic acid in
o-dichlorobenzene was maintained over the anhydrous
MgSO4 for 24 hours. A content of the main substance
in the used working solution determined by gas-liquid
chromatography (GLC) (after transferring in benzyl ether
according to [6]) was 99.3 ± 0.4% (n = 10, P = 0.95).
Technical grade cyclohexanol was purified from ethers
and cyclohexanone according to [7]. The content of the
main substance in the used material by GLC data was 99.5
± 0.1%. Valeric anhydride was obtained by a treatment of
the anhydrous sodium valerate by acid chloride of valeric
acid [8]. The product was treated by diazomethane
and subjected to rectification in a vacuum in an argon
flow for removing valeric acid. The content of the main
substance in the used material by GLC data was 99.5 ±
0.1%. A solvent (o-dichlorobenzene) was of pure gtrade
and it was rectified [7].
For revealing pathways of the formation and
alcoholysis of the mixed anhydrides containing the
residue of formic acid the kinetics of all stages of these
reactions should be studied.At the same time the presence
in real processes (e.g., at cyclohexane oxidation [5]) of
more than ten compounds with carboxyl groups and also
the presence of reactive water essentially complicated
the study of the kinetics of the whole complex of
series-parallel reactions producing esters. Under these
conditions an employment of the model reactions for the
study of the ester formation is reasonable.
The experiments on an interaction of the valeric
anhydride and cyclohexanol in the presence of
formic acid in the solution of o-dichlorobenzene were
conducted in a thermostated sealed ampoule. The
temperature maintained with an accuracyin of ±0.2°С.
In the previous experiments we established that the
starting rate of the reaction depended on an order
of the reagent mixing. The reproducible result was
reached by mixing of solutions of valeric anhydride
A target of this paper is the study of the kinetics of
the reactions proceeding at the alcoholysis of valeric
anhydride by cyclohexanol in the presence of formic acid.
Mixture of anhydrides formed in situ contains formic-
valeric anhydride including the residues of two important
acids of the oxidized cyclohexane.
466

KINETICS OF ALCOHOLYSIS OF VALERIC ANHYDRIDE
467
Scheme 1.
O
1
O
C
C
H
H
OH; k
+R
_
5
C
H
O
+HCOOH; k
4
HCOOH
O
O
O
R1
_
C
C
_
H
R
RCOOH;
k
4
O
O
+HCOOH; k
k2
RCOOH
1
O
O
1
H
R
C
C
_
OH
+R
_
O
O
R1
R
R
C
C
_
RCOOH ; k
1
O
'
k2
1
O
_
OH;
+R
_
k
3
HCOOH
C
R
O
R1
O
RCOOH
O
R1
in o-dichlorobenzene and a mixture of cyclohexanol
with formic acid in equipment operating according to
a principle of a stopped stream.
According to the assigned task we studied the inter-
action of valeric anhydride (0.31 M) with cyclohexanol
(0.332 M) in the presence of formic acid (0.21 M) in the
solution of o-dichlorobenzene in a temperature range of
60–100°С.
The reaction products, esters, were determined by GLC.
A decomposition of unreacted anhydrides by an excess of
methanol−pyridine mixture added just after a sampling
preceded the determination of cyclohexyl formate and
cyclohexyl valerate. Analysis of the reaction products
was performed in a column of 2000 × 3 mm with a nozzle
that was 5% silicone XE-60, on Khromaton N-AW
0.20−0.25 mm. An internal standard is hexadecane.
We calculated the parameters of kinetic equations by
using software implementing the least-squares method in
the Delphi 5.5 environment. The system of differential
equations was solved in each step by the Euler method.
The calculation was performed over the entire body of
data for the object under study. This made it possible to
improve the accuracy of determination of the activation
energy and the pre-exponential factor [9].
Obstacles caused by difficulties of the formic
anhydride presence arose in the course of development
of kinetic schemes required for a solution of an inverse
kinetic problem.
Transformations may be presented by a scheme
assuming the formation of formic anhydride on the
basis of existing concepts about mechanisms of the
transacylation of anhydrides by carboxylic acids and of
the alcoholysis of anhydrides by alcohols [1–4].
However a majority of sources rejects the possibility
of existence of the formic anhydride probably due to
its instability [10, 11]. Thus a simplified scheme that
excluded formation of formic anhydride was considered
as alternative.
