Kinetics of hydrolysis of bisoprolol hemifumarate in aqueous acidic solutions

Article abstract of DOI:10.1002/kin.20809

The kinetics of hydrolysis of bisoprolol hemifumarate in acidic conditions was studied using high-performance liquid chromatography. For this purpose, different hydrohalic acids and one weak carboxylic acid were used. The rate constants, the order of the reaction, and the activation parameters: enthalpy, entropy, and energy of activation were calculated. A proposition for the mechanism of degradation was provided.

Full text of DOI:10.1002/kin.20809

Kinetics of Hydrolysis of
Bisoprolol Hemifumarate in
Aqueous Acidic Solutions
MATEUSZ SZALKA,1 EDWARD ROKASZEWSKI,1 KRZYSZTOF KACZMARSKI2
1Product Development Department, ICN Polfa Rzeszo´w S.A., 35-959, Rzeszo´w, Poland
2Department of Chemical and Process Engineering, Rzeszo´w University of Technology, 35-959, Rzeszo´w, Poland
Received 31 January 2012; revised 13 November 2012; 28 June 2013; 7 July 2013; accepted 7 July 2013
DOI 10.1002/kin.20809
Published online 3 August 2013 in Wiley Online Library (wileyonlinelibrary.com).
ABSTRACT: The kinetics of hydrolysis of bisoprolol hemifumarate in acidic conditions was
studied using high-performance liquid chromatography. For this purpose, different hydrohalic
acids and one weak carboxylic acid were used. The rate constants, the order of the reaction,
and the activation parameters: enthalpy, entropy, and energyꢀCof activation were calculated. A
proposition for the mechanism of degradation was provided. 2013 Wiley Periodicals, Inc. Int
J Chem Kinet 45: 744–754, 2013
of 9.5 [3], the lipophilicity measured by a partition
coefficient puts bisoprolol somewhere between less
lipophilic atenolol and more lipophilic propranolol [4],
and this position is a key factor for the theoretically
ideal pharmacokinetic properties of bisoprolol. Biso-
prolol is stable at a pH above 5.0 also in strong alkaline
conditions.
In spite of the degradation studies [5] carried out
for this drug substance, there is no information on the
kinetics of hydrolysis in acidic aqueous solutions as
well as no proposition for a detailed mechanism of
degradation. The scope of this study is to demonstrate
an explanation for the mechanism of hydrolysis and
calculation of the activation parameters, which may
be important for preparation of stable drug product
formulations containing bisoprolol hemifumarate and
compatible excipients.
INTRODUCTION
Bisoprolol hemifumarate is a very popular drug sub-
stance used in the treatment of many cardiovascular
diseases such as hypertension, arrhythmia, and coro-
nary failure. Bisoprolol belongs to the beta-blockers
group, which inhibits the synthesis of catecholamines
(i.e., adrenaline) reducing their concentration in a hu-
man organism. Beta-blockers are also commonly used
as illegal doping agents; they reduce tremors and car-
diac frequency, significantly improving the physical
performance [1,2]. Chemically bisoprolol is a deriva-
tive of aminopropanol and is used as a racemic mixture
for therapeutic purposes. The full formula is presented
in Fig. 1.
The lipophilic character of this drug substance is
mainly determined by its aromatic ring. The alka-
line properties, on the other hand, depend on the
alkanoamine chain. The bisoprolol base has a pKa
Krzek et al. [6] found a correlation between the po-
larity of beta-blockers and their rate of degradation.
According to the studies carried out for atenolol, ace-
butolol, and propranolol, the stability of beta-blockers
increases with the increasing lipophilicity. The most
stable is propranolol, then acebutolol and atenolol.
Correspondence to: Mateusz Szalka; email: mateusz.szalka@
valeant.com
C
ꢀ
2013 Wiley Periodicals, Inc.

KINETICS OF HYDROLYSIS OF BISOPROLOL HEMIFUMARATE
745
Table I Gradient Program for the HPLC Method
Time (min)
Mobile Phase A (%) (v/v)
0 → 12
57
12 → 21
21 → 22
22 → 30
57 → 30
30 → 57
57
Figure 1 Structure of bisoprolol hemifumarate.
presented in Table I. The mobile phase A was prepared
by adding 1.36 g of potassium dihydrogen phosphate
and 1 mL of triethylamine to 1 dm3 of purified water;
the pH of this solution was adjusted to 5.5 by diluted
(8.5% v/v) phosphoric acid. The mobile phase B was
HPLC-grade methanol.
