An ion content detection method based on potentiometric titration

Abstract

The application discloses a kind of ion content detection methods based on potentiometric titration method, and the method specifically includes the following steps: S1, the sample to be tested is weighed and dissolved into the solution to be measured and placed in titration cell;S2, titrant is dropped into titration cell by burette;S3, the volume reading of titrant in burette and the potential value of corresponding potential measuring instrument are recorded;S4, the first derivative and second derivative of potential to volume are calculated according to the recorded volume and potential value data, S5, the volume of titrant at stoichiometric point is calculated by interpolation method, the ion content to be measured in the sample to be tested is obtained, and the detection of ion content to be measured is completed.The method of the application improves the potentiometric titration method, realizes unequal volume titrant titration, changes the traditional potentiometric titration method from equal volume titration to equal volume titration or unequal volume titration for detecting ion content, and improves the efficiency of ion content detection.

Description

Technical Field

[0001] This invention belongs to the field of chemical analysis technology, specifically relating to a method for detecting ion content based on potentiometric titration. Background Technology

[0002] Potentiometric titration, also known as the second derivative method, is a method of determining the titration endpoint by measuring the change in potential during titration. Depending on the indicating electrode, potentiometric titration is classified into acid-base titration, redox titration, complexometric titration, and precipitation titration. In acid-base titration, a glass electrode can be used as the indicating electrode; in redox titration, a platinum electrode; in complexometric titration, a mercury electrode; and in precipitation titration, a silver electrode. The measuring instrument includes a burette, titration cell, indicating electrode, reference electrode, stirrer, and an electromotive force measuring instrument, such as a potentiometer or pH meter. The testing principle is as follows: A reference electrode and an indicator electrode are inserted into the solution to form a working cell. As the titrant is added, a continuous chemical reaction occurs, causing changes in the concentration of the analyte ion. Correspondingly, the potential of the indicator electrode changes. Before and after the titration endpoint, the concentration of the analyte ion changes continuously by n orders of magnitude, causing a sudden jump in potential. The volume of titrant added each time and the potential are recorded, and a voltage-volume curve is plotted. The volume at which the slope is maximum is the volume of titrant consumed. Given the concentration and volume of the titrant consumed, the number of moles (amount of substance) of the titrant is calculated. This is then converted to the number of moles of the analyte ion using the coefficients of the chemical reaction equation. By looking up the molecular weight of the analyte ion, the mass of the analyte ion can be obtained, and thus the mass fraction of the analyte ion in the sample can be determined.

[0003] To find the volume at the point of maximum slope on the voltage-volume curve, the quadratic derivative method is commonly used. The derivative is the old name for the second derivative. The principle behind using the quadratic derivative method to calculate the volume at the equivalence point is as follows: the voltage-volume curve (EV curve) is an S-shaped curve. This S-shape trend is initially flat, then becomes steeper, and finally flat again, which means the slope (i.e., steepness) is... The slope of the original function first increases and then decreases; the slope is the derivative. The slope of the original function is the ordinate value of the first derivative, and the slope of the first derivative is the ordinate value of the second derivative. The derivative is the function obtained by differentiating the original function. More specifically, the first derivative is the function obtained by differentiating the original function, and the second derivative is the function obtained by differentiating the first derivative. The derivative is the differential curve. Therefore, the slope of the original function (EV curve) first increases and then decreases, so the slope of the first derivative (EV curve)... The ordinate value of the curve also increases first and then decreases. Previous studies have shown that this first derivative function is a herringbone curve; the trend of this herringbone curve is to increase first and then decrease, which means that the slope (i.e., steepness) is... It is first positive and then becomes negative; and the slope of the first derivative is the ordinate value of the second derivative, so the first derivative ( If the slope of the curve is initially positive and then becomes negative, then the second derivative function ( The vertical coordinate value of the curve is initially positive and then becomes negative. Previous studies have shown that the second derivative function is approximately a straight line near the equivalence point; this straight line intersects the horizontal axis.

[0004] The equivalence point is the titration point at which the analyte ions are exhausted, causing a sudden jump in potential. Therefore, the equivalence point is the inflection point (the point with the steepest slope) of the EV curve, and also the first derivative curve. The maximum point (peak) of the curve, or the second-order derivative curve ( The intersection of the curve and the horizontal axis (i.e., the point where the vertical axis is 0). The volume of the titrant at the potential jump is calculated using interpolation, i.e., the volume of the titrant at the equivalence point, which is the horizontal axis value (volume value) when the vertical axis of the second derivative curve is 0. The problem is transformed into: given the volume before the equivalence point is V1, and the second derivative of the potential with respect to volume before the equivalence point is... The volume after the equivalence point is V2, and the second derivative of the potential with respect to volume after the equivalence point is... Find the volume when the second derivative of the potential with respect to volume is 0. As mentioned before, the second derivative curve near the equivalence point is a straight line m, and the coordinates of the left endpoint L of the line m are (V1, ..., V2). The coordinates of the right endpoint R are (V2, The left endpoint L has a positive ordinate, and the right endpoint R has a negative ordinate. The intersection point A of line m and the x-axis is (Ve, 0). A perpendicular line p is drawn from the left endpoint L of line m to the x-axis, intersecting the x-axis at point B. Then, a line q is drawn parallel to the x-axis from the right endpoint R of line m. The intersection point C of the perpendicular line p and the parallel line q is (V1, 0). Points L, B, and A form triangle LBA, and points L, C, and R form triangle LCR. Therefore, triangles LBA and LCR are similar triangles. According to the principle of similar triangles, we have... Then there is,

[0005] However, when using potentiometric titration to determine the content of analyte ions (or substances) in a test sample, before the equivalence point, the volume of titrant added each time is relatively large, such as 0.5 mL; near the equivalence point, the volume added each time is only 0.10 mL. This may cause the ΔV at the potential jump to be unequal, thus making it impossible to determine the second derivative of potential with respect to volume. The corresponding titrant volume is the original V. i Or V i The two assumed titration points V before and after i-0.5 Vi+0.5 The intermediate value, where i represents the i-th titration point; moreover, during potentiometric titration, the first derivative of the potential with respect to volume is prone to having multiple maximum values, making it impossible to determine the endpoint. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art and provide an ion content detection method based on potentiometric titration. The method of this invention improves the potentiometric titration method by realizing titration with unequal volumes of titrant, thus changing the traditional potentiometric titration method from requiring equal volume titration to detecting ion content by equal or unequal volume titration, thereby improving the efficiency of ion content detection.

[0007] To achieve the above-mentioned objectives, the technical solution provided by this invention patent is as follows:

[0008] A method for detecting ion content based on potentiometric titration, the method specifically includes the following steps:

[0009] S1, Weigh the sample to be tested and dissolve it into a solution to be tested and place it in the titration cell. Place a magnetic stirring rod in the titration cell and place the titration cell on a magnetic stirrer.

[0010] S2, add titrant to the titration cell through the burette, record the initial reading of the titrant volume in the burette, and at the same time turn on the magnetic stirrer and stir the solution in the titration cell with the magnetic stirring rod;

[0011] S3. Measure the change in potential value during titration in the titration cell using a potentiometer. Record the volume reading of the titrant in the burette and the corresponding potential value of the potentiometer after each addition of titrant. As the stoichiometric point approaches, the increase in potential of the potentiometer increases rapidly; at this point, reduce the amount of titrant added to the titration cell each time. When the potential of the potentiometer changes abruptly, the stoichiometric point has passed; continue adding titrant to the titration cell until the potential change of the potentiometer becomes gradual, then stop adding titrant.

