物理化学学报(Wuli Huaxue Xuebao)
Acta Phys. -Chim. Sin. 2012, 28 (5), 1030-1036
1030
doi: 10.3866/PKU.WHXB201203025
[Article]
May
www.whxb.pku.edu.cn
紫外-可见吸收光谱结合高斯多峰拟合技术测定甲基红酸离解常数
张建华
刘
琼
陈玉苗
刘兆清
徐常威*
(广州大学化学化工学院, 广州 510006)
摘要:
在一定 pH 值范围内, 甲基红(MR)水溶液紫外-可见吸收光谱特征是酸式甲基红(HMR)最大吸收峰
((530±15) nm)与碱式甲基红(MR-)最大吸收峰((435±20) nm)叠合在一起. 本文用高斯多峰拟合技术实现了
HMR 和 MR- 叠合峰的分峰拟合计算. 拟合计算输出两个吸收峰的积分面积即峰强度 A1 和 A2, A1 和 A2 之比与
MR- 和 HMR 浓度之比. 进而计算甲基红水溶液酸离解平衡常数 pKa. 用本方法测量 298.15 K 时的 pKa 值为
4.76. 拟合优度高, 拟合度 R2、拟合优度χ2 分别达到 0.998 和 10-5 以下. 深入探讨了表面活性剂十二烷基硫酸钠
(SDS)、十六烷基三甲基溴化铵(CTAB)聚集行为对甲基红 pKa 的影响. 与传统分光光度测量方法相比, 紫外-可
见吸收光谱结合高斯多峰拟合技术结果更可靠, 测量步骤和数据处理过程更简单, 更具有普适性.
关键词:
甲基红; 紫外-可见吸收光谱; 叠合峰; 酸离解常数; 高斯多峰拟合
中图分类号:
O648
Determination of Acid Dissociation Constant of Methyl Red by
Multi-Peaks Gaussian Fitting Method Based on UV-Visible
Absorption Spectrum
ZHANG Jian-Hua
LIU Qiong
CHEN Yu-Miao
LIU Zhao-Qing
XU Chang-Wei*
(School of Chemistry and Chemical Engineering, Guangzhou University, Guangzhou 510006, P. R. China)
Abstract: UV-visible electronic absorption spectra of methyl red (MR) aqueous solutions are characterized
by the overlap of a principal peak at λmax ((520±15) nm) with a shoulder peak at λmax ((435±20) nm), which
are assigned to acidic species (HMR) and basic species of methyl red, respectively. In this study, the
spectra and the integrated absorbance of the MR- and HMR peaks (denoted A1 and A2, respectively) were
interpreted using a new multi-peaks Gaussian fitting method. From the absorbance ratio A1/A2 and the
concentration ratio cMR-/cHMR, the average acid dissociation constant (pKa) was determined as 4.76 at 298.15
K. The goodness is high and the values of R2 (degree of fitting) and χ2 (chi-square test for goodness of fit)
were 0.998 and below 10-5, respectively. The effects of aggregation behavior of sodium dodecyl sulfate
(SDS) and cetylammonium bromide (CTAB) on pKa were also investigated via this method. The multi-peaks
Gaussian fitting method was shown to determine pKa more reliably and simply than traditional
spectrophotometric techniques.
Key Words:
Methyl red; UV-visible absorption spectrum;
Multi-peaks Gaussian fitting
Overlap peak; Acid dissociation constant;
Received: December 22, 2011; Revised: March 1, 2012; Published on Web: March 2, 2012.
∗
Corresponding author. Email: cwxuneuzsu@126.com; Tel: +86-20-39366908.
The project was supported by the National Natural Science Foundation of China (20903028), Scientific Research Foundation for Returned Scholars
from Ministry of Education of China, and Scientific Research Foundation for Yangcheng Scholar, China (10A041G).