The analyzed drugs significantly differ in log P val-
ues. According to Carda-Broch and Berthod [7] the
log P for propranolol is 1.16, acebutolol −0.40, and
atenolol −0.83, whereas the log P of bisoprolol is 0.04.
The scope of this study was also to determine whether
bisoprolol fits into this correlation.
Validation of the Analytical Method
EXPERIMENTAL
Instrumentation
The HPLC method was validated according to Inter-
national Conference on Harmonisation of Technical
Requirements for Registration of Pharmaceuticals for
Human Use guidelines; the results for all important
parameters are presented below.
The limit of detection was set to 0.014 μg/mL and
the limit of quantitation 0.048 μg/mL and linearity
(peak areas vs. the concentration of bisoprolol) with
the regression factor r = 1.00. Repeatability, measured
as a deviation from peak areas, is characterized by
relative standard deviation not more than 2.0%. Accu-
racy, measured by a recovery method, falls within the
range from 95.0% to 105.0%. The analytical method
is specific, accurate, precise, and linear.
A HPLC Waters 2659 separations module (maximum
operating pressure 345 bar) with a photodiode ar-
ray detector (PDA 2998) from Waters (Milford, MA)
was used. An EC Nucleosil column, 100–5 C18 HD,
5 μm, 250 × 4.6 mm, was supplied by Macherey-Nagel
(Du¨ren, Germany).
Materials
Triethylamine (≥99.5%, HPLC grade) was supplied
by Sigma Aldrich (Steinheim, Germany). Methanol
of HPLC grade, orthophosphoric acid p.a. (85%), and
anhydrous potassium dihydrogen phosphate p.a. were
supplied by POCH S.A. (Gliwice, Poland).
Kinetic Testing
Fumaric acid (>99%) and hydroiodic acid (57%)
were supplied by Acros Organics (Geel, Belgium). Hy-
drochloric acid (35–38%), hydrobromic acid (48%),
sodium chloride (p.a.), potassium bromide (p.a.),
and potassium iodide (p.a.) were supplied by POCH
S.A. (Gliwice, Poland). Bisoprolol hemifumarate,
working standard, was synthesized at ICN Polfa Rzes-
zow S.A. (Rzeszo´w, Poland).
Kinetic measurements were studied in the aqueous
acidic solutions for the initial concentration of biso-
prolol 1.3 × 10−3 mol·dm−3 (1.0 mg/mL) if not stated
otherwise. The temperatures for hydrohalic acids were
323.2, 333.2, and 343.2 K. The degradation of biso-
prolol in fumaric acid occurred much more slowly,
so the solutions were tested at higher temperatures,
353.2, 358.2, and 363.2 K. This temperature addition-
ally guaranteed complete dissolution of fumaric acid in
water. Three different hydrohalic acids were tested: hy-
drochloric, hydrobromic, and hydroiodic acids. Biso-
prolol contains several ether linkages, and thus a pro-
tonation of various ether oxygen atoms followed by a
nucleophilic attack may result in many different degra-
dation products. The acid strength is also an important
factor in the cleavage of ethers; hydroiodic and hy-
drobromic acids may be strong enough to cleave ether
linkages that are often resistant to hydrochloric acid.
After the assumed experimental time intervals, 2.0 mL
Analytical Method
Gradient elution high-performance liquid chromatog-
raphy (HPLC) was applied for the analysis of reaction
mixtures with the EC Nucleosil column, 100–5 C18
HD, 5 μm, 250 × 4.6 mm. The flow rate was set to
0.8 mL/min, the UV light absorbance at 225 nm wave-
length, column temperature at 50◦C, and sample injec-
tion volume at 10 μL. The time of a single analysis, 30
min, was determined by the gradient elution program
International Journal of Chemical Kinetics DOI 10.1002/kin.20809

746
SZALKA, ROKASZEWSKI, AND KACZMARSKI
Figure 2 The pseudo–first-order hydrolysis reaction of bisoprolol hemifumarate.
of a reaction mixture was withdrawn from a reaction
vessel and placed in the thermostated autosampler of
the HPLC system. The autosampler temperature was
set to 278.2 K to rapidly slow down the reaction; the
samples were injected immediately after withdrawal.