In the case of realization of Scheme 1 the kinetics
of the reaction product accumulation and the initial
compound consumption may be described by a set of
differential equations:
We used software Hyperchem 8.04 for quantum
chemical computations and also semi-empirical method
MINDO3.
d[HC(O)OC(O)R]
= k1[RC(O)OC(O)R][HCOOH]− k−1[HC(O)OC(O)R][RCOOH]
dt
1
'
− (k2 + k2 )[HC(O)OC(O)R][R OH]− k4[HC(O)OC(O)R][HCOOH]
(1)
+ k−4[HC(O)OC(O)H][RCOOH],
d[RC(O)OC(O)R]
= k1[RC(O)OC(O)R][HCOOH]− k−1[HC(O)OC(O)R][RCOOH]
+k3[RC(O)OC(O)R][R1OH],
dt
(2)
(3)
d[HCOOR1]
= k2[HC(O)OC(O)R][R1OH]+ k5[HC(O)OCOH][R1OH] ,
dt
RUSSIAN JOURNAL OF APPLIED CHEMISTRY Vol. 82 No. 3 2009

468
KOTEL’NIKOVA et al.
d[RCOOR1]
1
1
(4)
(5)
'
= k2[HC(O)OC(O)R][R OH]+ k3[RC(O)OC(O)R][R OH],
dt
d[RCOOH]
= k1[RC(O)OC(O)R][HCOOH]− k−1[HC(O)OC(O)R][RCOOH]
dt
1
1
(O)OC(O)R]
+ k2 [HC(O)OC(O)R][R OH]+k3[RC(O)OC(O)R][R OH]+k4 [HC
× [HCOOH]− k−4[HC(O)OC(O)H][RCOOH],
d[HCOOH]
−
= k1[RC(O)OC(O)R][HCOOH]− k−1[HC(O)OC(O)R][RCOOH]
dt
1
'
− k2[HC(O)OC(O)R][R OH]+ k4[HC(O)OC(O)R][HCOOH]− k−4[HC(O)OC(O)H]
Ч[RCOOH] − k [HC(O)OC(O)H][R1OH],
(6)
(7)
(8)
× [
5
d[HC(O)OC(O)H]
= k4[HC(O)OC(O)R][HCOOH]− k−4[HC(O)OC(O)H][RCOOH]
dt
− k5[HC(O)OC(O)H][R1OH],
d[R1OH]
1
1
'
−
= (k2 + k2 )[HC(O)OC(O)R][R OH]+ k3[RC(O)OC(O)R][R OH]
dt
+k5[HC(O)OC(O)H][R1OH],
where k1, k–1, k4, k–4 are the rate constants of the direct and
the inverse reactions of the formation of formic-valeric
anhydride, and formic anhydride; k2, k 2 are rate constants
of reaction of cyclohexyl formate and ciclohexyl valerate
formation according to alcoholysis of mixed anhydride by an
alcohol, respectively; k3, k5 are rate constants of cyclohexyl
valerate and cyclohexyl formate formation according to
alcoholysis of appropriate anhydride by cyclohexanol.
In the case of realization of Scheme 2 kinetics
of the reaction product accumulation and the initial
compound consumption may be described by a set
of equations
d[HC(O)OC(O)R]
= k1[RC(O)OC(O)R][HCOOH]− k−1[HC(O)OC(O)R][RCOOH]
dt
1
(9)
'
− (k2 + k2 )[HC(O)OC(O)R][R OH],
d[RC(O)OC(O)R]
−
= k1[RC(O)OC(O)R][HCOOH]− k−1[HC(O)OC(O)R][RCOOH]
+k3[RC(O)OC(O)R][R1OH],
dt
(10)
Scheme 2.
O
k2
C
C
H
R
_
_
RCOOH
1
OR1
O
+R OH
+HCOOH; k
1
C
O
C
O
R
H
O
'
k
2
_
_
RCOOH ; k
1
HCOOH
R
C
O
C
O
R
OR1
1
O
OH;
+R
_
k
3
O
R C
RCOOH
OR1
RUSSIAN JOURNAL OF APPLIED CHEMISTRY Vol. 82 No. 3 2009

KINETICS OF ALCOHOLYSIS OF VALERIC ANHYDRIDE
469
(11)
d[HCOOR1]
= k2[HC(O)OC(O)R][R1OH],
dt
d[RCOOR1]
1
1
(12)
(13)
'
= k2[HC(O)OC(O)R][R OH]+ k3[RC(O)OC(O)R][R OH],
dt
d[RCOOH]
= k1[RC(O)OC(O)R][HCOOH]− k−1[HC(O)OC(O)R][RCOOH]
dt
+k2[HC(O)OC(O)R][R1OH]+ k3[RC(O)OC(O)R][R1OH],
d[HCOOH]
−
= k1[RC(O)OC(O)R][HCOOH]− k−1[HC(O)OC(O)R][RCOOH]
dt
1
(14)
(15)
'
− k2[HC(O)OC(O)R][R OH],
d[R1OH]
1
1
'
−
= (k2 + k2 )[HC(O)OC(O)R][R OH]+ k3[RC(O)OC(OO)R][R OH].