国家自然科学基金(20903028), 留学回国人员科研启动基金及羊城学者青年科研骨干培养对象项目(10A041G)资助
Ⓒ Editorial office of Acta Physico-Chimica Sinica
No.5
1
ZHANG Jian-Hua et al.: Determination of pKa of Methyl Red by Multi-Peaks Gaussian Fitting Method
Introduction
The acid-base ionization equilibrium exists in aqueous solution of many organic dyes. Acid dissociation constant is a very
important parameter to indicate degree of ionization at the different pH values in acidic organic dye solutions.1-3 The acidbase ionization equilibrium of organic dyes and the determination of acid dissociation constant in aqueous solution are of
great significance for many practical applications and scientific
research areas such as acid-base titration, complex formation,
solvent extractions, capillary electrophoresis,4 chromatographic
retention characteristics,5,6 potentiometric titration, fabric dyeing and finishing,7 environmental monitoring and protection,8-12
drug research and development. In particular, drug synthesis,
production, purification, formulation, dissolution, absorption,
distribution and metabolism processes are closely related with
the pKa.13,14 Many determination methods for acid dissociation
constants of organic dyes have been developed.3,15-17 The most
commonly used methods are potentiometric titration,5,18-21 conductivity,22,23 capillary electrophoresis,15 capillary electrophoresis mass spectrometry,24 nuclear magnetic resonance spectroscopy,25-28 liquid chromatography,6,16,29 infrared spectroscopy,30,31
Raman scattering,32 fluorescence spectroscopy,33,34 UV-visible
spectrophotometry,35-37 theoretical calculation38 and so on. Among
them, spectrophotometric method has high precision and accuracy. The linear relationship between absorbance and concentration of color solution with a certain thickness is determined
by Lambert-Beerʹs law, which gives a theoretical foundation of
the spectrophotometric determination of the pKa of an acidbase indicator.
In 1958, Tobey39 determined the pKa of methyl red using singlewavelength spectrophotometry and the pKa is 5.02 at 300.35
K. Since then, a lot of work to determine the pKa of organic
dyes using single-wavelength spectrophotometry has been reported.3,35-37 Single-wavelength spectrophotometry is very suitable to determine the position of absorption peaks of acid and
base species which are separated. However, in most cases, the
maximum absorption peaks of acid and base species are association with each other in organic dye aqueous solutions. This situation leads to difficulties in data processing and determination
of the pKa.3 The multi-wavelengths spectrophotometric method
has been adopted to determine the value of pKa.4,40,41 Target factor analysis,4 rank annihilation factor analysis42,43 and other
methods6,44 have been developed to deduce the pKa values from
the multi-wavelengths spectrophotometric data obtained at different pH values.
UV-visible absorption spectra of methyl red were measured
at different pH values regulated by a series of acetic acid
(HAc)-sodium acetate (NaAc) buffer solutions with different
concentrations and characterized by an overlap of a principal
peak of acidic specie of methyl red (HMR) at 520-550 nm and
a shoulder peak of basic specie of methyl red (MR-) at
425-460 nm. A multi-peaks Gaussian fitting method based on
Origin from Microcal Company was used to interpret the spec-
1031
tra in this study. The multi-peaks Gaussian fitting calculation45-47 on the overlap peaks gave the integrated absorbance ratio A1/A2, then the pKa of methyl red was obtained.
The studies on organic dye-surfactant interactions in aqueous buffered systems are of great importance in analytical
chemistry, pesticide efficiency, pharmaceutical development,
fabric dyeing and so on. Therefore, a new procedure based on
multi-peaks Gaussian fitting method was firstly performed in
dye-surfactant interactions of methyl red with sodium dodecyl
sulfate (SDS), cetylammonium bromide (CTAB), which will
enrich research methods in this research area.
2
Experimental
2.1 Reagents
Methyl red, anhydrous NaAc, CTAB, SDS were of analytical grade and purchased from Sigma-Aldrich. Ethanol, HAc,
HCl were of analytical grade and purchased from Guangzhou
chemical reagent factory. All solutions were prepared with distilled water.
(1) All the solutions of methyl red were prepared according
to the literature37 and the pH values were achieved using a certain concentration of NaAc-HAc buffer solution.
(2) A series of methyl red solutions with SDS were prepared
by a concentration range of SDS from 0.001 to 0.018 mol·L-1
and the concentration of methyl red was fixed.
(3) Instead of SDS, a series of methyl red solutions with
CTAB were prepared by the concentration of CTAB at 0.0001
mol·L-1 (below the critical micelle concentration (CMC) of
CTAB) and 0.001 mol·L-1 (above the CMC of CTAB) and the
concentration of methyl red was fixed.