The peak areas of bisoprolol were measured for each
determination and compared to the initial conditions.
A temporary concentration of bisoprolol hemifumarate
b = [B]/[B]0 during the reaction was determined as a
ratio of peak areas, b = [B]/[B]0 = [Area]t/[Area]0,
where [Area]0 is the area at the beginning of the re-
action, [Area]t is the peak area at the assumed time
point, [B]0 is the concentration of bisoprolol at the
beginning of measurement, and [B] is the temporary
concentration of bisoprolol at the assumed time point.
The total order, the rate of a reaction, the half-life
time, and the activation parameters are presented in the
next section. An explanation for the reaction mecha-
nism is provided.
pseudo–first-order reaction as presented in Fig. 2. The
linear functions of ln([B0]/[B]) plotted against the reac-
tion time are characterized by good regression coeffi-
cients, r > 0.99. The fastest reaction rate was obtained
for hydroiodic, hydrobromic, and hydrochloric acids
in a decreasing order. The slowest reaction was ob-
served for a weak carboxylic acid. Surprisingly, only
one degradation product arising due to the hydrolysis of
the benzyl ether linkage was observed. The other ether
connections remained unchanged, even when stronger
acids (HBr and HI) were applied. As we can notice,
the rate of hydrolysis of the benzyl ether linkage in
bisoprolol directly depends on the acid strength and
the type of a nucleophile. The initial concentrations
of bisoprolol, the reaction temperatures, and obtained
results are presented in Fig. 2. and Table II.
At the constant initial concentration of bisoprolol
hemifumarate (about 1.3 × 10−3 mol·dm−3), the in-
fluence of temperature (333.2, 343.2, and 353.2 K)
and the concentration of hydrohalic acid on reaction
rates was determined. The concentrations of hydro-
halic acids varied from 0.1 to 1.0 mol·dm−3. As seen
in Fig. 3, the effective rate constants of this reaction
are the quadratic function of a concentration of hydro-
halic acid according to Eq. (1). In our experiments, the
concentration of a nucleophile [X−] was equal to the
RESULTS AND DISCUSSION
In the aqueous solutions of hydrohalic acids, HX
(HX = HCl, HBr, or HI), and in the solutions of fumaric
acid, bisoprolol hydrolyzes according to the kinetics of
International Journal of Chemical Kinetics DOI 10.1002/kin.20809

KINETICS OF HYDROLYSIS OF BISOPROLOL HEMIFUMARATE
747
concentration of [H3O+] (excluding the experiments
with added salts); thus Eq. (1) may be simplified to
Eq. (2), where k1 is a kinetic rate constant of hydrol-
ysis according to the mechanism of the nucleophilic
substitution type 1 (SN1) and k2 is a kinetic rate con-
stant of hydrolysis according to the mechanism of the
nucleophilic substitution type 2 (SN2). As we can no-
tice from Fig. 3, the k1 rate constant slightly differs for
all three hydrohalic acids; this is because the SN1-type
mechanism involves only a protonation of the benzyl
ether oxygen atom and then a spontaneous cleavage of
this linkage. There is no involvement of a nucleophile
in the SN1 mechanism; thus the reaction rates directly
depend on the acid strength and its concentration. All
hydrohalic acids are strong acids, which dissociate al-
most completely in the aqueous solutions; however,
the level of dissociation may insensibly vary between
them. The highest value of pKa has the strongest hy-
droiodic acid (pKa = −10) [8], then hydrobromic
acid (pKa = −9) [8], and the lowest value has hy-
drochloric acid (pKa = −7) [9]. There are no important
differences in the calculated dissociation of HI and
HBr at the concentrations from 0.1 to 1.0 mol·dm−3
,
whereas the dissociation of HCl is slightly lower. The
numbers of protonated molecules of bisoprolol are sim-
ilar in the experiments with HI and HBr; thus k1 rate
constants of the SN1 mechanism are almost the same.