[0012] S4. Calculate the first and second derivatives of the potential with respect to volume based on the recorded volume reading of the titrant in the burette and the corresponding potential value of the potential measuring instrument. Obtain the maximum value of the first derivative and two second derivatives near the maximum value of the first derivative. These two second derivatives are adjacent, one is positive and the other is negative. Obtain the two volumes corresponding to these two second derivatives.

[0013] S5. Calculate the volume of the titrant at the stoichiometric point using interpolation. Based on the obtained volume of the titrant at the stoichiometric point, obtain the content of the analyte ion in the test sample, thus completing the detection of the analyte ion content.

[0014] Furthermore, the potential measuring instrument includes a potentiometer, a reference electrode, and an indicating electrode. The potentiometer is connected to the reference electrode and the indicating electrode, respectively, and is used to display the potential change in the titration cell.

[0015] Furthermore, the specific steps for titrating the titration cell using the burette in step S3 are as follows:

[0016] S31, when titrating with equal volumes of titrant added to the titration cell before and after the stoichiometric point, calculate the first and second derivatives of the potential with respect to volume using the ordinary method;

[0017] S32. When titrating with unequal volumes of titrant added to the titration cell before and after the stoichiometric point, the first derivative of the potential with respect to volume is first calculated using the ordinary method. When the maximum value of the first derivative of the potential with respect to volume is not unique, the first and second derivatives of the potential with respect to volume are calculated using the improved method. When the maximum value of the first derivative of the potential with respect to volume is unique, the second derivative of the potential with respect to volume is calculated using the ordinary method.

[0018] Furthermore, the specific formulas for calculating the first and second derivatives of the potential with respect to volume using the ordinary method are as follows:

[0019]

[0020]

[0021] i = 2, 3, 4, ..., n-1,

[0022] in, y′ represents the first derivative of the potential with respect to volume. i+0.5 y is the first derivative of the potential with respect to volume obtained by the ordinary method. i Let x be the potential value at the i-th titration point. i This represents the burette volume reading at the i-th titration point. y″ represents the second derivative of the potential with respect to volume. i Let i represent the second derivative of the potential with respect to volume obtained by the ordinary method, where i represents the i-th set of volume and potential data, and n represents the total n sets of volume and potential data.

[0023] Furthermore, the specific formulas for calculating the first and second derivatives of the potential with respect to volume using the improved method are as follows:

[0024]

[0025]

[0026] i = 2, 3, 4, ..., n-1,

[0027] in, f′(x) represents the first derivative of the potential with respect to volume.i f(x) is the first-order derivative of the potential with respect to volume obtained by the improved method. i Let x be the potential value at the i-th titration point. i This represents the burette volume reading at the i-th titration point. f″(x) represents the second derivative of the potential with respect to volume. i ) represents the second derivative of the potential with respect to volume obtained by the improved method, where i represents the i-th set of volume and potential data; n represents a total of n sets of volume and potential data.

[0028] Furthermore, the specific steps for calculating the first and second derivatives of the potential with respect to volume using the improved method are as follows:

[0029] S41, use Taylor's formula to express the relationship between potential and volume when the volume is near x0.

[0030] Where f(x) is the electric potential and x is the volume;

[0031] S42, treating x1 as x and x2 as x0, according to Taylor's formula in S41 and taking the first three terms of Taylor's formula, we get:

[0032]

[0033] Where, f′(x2)=f 1 (x2), f″(x2)=f 2 (x2);

[0034] Treating x3 as x and x2 as x0, according to Taylor's formula in S41 and taking the first three terms of Taylor's formula, we get:

[0035]

[0036] According to (1) and (2):

[0037]

[0038]

[0039] S44, replace x2 with x in formula S43. i x1 replaced with x i-1 x3 replaced with x i+1 f(x2) replaced by f(x) i ), f(x1) replaced by f(x) i-1 ), f(x3) replaced with f(x) i+1 To obtain the formulas for the first and second derivatives:

[0040]

[0041]

[0042] i = 2, 3, 4, ..., n-1

[0043] Where i: the i-th set of volume and potential data, and n: a total of n sets of volume and potential data.

[0044] Furthermore, in S5, the volume of titrant at the stoichiometric point is the volume of titrant consumed when the second derivative of potential with respect to volume is 0, as specified in the formula:

[0045]

[0046] Among them, V e V0 is the volume of titrant consumed when the second derivative is 0, and V1 is the volume of titrant before the stoichiometric point. V2 is the second derivative of the potential with respect to volume before the stoichiometric point, and V2 is the volume of titrant after the stoichiometric point. V0 is the second derivative of the potential with respect to volume after the stoichiometric point, and V0 is the initial reading of the titrant volume in the burette.

[0047] Furthermore, in step S5, the content of the analyte ion in the test sample is the percentage of the analyte ion content to the mass of the test sample, and the specific formula is as follows:

[0048]

[0049] Where, ω x C represents the mass fraction of the analyte ion x in the test sample. T V represents the concentration of the titrant. e M is the volume of titrant consumed. x m is the molecular weight of the ion to be measured. 试样 Let be the mass of the sample. The chemical reaction equation between the analyte ion x and the titrant T is ax + bT = cA + dB.

[0050] Based on the above technical solution, the ion content detection method based on potentiometric titration of this invention has achieved the following technical advantages through practical application:

[0051] 1. The present invention provides an ion content detection method based on potentiometric titration. By improving the potentiometric titration method, it enables titration with unequal volumes of titrant, changing the traditional potentiometric titration method from requiring equal volume titration to enabling the detection of ion content with either equal or unequal volume titration, thereby improving the efficiency of ion content detection.

[0052] 2. This invention provides an ion content detection method based on potentiometric titration. Through an improved method, it addresses the problem in conventional potentiometric titration where the maximum value of the first derivative is not unique and the titration endpoint cannot be determined. It also solves the problem in conventional potentiometric titration where the volume corresponding to the second derivative cannot be determined when titrating unequal volumes. This improves the accuracy of ion detection, reduces the number of experimental repetitions, and increases detection efficiency.

[0053] 3. The potentiometric titration method in the ion content detection method based on potentiometric titration of this invention is applicable to all types of potentiometric titration, including acid-base titration, redox titration, complexometric titration and precipitation titration, and is suitable for the determination of different ion contents, thus improving the scope of application.

