A method and device for determining the number of moles of dissolved gas, and a membrane inlet mass spectrometer
By constructing a conversion model between signal value and mole number, the problem of low conversion efficiency of membrane injection mass spectrometry measurement results was solved, achieving efficient determination of dissolved gas mole number, improving detection efficiency and process standardization.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- BEIJING WATER SCI & TECH INST
- Filing Date
- 2026-02-28
- Publication Date
- 2026-05-29
AI Technical Summary
In the existing technology, membrane sample mass spectrometers cannot efficiently convert the measurement results from mbar to the commonly used unit μmol when measuring the concentration of dissolved gases in a liquid system.
A conversion model between signal values and mole counts is constructed, and the signal values output by the membrane mass spectrometer are directly converted into mole counts using deep learning models or relational functions.
It has achieved automatic conversion and standardization of the detection process, improved data processing efficiency, reduced cumbersome calibration experiments, and significantly improved detection efficiency.
Smart Images
Figure CN122109266A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of data processing technology, specifically to a method, apparatus, and membrane injection mass spectrometer for determining the molar number of dissolved gases. Background Technology
[0002] Membrane inlet mass spectrometry (MIMS) is a highly sensitive detection technique widely used to determine the concentration of dissolved nitrogen in liquid systems.
[0003] However, when using membrane sample mass spectrometry to determine the concentration of dissolved gases, such as nitrogen, in a liquid system, the measured substances are generally nitrogen isotopes (e.g., nitrogen isotopes). 28 N2, 29 N2, 30 The signal value of N2 is expressed in mbar. Currently, converting the unit from mbar to the commonly used unit μmol requires an experimental conversion process, which is inefficient. Summary of the Invention
[0004] This invention provides a method, apparatus, and membrane injection mass spectrometer for determining the molar number of dissolved gases, thereby solving the problem of low efficiency in the prior art when converting the measurement results of membrane injection mass spectrometers from mbar to μmol.
[0005] In a first aspect, the present invention provides a method for determining the number of moles of dissolved gas, the method comprising:
[0006] Acquire the dissolved target gas signal value output by the membrane injection mass spectrometer; Construct a conversion model; the conversion model characterizes the relationship between signal value and number of moles; Input the dissolved target gas signal value into the conversion model to determine the number of moles of dissolved target gas.
[0007] This invention obtains the molar number of the dissolved target gas by acquiring the signal value of the dissolved target gas and directly inputting it into a constructed conversion model between signal value and molar number. This method not only enables automatic conversion and improves data processing efficiency, but also standardizes the detection process. Once the model is built, subsequent input of the detection signal value is sufficient to quickly output the molar number, eliminating the need for repeated, tedious calibration experiments and significantly improving detection efficiency.
[0008] In one alternative implementation, constructing the transformation model includes: Identify at least one set of target samples, in which the concentration of the target gas differs among the target samples; Determine the reference signal value and reference molar number of the target gas in each target sample at different temperatures; The conversion model is determined based on the reference signal value and the number of reference moles.
[0009] In one alternative implementation, the conversion model is determined based on the reference signal value and the reference number of moles, including: The conversion model is obtained by fitting the reference signal value and the number of reference moles.
[0010] In one optional embodiment, the target samples are in two or more groups, and the target gas is nitrogen; each group of target samples includes: Synthetic helium containing a first preset concentration of nitrogen, synthetic air containing a second preset concentration of nitrogen, and synthetic nitrogen containing a third preset concentration of nitrogen.
[0011] In one optional implementation, the first preset concentration is 0.001%; the second preset concentration is 78%; and the third preset concentration is 99.99%.
[0012] In one optional implementation, determining the reference molar number of the target gas in each target sample includes: The reference molar number of nitrogen in the synthesized helium was determined to be 0; Determine the molar volume of synthesized nitrogen; based on the molar volume, determine the reference number of nitrogen moles in the synthesized nitrogen. The reference molar number of nitrogen in the synthetic air is determined based on the reference molar number of nitrogen in the synthetic nitrogen gas.
