Method for determining molar absorption coefficient of bisulfate ions in solution

Abstract

The invention discloses a method for determining the molar absorption coefficient of bisulfate ions in a solution. The method comprises the following steps: analyzing ultraviolet absorption spectrums of sulfuric acid, sodium hydrogen sulfite and sodium sulfate solutions by adopting an ultraviolet-visible spectrophotometric method, and calculating molar absorption coefficients of HSO4 <-> under different wavelengths by integrating absorbance values and ionization constants of HSO4 <-> in different solutions. The method for calculating the molar absorption coefficient of HSO4 <-> in the wavelength range of 189-200 nm is established by measuring the absorbance of a series of low-concentration solutions containing sulfuric acid, sodium hydrogen sulfate and sodium sulfate. Then, the total sulfur content in the binary mixture of sodium sulfate / sulfuric acid and sodium hydrogen sulfate / sulfuric acid is determined by utilizing the numerical values, and compared with an experimental result, the relative error is 3.82% + / -2.11%, so that the reliability of the determination method disclosed by the invention is proved.

Description

Technical Field

[0001] This invention relates to the field of molar absorption coefficient determination technology, and specifically to a method for determining the molar absorption coefficient of bisulfate ions in solution. Background Technology

[0002] Coal is a primary energy source for humankind. Flue gas from coal-fired power plants is rich in sulfur trioxide (SO3), a major source of atmospheric dust plumes, acid rain, and particulate pollution. When cooled to the acid dew point, the resulting sulfuric acid can corrode flue gas treatment equipment. Furthermore, during selective catalytic reduction (SCR), sulfuric acid reacts with ammonia to form ammonium sulfate (NH4HSO4) and ammonium sulfate ((NH4)2SO4), thereby reducing denitrification efficiency. Therefore, monitoring the SO3 content in flue gas is crucial.

[0003] Current methods for measuring sulfur trioxide in flue gas involve two steps: collection and detection. The main collection methods include controlled condensation, spiral coil methods, and isopropanol absorption, which focus on condensing or absorbing SO3 and converting it into a sulfuric acid solution. However, these methods are time-consuming and labor-intensive, making them unsuitable for rapid and dynamic monitoring.

[0004] Ultraviolet-visible spectrophotometry, based on the Lambert-Beer law, provides a simple and cost-effective method for rapid and direct evaluation of analytes. First, a calibration curve is established using standard sulfuric acid or sulfate solution, and the SO3 level in the flue gas is directly measured, subsequently used to estimate the actual SO3 concentration. However, this method may lead to inaccurate analytical results. As mentioned earlier, in addition to SO3, flue gas also contains large amounts of NH4HSO4 and (NH4)2SO4, which together form HSO4. - With SO4 2- A mixed solution. Furthermore, during the partial dissociation of sulfuric acid in the second step, HSO4 is also generated simultaneously. - and SO4 2- Therefore, relying solely on a single standard solution to determine SO3 content may lead to errors. A more suitable method is to utilize SO42-. 2- and HSO4 - The molar absorptivity is measured simultaneously with the concentration to obtain more accurate results.

[0005] SO4 2- It undergoes almost no hydrolysis reaction in water. Its molar absorptivity at various wavelengths can be easily determined using sulfate solutions of known concentrations. However, HSO4... - Partial dissociation occurs in aqueous solutions, a process significantly influenced by factors such as solution concentration and temperature. This dependence makes it difficult to directly determine its molar absorptivity using standard bisulfate solutions. Summary of the Invention

[0006] The purpose of this invention is to solve the aforementioned technical problems in the prior art and to provide a method for determining the molar absorption coefficient of hydrogen sulfate ions in solution.

[0007] To address the shortcomings of the aforementioned technical problems, the present invention adopts the following technical solution: A method for determining the molar absorptivity of bisulfate ions in solution employs ultraviolet-visible spectrophotometry to analyze the ultraviolet absorption spectra of sulfuric acid, sodium bisulfite, and sodium sulfate solutions. This method integrates the HSO4 content in different solutions. - The absorbance value and ionization constant of HSO4 were used to calculate the HSO4 content. - Molar absorptivity at different wavelengths.