[0054] 4. This invention provides a potentiometric titration-based method for detecting ion content, which can shorten titration time and ensure successful sample testing on the first attempt. Because the volume of titrant added each time decreases progressively, the volume of titrant added at the titration point before the equivalence point is often greater than the volume added at the titration point after the equivalence point. Conventional methods cannot determine the second derivative of potential with respect to volume. The corresponding titrant volume is the original V. i Or V i The two assumed titration points V before and after i-0.5 V i+0.5 The intermediate value, where i represents the i-th titration point, requires re-titration to ensure that the volume of titrant added at the titration point before and after the equivalence point is the same. Since the mass of each sample varies, the volume at the equivalence point will also differ, making it difficult to ensure that the volume of titrant added before and after the equivalence point is the same. To ensure the same volume of titrant added before and after the equivalence point, equal-volume titration must begin far from the equivalence point, and to ensure the accuracy of the equivalence point, a very small amount of titrant needs to be added each time near the equivalence point, resulting in a long titration time. The improved method allows for adding a larger amount of titrant initially, and then adding a smaller amount when the potential changes significantly. If the volume of titrant at the titration point before and after the equivalence point is not properly controlled, the second derivative of potential with respect to volume can be precisely calculated. The corresponding titrant volume is the original V. i No need for retesting; the improved method can achieve success on the first try. Attached Figure Description

[0055] Figure 1 This is a diagram of the potentiometric titration apparatus used in the ion content detection method based on potentiometric titration of the present invention. Detailed Implementation

[0056] To make the objectives, technical solutions, and advantages of this invention clearer, the invention is described below with reference to the accompanying drawings and specific examples. However, it should be understood that these descriptions are merely exemplary and not intended to limit the scope of the invention. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concept of the invention.

[0057] Examples 1-3 of the present invention are precipitation titrations, Example 4 is an acid-base titration, Example 5 is a complexation titration, and Example 6 is a redox titration.

[0058] The potentiometric titration method of this invention for ion content detection is applicable to all types of potentiometric titration, including acid-base titration, redox titration, complexometric titration, and precipitation titration. It is suitable for determining the content of different ions and has a wide range of applications. The unequal volume titration and improved method of this invention for solving ion content are applicable to ion content detection performed by acid-base titration, redox titration, complexometric titration, and precipitation titration.

[0059] The equal-volume titration mentioned does not mean that the titration is performed with equal volume throughout the entire titration process, but only around the stoichiometric point.

[0060] Example 1

[0061] The chloride ion content in concrete raw material admixtures is tested using the conventional method.

[0062] A chloride ion selective electrode was used as the indicator electrode, and a saturated calomel electrode was used as the reference electrode.

[0063] The specific steps are as follows: Weigh 4.6942g of the additive and put it into titration cell 4. Add 200mL of deionized water and dissolve it. Then add 4mL of nitric acid (1+1) (the volume ratio of concentrated nitric acid (68wt%) to deionized water is 1:1). Then add 10mL of 0.1mol / L NaCl standard solution. Put 0.1mol / L silver nitrate solution into burette 1 and titrate it into titration cell 4. Use a potential measuring instrument to measure the potential change of titration cell 4.

[0064] Add titrant to titration cell 4 through burette 1, record the initial reading of titrant volume in burette 1, and simultaneously turn on the magnetic stirrer and stir the solution in titration cell 4 with magnetic stirring rod 5.

[0065] The change in potential value during titration in titration cell 4 is measured using a potentiometer. Unequal volumes of titrant are added to titration cell 4 each time, and the volume reading of the titrant in burette 1 and the corresponding potential value of the potentiometer are recorded. As the stoichiometric point approaches, the increase in potential of the potentiometer accelerates, so the amount of titrant added to titration cell 4 each time from burette 1 is reduced. Before and after the stoichiometric point, it is not necessary to deliberately add equal volumes of titrant to titration cell 4 each time. When the potential of the potentiometer changes abruptly, the stoichiometric point has passed. At this point, unequal volumes of titrant are continued to be added to titration cell 4 until the potential change of the potentiometer becomes gradual, at which point the addition of titrant is stopped.

[0066] The first and second derivatives of potential with respect to volume are calculated using the ordinary method; the volume of titrant at the stoichiometric point is calculated by interpolation; and the content of the analyte ion in the test sample is obtained based on the volume of titrant at the stoichiometric point, thus completing the detection of the analyte ion content.

[0067] Blank experiment: The blank sample was 200 mL of deionized water, 4 mL of nitric acid (1+1) was added, 10 mL of 0.1 mol / L NaCl standard solution was added, and titrated with 0.1 mol / L silver nitrate solution.

[0068] Table 1 shows the potentiometric titration records for chloride ion detection with admixtures (ordinary method unequal volume titration).

[0069]

[0070]

[0071] From Table 1, the maximum value of the first derivative is y′. 23.5 =380, but it's unclear whether the data in the sixth column should be the average of the data in the fourth column or directly equal to the data in the second column. Specifically, is the volume corresponding to the second derivative of 866.67 at the titration point before the equivalence point directly the volume of the 23rd titration point in this row (30.5), or the average of the volumes of the 22.5th and 23.5th titration points before and after 866.67 (i.e., the average of 30.25 and 30.55, which is 30.4)? The volume corresponding to the second derivative -2100 at the equivalence point is equal to either the volume of the 24th titration point in this row (30.6) or the average of the volumes of the 23.5th and 24.5th titration points before and after -2100 (30.55 and 30.65 respectively). Therefore, we can determine that the volume corresponding to the second derivative -2100 is 30.6, but we cannot determine whether the volume corresponding to the second derivative 866.67 is 30.5 or 30.4.

[0072] An improved method was used to test the chloride ion content in the raw material admixtures of concrete.

[0073] The specific steps are as follows: Weigh 4.6942g of the additive and put it into titration cell 4. Add 200mL of deionized water and dissolve it. Then add 4mL of nitric acid (1+1) (the volume ratio of concentrated nitric acid (68wt%) to deionized water is 1:1). Then add 10mL of 0.1mol / L NaCl standard solution. Put 0.1mol / L silver nitrate solution into burette 1 and titrate it into titration cell 4. Use a potential measuring instrument to measure the potential change of titration cell 4.

[0074] Add titrant to titration cell 4 through burette 1, record the initial reading of titrant volume in burette 1, and simultaneously turn on the magnetic stirrer and stir the solution in titration cell 4 with magnetic stirring rod 5.

[0075] The change in potential value during titration in titration cell 4 is measured using a potentiometer. Before and after the stoichiometric point, it is not necessary to add equal volumes of titrant to titration cell 4 each time. The volume reading of the titrant in burette 1 and the corresponding potential value of the potentiometer are recorded. As the stoichiometric point approaches, the increase in potential of the potentiometer accelerates. The amount of titrant added to titration cell 4 each time from burette 1 is reduced, and more titrant is added to titration cell 4. When the potential of the potentiometer changes abruptly, the stoichiometric point has passed. At this point, titrant is added to titration cell 4 in unequal volumes until the potential change of the potentiometer becomes gradual, at which point the addition of titrant is stopped.

[0076] The first and second derivatives of potential with respect to volume are calculated using an improved method; the volume of titrant at the stoichiometric point is calculated by interpolation; and the content of the analyte ion in the test sample is obtained based on the volume of titrant at the stoichiometric point, thus completing the detection of the analyte ion content.

[0077] Blank experiment: The blank sample was 200 mL of deionized water, 4 mL of nitric acid (1+1) was added, 10 mL of 0.1 mol / L NaCl standard solution was added, and titrated with 0.1 mol / L silver nitrate solution.

[0078] Table 2 shows the potentiometric titration records for chloride ion detection with admixtures (modified method, unequal volume titration).