[0013] In one optional implementation, determining the reference signal value of the target gas in each target sample includes: Determine the first signal value of nitrogen in synthetic helium, the second signal value of nitrogen in synthetic air, and the third signal value of nitrogen in synthetic nitrogen in each group of target samples; use the average value of the first signal as the reference signal value of nitrogen in synthetic helium. Subtract the first signal value from the second signal value to obtain the reference signal value of nitrogen in the synthesized air; Subtracting the first signal value from the third signal value yields the reference signal value for nitrogen in the synthesized nitrogen gas.
[0014] In one alternative implementation, the conversion model is: ; Where a, b, and c are constants, and n is the number of moles. The value is the dissolved target gas signal, and T is the temperature of the water sample to be tested.
[0015] In a second aspect, the present invention provides a device for determining the molar number of dissolved gases, the device comprising: The acquisition module is used to acquire the dissolved target gas signal value output by the membrane sample mass spectrometer; The building block is used to construct the conversion model; the conversion model represents the relationship between the signal value and the number of moles. The conversion module is used to input the dissolved target gas signal value into the conversion model to determine the number of moles of dissolved target gas.
[0016] Thirdly, the present invention provides a membrane injection mass spectrometer, which is applicable to the method for determining the number of dissolved gases in any of the above aspects or embodiments.
[0017] It should be noted that the beneficial effects of the dissolved gas molar number determination device and membrane injection mass spectrometer provided in the embodiments of the present invention can be found in the description of the corresponding beneficial effects of the dissolved gas molar number determination method above, and will not be repeated here. Attached Figure Description
[0018] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.
[0019] Figure 1 This is a schematic flowchart of the first method for determining the number of moles of dissolved gas according to an embodiment of the present invention; Figure 2 This is a structural block diagram of a device for determining the number of moles of dissolved gas according to an embodiment of the present invention. Detailed Implementation
[0020] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0021] It is understood that before using the technical solutions disclosed in the various embodiments of the present invention, users should be informed of the types, scope of use, and usage scenarios of the personal information involved in the present invention and their authorization should be obtained in accordance with relevant laws and regulations through appropriate means.
[0022] The terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.
[0023] When using a membrane sample mass spectrometer (MIMS) (such as the HPR40 or pQA model) to determine the concentration of dissolved nitrogen in a liquid phase system, the results are generally as follows: 28 N2, 29 N2 and 30 The signal value of N2 (mbar) cannot be directly converted into the unit (μmol) commonly used in subsequent calculations, and there are few explicit calculation methods for this process.
[0024] In view of this, according to an embodiment of the present invention, a method for determining the number of moles of dissolved gas is provided. It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions. Furthermore, although a logical order is shown in the flowchart, in some cases, the steps shown or described may be executed in a different order than that shown here.
[0025] This embodiment provides a method for determining the molar number of dissolved gases, which can be used in membrane sample mass spectrometers, servers, terminals, mobile terminals, etc. Figure 1 This is a flowchart of a method for determining the number of moles of dissolved gas according to an embodiment of the present invention, as shown below. Figure 1 As shown, the process includes the following steps: Step S101: Obtain the dissolved target gas signal value output by the membrane injection mass spectrometer.
[0026] Membrane mass spectrometry (MMS) is a detection technology that combines membrane separation and mass spectrometry analysis. It can be used to detect and analyze gaseous components in solutions. It uses a selectively permeable membrane to transmit gases (such as nitrogen and oxygen) from the solution to the mass spectrometer for analysis, thereby providing their corresponding signal values. For example, it can obtain the signal values for nitrogen or oxygen.
[0027] Step S102: Construct a conversion model; the conversion model characterizes the relationship between signal value and number of moles.
[0028] Membrane mass spectrometry outputs results in mbar, which represents the gas pressure. For example, it can measure different isotopes in nitrogen (N2) molecules. 28 N2, 29 N2 and 30 The signal value of N2.28 N2, 29 N2 and 30 The N2 signal value actually represents the partial pressure of nitrogen under specific conditions, rather than its direct concentration (such as μmol / L).