On the other hand, the protonation of bisoprolol is
lower in hydrochloric acid solution, which explains
the lower k1 value.
The second mechanism of hydrolysis of bisoprolol
is the nucleophilic substitution type 2 and occurs si-
multaneously. It is described by k2 rate constants and
involves a protonation of the benzyl ether oxygen atom
and then the attack of a nucleophile (I−, Br−, or Cl−).
The rate of this reaction depends on the dissociation
of acids but also on the type of nucleophile. As can be
noticed from Fig. 3, the fastest reaction rate constants
were obtained for HI, HBr, and HCl in a decreasing or-
der. This confirms that the strength of the nucleophile
decreases in the order I−, Br−, Cl−.
The reaction rates determined for fumaric acid
(pKa1 = 3.03, pKa2 = 4.54) [10] were much slower
than for hydrohalic acids even at higher temperatures
(353.2, 358.2, and 363.2 K). There are two explana-
tions for this behavior. First, fumaric acid is a weak
carboxylic acid with a low dissociation level; thus the
low protonation of the benzyl oxygen atom in the biso-
prolol molecule inhibits the SN1 and SN2 reactions.
The second explanation is the lack of a strong nucle-
ophile in the reaction mixture that additionally slows
the nucleophilic substitution type 2. Water (reaction
solvent) and the anion of fumaric acid may act as nu-
cleophiles, but both are significantly weaker than the
International Journal of Chemical Kinetics DOI 10.1002/kin.20809

748
SZALKA, ROKASZEWSKI, AND KACZMARSKI
Figure 3 Impact of hydrohalic acid concentration on the effective rate constants of hydrolysis at 323.2 K.
served in 0.1 M KI solution (k0 = 7.4785 × 10−4 s−1),
halogen anions. The experiments carried out for fu-
maric acid will be omitted from further calculations
and discussion due to low reaction rates.
then in 0.1 M KBr (k0 = 7.2366 × 10−4
s
−1), and the
slowest reaction occurred in 0.1 M KCl (k0 = 6.8626 ×
10−4 −1). The ionic strength in all above-described
s
ꢀ
ꢁ
ꢀ
ꢁ ꢀ
ꢁ
ꢁ
k = k0 + k1 H3O+ + k2 H3O+ X−
(1)
(2)
experiments is constant; thus the rate of hydrolysis di-
rectly depends on the strength of the nucleophile (I− >
Br− > Cl−). Considering the reaction mechanism, we
have assumed that an increase in the concentration of
chloride ions (addition of KCl) enhances the proba-
bility of the SN2 reaction. The addition of the same
molar quantities of KBr or KI into the reaction vessel
improves the nucleophilic character of anions; I− and
Br− compete with Cl− in the SN2 reaction, increas-
ing its rate. No reaction occurred in the experiments in
which hydrohalic acids were substituted by appropriate
salts. This proves that the isopropoxyethoxide anion is
a poor leaving group (the lack of a stabilization of the
negative charge); thus the SN2 reaction requires a pro-
tonation of the benzyl oxygen atom to proceed. In all
reactions with hydrohalic acids, only benzyl halides
were observed as the degradation products.
ꢀ
ꢁ
ꢀ
2
k = k0 + k1 H3O+ + k2 H3O+
The obtained results are in agreement with the
knowledge about hydrolysis of benzyl ethers, which
may occur according to two important reaction mech-
anisms: nucleophilic substitution type 1 and type 2.
Both possible mechanisms of the degradation are pre-
sented in Fig. 4.
The hydrolysis of bisoprolol molecule according to
the SN2 reaction mechanism is presented in Fig. 4(a).
It begins with a protonation of the oxygen atom at the
benzyl ether linkage and then the attack of a nucle-
ophile on the benzyl carbon atom from the opposite
side to the leaving group (isopropoxyethanol). The di-
rect influence of a nucleophile was confirmed in the
experiments carried out in 0.5 M HCl with the addition
of various salts (0.1 M). The fastest reaction was ob-
The hydrolysis according to the SN1 mechanism is
described in Fig. 4(b); it also begins with a protonation
of oxygen atom at the benzyl ether, but a nucleophile
International Journal of Chemical Kinetics DOI 10.1002/kin.20809

KINETICS OF HYDROLYSIS OF BISOPROLOL HEMIFUMARATE
749
Figure 4 The mechanisms of degradation of bisoprolol in the aqueous acidic solutions. (a) Hydrolysis according to the
nucleophilic substitution type 2 mechanism (SN2), (b) hydrolysis according to the nucleophilic substitution type 1 mechanism
(SN1), and (c) termination of the SN1 reaction mechanism.