[0079]

[0080]

[0081]

[0082] From Tables 1 and 2, we can see that the second derivatives of the ordinary method and the improved method are exactly the same, but the corresponding x is different. The ordinary method uses x as a given value. 1.5 x2.5 y′ 1.5 y′ 2.5 ,use express The second derivative should correspond to x. 1.5 x 2.5 The intermediate value is still the original x2. Neither Appendix A of standard GB / T176-2017 nor Appendix A of GB / T 8077-2012 provides this value. It's worth noting that these two standards specify that the x corresponding to the second derivative y″2 is the original x2, only when Δx (i.e., x2-x1) is equal. They do not specify when Δx is unequal, and it's easy to assume that the x corresponding to y″2 is x2. 1.5 x 2.5 The intermediate value; the improved method is to use the given x1, x2, x3, f(x1), f(x2), f(x3) as the intermediate value; express The x corresponding to this second derivative is the original x². The ordinary method finds y″², y″³, and y″⁴, but the corresponding x is unknown. Still using the original x2, x3, and x4, the improved method finds f″(x2), f″(x3), and f″(x4), corresponding to the original x2, x3, and x4. The improved method proves that the x corresponding to y″2 in the ordinary method is the original x2. It is worth noting that listing the data... It can be known that x 2.5 It is the intermediate value between x2 and x3, as defined; but x2 is not x 1.5 and x 2.5 The middle value, because x2 is not the middle value of x1 and x3.

[0083] We prove, through an improved method, that the x corresponding to y″2 in the ordinary method is the original x2.

[0084]

[0085] Comparing the ordinary method and the improved method based on this formula: the second derivatives of the ordinary method and the improved method are exactly the same, but the corresponding x is different. The ordinary method assumes x is known. 1.5 x 2.5 y′ 1.5 y′ 2.5 ,use express The second derivative should correspond to x. 1.5 x 2.5The intermediate value is still the original x2. Neither Appendix A of standard GB / T176-2017 nor Appendix A of GB / T 8077-2012 provides this value. It's worth noting that these two standards specify that the x corresponding to the second derivative y″2 is the original x2, only when Δx (i.e., x2-x1) is equal. They do not specify when Δx is unequal, and it's easy to assume that the x corresponding to y″2 is x2. 1.5 x 2.5 The intermediate value. The improved method is to use the given x1, x2, x3, f(x1), f(x2), and f(x3) to find the intermediate value. express The x corresponding to this second derivative is the original x². The ordinary method finds y″², y″³, and y″⁴, but the corresponding x is unknown. We still use the original x2, x3, and x4. The improved method finds f″(x2), f″(x3), and f″(x4), and the corresponding x is the original x2, x3, and x4. We prove through the improved method that the x corresponding to y″2 in the ordinary method is the original x2. It is worth noting that listing the data... It can be known that x 2.5 It is the intermediate value between x2 and x3, as defined; but x2 is not x 1.5 and x 2.5 The middle value, because x2 is not x 1.5 and x 2.5 The median value.

[0086] Comparing the similarities and differences between the first derivative of the ordinary method and the first derivative of the improved method, f(x) is the potential representation of the improved method, and y is the potential representation of the ordinary method. We transform f(x) into a form containing y.

[0087]

[0088] Analysis of the meaning of this formula: When Δx is equal (x3-x2=x2-x1), f′(x2) is y′ 2.5 and y′ 1.5 The average value. When Δx is not equal, if x2 is closer to x3 but not closer to x1, then That is, y′ 1.5 It has a lower weight, y′ 2.5 It has a higher weight. Comparing the ordinary method and the improved method based on this formula: the ordinary method is based on the given x1, x2, y1, y2, and uses... express The x corresponding to this first derivative is an artificially defined x. 1.5 , That is, x 1.5 It is the intermediate value of x1 and x2, and is defined arbitrarily. The improved method is based on the given values ​​of x1, x2, x3, f(x1), f(x2), and f(x3), using... express The x corresponding to this first derivative is the original x². The ordinary method calculates y′. 1.5 y′ 2.5 y′ 3.5 The corresponding x is x 1.5 x 2.5 x 3.5 The improved method finds f′(x2), f′(x3), and f′(x4), where x is x2, x3, and x4 respectively.

[0089] The improved quadratic derivative method yields a second derivative of 866.67, corresponding to x = 30.5, which is the original value of x. The ordinary quadratic derivative method might mistakenly assume that x corresponds to 30.4, which is the midpoint between 30.25 and 30.55. Here, 30.25 is the midpoint between the original values ​​30 and 30.5, and 30.55 is the midpoint between the original values ​​30.5 and 30.6. In other words, the x corresponding to the second derivative of 866.67 obtained by the ordinary quadratic derivative method is the midpoint of the midpoints of the original values. When calculating y″2, the midpoint is used. The x corresponding to y″2 is x2, not x. 1.5 and x 2.5 The median value, because the curve y″ is at x 1.5 and x 2.5 The slope on the left side of the middle value is not necessarily equal to the slope on the right side; that is, x2 is not necessarily x. 1.5 and x 2.5 The intermediate value of y″2, where x2 is the most accurate value under the current conditions. In fact, x2 is x 1.5 and x 2.5 An approximation of the intermediate value.

[0090] Table 3 shows the potentiometric titration records for chloride ion detection with admixtures (ordinary method unequal volume titration; the sixth column V is the average value of the fourth column V).

[0091]

[0092]

[0093] The volume represented in the sixth column of Table 3 is calculated from the average of the fourth column. Based on Table 2 (Improved Method) and Table 3 (Ordinary Method), the equivalence point V of the ordinary method is: V = 30.40 + (30.60 - 30.40) × 866.67 / (866.67 - (-2100)) - 18.10 = 12.36 mL. The improved method determines that x corresponds to y″2 as x2 (see Table 2), therefore the equivalence point V of the improved method is: V = 30.50 + (30.60 - 30.50) × 866.67 / (866.67 - (-2100)) - 18.10 = 12.43 mL. The blank (200 mL deionized water + 4 mL nitric acid (1+1) + 10 mL 0.1 mol / L...) (NaCl standard solution) Experiment V0 = 9.85 mL. Ordinary potentiometric titration: Chloride ion content W(Cl-) = C(AgNO3)(V-V0) / 1000×35.45 / m×100 = 0.1×(12.36-9.85) / 1000×35.45 / 4.6942×100 = 0.190%; Improved potentiometric titration: W(Cl-) = C(AgNO3)(V-V0) / 1000×35.45 / m×100 = 0.1×(12.43-9.85) / 1000×35.45 / 4.6942×100 = 0.195%; Therefore, the relative error of chloride ion detection between the ordinary method and the improved method is (0.190-0.195) / 0.195×100 = -2.71%.

[0094] This example illustrates that in the conventional method, the volume of titrant added decreases with each drop as the test approaches the stoichiometric point, leading to test failure and requiring retesting. The improved method, however, allows for a successful test on the first attempt. In the ordinary method, near the stoichiometric point (maximum first derivative 380mV), the two second derivatives (one positive, one negative) are 866.67 and -2100. 866.67 is obtained from 30.25, 30.55, 120, and 380, calculated using the formula (380-120) / (30.55-30.25) = 866.67. Specifically, 30.25 and 120 are obtained from 30, 30.5, 188, and 248, calculated using the formula (30+30.5) / 2 = 30.25 and (248-188) / (30.5-30) = 120. Similarly, 30.55 and 380 are obtained from 30.5, 30.6, 248, and 286, calculated using the formula (30.5+30.6). (286-248) / (30.6-30.5) = 380; similarly, -2100 is obtained from 30.55, 30.65, 380, and 170, and the calculation formula is (170-380) / (30.65-30.55) = -2100, where 30.65 and 170 are obtained from 30.6, 30.7, 286, and 303, and the calculation formula is (30.6+30.7) / 2 = 30.65, (303-286) / (30.7-30.6) = 170; therefore, the titration points near the stoichiometric point are (30, 188), (30.5, 248), (30.6, 286), and (30.7, 303). In the ordinary method, near the stoichiometric point, the volume of titrant added each time changes from 0.5 mL to 0.1 mL. The volume corresponding to the second derivative 866.67 is unknown—whether it is 30.40 (the midpoint between 30.25 and 30.55) or 30.5 (directly the original data in the second column, see Table 1). A new sample needs to be taken for potentiometric titration. However, the mass of the sample taken each time is not necessarily exactly the same, so the volume of titrant consumed is not equal. It is impossible to predict the volume of titrant at the potential jump. It is possible that the volume of titrant added at the potential jump will still be unequal in the second titration.

