Compressed oxygen in drug stability experiments

Article abstract of DOI:10.1248/cpb.55.87

A drug stability experiment accelerated by compressed oxygen was established. The stability of 10% ascorbic acid solution as a model was studied and the kinetic parameters were obtained with the newly established experimental method. Because ascorbic acid degrades under both anaerobic and aerobic conditions, the total rate constant k_total can be expressed as: k_total=k_anaerobic+k_aerobic, where k _anaerobic and k_aerobic are the rate constants of anaerobic and aerobic degradations, respectively. The k_anaerobic can be expressed as k_anaerobic= A_anaerobic·exp(-E _a,anaerobic/RT) according to Arrhenius equation, and the k _aerobic was found to be k_aerobic= A _aerobic·exp(-E_a,aerobic/RT)·p_O2 in our study.

Full text of DOI:10.1248/cpb.55.87

January 2007
Chem. Pharm. Bull. 55(1) 87—91 (2007)
87
Compressed Oxygen in Drug Stability Experiments
Yan SHI, Xiancheng ZHAN,* Lie MA, Bing LIN, Linli LI, Chengrong LI, and Ning HE
Key Laboratory of Drug Targeting, West China School of Pharmacy, Sichuan University; No. 17, Section 3, Ren-Min-Nan-
Lu Rd., Chengdu, Sichuan 610041, P. R. China. Received September 8, 2006; accepted October 24, 2006
A drug stability experiment accelerated by compressed oxygen was established. The stability of 10% ascor-
bic acid solution as a model was studied and the kinetic parameters were obtained with the newly established
experimental method. Because ascorbic acid degrades under both anaerobic and aerobic conditions, the total
rate constant ktotal can be expressed as: ktotalꢀkanaerobicꢁkaerobic, where kanaerobic and kaerobic are the rate con-
stants of anaerobic and aerobic degradations, respectively. The kanaerobic can be expressed as kanaerobic
Aanaerobic·exp(ꢂEa,anaerobic/RT) according to Arrhenius equation, and the kaerobic was found to be kaerobic
Aaerobic·exp(ꢂEa,aerobic/RT)·pO2 in our study.
ꢀ
ꢀ
Key words drug stability experiment; compressed oxygen; degradation kinetics; ascorbic acid
In oxido-stability studies, some drugs are unstable to oxy- study have not been found in the literature.
gen, indicating that their stabilities depend mainly on the
In the present paper, kinetic studies were used to quantitate
pressure of oxygen (or the concentration of dissolved oxygen the influence of the pressure of oxygen on the oxidation rate
in solutions). The drugs that are unstable to both oxygen and of drugs. In order to save time, compressed oxygen were
heat should obviously depend on both the pressure of oxygen used in isothermal experiments. This kind of experiments has
and the storage temperature. In order to predict and improve not been found in drug stability studies, except in some lipid
2
4—26)
the stability of these drugs, it is important to study their oxi- oxidation in foods.
Ascorbic acid solution, used as a
dation rates, but a quantitative study of such phenomena has model drug, was incubated under a group of oxygen pres-
seldom been found in the literature because of theoretical sures and temperatures. The oxidation rate constants of the
and technological limitations. It was reported that some model drug at various temperatures were obtained and the re-
drugs were unstable (or stable) under an aerobic (or anaero- lationship among pressure of oxygen, temperature and degra-
1—11)
bic) condition,
found in the literature.
Antioxidant played a very important part in pharmaceuti- oxygen pressures was extrapolated.
however, the oxidation rate has not been dation rate constant was established. According to the rela-
tionship, the rate constant at room temperature and normal
cal preparations to protect drugs unstable to oxygen; how-
In our other studies which will be reported in separated
ever, the selection of antioxidants in pharmaceutical studies submissions, kinetics is used to quantitatively determine the
1
2—17)
is considerably empirical.
The theoretics found in the oxidation rate constants of some widely used antioxidants.
These studies are benefit to improve drug stability, deter-
literature was the comparison of the standard oxidation (or
reduction) potentials of antioxidants and that of drugs. Ac- mine the shelf life of drugs, and reduce the harm resulted
cording to the theoretics of physical chemistry, these stan- from excessive quantity of antioxidants.
dard potentials are related to DG and K, the increment of
standard Gibbs function and the equilibrium constant of the Theoretical
18)
0
19,21)
chemical reactions.
The criterion dG ꢀ0 carries over
According to the basement of physical chemistry, the oxi-
T,p
into chemistry as the remark that, at constant temperature dation of drugs can be described by some form of the follow-
and pressure, chemical reactions are spontaneous in the di- ing general equation:
2
0,22)
rection of decreasing Gibbs function.
Therefore, the
ꢃdcDrug
ꢃdcDrug
n
m
n
m
comparison of the standard potentials can only demonstrate a
possibility of the protection because the emphasis up to this
point has been on the equilibrium properties of substances in
pure or solution form.
ꢂkꢁc
p
or
ꢂkꢁc
c
Drug O2
(1)
Drug O2
dt
dt
where cDrug is the concentration of drug, pO2 the pressure of
oxygen, cO2 the concentration of oxygen, t the time, kꢁ the re-
action rate constant, n the reaction order of the drug, and m
that of oxygen. According to Eq. 1, drugs will in general
show a rate dependence on cDrug, pO2 or c . The p depend-
A competitive oxidation reaction between the antioxidant
and the protected drug occurred in a pharmaceutical prepara-
tion. Studying the rates of reactions is the practical impor-
tance of being able to predict how quickly a reaction mixture
O
O2
2
2
4—26)
ence was reported in studies of lipid oxidation in food.
23)
approaches equilibrium. Therefore, to determine the actual
priority of the competitive oxidations and compare the drug-
protect capacity of antioxidants, it is important to determine
their oxidation rate constant using chemical kinetics. A ratio
of oxygen consumed by antioxidants to that by protected
drugs can be calculated theoretically, provided the oxidation
rate constants of both antioxidants and protected drugs were
determined. Moreover, the amount of a drug protected by an-
tioxidant can be therefore calculated. Such viewpoint and
When pO2 or cO2 keeps constant, Eq. 1 can be expressed as:
ꢃdcDrug
n
(2)
ꢂkc
Drug
dt
where k is the apparent reaction rate constant. After integrat-
ing, Eq. 2 can be expressed as follows:
f(c)ꢂf(c )ꢃkt
(3)
0
∗
To whom correspondence should be addressed. e-mail: xczhan@mail.sc.cninfo.net
© 2007 Pharmaceutical Society of Japan