[0029] In related technologies, conversion is generally achieved through experiments, a process that is relatively cumbersome. This invention, however, directly constructs a conversion model beforehand that characterizes the relationship between signal values and mole counts, such as a deep learning model or a relational function. Specifically, a large amount of experimental sample data can be acquired, including the signal values output by a membrane mass spectrometer and the corresponding number of moles of dissolved gas. Then, the experimental sample data is used to train a deep learning model, such as a fully connected neural network, convolutional neural network, or recurrent neural network, to obtain the conversion model. Alternatively, signal values and corresponding mole counts of multiple standard samples with known concentrations can be collected, and a functional relationship can be established. Linear or nonlinear fitting methods can be used to establish the relationship between signal values and mole counts, thereby generating the conversion model.
[0030] Step S103: Input the dissolved target gas signal value into the conversion model to determine the number of moles of dissolved target gas.
[0031] In actual conversion, the dissolved nitrogen signal value output by the membrane sample mass spectrometer can be directly input into the conversion model to obtain the corresponding number of moles.
[0032] In this embodiment, the number of moles of the dissolved target gas can be obtained by acquiring the signal value of the dissolved target gas and directly inputting the signal value into the constructed conversion model between signal value and mole count. This method not only enables automatic conversion and improves data processing efficiency, but also standardizes the detection process. Once the model is built, subsequent input of the detection signal value is sufficient to quickly output the mole count, eliminating the need for repeated tedious calibration experiments and significantly improving detection efficiency.
[0033] This embodiment provides a method for determining the molar number of dissolved gases, which can be used in membrane sample mass spectrometers, servers, terminals, mobile terminals, etc. The process includes the following steps: Step S101: Obtain the dissolved target gas signal value output by the membrane sample mass spectrometer. For details, please refer to [link to relevant documentation]. Figure 1 Step S101 of the illustrated embodiment will not be described again here.
[0034] Step S102: Construct a conversion model; the conversion model characterizes the relationship between signal value and number of moles.
[0035] Specifically, step S102 above includes: Step S1021: Determine at least one set of target samples, where the concentration of the target gas in each target sample within the set is different.
[0036] In this embodiment, three sets of target samples are selected, and the target gas is nitrogen. Each set of target samples includes: synthetic helium containing a first preset concentration of nitrogen, synthetic air containing a second preset concentration of nitrogen, and synthetic nitrogen containing a third preset concentration of nitrogen. The first preset concentration is 0.001%; the second preset concentration is 78%; and the third preset concentration is 99.99%.
[0037] Each target sample was sealed in an airtight bottle of the same volume. These nine airtight bottles of constant volume were randomly divided into three groups, each filled with deionized water that had been thoroughly aerated with high-purity helium (synthetic helium in this embodiment, helium purity 99.999%), synthetic air (nitrogen purity 78%), and high-purity nitrogen (synthetic nitrogen in this embodiment, nitrogen purity 99.99%). The three groups of synthetic helium were numbered H1, H2, and H3, the synthetic air was numbered A1, A2, and A3, and the synthetic nitrogen was numbered N1, N2, and N3.
[0038] Step S1022: Determine the reference signal value and reference mole number of the target gas in each target sample.
[0039] In some optional embodiments, step S1022 includes: determining a first signal value of nitrogen in synthetic helium, a second signal value of nitrogen in synthetic air, and a third signal value of nitrogen in synthetic nitrogen in each group of target samples; using the average of the first signals as a reference signal value of nitrogen in synthetic helium; subtracting the first signal value from the second signal value to obtain a reference signal value of nitrogen in synthetic air; and subtracting the first signal value from the third signal value to obtain a reference signal value of nitrogen in synthetic nitrogen.
[0040] In this embodiment, the amount of dissolved nitrogen in water samples from 36 samples at different water temperatures (5℃, 10℃, 15℃, and 20℃) was determined using a Hiden pQA-MIMS membrane mass spectrometer. The reagent used was a 50% zinc chloride solution (ZnCl2, 50% w / w%).