[0095] This example illustrates that when the volume (ΔV) of the titrant is not equal in each titration near the equivalence point, ordinary potentiometric titration cannot determine the second derivative of potential with respect to volume. What is the corresponding V? The improved potentiometric titration method can accurately determine the second derivative of potential with respect to volume. The corresponding V value expands the traditional potentiometric titration method from requiring equal-interval titration to allowing for both equal-interval and unequal-interval titration.

[0096] Example 2

[0097] Blank experiment for detecting chloride ion content in concrete admixtures using the conventional method.

[0098] A chloride ion selective electrode was used as the indicator electrode, and a saturated calomel electrode was used as the reference electrode.

[0099] According to GB / T 8077-2012, the chloride ion content in admixtures is relatively low. In order to improve the detection sensitivity, a known amount of chloride ions is added to the admixture sample, and this amount of chloride ions is subtracted after detection. The detection test is to add water, then nitric acid, and finally sodium chloride solution to the admixture sample. The blank test is to add water, nitric acid, and then sodium chloride solution. This embodiment only performs the blank test.

[0100] The specific steps are as follows: Weigh 0g of the additive and put it into titration cell 4, add 200mL of deionized water, add 4mL of nitric acid (1+1) (the volume ratio of concentrated nitric acid (68wt%) to deionized water is 1:1), then add 10mL of 0.1mol / L NaCl standard solution, put 0.1mol / L silver nitrate solution into burette 1 and titrate it into titration cell 4, and use a potential measuring instrument to measure the potential change of titration cell 4;

[0101] Add titrant to titration cell 4 through burette 1, record the initial reading of titrant volume in burette 1, and simultaneously turn on the magnetic stirrer and stir the solution in titration cell 4 with magnetic stirring rod 5.

[0102] The change in potential value during titration in titration cell 4 is measured using a potentiometer. Before and after the stoichiometric point, an equal volume of titrant is added to titration cell 4 each time, and the volume reading of the titrant in burette 1 and the corresponding potential value of the potentiometer are recorded. As the stoichiometric point approaches, the increase in potential of the potentiometer accelerates, so the amount of titrant added to titration cell 4 each time from burette 1 is reduced, and an equal volume of titrant is added to titration cell 4. When the potential of the potentiometer changes abruptly, the stoichiometric point has passed. At this point, unequal volumes of titrant are added to titration cell 4 until the potential change of the potentiometer becomes gradual, at which point the addition of titrant is stopped.

[0103] The first and second derivatives of the potential with respect to volume are calculated using the ordinary method; the volume of the titrant at the stoichiometric point is calculated by interpolation; based on the volume of the titrant at the stoichiometric point obtained in the blank experiment, the content of the analyte ion in the test sample is obtained (this step has been exemplified in Example 1; in this example, only the volume at the equivalence point of the blank titration is obtained, and the content of the analyte ion is not calculated), thus completing the detection of the content of the analyte ion.

[0104] Table 4 shows the blank potentiometric titration records for chloride ion detection with admixtures (ordinary method, equal volume titration).

[0105]

[0106] From Table 4, the volume at the equivalence point of the ordinary method is: V = 38.8 + (38.9 - 38.8) × 3500 / (3500 - (-800)) - 29 = 9.88 mL.

[0107] Blank experiment for detecting chloride ion content in concrete raw material admixtures using an improved method.

[0108] The specific steps are as follows: Weigh 0g of the additive and put it into titration cell 4, add 200mL of deionized water, add 4mL of nitric acid (1+1) (the volume ratio of concentrated nitric acid (68wt%) to deionized water is 1:1), then add 10mL of 0.1mol / L NaCl standard solution, put 0.1mol / L silver nitrate solution into burette 1 and titrate it into titration cell 4, and use a potential measuring instrument to measure the potential change of titration cell 4;

[0109] Add titrant to titration cell 4 through burette 1, record the initial reading of titrant volume in burette 1, and simultaneously turn on the magnetic stirrer and stir the solution in titration cell 4 with magnetic stirring rod 5.

[0110] The change in potential value during titration in titration cell 4 is measured using a potentiometer. Before and after the stoichiometric point, an equal volume of titrant is added to titration cell 4 each time, and the volume reading of the titrant in burette 1 and the corresponding potential value of the potentiometer are recorded. As the stoichiometric point approaches, the increase in potential of the potentiometer accelerates; therefore, the amount of titrant added to titration cell 4 each time from burette 1 is reduced, and more titrant is added to titration cell 4. When the potential of the potentiometer changes abruptly, the stoichiometric point has passed; at this point, an equal volume of titrant is continued to be added to titration cell 4 until the potential change of the potentiometer becomes gradual, at which point the addition of titrant is stopped.

[0111] The first and second derivatives of the potential with respect to volume are calculated using an improved method; the volume of the titrant at the stoichiometric point is calculated by interpolation; based on the volume of the titrant at the stoichiometric point obtained in the blank experiment, the content of the analyte ion in the test sample is obtained (this step has been illustrated in Example 1; in this example, only the volume at the equivalence point of the blank titration is obtained, and the content of the analyte ion is not calculated), thus completing the detection of the content of the analyte ion.

[0112] Table 5 shows the potentiometric titration records for chloride ion detection with admixtures (modified method, equal volume titration).

[0113]

[0114]

[0115] From Table 5, the volume at the equivalence point of the improved method is: V = 38.8 + (38.9 - 38.8) × 3500 / (3500 - (-800)) - 29 = 9.88 mL.

[0116] The fact that the equivalence point volumes obtained from Tables 4 and 5 are equal indicates that the results obtained by the ordinary method and the improved method are the same when titrating with equal volumes.

[0117] Example 3

[0118] Determination of acid-soluble chloride ion content in hardened concrete using conventional methods:

[0119] A chloride ion selective electrode was used as the indicator electrode, and a saturated calomel electrode was used as the reference electrode.

[0120] The specific steps are as follows: Sampling: Take three samples of no less than 200g each from the hardened concrete, remove the stones from the samples, crush the samples and mix them evenly, grind them until they all pass through a 0.16mm sieve, place them in an oven at 105℃±5℃ for 2 hours, and then place them in a desiccator to cool to room temperature.

[0121] Weighing and processing the sample: Weigh 20.00g of finely ground mortar powder, accurate to 0.01g, place it in a 250mL Erlenmeyer flask, add 100mL of (1+7) nitric acid solution, stopper the flask, shake vigorously for 1-2 minutes, soak for 24 hours, and then filter with rapid quantitative filter paper to obtain the filtrate; shake the Erlenmeyer flask during the process.