8
8
Vol. 55, No. 1
where c is the residual concentration at time t, c the initial concentration solution. Therefore, the ionic strength was not
0
concentration, and f(c) the concentration function, which de- controlled in our experiments.
pends on the reaction order. For zero-, first- and second-order
Measuring Oxygen Pressure Because of the difficulty
reactions, f(c) is c, ln c, and ꢃ1/c, respectively.
in measuring the concentration of dissolved oxygen in
According to Eq. 3, the rate constant k can be obtained bombs, p , the pressure of oxygen in a state of equilibrium,
O
2
from the slope of a plot of f(c) versus t. In experiments, we was measured instead.
can place samples into oxygen bombs and pressurize the
The difference between the internal pressure of a bomb
bombs with oxygen to a specific pressure. Then incubating and the external barometric pressure was measured by a
the bombs isothermally and measuring the samples at each highly accurate pressure meter. The barometric pressure was
suitable interval, respectively.
measured with a Fortin type mercurial barometer. Then the
For a drug that is unstable to both oxygen and heat, the k is measured value of barometric pressure was corrected by the
the function of oxygen pressure and temperature:
location-dependent latitude, height and the ambient tempera-
ture because they influenced the specific gravity of mercury.
Isothermal Experiments under Compressed Oxygen
kꢂf(p , T)
(4)
O
2
The relationship between rate constant and oxygen pressure The oxidation rate of ascorbic acid is catalyzed by metal
29)
and temperature can be obtained by repeating the above incu- ions. In order to avoid the contact of metal ions, an exact
bating experiment under a group of oxygen pressures and volume of 2 ml of the 10% ascorbic acid solution was trans-
temperatures.
ferred to a 50-ml beaker. Then the beaker was placed into an
oxygen bomb. About 30 such bombs were pressurized with
oxygen to a specific pressure and put into a thermostatic oven
Experimental and Results
Instruments and Drugs Thirty oxygen bombs (pressur- at the beginning of the experiment. Three bombs were taken
ized-stainless-steel-container) were used and are shown in out of the thermostatic oven at each suitable interval and the
Fig. 1.
A highly accurate pressure meter (YB-150, the measure- metrically.
ment range is 0—6 MPa, the accuracy of pressure is 0.25%, The experimental temperatures and oxygen pressures were
residual concentrations of the samples were measured iodo-
3
0,31)
Yangquan, China), a Fortin type mercurial barometer (the ac- 15 °C, 25 °C, 35 °C, 45 °C (or 288.15, 298.15, 308.15,
curacy is ꢄ0.2 mmHg, Jiaxing, China), a pH Meter (Delta- 318.15 K) and 0.597 MPa, 1.097 MPa, 1.597 MPa, 2.097
3
20, Shanghai, China), and an isothermal heating oven with MPa, respectively. The experimental results are shown in
high precision (the accuracy, precision, and reproducibility of Figs. 2—5.
temperature are ꢀꢄ0.5 °C in the range of room temperature Ascorbic acid is unstable in aqueous solutions. It is re-
ported that the degradation of ascorbic acid obeys apparent
27)
to 100 °C; self-made) were used.
Ascorbic acid was received from Chengdu Chemical Com- zero-order kinetics in high concentration, such as 10% or
pany and of analytical grade. It contains ꢅ99.7% of C H O .
6
8
6
Oxygen was of medical application grade. It contains
ꢅ99.0% of O . The Other reagents used were of analytical
2
grade.
Preparation of 10% (0.567 mol/l) Ascorbic Acid Solu-
tion A 50 g quantity of ascorbic acid was dissolved in
4
50 ml water. The pH was adjusted to 6.8 with NaOH. Then
the solution was diluted with water to a total volume of
00 ml. Because ascorbic acid and ascorbate is a good pair of
5
buffer, the pH change is ꢀ0.2 pH after each incubation. So
no other buffer was used in our experiment.
It is reported that the degradation of high concentration
ascorbic acid solution is little ionic strength dependent,
Fig. 2. The Residual Concentrations of Ascorbic Acid Solutions at 15 °C
The oxygen pressures were 0.597 MPa (a), 1.097 MPa (b), 1.597 MPa (c), 2.097 MPa
28)
and, it is difficult to control the ionic strength in such high (d), respectively.
Fig. 3. The Residual Concentrations of Ascorbic Acid Solutions at 25 °C
The oxygen pressures were 0.597 MPa (a), 1.097 MPa (b), 1.597 MPa (c), 2.097 MPa
(d), respectively.
Fig. 1. The Outside Drawing and Profile Chart of the Oxygen Bomb