2.2 Apparatus
UV-visible absorption spectra were recorded on Shimadzu
UV2550-UV-visible spectrophotometer (Japan) equipped with
10 mm path length quartz cell. Distilled water was used as reference solution. All the spectra were obtained between 320 and
750 nm and the sampling interval was 0.5 nm. The pH values
of the solutions were measured by PHSJ-4A-type PH meter furnished with a combined glass electrode (Shanghai Precision Division-Shanghai Lei magnetic) which was pre-calibrated with
at least two buffer solutions at pH 4.00 and 10.00. Each pH value was obtained from the average of three measurements. All
pH values and spectra were measured at a constant temperature
which was controlled by a super-heated water circulating thermostat bath. The measurement data were imported into PC
with Microcal Origin 7.0 for data processing.
2.3 Multi-peaks Gaussian fitting method
The UV-visible spectrum data were imported and plotted
with Origin 7.5 software. When menu command of Analysis/
Fit Multi-Peaks/Gaussian was selected, a dialog box with the
number and the initial half-width estimated default values of the
peaks appeared in the current graphics window. After doubleclicking the mouse at 425 and 520 nm of the spectra respectively, Origin 7.5 automatically completed a multi-peaks Gaussian
1032
fitting procedure on certain spectra and gave the line-shape
parameters of the UV-visible spectra in the result window.
3
Vol.28
Acta Phys. -Chim. Sin. 2012
Table 1
pH
Results and discussion
3.1 Principle of multi-peaks Gaussian fitting method
Ionization equilibrium of methyl red in aqueous solution is
given as the following equation
HMR⇌MR-+H+
(1)
red
yellow
The pH value range of color change of methyl red in aqueous
solution is well known as 4.4-6.2. When pH values are 4.63,
4.93, 5.39, 5.68, the UV-visible absorption spectra and their
multi- peaks Gaussian fitting results are shown in Fig.1. It is
shown that integrated absorbance A1 of base MR- peaks increases and integrated absorbance A2 of acid HMR peaks decreases
with the increase of pH value. The increase and decrease of the
integrated absorbance of the MR- and HMR are objectively
due to the change of the relative concentrations of MR- and
HMR.
Existence simultaneously of HMR and MR- in methyl red
solution results in spectra with two peaks at a certain pH value.
Multi-peaks Gaussian fitting on the spectra with two peaks satisfies following equation
A1
y = y0 +
exp(-2((x - λ max1)/w1)2) +
w1 π 2
A2
exp( - 2((x - λ max2)/w 2)2)
(2)
w2 π 2
where, y0 is baseline, λmax1 and λmax2 are the maximum absorption
wavelengths, w1 and w2 are half peak widths, A1 and A2 are the
integrated absorbances of the two peaks for MR- and HMR.
Multi-peaks Gaussian fitting method based on the spectra
Fig.1
Results of the multi-peaks Gaussian fitting method on
the spectra of methyl red solution at different
pH values and 298.15 K
A1
A2
λmax1/nm λmax2/nm w1/nm w2/nm Height1 Height2
456.5
532.0
122.0
66.3
0.30
0.85
0.997
4.93 46.01 43.12
448.9
535.1
120.5
63.1
0.38
0.59
0.998
5.39 52.40 21.81
445.5
541.8
124.7
46.2
0.46
0.27
0.996
5.68 55.83 11.81
436.5
546.9
114.0
46.2
0.49
0.15
0.997
Height1 and Height2 are the heights of absorbance peaks for MR- and HMR.
gives the λmax1, λmax2, w1, w2, A1, A2 and these data are listed in
Table 1.
3.2 Relationship between pKa and the relative
integrated absorbance
Acid dissociation constant of methyl red is given as following equation
[H+][MR -]
Ka =
(3)
[HMR]
thus pKa = pH - lg
where
[MR -]
[HMR]
A1 ε1[MR -]
=
A 2 ε 2[HMR]
(4)
(5)
[MR -] ε 2 A1
=
(6)
[HMR] ε1 A 2
where, ε1 and ε2 are the molar absorption coefficients of MRand HMR, respectively. Then, the methyl red absorption spectra (Fig.2) were measured in base (pH=9) and acid (pH=2) conditions respectively.