[0122] Test: Transfer 20 mL of filtrate, add 100 mL of distilled water, then add 20 mL of starch solution (10 g / L) and place it in titration cell 4, and titrate with 0.01 mol / L silver nitrate standard solution;

[0123] Add titrant to titration cell 4 through burette 1, record the initial reading of titrant volume in burette 1, and simultaneously turn on the magnetic stirrer and stir the solution in titration cell 4 with magnetic stirring rod 5.

[0124] The change in potential value during titration in titration cell 4 is measured using a potentiometer. Before and after the stoichiometric point, an equal volume of titrant is added to titration cell 4 each time, and the volume reading of the titrant in burette 1 and the corresponding potential value of the potentiometer are recorded. As the stoichiometric point approaches, the increase in potential of the potentiometer accelerates; therefore, the amount of titrant added to titration cell 4 each time from burette 1 is reduced, and more titrant is added to titration cell 4. When the potential of the potentiometer changes abruptly, the stoichiometric point has passed; at this point, an equal volume of titrant is continued to be added to titration cell 4 until the potential change of the potentiometer becomes gradual, at which point the addition of titrant is stopped.

[0125] The first and second derivatives of potential with respect to volume are calculated using the ordinary method; the volume of titrant at the stoichiometric point is calculated by interpolation; and the content of the analyte ion in the test sample is obtained based on the volume of titrant at the stoichiometric point, thus completing the detection of the analyte ion content.

[0126] Blank experiment: The blank sample was 100 mL of deionized water, 20 mL of nitric acid (1+7) was added, 20 mL of starch solution (10 g / L) was added, and titrated with 0.01 mol / L silver nitrate solution.

[0127] Table 6 shows the potentiometric titration records for detecting acid-soluble chloride ions in hardened concrete (ordinary method, equal volume titration).

[0128]

[0129]

[0130] As shown in Table 6, the potential jump during the ordinary titration process is not obvious, and the first derivative has multiple maximum values, making it impossible to determine the endpoint.

[0131] An improved method was used to detect the acid-soluble chloride ion content in hardened concrete.

[0132] The specific steps are as follows: Sampling: Take three samples of no less than 200g each from the hardened concrete, remove the stones from the samples, crush the samples and mix them evenly, grind them until they all pass through a 0.16mm sieve, place them in an oven at 105℃±5℃ for 2 hours, and then place them in a desiccator to cool to room temperature.

[0133] Weighing and processing the sample: Weigh 20.00g of finely ground mortar powder, accurate to 0.01g, place it in a 250mL Erlenmeyer flask, add 100mL of (1+7) nitric acid solution, stopper the flask, shake vigorously for 1-2 minutes, soak for 24 hours, and then filter with rapid quantitative filter paper to obtain the filtrate; shake the Erlenmeyer flask during the process.

[0134] Test: Transfer 20 mL of filtrate, add 100 mL of distilled water, then add 20 mL of starch solution (10 g / L) and place it in titration cell 4, and titrate with 0.01 mol / L silver nitrate standard solution;

[0135] Add titrant to titration cell 4 through burette 1, record the initial reading of titrant volume in burette 1, and simultaneously turn on the magnetic stirrer and stir the solution in titration cell 4 with magnetic stirring rod 5.

[0136] The change in potential value during titration in titration cell 4 is measured using a potentiometer. Before and after the stoichiometric point, an equal volume of titrant is added to titration cell 4 each time, and the volume reading of the titrant in burette 1 and the corresponding potential value of the potentiometer are recorded. As the stoichiometric point approaches, the increase in potential of the potentiometer accelerates; therefore, the amount of titrant added to titration cell 4 each time from burette 1 is reduced, and more titrant is added to titration cell 4. When the potential of the potentiometer changes abruptly, the stoichiometric point has passed; at this point, an equal volume of titrant is continued to be added to titration cell 4 until the potential change of the potentiometer becomes gradual, at which point the addition of titrant is stopped.

[0137] The first and second derivatives of potential with respect to volume are calculated using an improved method; the volume of titrant at the stoichiometric point is calculated by interpolation; and the content of the analyte ion in the test sample is obtained based on the volume of titrant at the stoichiometric point, thus completing the detection of the analyte ion content.

[0138] Blank experiment: The blank sample was 100 mL of deionized water, 20 mL of nitric acid (1+7) was added, 20 mL of starch solution (10 g / L) was added, and titrated with 0.01 mol / L silver nitrate solution.

[0139] Table 7 shows the potentiometric titration records for detecting acid-soluble chloride ions in hardened concrete (modified method, equal volume titration).

[0140]

[0141]

[0142] Improved method: Equivalence point V = 48.90 - 43.00 = 5.90 mL. The volume of titrant consumed in the blank experiment (20 mL nitric acid (1+7) + 20 mL starch solution (10 g / L) + 100 mL deionized water) was measured to be V0 = 1.45 mL. Percentage of chloride ions in the mortar mass:

[0143]

[0144] Concrete mix proportion (kg / m³) 3 ): Water = 175, Cement = 230, Mineral powder = 70, Fly ash = 50, Sand = 800; Based on the calculated percentage of chloride ions in the mortar mass, calculate the percentage of chloride ions in the cementitious material mass:

[0145]

[0146] The purpose of calculating the percentage of chloride ions in the mass of cementitious materials is to provide a unified reference for comparison, as specified in standard JGJ / T 322-2013, which uses the percentage of chloride ions in the mass of cementitious materials to represent the acid-soluble chloride ion content of hardened concrete.

[0147] This example illustrates that the conventional potentiometric titration method cannot determine the endpoint, while the improved potentiometric titration method has a unique endpoint.

[0148] Example 4

[0149] Determination of the effective content of the antioxidant ethoxyquinoline in feed using the conventional method.

[0150] The original potentiometric titration data were extracted from the paper "Determination of Ethoxyquinoline Content in Powder by Potentiometric Titration - Lin Lishan". Sample processing methods followed the group standard "Mixed Feed Additive Ethoxyquinoline (Powder)" (TCFIAS 3011-2023). As stated in section 6.2.1 of TCFIAS 3011-2023, the titration of ethoxyquinoline with perchloric acid is a neutralization reaction, i.e., acid-base neutralization titration. A glass electrode was used as the indicator electrode, and a saturated calomel electrode as the reference electrode.

[0151] The specific steps are as follows: Weighing and processing the sample: Accurately weigh 0.2111g of ethoxyquinoline powder sample, accurate to 0.0001g, place it in titration cell 4 (e.g., a 100mL beaker), add 5mL of glacial acetic acid (analytical grade), and add 2mL of acetic anhydride (analytical grade) to titration cell 4;

[0152] Test: Add 0.1 mol / L perchloric acid standard solution to burette 1 for titration;

[0153] Add titrant to titration cell 4 through burette 1, record the initial reading of titrant volume in burette 1, and simultaneously turn on the magnetic stirrer and stir the solution in titration cell 4 with magnetic stirring rod 5.