is not involved in the further step. The cleavage of
the benzyl ether linkage occurs spontaneously to form
a benzylic carbocation and isopropoxyethanol as the
leaving group. Benzyl carbocations are stabilized by
the ꢁ electron resonance from the aromatic ring and
the solvation by polar protic solvents such as water.
Finally, Fig. 4(c) presents the termination of the
SN1 reaction mechanism, attack of a nucleophile on
the carbocation, and formation of benzyl halides.
In addition, we have carried out a set of experi-
ments for various initial concentrations of bisoprolol
hemifumarate ranging from 1.3 × 10−3 to 2.6 × 10−1
mol·dm−3 in 1.0 mol·dm−3 solution of hydrochloric
acid. These studies were performed to test the influ-
ence of the initial concentration of bisoprolol on the
effective rate of hydrolysis. In all experiments,
ln([Bo]/[B]) was a linear function of time (with re-
gression coefficients higher than 0.99), indicating the
pseudo–first-order reaction in relation to bisoprolol
(according to Eq. (5)). It may be noticed from Fig. 5
that the effective rate constants decrease with the in-
crease of the concentration of bisoprolol hemifumarate.
It was assumed that participation of the SN1 and SN2
mechanisms is different for various initial concentra-
tions of bisoprolol; thus the effective rate constant k0
is influenced by various participations of k1 and k2
rate constants. The results obtained for different initial
concentrations of bisoprolol are presented in Fig. 5 and
Table III.
ꢀ
ꢁ
ꢀ
ꢁ ꢀ
ꢁ
d Bisoprolol
−
= k1 Bisoprolol H3O+
dt
ꢀ
ꢁ ꢀ
ꢁ
2
+ k2 Bisoprolol H3O+ (3)
ꢀ
ꢁ
ꢂ
ꢃ
ꢀ
ꢁ
ꢀ
ꢁ
d Bisoprolol
2
−
= k1 H3O+ + k2 H3O+
dt
ꢀ
ꢁ
· Bisoprolol
(4)
ꢀ
ꢁ
ꢀ
ꢁ
d Bisoprolol
−
= k0 Bisoprolol ,
dt
International Journal of Chemical Kinetics DOI 10.1002/kin.20809

750
SZALKA, ROKASZEWSKI, AND KACZMARSKI
Figure 5 Determination of the reaction order in relation to bisoprolol.
Table III Influence of the Bisoprolol Hemifumarate
Concentration on the Reaction Rate Constants
(in 1 mol.dm−3 HCl Solution)
Temperature 333.2 K
[B0] mol·dm−3
bn
r2 (n)
(k ꢀI) (× 10−3 s−1
)
1.3168 × 10−3 0.01 0.99 (4)
2.6411 × 10−3 0.01 0.99 (4)
6.5450 × 10−3 0.01 0.99 (4)
1.3038 × 10−2 0.01 0.99 (4)
2.6597 × 10−2 0.02 0.99 (4)
6.2541 × 10−2 0.04 0.99 (4)
1.3075 × 10−1 0.10 0.99 (4)
1.9562 × 10−1 0.21 0.99 (4)
2.6141 × 10−1 0.35 0.99 (4)
1.43 0.02
1.34 0.05
1.39 0.04
1.27 0.05
1.10 0.07
0.91 0.05
0.63 0.03
0.43 0.01
0.290 0.004
Figure 6 The order of a reaction in hydrohalic acid (isola-
tion method).