[0008] As a further optimization of the method for determining the molar absorption coefficient of bisulfate ions in solution according to the present invention, the method specifically includes the following steps: S1. Prepare sulfuric acid solutions of different concentrations and measure their absorbance using a spectrophotometer. Sodium sulfate solutions of different concentrations were prepared, and their absorbance was measured using a spectrophotometer. SO4 is calculated using formula (1). 2- Molar absorptivity at a specific wavelength ; (Formula 1) S2, combine formula (2) and Substituting into formula (3), HSO4 is obtained through nonlinear fitting. - molar absorptivity ; (Formula 2) (Formula 3).

[0009] As a further optimization of the method for determining the molar absorption coefficient of bisulfate ions in solution according to the present invention: the sulfuric acid and sodium sulfate solutions are prepared in a concentration range of 0.001 M to 0.045 M with a gradient of 0.001 M intervals, and in a concentration range of 0.1 M to 0.5 M with a gradient of 0.1 M intervals.

[0010] As a further optimization of the method for determining the molar absorption coefficient of hydrogen sulfate ions in solution according to the present invention: the sulfuric acid and sodium sulfate used in the preparation of the sulfuric acid and sodium sulfate solution are both of analytical grade, and the solvent used is ultrapure water.

[0011] As a further optimization of the method for determining the molar absorption coefficient of bisulfate ions in solution according to the present invention: when detecting absorbance, the concentration range is 0.001 M to 0.045 M, and a 1 cm cuvette is used for measurement; when the concentration is between 0.1 M and 0.5 M, a 1 mm cuvette is used for measurement.

[0012] As a further optimization of the method for determining the molar absorption coefficient of hydrogen sulfate ions in solution according to the present invention: all mathematical calculations and fitting processes were performed in Matlab.

[0013] This invention has the following beneficial effects: By measuring the absorbance of a series of low-concentration solutions containing sulfuric acid, sodium bisulfate, and sodium sulfate, this invention establishes a method for calculating HSO4. - The method for determining the molar absorptivity in the wavelength range of 189 nm to 200 nm was then used. These values ​​were subsequently used to determine the total sulfur content in binary mixtures of sodium sulfate / sulfuric acid and sodium bisulfate / sulfuric acid, with a relative error of 3.82% ± 2.11% compared to experimental results, confirming the reliability of the method of the present invention. Attached Figure Description

[0014] Figure 1 UV absorption spectra of sulfuric acid (a), sodium bisulfate (b), and sodium sulfate (c) in solutions ranging from 0.001 M to 0.045 M; Figure 2 (a) shows the relationship between absorbance and concentration of sulfuric acid, sodium bisulfate, and sodium sulfate at a wavelength of 189 nm. The corresponding standard deviations are marked with error bands, and low-resolution spectral data are marked in blue. (b) shows the relationship between absorbance and concentration of sodium sulfate at different wavelengths from 189 nm to 200 nm. Spectral data that deviate from linearity are marked in blue. Figure 3 for A schematic diagram of the calculation process; Figure 4 (a) represents HSO4 in sulfuric acid solution. - The relationship curve of dissociation fractions Based on the literature, the concentration range is 0.001-0.3M; (b) is HSO4 in sulfuric acid solution. - The relationship curve of dissociation fraction was derived, showing a concentration range of 0.001-0.3M; (c) shows the relationship between the concentration equilibrium constant and ionic strength of sodium bisulfate solution; (d) is the fitted curve; (e) is a comparison graph of the calculated slope derived from (d) and the experimental slope derived from the spectral data of NaHSO4 solution; (f) is... and Scatter plot fitted in the wavelength range of 189 nm to 200 nm; Figure 5To compare the experimental and fitted values ​​of the total sulfur content in the two-component mixed solution, the number above each set of data represents the relative error: (fitted data - experimental data) / experimental data × 100%. Detailed Implementation

[0015] To better understand the present invention, the following embodiments further illustrate the content of the present invention, but the content of the present invention is not limited to the following embodiments.