When the value of pH is 9, there is only MR- in methyl red
solution and the [MR-]=C, then
A1=ε1[MR-]=ε1C
(7)
When the value of pH is 2, there is only HMR in methyl red so-
UV-visible absorption spectra of methyl red at different pH values and their multi-peaks Gaussian fitting results
experiment,
R2
4.63 28.80 76.43
fitting,
MR-,
HMR
No.5
ZHANG Jian-Hua et al.: Determination of pKa of Methyl Red by Multi-Peaks Gaussian Fitting Method
Fig.2 UV-visible absorption spectra of methyl red solution
measured in basic (pH=9) and acid (pH=2) solutions
lution and [HMR]=C, then
A2=ε2[HMR]=ε2C
(8)
Setting ε=ε1/ε2 and A1 or A2 are obtained with the same concentration of methyl red, then
ε=A1/A2
(9)
The value of ε is obtained as 0.56.
From Eqs.(4)-(8), pKa can be calculated from Eq.(10)
[MR -]
ε A
A
pKa = pH - lg
= pH - lg 2 1 = pH + lgε -lg 1 (10)
ε1 A 2
A2
[HMR]
A
pH = lg 1 + pKa - lgε
(11)
A2
The value of pKa is obtained from Eq.(10) at different pH values. The Multi-peaks Gaussian Fitting results are shown in Table 2.
3.3 Error analysis for determination of pKa
It is very clear that the values of pKa listed in Table 2 are
slightly lower than the values (4.90 ± 0.20) in literature.39,42,48
However, the results are within the error range for the values
of pKa and prove the reliability of multi-peaks Gaussian fitting
Table 2
Relationship between Ka and temperature
T/K
No.
A1/A2
lg(A1/A2)
pH
pKa
Average of pKa
298.15
1
0.38
-0.42
4.63
4.79
4.76
2
0.89
-0.05
4.95
4.74
3
2.40
0.38
5.39
4.75
4
4.73
0.67
5.68
4.75
1
0.52
-0.28
4.65
4.68
2
1.01
0.00
4.97
4.71
3
2.50
0.40
5.36
4.71
4
4.78
0.68
5.63
4.69
1
0.50
-0.30
4.58
4.62
2
0.99
-0.01
4.90
4.65
3
2.47
0.39
5.30
4.65
4
4.75
0.68
5.62
4.68
1
0.48
-0.32
4.56
4.62
2
0.95
0.02
4.88
4.64
3
2.44
0.39
5.28
4.63
4
4.69
0.67
5.58
4.65
1
0.46
-0.34
4.54
4.62
2
0.93
-0.03
4.86
4.63
3
2.40
0.38
5.25
4.61
4
4.72
0.67
5.54
4.60
303.15
308.15
313.15
318.15
1033
method for determination of pKa. The concentrations of MRand HMR in solutions are determined by the curves for absorbance of maximum absorption wavelength at 425 nm for MRand that at 520 nm for HMR. However the concentrations of
MR- and HMR are determined by the methyl red color range
which are unreliable because of blue shift of MR- and red shift
of HMR absorption peak.18 The absorption peak of MR- bluely
shifts from 456 to 436 nm and the absorption peak of HMR
redly shifts from 531 to 546 nm when the pH value increases
from 4.63 to 5.68 in Table 1. The shifts of absorption peaks
make the relationship of the concentration and absorbance diverge obviously from the standard curve and cause about
±(3%-5%) systematic error for pKa measurement which is higher than true value.
A multi-peaks Gaussian fitting based on the absorption spectra of methyl red within the color change interval has been
made and gives the relative integrated absorbance of MR- and
HMR absorption peaks which is used to determine the relative
concentration of MR- and HMR instead of using the unreliable
standard curves obtained from the acid and base conditions in
this study. So the pKa measurement results are more reliable
and repeatable.
3.4 Thermodynamics on ionization equilibrium of
methyl red
The pKa values of methyl red were determined by UV-visible absorption spectroscopy with multi-peaks Gaussian fitting
method at different temperatures and shown in Table 2. The
values of pKa decrease considerably with increase of temperature, which is consistent with the literature.49 Generally it is believed that the increase of temperature promotes ionization of
organic dyes and leads to decrease of pKa.