January 2007
89
Fig. 4. The Residual Concentrations of Ascorbic Acid Solutions at 35 °C
The oxygen pressures were 0.597 MPa (a), 1.097 MPa (b), 1.597 MPa (c), 2.097 MPa
Fig. 5. The Residual Concentrations of Ascorbic Acid Solutions at 45 °C
(d), respectively.
The oxygen pressures were 0.597 MPa (a), 1.097 MPa (b), 1.597 MPa (c), 2.097 MPa
d), respectively.
(
Table 1. The Degradation Rate Constants of Ascorbic Acid Solution at Experimental Temperatures and Pressures of Oxygen
T
K)
pO2
(MPa)
ktotal
[mol/(l ·h)]
kanaerobic
[mol/(l ·h)]
kaerobic
[mol/(l ·h)]
|
r|
(
288.15
298.15
308.15
318.15
0.597
0.0105
0.0142
0.0202
0.0247
0.0195
0.0297
0.0421
0.0477
0.0325
0.0460
0.0626
0.0729
0.0490
0.0684
0.0919
0.1126
0.0043
0.0086
0.0164
0.0228
0.0062
0.0099
0.0159
0.0204
0.0109
0.0211
0.0335
0.0391
0.0161
0.0296
0.0462
0.0565
0.0262
0.0456
0.0691
0.0898
0.9988
0.9989
0.9998
0.9997
0.9997
0.9995
0.9987
0.9988
0.9994
0.9996
0.9995
0.9987
0.9994
0.9989
0.9998
0.9996
1
1
2
.097
.597
.097
0.597
1
1
2
.097
.597
.097
0.597
1
1
2
.097
.597
.097
0.597
1
1
2
.097
.597
.097
3
2)
2
5%, and obeys apparent first-order kinetics in low con-
29)
centration, such as 2.5%, 1.5%, 0.5% etc. From the lines in
Figs. 2—5, the degradation of 10% ascorbic acid solution
obeys apparent zero-order kinetics in our experiments:
cꢂc ꢃkt
(5)
0
It is reported that the degradation of ascorbic acid occurs
under either aerobic or anaerobic condition, giving different
29)
degradants. Under aerobic condition the ascorbic acid is
oxidized to dehydroascorbic acid followed by hydrolysis and
oxidation to give diketogulonic acid and oxalic acid. Under
anaerobic condition, it undergoes dehydration and hydrolysis
29)
to give furfural and carbon dioxide.
aerobic
dehydroascorbic acid, diketogulonic acid, etc.
Fig. 6. Relationships between ktotal and pO2
ꢀ: 15 °C, ꢁ: 25 °C, ꢂ: 35 °C, ꢃ: 45 °C.
L-ascorbic acid
furfural, carbon dioxide
anaerobic
sure was obtained from slope of each line in Figs. 2—5 and
So it is suggested that the total degradation can be divided is listed in Table 1.
into two parallel reactions: the anaerobic and aerobic reac-
Kinetic Parameters of Ascorbic Acid Solution under
tion. Therefore, the total degradation rate constant ktotal can Anaerobic Condition From the data in Table 1, four linear
be expressed as:
regression lines, shown in Fig. 6, can be obtained by plotting
ktotal versus pO for each experimental temperature, respec-
tively. The rate constants under anaerobic condition kanaerobic
ktotalꢂkanaerobicꢆkaerobic
(6)
2
The ktotal at each experimental temperature and oxygen pres- are the intercepts of these lines and are also listed in Table 1.