ꢀ
ꢁ
ꢀ
ꢁ
2
where k0 = k1 H3O+ + k2 H3O+
(5)
The order of reaction in relation to a hydrohalic
acid may be confirmed mathematically. The kinetic
equation (6) may be further reduced to Eq. (7) by us-
ing high excess of hydrochloric acid. The experiments
were carried out for eight different concentrations of
hydrochloric acid ranging from 0.1 to 2.0 mol·dm−3 at
323.2 and 333.2 K and for the initial concentration of
bisoprolol 1.3 × 10−3 mol·dm−3. The order of a reac-
tion in hydrohalic acid may be determined from Eq. (8)
and Fig. 6. The graph of ln k plotted against ln [HX]
International Journal of Chemical Kinetics DOI 10.1002/kin.20809

KINETICS OF HYDROLYSIS OF BISOPROLOL HEMIFUMARATE
has a slope z and an intercept ln kꢁ . The calculated or-
751
der of the reaction (z) was approximately 1.5 (1.49 for
323.2 K and 1.46 for 333.2 K), indicating that there are
two possible reaction mechanisms: the first involving
only the hydronium ion and the second involving the
hydronium ion and appropriate nucleophile. This is in
conformance with our explanation of a hydrolysis by
the nucleophilic substitution types 1 and 2. At this
point, it is important to highlight that the overall
reaction order in hydrohalic acid is an average value es-
timated for the reactions carried in 0.1–2.0 mol/dm−3
HCl solutions. At very low acid concentrations, the
SN1 mechanism may dominate, whereas at high acid
concentrations the reaction will appear as second
order in HX (the SN2 mechanism). In fact, the data
in Fig. 6 appear slightly curved, confirming that the
reaction order in HX may change with the concentra-
tion of the catalyst:
Figure 7 The linear form of the Eyring equation for three
hydrohalic acids.
ꢀ
ꢁ
v = kꢁ · Bisoprolol · [HX]z
(6)
of the SN2 mechanism in more concentrated solutions.
This phenomenon was also confirmed by a decrease
in the entropy of activation in the concentration range
from 0.5 to 1.0 mol·dm3 (compare with ꢀH= and
ꢀS= values for the SN1 and SN2 reaction presented in
Table VI). Summarizing the obtained results, we con-
clude that at low concentration of HX the SN1 mech-
anism is favored, whereas at high acid concentration
the SN2 mechanism dominates. All obtained results are
presented in Table IV.
ꢀ
ꢁ
v = k · Bisoprolol ; where k = kꢁ · [HX]z (7)
ln k = ln kꢁ + z ln [HX]
(8)
We have mainly focused on the hydrolysis of biso-
prolol hemifumarate; however, the kinetic studies car-
ried out for the bisoprolol base (free amine) proved that
there is no influence of fumaric acid on the reaction
rate. The measurements were carried out at 333.2 K
in 1.0 and 0.1 mol·dm−3 solutions of hydrochloric
acid and 1.3 × 10−3 mol·dm−3 initial concentration
of bisoprolol hemifumarate and bisoprolol base. The
effective rate constant (k) obtained in 1.0 mol·dm−3
HCl solution was 1.4316 × 10−3 s−1 for bisoprolol
hemifumarate and 1.4344 × 10−3 s−1 for the bisopro-
lol base. In 0.1 mol·dm−3 solution of hydrohalic acid,
k
ꢀH=
R
1
kb
h
ꢀS=
R
ln = −
·
+ ln
+
(9)
T
T
In addition, we used available software to carry
out the modeling to estimate the activation parame-
ters for the two reaction pathways individually. The
main model of the examined reaction was based on
a quadratic function of Eq. (2) and the Arrhenius
equation (10). The full description of our model is
presented in Eq. (11), where A is a preexponential fac-
tor estimated empirically, Ea is the Arrhenius energy of
activation, R is a gas constant, and T is a temperature.
Equation (11) was solved numerically, simultaneously
for all different experiments (all different initial con-
ditions) at a given temperature. The model parame-
ters were estimated by minimizing the sum of squares
between experimental and theoretical values. For the
nonlinear least-squares curve fitting, the Levenberg–
Marquardt procedure modified by Fletcher [12] was
used. The assessment of statistical significance of esti-
mated values parameters at a fixed scan rate was based
on the Student t test at the 0.05 significance level.
The estimation was carried out for the data obtained
for three hydrohalic acids at 323.2 K. Results are pre-
sented in Table V. Similar results were obtained at the
the rate constants for fumaric salt (6.0345 × 10−5 s−1
)
and bisoprolol base (6.0088 × 10−5
s
−1) were almost
the same. It was assumed that the dissociation of a
weak carboxylic acid was inhibited in the presence of
a strong hydrohalic acid and had no significant influ-
ence on the effective rate of hydrolysis.