[0154] The change in potential value during titration in titration cell 4 is measured using a potentiometer. Before and after the stoichiometric point, an equal volume of titrant is added to titration cell 4 each time, and the volume reading of the titrant in burette 1 and the corresponding potential value of the potentiometer are recorded. As the stoichiometric point approaches, the increase in potential of the potentiometer accelerates; therefore, the amount of titrant added to titration cell 4 each time from burette 1 is reduced, and more titrant is added to titration cell 4. When the potential of the potentiometer changes abruptly, the stoichiometric point has passed; at this point, an equal volume of titrant is continued to be added to titration cell 4 until the potential change of the potentiometer becomes gradual, at which point the addition of titrant is stopped.

[0155] The first and second derivatives of potential with respect to volume are calculated using the ordinary method; the volume of titrant at the stoichiometric point is calculated by interpolation; and the content of the analyte ion in the test sample is obtained based on the volume of titrant at the stoichiometric point, thus completing the detection of the analyte ion content.

[0156] Table 8 shows the potentiometric titration records for detecting the effective content of the antioxidant ethoxyquinoline in feed (ordinary method, equal volume titration).

[0157]

[0158]

[0159] Standard method: Equivalence point V = 5.00 + (5.10 - 5.00) × (800 - 0) / (800 - (-500)) - 0.00 = 5.06 mL. Percentage of effective content of ethoxyquinoline in the sample by mass:

[0160]

[0161] Where ω is the ethoxyquinoline content (%), c is the concentration of the perchloric acid standard titration solution (mol / L), V is the volume of perchloric acid standard solution consumed by sample V (mL), and M is the ethoxyquinoline content (C0). 14 H 19 The molar mass (g / mol) of NO is given by m, where m is the mass (g) of the sample.

[0162] Determination of the effective content of the antioxidant ethoxyquinoline in feed using the conventional method.

[0163] The original potentiometric titration data were taken from the paper "Determination of Ethoxyquinoline Powder Content by Potentiometric Titration_Lin Lishan". In order to achieve unequal volume titration before and after the stoichiometric point, the data of the three titration points of 4.70, 4.80 and 4.90 were deleted. The sample processing method refers to the group standard "Mixed Feed Additive Ethoxyquinoline (Powder)" (TCFIAS 3011-2023).

[0164] The specific steps are as follows: Weighing and processing the sample: Accurately weigh 0.2111g of ethoxyquinoline powder sample, accurate to 0.0001g, place it in titration cell 4 (e.g., a 100mL beaker), add 5mL of glacial acetic acid (analytical grade), and add 2mL of acetic anhydride (analytical grade) to titration cell 4;

[0165] Test: Add 0.1 mol / L perchloric acid standard solution to burette 1 for titration;

[0166] Add titrant to titration cell 4 through burette 1, record the initial reading of titrant volume in burette 1, and simultaneously turn on the magnetic stirrer and stir the solution in titration cell 4 with magnetic stirring rod 5.

[0167] The change in potential value during titration in titration cell 4 is measured using a potentiometer. Before and after the stoichiometric point, it is not necessary to add an equal volume of titrant to titration cell 4 each time; the volume reading of the titrant in burette 1 and the corresponding potential value of the potentiometer are recorded. As the stoichiometric point approaches, the increase in potential of the potentiometer accelerates; therefore, the amount of titrant added to titration cell 4 each time from burette 1 is reduced, and more titrant is added to titration cell 4. When the potential of the potentiometer changes abruptly, the stoichiometric point has passed; at this point, an equal volume of titrant is added to titration cell 4 until the potential change of the potentiometer becomes gradual, at which point the addition of titrant is stopped.

[0168] The first and second derivatives of potential with respect to volume are calculated using the ordinary method; the volume of titrant at the stoichiometric point is calculated by interpolation; and the content of the analyte ion in the test sample is obtained based on the volume of titrant at the stoichiometric point, thus completing the detection of the analyte ion content.

[0169] Table 9 shows the potentiometric titration records for detecting the effective content of the antioxidant ethoxyquinoline in feed (ordinary method, unequal volume titration).

[0170]

[0171]

[0172] Ordinary method: Equivalence point V = 4.93 + (5.10 - 4.93) × (790 - 0) / (790 - (-500)) - 0.00 = 5.03 mL. Percentage of effective content of ethoxyquinoline in the sample by mass:

[0173]

[0174] Where ω is the ethoxyquinoline content (%), c is the concentration of the perchloric acid standard titration solution (mol / L), V is the volume of perchloric acid standard solution consumed by the sample (mL), and M is the ethoxyquinoline content (C0). 14 H 19 The molar mass (g / mol) of NO is given by m, where m is the mass (g) of the sample.

[0175] Determination of the effective content of the antioxidant ethoxyquinoline in feed using an improved method.

[0176] The original potentiometric titration data were taken from the paper "Determination of Ethoxyquinoline Powder Content by Potentiometric Titration_Lin Lishan". In order to achieve unequal volume titration before and after the stoichiometric point, the data of the three titration points of 4.70, 4.80 and 4.90 were deleted. The sample processing method refers to the group standard "Mixed Feed Additive Ethoxyquinoline (Powder)" (TCFIAS 3011-2023).

[0177] The specific steps are as follows: Weighing and processing the sample: Accurately weigh 0.2111g of ethoxyquinoline powder sample, accurate to 0.0001g, place it in titration cell 4 (e.g., a 100mL beaker), add 5mL of glacial acetic acid (analytical grade), and add 2mL of acetic anhydride (analytical grade) to titration cell 4;

[0178] Test: Add 0.1 mol / L perchloric acid standard solution to burette 1 for titration;

[0179] Add titrant to titration cell 4 through burette 1, record the initial reading of titrant volume in burette 1, and simultaneously turn on the magnetic stirrer and stir the solution in titration cell 4 with magnetic stirring rod 5.

[0180] The change in potential value during titration in titration cell 4 is measured using a potentiometer. Before and after the stoichiometric point, it is not necessary to add an equal volume of titrant to titration cell 4 each time; the volume reading of the titrant in burette 1 and the corresponding potential value of the potentiometer are recorded. As the stoichiometric point approaches, the increase in potential of the potentiometer accelerates; therefore, the amount of titrant added to titration cell 4 each time from burette 1 is reduced, and more titrant is added to titration cell 4. When the potential of the potentiometer changes abruptly, the stoichiometric point has passed; at this point, an equal volume of titrant is added to titration cell 4 until the potential change of the potentiometer becomes gradual, at which point the addition of titrant is stopped.

[0181] The first and second derivatives of potential with respect to volume are calculated using an improved method; the volume of titrant at the stoichiometric point is calculated by interpolation; and the content of the analyte ion in the test sample is obtained based on the volume of titrant at the stoichiometric point, thus completing the detection of the analyte ion content.

[0182] Table 10 shows the potentiometric titration records for detecting the effective content of the antioxidant ethoxyquinoline in feed (modified method, unequal volume titration).

[0183]

[0184] Improved method: Equivalence point V = 5.00 + (5.10 - 5.00) × (790 - 0) / (790 - (-500)) - 0.00 = 5.06 mL. Percentage of effective content in ethoxyquinoline relative to the sample mass:

[0185]

[0186] Where ω is the ethoxyquinoline content (%), c is the concentration of the perchloric acid standard titration solution (mol / L), V is the volume of perchloric acid standard solution consumed by the sample (mL), and M is the ethoxyquinoline content (C0). 14 H 19 The molar mass (g / mol) of NO is given by m, where m is the mass (g) of the sample.