9
0
Vol. 55, No. 1
Table 2. Kinetic Parameters of Ascorbic Acid Solution
Aanaerobic
Ea, anaerobic
Aaerobic
Ea, aerobic
[mol/(l·h)]
(kJ/mol)
[mol/(l·h ·MPa)]
(kJ/mol)
5
4
2
.97ꢇ10
43.10
4.67ꢇ10
36.70
Table 3. The Values of B at Various Temperatures
T
B
(K)
mol/(l·h ·MPa)
2
2
3
3
88.15
98.15
08.15
18.15
0.0097
0.0194
0.0276
0.0428
Fig. 7. Relationship between ln kanaerobic and 1/T
Based on the Arrhenius equation, a straight line was ob-
tained by plotting ln kanaerobic versus 1/T (shown in Fig. 7).
Therefore, kanaerobic can be expressed as:
Ea,anaerobic
(7)
lnkanaerobicꢂln Aanaerobic
ꢃ
RT
where Ea, anaerobic and Aanaerobic are the activation energy and
pre-exponential factor of the degradation under anaerobic
conditions, respectively. From the slope and the intercept of
the ln kanaerobicꢀ1/T line, Ea, anaerobic and Aanaerobic, respectively,
can be determined (values listed in Table 2).
Kinetic Parameters of Ascorbic Acid Solution under
Aerobic Condition According to Eq. 6 kaerobic can be cal-
culated as:
Fig. 8. Relationship between ln B and 1/T
our experiments are comparable with the reported ones at the
kaerobicꢂktotalꢃkanaerobic
(8)
32)
similar pH value: Ea, anaerobicꢂ49.51 kJ/mol (pHꢂ6.85) and
The values of kaerobic are also listed in Table 1. Because of Ea, aerobicꢂ32.64 kJ/mol (pHꢂ6.6).29)
the linear relationship between ktotal and pO2 (shown in Fig. 6),
kaerobic is proportional to p :
Finally, the total degradation rate constant ktotal can be re-
arranged as:
O
2
kaerobic=B·pO2
(9)