The activation parameters were calculated using the
Eyring equation [11]. Figure 7 is a graphical presen-
tation of a linear form of the Eyring equation (9)
for different hydrohalic acids at the concentration
1.0 mol·dm−3 at temperatures 323.2, 333.2, and 343.2
K. The enthalpy and entropy of activation were calcu-
lated from a plot of ln(k/T) versus 1/T; this function
ꢄ
is a straight line with a slope of (−ꢀH= R) and an
ꢄ
ꢄ
intercept (ln kb h + ꢀS= R). The enthalpy of activa-
tion decreases with an increase of the concentration
of hydrohalic acid; this indicates larger participation
International Journal of Chemical Kinetics DOI 10.1002/kin.20809

752
SZALKA, ROKASZEWSKI, AND KACZMARSKI
Table IV Enthalpy and Entropy of Activation for Different Hydrohalic Acids Calculated from a Linear Form of the
Eyring Equation (9)
Hydrohalic Acid
HCl
Parameter
0.1 mol·dm−3
0.5 mol·dm−3
1.0 mol·dm−3
ꢀH= (kJ/mol)
ꢀS= (J/K·mol)
ꢀH= (kJ/mol)
ꢀS= (J/K·mol)
ꢀH= (kJ/mol)
ꢀS= (J/K·mol)
109.5
2.4
105.7
− 7.8
109.4
2.2
104.4
4.4
99.2
− 8.8
106.2
13.5
98.4
− 4.9
94.7
HBr
HI
− 13.0
91.5
− 21.5
Table V Activation Parameters Estimated by a Reaction Model (11) for Three Different Hydrohalic Acids at 323.2 K
Ea Calculated Ea Calculated
Rate Constant Preexponential
Preexponential
Factor for the
SN2
for the SN1
Reaction
exp (Ea2/RT ) Mechanism, Mechanism,
(s−1
Ea1 (kJ/mol) Ea2 (kJ/mol)
for the SN2
Reaction
of Reverse
Factor for the
SN1
k1 = A1 ·
k2 = A2 ·
Hydrohalic Reaction, k0
exp (Ea1/RT )
Acid
(s−1
)
Mechanism, A1
(s−1
)
Mechanism, A2
)
HCl
HBr
HI
−1.75 × 10−6
−1.44 × 10−6
−1.66 × 10−6
1.155 × 1014 1.630 × 10−4 3.186 × 1011 2.950 × 10−4 110.4 4.9
93.0 5.1
4.649 × 1014 1.822 × 10−4 1.447 × 1011 5.202 × 10−4 107.7 17.7 89.4 11.2
4.243 × 1014 1.374 × 10−4 2.873 × 1010 6.566 × 10−4 114.7 19.3 84.4 8.0
The modeling was carried out for the results ob-
tained at three temperatures, 323.2, 333.2, and 343.2 K,
at three different concentrations of hydrohalic acids,
0.1, 0.5, 1.0 mol·dm−3. The estimated k1 and k2 rate
constants were then introduced to the Eyring equa-
tion to calculate the enthalpy and entropy of activation
for the SN1 and SN2 reactions individually; results are
presented in Table VI. The negative values of the en-
tropy of activation for the SN2 reaction indicate that the
transition state is more ordered than molecules in a
ground state. It stays in conformance with the mecha-
nism of the SN2 reaction where a nucleophile may at-
tack on the protonated bisoprolol molecule only from
the opposite side to the leaving group. On the other
hand, positive values of the entropy of activation for the
SN1 mechanism confirm that the reactant in a ground
state (a protonated form of bisoprolol) is more ordered
than in a transition state.
Finally, a comparison of the half-lives of atenolol,
acebutolol, and propranolol (1 M HCl, 333.2 K), which
are, respectively, 0.84, 4.29, and 385 h, with the half-
life of bisoprolol 0.13 h, indicates that the stability
of beta-blockers does not depend on a lipophilicity as
indicated by Krzek et al. The stability mainly depends
on the reactivity of functional groups contained in the
molecule.