A few of thermodynamic models have been developed for
acid dissociation equilibrium of oganic dyes.49 Here, the‘density’model has been selected.49 The standard Gibbs free energy
of reaction (ΔrG 􀱉) for the ionization equilibrium of methyl red
satisfies the following Eq.(12)
⊖
lgKa=-pKa ln10= -Δ r G /(RT) =
4.70
4.65
4.63
4.61
(12)
a + b/T + c/T 2 + d/T 3 + (e + f/T + g/T 2)ln ρ w
where pKa=-lgKa, ρw is water density (kg·m-3), T is the thermodynamic temperature (K), and a-g are model parameters. The
relationship between the lgKa and 1/T is shown in Fig.3. The
ΔrG 􀱉 obtained from Eq.(12) with parameters which were obtained from non-linear curve fitting on data of Fig.3 with
change of temperature is shown in Fig.4. The ΔrG 􀱉 increases
with increase of temperature and is consistent with the literature.49
3.5 Effect of surfactants on pKa
3.5.1 SDS-methyl red system
The variety of CMC of surfactants can be measured accurately by UV-visible absorption spectrum combined with multipeaks Gaussian fitting method in order to study their aggregation behavior.45 To study the effects of aggregation behavior of
surfactant on pKa, SDS-methyl red and CTAB-methyl red aque-
1034
Vol.28
Acta Phys. -Chim. Sin. 2012
Table 3 Spectrum line-shape parameters of methyl red with
different concentrations of SDS at 298.15 K and pH=5.40
CSDS/(mol·L-1)
Fig.3 Relationship between lgKa and 1/T
Fig.4 Relationship between ΔrG􀱉 and temperature
ous solution systems were selected. Fig.5 shows the relationships between pKa of methyl red and the SDS concentration at
different temperatures. The values of pKa decrease considerably with the increase of temperature, indicating that the ionization equilibrium of methyl red moves to the right in the existence of anionic surfactant SDS. When the SDS concentration
is lower than the CMC, no significant change of pKa values is
observed. When the SDS concentration is higher than the
CMC, pKa values increase with the increase of SDS concentration. It is undoubted that the pKa is sensitive to the CMC and
used for determination of the CMC of SDS, for example the
CMC of SDS are 8.54×10-3, 8.68×10-3, 8.82×10-3, 9.66×10-3
mol·L-1 at 303.15, 308.15, 313.15, 318.15 K, respectively,
which are consistent with the literature.50
Fig.5
Relationships between pKa of methyl red and the SDS
concentration at different temperatures
A1
A2
λmax1/nm
λmax2/nm
w1/nm
w2/nm
0.001
31.28
6.95
443.8
542.8
123.5
52.0
0.002
31.62
7.11
444.5
542.7
124.3
51.2
0.004
31.88
7.13
444.5
542.7
124.7
51.2
0.006
31.93
6.95
444.2
543.0
124.6
50.9
0.008
32.22
6.88
444.3
543.1
125.2
50.9
0.010
31.99
7.60
445.2
542.1
125.2
52.2
0.012
30.83
8.00
446.0
540.9
123.6
53.8
0.014
30.45
9.17
447.9
539.1
123.8
55.6
0.016
29.79
9.59
446.9
538.7
121.7
57.3
0.018
28.12
10.01
449.5
537.9
120.0
58.1
In order to investigate further effect of SDS on ionization
equilibrium of methyl red in solution, a multi-peaks Gaussian
fitting method on UV-visible spectra of the series of solutions
(pH=5.40) containing different concentrations of SDS from
0.001 to 0.018 mol·L-1 gives spectral line-shape parameters
such as A1 and A2, λmax1 and λmax2, w1 and w2 of MR- and HMR at
298.15 K in Table 3.
The spectral line-shape parameters listed in Table 3 are sensitive to the SDS concentration and changes suddenly at CMC of
SDS which are shown in Fig.6 and Fig.7. The red shift of λmax1
and blue shift of λmax2 with the increase of the SDS concentration are observed and more obvious after formation of the SDS
micelle. There is a sudden change at 0.0083 mol·L-1 in Fig.6
and Fig.7. At first, the λmax1 of MR- absorption peak increases
slowly and then increases quickly with the increase of SDS
concentration. Sudden change occurs at the CMC of SDS. The
change of λmax2 is exactly the opposite with λmax1. The w1 of MRabsorption peak increases then decreases quickly with the increase of SDS concentration. Sudden change occurs at the
CMC of SDS. The change of w2 is exactly the opposite with
w1. Generally, relationship between spectral line-shape parameters such as A1, A2, λmax1, λmax2, w1, w2 and concentration of surfac-
Fig.6 Dependence of the maximum absorption wavelengths of
MR- and HMR on the concentration of SDS at 298.15 K
No.5
ZHANG Jian-Hua et al.: Determination of pKa of Methyl Red by Multi-Peaks Gaussian Fitting Method
Table 4
Spectrum line-shape parameters and effect of aggregation behavior of CTAB on pKa of methyl red with different concentra
CCTAB/(mol·L-1)
0.0001
0.001
No.