Ea,anaerobic
RT


Ea,aerobic
RT

ktotalꢂ Aanaerobic ⋅exp ꢃ
ꢆ Aaerobic ⋅exp ꢃ
⋅ pO2




where B is the slope of each line in Fig. 6 and listed in Table
. It is evident that the higher the temperature, the larger the




3
(12)
value of B; therefore, B is also a function of temperature.
Then, we supposed the temperature dependence of B
might be expressed as the following form, similar to the Ar-
rhenius equation:
According to Eq. 12, k0.9, 298 K, 0.0204 MPa, the degradation rate
constant of ascorbic acid solution at room temperature
25 °C) and normal pressure of oxygen (0.097ꢇ21%ꢂ
(
0
.02037 MPa) can be obtained, and therefore the t , the time
0
.9
for the c to decrease to 90% at 25 °C and 0.02037 MPa, can
be estimated.

Ea,aerobic

Ea,aerobic
RT
Bꢂ Aaerobic ⋅ exp ꢃ
or ln Bꢂln Aaerobicꢃ



RT


E


E

(10)
a,anaerobic
a,aerobic
k298K,0.0204MPaꢂ Aanaerobic ⋅exp ꢃ
ꢆ Aaerobic ⋅exp ꢃ
⋅ pO2





RT


RT

Thus, kaerobic can be expressed as:

ꢃ 43100


5
ꢂ2.97ꢇ10 ⋅exp


Ea,aerobic
RT

 8.314ꢇ298.15 
kaerobicꢂ Aaerobic ⋅exp ꢃ
⋅ pO2
(11)





ꢃ36700


4
ꢆ 4.67ꢇ10 ⋅exp
ꢇ0.02037

where Ea, aerobic and Aaerobic are the activation energy and pre-
exponential factor of the degradation under aerobic condi-
tions, respectively.
According to Eq. 10, a straight line, with correlation coef-
ficient rꢂ0.9924, was obtained by plotting ln B versus 1/T

8.314ꢇ298.15 
ꢃ3
ꢂ8.70ꢇ10 mol/(l⋅h)
c0ꢃ0.9⋅c0
0.1⋅c0
0.1ꢇ0.567
t0.9
ꢂ
ꢂ
ꢂ
ꢂ6.52 h
ꢃ3
k
k
8.70ꢇ10
This calculated t0.9 was confirmed to be 7.5 h by a room
temperature storage testing.
(shown in Fig. 8). From the slope and the intercept of the
ln Bꢀ1/T line, Ea, aerobic and Aaerobic, respectively, were deter-
mined (values also listed in Table 2).
Acknowledgement The authors are grateful to the National Science
Because the degradation of ascorbic acid is very pH de- Foundation of China for financial support.
pendent, the estimates for the activation energies obtained by

January 2007
91
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