dt
Considering the experiments at jth temperature the
values of the appropriate rate constants may be expressed
by the following equation:
With the help of obtained values of equilibrium con-
centrations for valeric acid [RCOOH]p, and the starting
concentrations of valeric anhydride [RC(O)OC(O)R]0,
and formic acid [HCOOH]0 by the following formula:
⎛
⎜
⎞
[RCOOH]2n
Kp =
E
1
1
ln k j = ln ki +
−
.
(16)
⎟
⎟
⎠
⎜
R T Tj
i
⎝
([RC(O)OC(O)R]0 −[RCOOH]p )
[RCOOH]2n
(17)
×
Although according to data of [12] valeric acid does
not influence the rate of alcoholysis of valeric anhydride
by cyclohexanol it can be assumed that the stronger
formic acid possesses ability for influencing some stage
of the kinetic schemes 1, 2. Hence we suggested that
effective constants of the stages of Scheme 1, 2 depend
linearly on the formic acid concentration.
([HCOOH]0 −[RCOOH]p )
the values of the eqiuilibrium constants for reaction
of formic-valeric anhydride formation from valeric
anhydride and formic acid in the case of Scheme 2
realization were determined (Table 1).
The temperature dependence of this constant was
computed on the basis of data presented in Table 1.
A preliminary treatment of the experimental data
using both equations (1)–(8), (16) and equations (9)–(16)
showed that in all cases a sum of constants k2 and k–2
was essentially higher then k–1, i.e. under conditions of
the experiment the reaction of formic-valeric anhydride
formation from a symmetric anhydride and formic acid was
become practically irreversible and that led to diminishing
accuracy at computation of k–1. In specific experiments
an equilibrium constant for the reaction of formic-valeric
anhydride formation (ratio k1/k–1) was determined to
increase the reliability of computation of k–1.
−1
±
22411 3 kJ mol
(18)
ln K = ln(15773.35 ± 0.01) −
.
RT
Naturally the equilibrium constants of the kinetic
scheme 1 cannot be computed by equation (18) but it
can be used in calculation as the first approximation. The
values of the effective rate constants, activation energies,
and pre-exponential factors for the stages of the kinetic
scheme 1, 2 (Table 2) were calculated by solution of the
inverse problem taking into account equation (18). The
calculation showed that formic acid practically did not
influence the effective rate constants of the stages both
of Scheme 1 and Scheme 2.
Valeric acid concentrations in equilibrium mixture
at the interaction of formic acid (0.21 M) and valeric
anhydride (0.169 M) in the solution of o-dichlorobenzene
in the temperature range of 90–150°С are presented in
Table 1.
Computed accumulation curves of cyclohexyl formate
and cyclohexyl valerate corresponding to obtained sets of
RUSSIAN JOURNAL OF APPLIED CHEMISTRY Vol. 82 No. 3 2009

470
KOTEL’NIKOVA et al.
Table 1. Effects of the temperature on the equilibrium con-
centrations of the valeric acid and on the equilibrium con-
stants of the interaction reactions of the valeric anhydride and
formic acid
show that in the case of Scheme 1 activation energy of
the stages at alcoholysis of valeric anhydride producing
cyclohexyl formate (111.23 ± 0.03 kJ mol–1) and cyclo-
hexyl valerate (117.36 ± 0.35 kJ mol–1) are essentially
higher than activation energy of alcoholysis of valeric
anhydride (61.5 kJ mol–1) [9]. Moreover at calculation
by kinetic scheme 1 activation energy for transacylation
of formic-valeric anhydride by formic acid (136.74 ±
0.21 kJ mol–1) appears almost twice higher than activation
energy for transacylation of valeric anhydride by formic
acid. Hence from the point of view of physical sense some
preference can be given to kinetic scheme 2
Data of Table 2 confirm existing ideas concepts
prevailing formation of formates in alcoholysis of
mixed anhydrides including the residue of formic acid
[5]. Apparently that is understood by a character of an
electron density distribution on a functional group of
mixed anhydride that governs capability of this group
to a nucleophilic attack. Values of atomic charges in
molecules of (a) formic, (b) formic-valeric, and (c) valeric
anhydrides are presented on Scheme 3.