[0041] Taking group H as an example, the nitrogen content in the synthesized helium was measured. 28 N2, 29 N2 and 30 The signal value of N2, measured in three groups of H. 28 N2, 29 N2 and 30 The signal values of N2 were averaged separately. Since nitrogen in water is produced by... 28 N2, 29 N2 and 30Since it is composed of N2, the total signal value of nitrogen measured by group H can be calculated based on the following formula: ;in, These represent the three sets of measurements. 28 N2, 29 N2 and 30 The average value of the N2 signal. The total signal of nitrogen here. This is the first signal value of nitrogen in the synthesized helium in this embodiment; the second and third signal values are obtained similarly. The above steps are repeated for the signal values measured in groups A and N to obtain the corresponding total signal values.
[0042] Furthermore, after obtaining the total signal values corresponding to groups A and N, the total signal value of nitrogen measured in group H can be subtracted from each to subtract the background value, thus obtaining the corrected total signal value P. 校 For details, please refer to Table 1.
[0043] Table 1
[0044] In this embodiment, subtracting the background value can effectively eliminate system interference caused by non-target nitrogen, ensuring that the final signal value only reflects the content of target nitrogen dissolved in the water sample.
[0045] In some optional embodiments, step S1022 includes: determining that the reference molar number of nitrogen in the synthesized helium is 0; determining the molar volume of the synthesized nitrogen; determining the reference molar number of nitrogen in the synthesized nitrogen based on the molar volume; and determining the reference molar number of nitrogen in the synthesized air based on the reference molar number of nitrogen in the synthesized nitrogen.
[0046] In this embodiment, for synthetic helium, the number of helium moles in the airtight bottle after helium aeration is set to 0. In this embodiment, the number of nitrogen moles in the high-purity helium-aerated water sample is defined as 0, which can be used as a blank control benchmark for detection, ensuring the accuracy of the curve intercept and eliminating the influence of systematic errors on the quantitative results.
[0047] For synthesized nitrogen, the number of moles of nitrogen is calculated based on the following formula: ; in, This indicates the volume (mL / L) of saturated nitrogen dissolved in the water sample. The values represent the molar volume (L / mol) of an ideal gas under standard atmospheric pressure. Table 2 shows the variation of the saturated dissolved volume and molar volume of nitrogen with temperature. Table 2
[0048] In this embodiment, high-concentration nitrogen can be used as a high-concentration benchmark for the multiple linear regression model, corresponding to the high signal value detected by MIMS, which can support the upper limit of the linear range of the curve.
[0049] For synthetic air, since nitrogen accounts for approximately 78% of the total air volume, the number of moles of air in the airtight bottle after aeration is calculated based on the following formula: In this embodiment, the number of nitrogen moles in the synthetic air can be used as the medium concentration benchmark in the multiple linear regression model, corresponding to the nitrogen concentration range commonly found in natural water bodies, thus ensuring the applicability of the method to conventional water samples.
[0050] Step S1023: Fit the reference signal value and the number of reference moles to obtain the conversion model.
[0051] In this embodiment, a multiple linear regression model was established based on the 36 valid samples in Table 1 to determine the number of moles of dissolved gas.
[0052] In the process of constructing the conversion model, without correcting the total signal value of nitrogen, in some optional implementations, the conversion model can be: ; In the process of constructing the conversion model, when correcting the total signal value of nitrogen, in some optional implementations, the conversion model is as follows: ; Where n is the number of moles, The signal value that needs to be converted to molar number is the dissolved target gas signal value in this embodiment, and T is the temperature of the water sample to be tested.
[0053] In this embodiment, a multiple linear regression model is constructed to compare the measured signal value with the solubility of the gas at a standard atmospheric pressure and corresponding experimental temperature, thereby obtaining a conversion calculation formula for the signal value (mbar) and the number of moles (μmol).