[0016] A method for determining the molar absorptivity of bisulfate ions in solution employs ultraviolet-visible spectrophotometry to analyze the ultraviolet absorption spectra of sulfuric acid, sodium bisulfite, and sodium sulfate solutions. This method integrates the HSO4 content in different solutions. - The absorbance value and ionization constant of HSO4 were used to calculate the HSO4 content. - Molar absorptivity at different wavelengths.

[0017] Figure 1 The ultraviolet absorption spectra of sulfuric acid, sodium bisulfate, and sodium sulfate solutions with concentrations between 0.001 M and 0.045 M were obtained. All measurements were performed at a 1 cm optical path. To avoid exceeding the detection limit of the spectrophotometer, solutions with concentrations between 0.1 M and 0.5 M were measured at a 1 mm optical path.

[0018] pass Figure 1 It can be seen that at a concentration of 0.045 M, the maximum absorption wavelengths of sulfuric acid, sodium bisulfate, and sodium sulfate are located at 188 nm, 188.5 nm, and 189 nm, respectively, indicating a slight redshift. This redshift is attributed to the gradual increase in absorbance values ​​and the corresponding increase in stray light interference within the spectrophotometer, leading to spectral distortion and an eigenvalue redshift. Therefore, to obtain accurate and reliable absorbance coefficient results, high absorbance data that deviates from the Lambert-Beer law should be avoided for spectral analysis.

[0019] It should be noted that the sulfuric acid, sodium bisulfate, and sodium sulfate were all analytical grade and purchased from Sinopharm Chemical Reagent Co., Ltd. in Beijing, China. Ultrapure water was used as the solvent. Solutions were prepared in 0.001 M increments within the concentration range of 0.001 M to 0.045 M, and in 0.1 M increments within the concentration range of 0.1 M to 0.5 M.

[0020] Spectral data were acquired under a nitrogen-protected environment using a T10CS UV-Vis spectrophotometer equipped with dual monochromators (Beijing Pujinji General Instrument Co., Ltd., China) to avoid oxygen interference. This experimental setup has been described in detail in previous reference 19. Based on the spectrophotometer's optimal absorbance detection range, a 1 cm cuvette was used for concentration measurements from 0.001 M to 0.045 M, and this size was also used for binary mixed solutions. When the concentration was between 0.1 M and 0.5 M, a 1 mm cuvette was used for measurement.

[0021] Sulfuric acid, as a dicarboxylic acid, undergoes almost complete first ionization (Ka1≈1000), while its second ionization is only partial (Ka2≈0.01). These processes are represented by the following chemical equilibrium equation: In dilute solutions, due to the relatively large first ionization constant, SO42- 2- The hydrolysis effect is negligible, which means that sodium sulfate solution is mainly composed of SO42-. 2- Composition. Conversely, sulfuric acid and sodium bisulfate solutions both contain HSO4. - and SO4 2- This forms a biphasic ionic composition. When the solution concentration is , the absorbance of the three solutions at a specific wavelength exhibits the following relationship (from top to bottom, Equations 1-3): , and The absorbance values ​​represent the absorbance of sulfuric acid, sodium bisulfate, and sodium sulfate solutions with concentrations of , respectively.

[0022] and They represent HSO4 - and SO4 2- The molar absorptivity at a specific wavelength.

[0023] and And respectively represent HSO4 - The degree of dissociation in sulfuric acid solution and sodium bisulfate solution.

[0024] In the acidic environment of sulfuric acid solution, the first dissociation produces H3O. + A large presence of HSO4 will inhibit - Further dissociation results in a lower degree of dissociation in sulfuric acid solution compared to sodium bisulfate solution. Despite these differences, as shown in the following equation (Equation 4), HSO4 - The equilibrium constant for dissociation remains consistent in both solutions.

[0025] The above four equations serve as the basis for deriving HSO4. - The fundamental elements of molar absorptivity. For accurate results, the choice of dataset is crucial. First, it is essential to maximize the differentiation... , and The numerical difference. Figure 2 (a) shows the correlation between absorbance and concentration of sulfuric acid, sodium bisulfate and sodium sulfate solutions at a wavelength of 189 nm. Figure 2 As shown in (b), an overlapping region is visible, and the absorbance of the three solutions exhibits similarity at concentrations below 0.01 M. This similarity mainly stems from HSO4. - The extensive ionization of SO42- at extreme dilutions in sulfuric acid and sodium bisulfate solutions results in... 2- It becomes the dominant anion in these solutions. Therefore, data points with concentrations below 0.01 M were excluded.