Figure 8 The exemplary graphical fit presenting estimation
of results obtained for hydrobromic acid at 323.2 K.
temperatures 333.2 and 343.2 K. The exemplary graph-
ical fit obtained after evaluation of the results for HBr
at 0.1, 0.5, and 1.0 M at 323.2 K is presented in Fig. 8.
k = Ae−E /RT
(10)
a
d[Bisoprolol]
=
dt
ꢅ
ꢅ
ꢀ
ꢆ
ꢀ
ꢁ
Ea1
RT
− k0 + A1 exp
H3O+
ꢅ
ꢆ
ꢆ
CONCLUSIONS
ꢁ
Ea2
2
+ A2 exp
H3O+
RT
ꢁ
In this article, we presented the results of the
pseudo–first-order kinetics of hydrolysis of bisoprolol
ꢀ
· Bisoprolol
(11)
International Journal of Chemical Kinetics DOI 10.1002/kin.20809

KINETICS OF HYDROLYSIS OF BISOPROLOL HEMIFUMARATE
753
Table VI Activation Parameters for Hydrolysis of Bisoprolol According to the SN1 and SN2 Mechanisms
Hydrolysis According to
the SN1 Mechanism
Hydrolysis According to
the SN2 Mechanism
Hydrohalic Acid
HCl
Parameter
ꢀH= (kJ/mol)
ꢀS= (J/K·mol)
ꢀH= (kJ/mol)
ꢀS= (J/K·mol)
ꢀH= (kJ/mol)
ꢀS= (J/K·mol)
117.6
45.7
112.2
28.9
120.9
54.4
84.5
− 51.7
85.7
HBr
HI
− 42.9
80.4
− 57.2
hemifumarate in the aqueous acidic solutions. The in-
fluence of three different hydrohalic acids and a weak
carboxylic acid was tested. There are two possible re-
action mechanisms of hydrolysis: the nucleophilic sub-
stitution types 1 and 2. As may be predicted, the SN2
mechanism occurs more readily at high acid concen-
trations, whereas at low acid concentrations the SN1
mechanism dominates. It was proved that the attack of
the nucleophile in the SN2 mechanism enhances sepa-
ration of a leaving group and improves the reaction rate.
The nucleophile entity is not engaged in the SN1 mech-
anism; thus a cleavage of the ether linkage occurs spon-
taneously, separating the reactive benzyl carbocation
from isopropoxyethanol. The SN1 reaction requires
higher energy of activation. The detailed explanation
of both reaction mechanisms was provided. Equation
(11) based on the Arrhenius equation presents a general
model for the hydrolysis of bisoprolol, which was used
to estimate the activation parameters by a specialized
software.
Only benzyl halides were observed as the
final products of a hydrolysis catalyzed by hy-
drohalic acids; these compounds may further re-
act to form (RS)-1-(4-hydroxymethyl-phenoxy)-3-
isopropylaminopropan-2-ol (impurity A of bisoprolol).
Our studies confirm that impurity A may arise in drug
product preparations due to the hydrolysis of the biso-
prolol molecule. No other degradation products ap-
peared; even hydrobromic or hydroiodic acids did not
cleave the phenol ether linkage, which seems to be
very stable in this molecule. Finally, the stability of
beta-blockers depends not on the lipophilicity but on
the reactivity of functional groups in the molecule.
bn
Relative concentration of
bisoprolol for the last point of
determination
Energy of activation
Energy of activation of the nu-
cleophilic substitution type 1
Energy of activation of the nu-
cleophilic substitution type 2
Planck constant
Ea
Ea1
Ea2
h
k
k1
Rate constant
Rate constant of the nucle-
ophilic substitution type 1
Rate constant of the nucle-
ophilic substitution type 2
Boltzmann constant
Partition coefficient
Number of determinations
Regression coefficient
Gas constant
Nucleophilic substitution
type 1
Nucleophilic substitution
type 2
Temperature, K
Reaction rate
Order of reaction in relation
to hydrohalic acid
Enthalpy of activation
Entropy of activation
k2
kb
log P
n
r
R
SN1
SN2
T
v
z
ꢀH=
ꢀS=
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754
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International Journal of Chemical Kinetics DOI 10.1002/kin.20809