[0054] The transformation model constructed based on the uncorrected signal values showed an overall goodness-of-fit test of F=4529.74 (P<0.0001), indicating a highly significant model with strong statistical explanatory power. The coefficient of determination R²=0.9963, and the adjusted R²=0.9960, meaning the model explains 99.6% of the dependent variable variation, demonstrating excellent fit. The sum of squared residuals was 0.0473, indicating a small prediction error. All independent variables passed the highly significant test (P<0.0001), and the signal values ( The value of t = 61.06 shows a highly significant positive correlation with the number of moles, making it the core dominant variable. After logarithmic transformation, the value of temperature (T) is t = -9.26, showing a highly significant negative correlation. This result is consistent with the thermodynamic law that nitrogen solubility decreases with increasing temperature, thus enhancing the theoretical rationality of the model.
[0055] The transformation model constructed based on the corrected signal values showed an overall goodness-of-fit test with F=4529.74 (P<0.0001), indicating a highly significant model with good statistical explanatory power. R²=0.9857, and the adjusted R²=0.9849, explaining 98.5% of the dependent variable variation, demonstrating excellent goodness of fit. The sum of squared residuals was 0.0636, indicating a low level of model prediction error.
[0056] The conversion model constructed in this embodiment has high statistical significance and good fit, and is suitable for the accurate quantification of the number of dissolved gas moles in the liquid phase.
[0057] Step S103: Input the dissolved target gas signal value into the conversion model to determine the number of moles of the dissolved target gas. For details, please refer to [link to relevant documentation]. Figure 1 Step S103 of the illustrated embodiment will not be described again here.
[0058] In this embodiment, the calibration using low, medium, and high concentration gradients, combined with background signal subtraction, effectively eliminates instrument noise and environmental interference, making the multiple linear regression fitting of signal value, temperature, and mole count more accurate, and significantly improving the accuracy and reliability of establishing the relationship between signal value, temperature, and mole count.
[0059] This embodiment also provides a membrane injection mass spectrometer, which is applicable to the method for determining the number of dissolved gases in any of the above embodiments.
[0060] The membrane sample introduction mass spectrometer provided by this invention obtains the signal value of the dissolved target gas and directly inputs it into a constructed conversion model between signal value and molar number to obtain the molar number of the dissolved target gas. This membrane sample introduction mass spectrometer not only achieves automatic conversion and improves data processing efficiency, but also standardizes the detection process, significantly improving detection efficiency.
[0061] This embodiment also provides a device for determining the molar number of dissolved gases, which is used to implement the above embodiments and preferred embodiments; details already described will not be repeated. As used below, the term "module" can refer to a combination of software and / or hardware that performs a predetermined function. Although the device described in the following embodiments is preferably implemented in software, hardware implementation, or a combination of software and hardware, is also possible and contemplated.
[0062] This embodiment provides a device for determining the molar number of dissolved gases, such as... Figure 2 As shown, it includes: The acquisition module 201 is used to acquire the dissolved target gas signal value output by the membrane sample mass spectrometer; Module 202 is used to construct the conversion model; the conversion model represents the relationship between the signal value and the number of moles. The conversion module 203 is used to input the dissolved target gas signal value into the conversion model to determine the number of moles of the dissolved target gas. Specifically, it is used to fit the reference signal value and the reference number of moles to obtain the conversion model.
[0063] In some alternative implementations, the conversion model is as follows: Where a, b, and c are constants, and n is the number of moles. The value is the dissolved target gas signal, and T is the temperature of the water sample to be tested.
[0064] In some alternative implementations, the building module 202 includes: The sample determination unit is used to determine at least one set of target samples, in which the concentration of the target gas is different in each target sample within the set; The parameter determination unit is used to determine the reference signal value and reference mole number of the target gas in each target sample at different temperatures; The conversion unit is used to determine the conversion model based on the reference signal value and the number of reference moles.
[0065] In some optional embodiments, there are two or more target samples, and the target gas is nitrogen; each target sample includes: synthetic helium containing a first preset concentration of nitrogen, synthetic air containing a second preset concentration of nitrogen, and synthetic nitrogen containing a third preset concentration of nitrogen.