the constants quite closely describe experi-mental values
of these ester concentrations both for kinetic scheme 1
and for kinetic scheme 2 (see the figure). Smaller value
of the sum of squared deviations for Scheme 1 can not
be governing factor at selection from two alternative
schemes since a scheme with larger number of parameters
as a rule better describes an experiment. Data of Table 2
Table 2. Results of the calculation of the rate constants, activation energies, and pre-exponential factors of the stages in the
kinetic schemes 1 and 2
4.04 ×10−3
RUSSIAN JOURNAL OF APPLIED CHEMISTRY Vol. 82 No. 3 2009

KINETICS OF ALCOHOLYSIS OF VALERIC ANHYDRIDE
(c)
471
(a)
(b)
(d)
Experimental values of the concentrations c (M) and calculated curves of cyclohexyl formate accumulation (a, c) and cyclohexyl valer-
ate (b, d) at various temperature. (τ) time (min); Т (°С): (1) 60, (2) 70, (3) 80, (4) 100. (a, b) Scheme 1, (c, d) Scheme 2.
Scheme 3.
(b)
(a)
−
−
−
−
−
−
−
−
−
−
(c)
−
−
−
−
RUSSIAN JOURNAL OF APPLIED CHEMISTRY Vol. 82 No. 3 2009

472
KOTEL’NIKOVA et al.
Quantum chemical calculation for the molecules of
REFERENCES
formic, valeric, and formic-valeric anhydrides evidences
the correlation between the value of the positive charge
on the carboxylic carbon and a relative yield of the
appropriate ester. It is important that formic acid forming
simultaneously with cyclohexyl valerate at alcoholysis
of formic-valeric anhydride by cyclohexanol is involved
in the reaction cycle of transformations till the complete
exhaustion of it or anhydrides.
1. Perkel’, A.L., Voronina, S.G., and Freidin, B.G., Uspekhi
Khimii, 1994, vol. 63, no. 9, pp. 793–796.
2. Freidin, B.G. and Perkel’, A.L., Zh. Prikl. Khim., 1980,
vol. 53, no. 4, pp. 861–866.
3. Perkel’, A.L., Freidin, B.G., Neginskaya, R.V. et al., Zh.
Prikl. Khim., 1985, vol. 58, no. 7, pp. 1572–1577.
4. Perkel, A.L., Buneeva, E.I., and Voronina, S.G., Oxid.
Commun, 2000, vol. 23, no. 1, pp. 12–28.
It may be assumed that the obtained temperature
dependencies of the rate constants for the stages of
alcoholysis of mixed anhydrides are useful for ester
formation simulation both of cyclohexane oxidation and
of other industrial processes of a liquid-phase oxidation
by molecular oxygen.
5. Kotel’nikova, T.S., Voronina, S.G., and Perkel’, A.L., Zh.
Prikl. Khim., 2006, vol. 79, no. 3, pp. 424–428.
6. Kotel’nikova, T.S., Vdovenko, O.V., Voronina, S.G., and
Perkel’, A.L., Zh. Anal. Khim., 2006, vol. 61, no. 4,
pp. 370–374.
7. Weissberger, A., Proskauer, E.S., Riddick, J.A., and
Toops, E.E., Jr., Organic Solvents: Physical Properties
and Methods of Purification, New York: Intersci., 1955,
2nd ed.
CONCLUSIONS
8. Weygand-Hilgetag Organisch-chemische Experimentier-
kunst, Hilgetag, G. and Martini, A., Eds., Leipzig: Johann
Ambrosius Barth, 1964, 3rd ed.
9. Kotel’nikova, T.S., Revkov, O.A., Voronina, S.G., and
Perkel’, A.L., Vestn. KuzGTU, 2006, no. 5, pp. 105–107.
10. Neiland, O.Ya. Organicheskaya khimiya (Organic
Chemistry), Moscow: Vyssh. Shkola, 1990. 751 p.
11. Fieser L. F., and Fieser, M., Advanced Organic Chemistry,
New York: Reinhold, 1962.
1. The temperature dependences of the rate
constants for the stage of alcoholysis of valeric
anhydrides by cyclohexanol in the presence of formic
acid were calculated by the solution of the inverse kinetic
problem.
2. Prevailing formation of formates at alcoholysis of
anhydrides in the presence of formic acid is understood
through the features of alcoholysis of mixed anhydrides
including formyl group and correlates with charge on
carbonyl atoms of anhydride carbon.
12. Nosacheva, I.M., Revkov, O.A., and Perkel’, A.L., Vestn.
KuzGTU, 2004, no. 3, pp. 78–81.
RUSSIAN JOURNAL OF APPLIED CHEMISTRY Vol. 82 No. 3 2009