A1/A2
lg(A1/A2)
pH
pKa
Average of pKa
1
0.45
-0.35
4.62
4.71
4.67
2
0.94
-0.03
4.88
4.65
3
2.81
0.45
5.38
4.67
4
5.30
0.74
5.67
4.67
1
8.83
0.94
4.61
3.41
2
25.10
1.40
4.89
3.23
3
absorption peak of MR-
5.37
-
-
4
absorption peak of MR-
5.66
-
-
tant has been used by us for CMC determination.45
3.5.2 CTAB-methyl red system
CTAB with methyl red system is much more complicated
than SDS with methyl red system. The UV-visible absorption
spectrum of CTAB with methyl red solution is shown in Fig.8
when CTAB concentration is bellow and above the CMC. Table 4 gives the spectrum line-shape parameters and the effect
of aggregation behavior of CTAB on the pKa of methyl red solutions at 303.15 K.
When the CTAB concentration is 0.0001 mol·L-1 which is
bellow the CMC of CTAB, the UV-visible absorption spectrum
of CTAB with methyl red solution is similar with that of methyl red solution. However, the pKa value of methyl red with
0.0001 mol·L-1 CTAB obtained by multi-peaks Gaussian fitting method is 4.67 which is 0.09 lower than that of the methyl
red (4.76) at the same temperature. Furthermore, pKa value decreases slowly with the increase of CTAB concentration. When
the CTAB concentration is 0.001 mol·L-1, the pKa value decreases rapidly to below 3.32 and the color of solution system
changes completely from red to yellow at the same time, which
indicates that there is mainly MR- species in the solution.
These results illustrate that formation of the CTAB micelle can
changes the range of changed color of methyl red from
Fig.8
Dependence of the half-widths of MR- and HMR on the
concentration of SDS at 298.15 K
3.32
UV-visible absorption spectra of methyl red solution with
different concentrations of CTAB at 303.15 K
4.4-6.2 to 3.0-5.0 and makes the pKa value of methyl red decrease remarkably. Generally the significant decrease of pKa
value is attributed to electrical double layer of CTAB micelle
which absorbs selectively MR- and makes the ionization equilibrium of methyl red move obviously to the right.
4
Fig.7
1035
Conclusions
In this study, a multi-peaks Gaussian fitting method based
on the UV-visible absorption spectra is firstly used to determine the pKa value of organic dyes such as methyl red. The reliability of the method is adequately proved by an excellent
agreement of the measurement results with literature. There are
several advantages, such as the easy operational procedure, explicit physical meaning, and the accurate measurement results
for the method.
The relative concentration of the MR- and HMR in solution
has been determined by the relative integrated absorbance calculated from multi-peaks Gaussian fitting method based on the
UV-visible spectra. This method avoids successfully the systematic error of 3%-5% of pKa measurement from the standard curves which is established from the absorbance of MRmaximum absorption wavelength at 425 nm and HMR maximum absorption wavelength at 520 nm versus concentration of
MR- and HMR at the methyl red color range, respectively.
1036
Moreover, the effect of SDS and CTAB on ionization equilibrium of methyl red also has been studied and some reliable results with the method have been obtained. The spectral lineshape parameters such as A1, A2, λmax1, λmax2, w1 and w2 of MRand HMR that obtained from multi-peaks Gaussian fitting
method on the UV-visible spectra of SDS-methyl red and
CTAB-methyl red solutions have been firstly discovered to be
sensitive to aggregation behavior of surfactants SDS and
CTAB. The CMC values can be determined by the dependence
of the three sets of parameters on the surfactant concentration
which should support each other.
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