[0026] also, It is determined by least squares fitting of equation (3), so the relationship between absorbance and concentration should be kept as linear as possible. Figure 2 (b) shows the relationship between absorbance and concentration of sodium sulfate in the wavelength range of 189 nm–200 nm (intervals of 0.5 nm). However, in the wavelength region of 189 nm–191.5 nm, where the absorbance is relatively strong, the relationship between absorbance and concentration begins to deviate from the linear region of the Lambert-Beer law when the concentration exceeds 0.02 M. Correspondingly, there is no significant shift in the 192 nm–200 nm range because the absorbance is relatively low at this wavelength. In short, to minimize calculation errors, Figure 2 The data points in the blue areas of (a) and (b) were not used for subsequent fitting.

[0027] The fitting process is as follows: The secondary dissociation constant of sulfuric acid has been documented in existing technologies, obtained through conductivity, Raman spectroscopy, and other experimental methods. The values ​​obtained from different experimental methods are very close and widely accepted; some data from the literature are summarized in [reference needed]. Figure 4 (a). By fitting data in the concentration range of 0-0.05 M, we obtained the concentration of HSO4 in sulfuric acid. - The logarithmic relationship between degree of dissociation and concentration, where Ri 2 >0.998. This fitted curve helped us obtain the degree of secondary dissociation of sulfuric acid at any concentration.

[0028] SO4 is calculated using formula (1) 2- Molar absorptivity at a specific wavelength ; (Formula 1) Formula (2) and Substituting into formula (3), HSO4 is obtained through nonlinear fitting. - molar absorptivity ; (Formula 2) (Formula 3).

[0029] Obtained using equation (4) (HSO4 at various concentrations) - The degree of dissociation in sodium bisulfate), the results are as follows: Figure 4 As shown in (b), then , and Substituting these values ​​into equation (2), the absorbance values ​​at each concentration can be calculated. .

[0030] Verification: The method includes obtaining the slope of the concentration curve in the above steps and comparing it with the slope of the experimental absorbance and concentration of sodium bisulfate solution.

[0031] The verification process involves three important parameters. , and . It is HSO4 - The dissociation fraction in sodium bisulfate solution. The relationship with the concentration equilibrium constant K is as follows: Using the formula above, the K value can be derived within the concentration range of 0.01 M to 0.045 M. The K value is affected not only by temperature but also by ionic strength. Figure 4 (c) shows the drawing Curve, in which, , This represents the square root of the ionic strength. The curve reveals... and The linear relationship between them, especially at lower ionic strengths ( (Less than 0.2) shows a significant linear relationship. When the ionic strength is extrapolated to zero, the corresponding activity balance constant K a This can be calculated. The y-intercept of the fitted line is 1.99, corresponding to K... aThe value is 0.0102. This value is consistent with the second dissociation constant of sulfuric acid (1.99) reported in the literature.

[0032] Obtained through equation (2) The value and concentration show a strong correlation, such as Figure 4 The fitted lines are shown in (d). The R-squared values ​​for all fitted lines are... 2 All values ​​exceeded 0.999, indicating a near-perfect predictive relationship. This set of fitted lines yielded a set of slope values, labeled 'calculated slope'. Similarly, by linearly fitting the experimentally measured absorbance values ​​of sodium bisulfate solution to its concentration, we obtained another set of slope values, called 'experimental slope'. The comparison results of the two sets of slopes are as follows... Figure 4 As shown in (e), the difference between the two sets of slopes is extremely small, with a maximum relative error of only 2.71%. This indicates that using parameters... , and Calculated The numerical values ​​are very close to the experimentally measured absorbance of sodium bisulfate solution, further confirming that the absorbance obtained from equation (1) is accurate. and It has high reliability.