[0066] In some optional implementations, the parameter determination unit is specifically used to: determine that the reference molar number of nitrogen in the synthesized helium is 0; determine the molar volume of the synthesized nitrogen; determine the reference molar number of nitrogen in the synthesized nitrogen based on the molar volume; and determine the reference molar number of nitrogen in the synthesized air based on the reference molar number of nitrogen in the synthesized nitrogen. It is also specifically used to: determine the first signal value of nitrogen in the synthesized helium, the second signal value of nitrogen in the synthesized air, and the third signal value of nitrogen in the synthesized nitrogen in each group of target samples; use the average of the first signals as the reference signal value of nitrogen in the synthesized helium; subtract the first signal value from the second signal value to obtain the reference signal value of nitrogen in the synthesized air; and subtract the first signal value from the third signal value to obtain the reference signal value of nitrogen in the synthesized nitrogen.
[0067] The dissolved gas molar number determination device provided in this embodiment of the invention can execute the dissolved gas molar number determination method provided in any embodiment of the invention, and has the corresponding functional modules and beneficial effects for executing the method. Further functional descriptions of the above modules and units are the same as in the corresponding embodiments described above, and will not be repeated here.
[0068] Although embodiments of the invention have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the invention, and such modifications and variations all fall within the scope defined by the appended claims.
Claims
1. A method for determining the number of moles of dissolved gas, characterized in that, The method includes: Acquire the dissolved target gas signal value output by the membrane injection mass spectrometer; Construct a conversion model; the conversion model characterizes the relationship between signal value and number of moles; The dissolved target gas signal value is input into the conversion model to determine the number of moles of dissolved target gas.
2. The method according to claim 1, characterized in that, The construction and transformation model includes: Identify at least one set of target samples, wherein the concentration of the target gas is different in each of the target samples within the set; Determine the reference signal value and reference molar number of the target gas in each of the target samples at different temperatures; The conversion model is determined based on the reference signal value and the reference number of moles.
3. The method according to claim 2, characterized in that, Determining the conversion model based on the reference signal value and the reference number of moles includes: The conversion model is obtained by fitting the reference signal value and the reference number of moles.
4. The method according to claim 2, characterized in that, The target samples are in two or more groups, and the target gas is nitrogen; each group of the target samples includes: Synthetic helium containing a first preset concentration of nitrogen, synthetic air containing a second preset concentration of nitrogen, and synthetic nitrogen containing a third preset concentration of nitrogen.
5. The method according to claim 4, characterized in that, The first preset concentration is 0.001%; the second preset concentration is 78%; and the third preset concentration is 99.99%.
6. The method according to claim 5, characterized in that, Determining the reference molar number of the target gas in each of the target samples includes: The reference molar number of nitrogen in the synthesized helium was determined to be 0; Determine the molar volume of the synthesized nitrogen gas; based on the molar volume, determine the reference number of nitrogen moles in the synthesized nitrogen gas; The reference molar number of nitrogen in the synthetic air is determined based on the reference molar number of nitrogen in the synthetic nitrogen gas.
7. The method according to claim 5, characterized in that, Determining the reference signal value of the target gas in each of the target samples includes: In each group of target samples, determine the first signal value of nitrogen in the synthesized helium, the second signal value of nitrogen in the synthesized air, and the third signal value of nitrogen in the synthesized nitrogen; use the average of the first signals as the reference signal value of nitrogen in the synthesized helium. Subtract the first signal value from the second signal value to obtain the reference signal value of nitrogen in the synthetic air; Subtracting the first signal value from the third signal value yields the reference signal value of nitrogen in the synthesized nitrogen gas.
8. The method according to claim 1, characterized in that, The conversion model is as follows: ； Where a, b, and c are constants, and n is the number of moles. The value of the dissolved target gas signal is given, and T is the temperature of the water sample to be tested.
9. A device for determining the number of moles of dissolved gas, characterized in that, The device includes: The acquisition module is used to acquire the dissolved target gas signal value output by the membrane sample mass spectrometer; A building module is used to construct a conversion model; the conversion model represents the relationship between signal values and the number of moles. The conversion module is used to input the dissolved target gas signal value into the conversion model to determine the number of moles of dissolved target gas.
10. A membrane sample introduction mass spectrometer, characterized in that, The membrane sample introduction mass spectrometer is applicable to the method for determining the number of moles of dissolved gas as described in any one of claims 1 to 8.