[0033] Figure 4 (f) demonstrates and The scatter plots fitted in the wavelength range of 189 nm to 200 nm are summarized in the table below.

[0034] As shown in the figure, HSO4 - and SO4 2- The absorbance of HSO4 decreases with increasing wavelength. Within this wavelength range, the absorbance of HSO4... - The molar absorptivity is approximately 1 to 20 L·mol⁻¹ -1 ·cm -1 SO4 2- The range is from 5 to 80 L·mol -1 ·cm -1 Between. SO4 2- The absorbance of HSO4 - It is 4 to 7 times stronger, with an average multiple of 5.9 times. SO4 2- The absorbance of [the substance] is significantly higher than that of HSO4. - This may be related to the configurations of the two ions.

[0035] In industrial liquid compositions, such as extracts from coal flue gas, sulfur is typically present as HSO4. - and SO4 2-The mixture exists in a mixed form. In spectrophotometry, the molar absorptivity of both ions is obtained simultaneously. and Accurate quantification of total sulfur content is a necessary prerequisite. Sodium sulfate / sulfuric acid mixed solutions and sodium bisulfate / sulfuric acid mixed solutions with different concentration ratios were selected, and the absorbance values ​​of the mixed solutions were obtained at wavelengths of 189 nm-200 nm. Based on the following formula, combined with... Figure 4 The molar absorption coefficient in (f) and the data in the table above are fitted together.

[0036] Indicates the absorbance of a binary mixture. and These represent the HSO4 in the mixed solution. - and SO4 2- The concentration, and This represents residual matrix.

[0037] The fitting process involves linear regression analysis. The comparison results between the fitted values ​​and experimental values ​​are as follows: Figure 5 As shown, the relevant data is summarized in the table below.

[0038] Through a comprehensive comparative analysis of the experimental data, we draw the following conclusions: the total sulfur content obtained by the fitting method is in high agreement with the experimental results, with an average relative error of only 3.82% and a root mean square error (RMSE) of 2.11%.

[0039] The specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various modifications or variations within the scope of the claims, which do not affect the essence of the present invention.

Claims

1. A method of determining the molar absorption coefficient of bisulfite ions in a solution, characterized by: The UV absorption spectra of sulfuric acid, sodium bisulfite and sodium sulfate solution were analyzed by UV-Vis spectrophotometry. The molar absorption coefficient of hydrogen sulfite at different wavelengths was calculated by integrating the absorbance value of hydrogen sulfite in different solutions and its ionization constant.

2. A method of determining the molar absorptivity of bisulphite ions in a solution as claimed in claim 1, wherein, The method comprises the following steps: S1, configure different concentrations of sulfuric acid solution, and use spectrophotometer to detect its absorbance , configure different concentrations of sodium sulfate solution, and use spectrophotometer to detect its absorbance , calculate SO4 2- Molar absorption coefficient at a specific wavelength ; (Formula 1) S2, formula (2) and Substituting formula (3) into formula (2), the molar absorption coefficient of bisulfate was obtained by nonlinear fitting ; (Formula 2) (Formula 3).

3. A method of determining the molar absorptivity of bisulphite ions in a solution as claimed in claim 2, wherein: The sulfuric acid and sodium sulfate solution is prepared in a concentration range of 0.001 M to 0.045 M at intervals of 0.001 M and in a concentration range of 0.1 M to 0.5 M at intervals of 0.1 M.

4. A method of determining the molar absorptivity of bisulphite ions in a solution as claimed in claim 2, wherein: The sulfuric acid and sodium sulfate used in the preparation of the sulfuric acid and sodium sulfate solution are both of analytical purity, and the solvent used is ultrapure water.

5. A method of determining the molar absorptivity of bisulphite ions in a solution as claimed in claim 3, wherein: When detecting the absorbance, the concentration measurement range is 0.001 M to 0.045 M, and the measurement is performed using a 1 cm cuvette. When the concentration is between 0.1 M and 0.5 M, the measurement is performed using a 1 mm cuvette.

6. A method of determining the molar absorptivity of bisulphite ions in a solution as claimed in claim 2, wherein: All mathematical calculations and fitting processes are completed in Matlab.

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