[0187] Therefore, the equivalence point volume obtained by the ordinary equal-volume titration method (see Table 8) is 5.06 mL, the equivalence point volume obtained by the ordinary unequal-volume titration method (see Table 9) is 5.03 mL, and the equivalence point volume obtained by the improved unequal-volume titration method (see Table 10) is also 5.06 mL. The ordinary equal-volume titration method has three additional titration points at 4.70, 4.80, and 4.90, and takes longer, but is the most accurate. The ordinary unequal-volume titration method does not have these three titration points, takes less time, but the test results are lower. The ordinary equal-volume titration method does not have these three titration points, takes less time, and the test results are accurate.

[0188] Example 5

[0189] Determination of calcium and magnesium content in tap water using the ordinary method

[0190] The original data from the potentiometric titration were extracted from the paper "Determination of Tap Water Hardness by Potentiometric Titration—An Improvement of an Instrumental Analysis Experiment_Wang Huanying". Sample processing methods followed the national standard "Determination of Total Calcium and Magnesium in Water" (GB 7477-87). As stated in the second sentence of Section 3, Complexometric Titration, of the paper "Recent Research Progress in Potentiometric Titration_Wu Chunqing," which states that "the most widely used application of complexometric titration is the determination of water hardness," the titration of calcium and magnesium ions with EDTA belongs to complexometric titration. A calcium ion selective electrode was used as the indicator electrode, and an Ag / AgCl electrode was used as the reference electrode.

[0191] The specific steps are as follows: Weighing and processing the sample: Accurately weigh 50.00 mL of water sample into titration cell 4 (e.g., a 100 mL beaker), add 20 mL of auxiliary complexing solution (0.035 mol / L trihydroxyaminomethane (TRIS) - 0.055 mol / L acetylacetone (HAA) solution), and mix well;

[0192] Test: Add 0.02 mol / L EDTA standard solution to burette 1 for titration;

[0193] Add titrant to titration cell 4 through burette 1, record the initial reading of titrant volume in burette 1, and simultaneously turn on the magnetic stirrer and stir the solution in titration cell 4 with magnetic stirring rod 5.

[0194] The change in potential value during titration in titration cell 4 is measured using a potentiometer. Unequal volumes of titrant are added to titration cell 4 each time, and the volume reading of the titrant in burette 1 and the corresponding potential value of the potentiometer are recorded. As the stoichiometric point approaches, the increase in potential of the potentiometer accelerates; therefore, the amount of titrant added to titration cell 4 each time from burette 1 is reduced, and more titrant is added to titration cell 4. When the potential of the potentiometer changes abruptly, the stoichiometric point has passed; at this point, equal volumes of titrant are continued to be added to titration cell 4 until the potential change of the potentiometer becomes gradual, at which point the addition of titrant is stopped.

[0195] The first and second derivatives of potential with respect to volume are calculated using the ordinary method; the volume of titrant at the stoichiometric point is calculated by interpolation; and the content of the analyte ion in the test sample is obtained based on the volume of titrant at the stoichiometric point, thus completing the detection of the analyte ion content.

[0196] Table 11 shows the potentiometric titration records for detecting calcium and magnesium content in tap water (ordinary method unequal volume titration).

[0197]

[0198] As shown in Table 11, in complexometric titration, the potential of the solution in the titration cell gradually decreases with the increase of the titrant volume. Therefore, the EV curve of complexometric titration is a gradually decreasing S-shaped curve with a negative slope. The absolute value of the slope is largest at the potential jump, hence the first derivative curve... The lowest point is the equivalence point, that is, the minimum value of the first derivative is the potential jump point. From the experimental section of Section 1, line 10 of the paper "Determination of Water Hardness by Potentiometric Titration - An Improvement of Instrumental Analysis Experiment_Wang Huanying", which states "In acetone-Tris medium, two titration endpoints for calcium and magnesium were obtained respectively during titration", and the last sentence of Section 2.1 of the paper "Continuous Determination of Calcium and Magnesium in Water by Potentiometric Titration_Lu Haiyan", which states "The first potential jump point corresponds to the calcium content, and the difference between the second potential jump point and the first potential jump point corresponds to the magnesium content", it can be seen that the two minimum values ​​of the first derivative in Table 11, -119 and -62.14, are two potential jump points.

[0199] Standard method: First jump point -119 equivalence point V = 2.03 + (2.51 - 2.03) × (0 - (-239.46)) / (224.21 - (-239.46)) = 2.28 mL. Second jump point -62.14 equivalence point volume V = 3.04 + (3.57 - 3.04) × (0 - (-92.99)) / (66.57 - (-92.99)) = 3.35 mL.

[0200] As stated in Section 2.1 of the paper "Continuous Determination of Calcium and Magnesium in Water by Potentiometric Titration - Lu Haiyan", calcium ions react with EDTA in a 1:1 ratio, and magnesium ions react with EDTA in a 1:1 ratio as well. Therefore, the calcium or magnesium ion content (mg / L) in tap water is:

[0201]

[0202] Where ω is the calcium or magnesium ion content in tap water (mg / L), c is the concentration of the EDTA standard titration solution (mol / L), V is the volume of EDTA standard solution consumed by the sample (mL), and M is the calcium ion concentration (Ca). 2+ or magnesium ions (Mg 2+ The molar mass (g / mol) of the sample is given by v, where v is the volume (mL) of the sample.

[0203] Ordinary method: Calcium ion content in tap water: ω=0.02×2.28×40.078 / 50×1000=36.55mg / L, Magnesium ion content in tap water: ω=0.02×(3.35-2.28)×24.305 / 50×1000=10.40mg / L.

[0204] Determination of calcium and magnesium content in tap water using an improved method

[0205] The original data from the potentiometric titration were taken from the paper "Determination of Water Hardness by Potentiometric Titration—An Improvement of an Instrumental Analysis Experiment_Wang Huanying". The sample processing method followed the national standard "Determination of Total Calcium and Magnesium in Water" (GB 7477-87). From the second sentence of Section 3, Complexometric Titration, in the paper "Recent Research Progress in Potentiometric Titration_Wu Chunqing", which states that "the most widely used application of complexometric titration is the determination of water hardness," it can be seen that the titration of calcium and magnesium ions with EDTA belongs to complexometric titration.

[0206] The specific steps are as follows: Weighing and processing the sample: Accurately weigh 50.00 mL of water sample into titration cell 4 (e.g., a 100 mL beaker), add 20 mL of auxiliary complexing solution (0.035 mol / L trihydroxyaminomethane (TRIS) - 0.055 mol / L acetylacetone (HAA) solution), and mix well;

[0207] Test: Add 0.02 mol / L EDTA standard solution to burette 1 for titration;

[0208] Add titrant to titration cell 4 through burette 1, record the initial reading of titrant volume in burette 1, and simultaneously turn on the magnetic stirrer and stir the solution in titration cell 4 with magnetic stirring rod 5.

[0209] The change in potential value during titration in titration cell 4 is measured using a potentiometer. Unequal volumes of titrant are added to titration cell 4 each time, and the volume reading of the titrant in burette 1 and the corresponding potential value of the potentiometer are recorded. As the stoichiometric point approaches, the increase in potential of the potentiometer accelerates; therefore, the amount of titrant added to titration cell 4 each time from burette 1 is reduced, and more titrant is added to titration cell 4. When the potential of the potentiometer changes abruptly, the stoichiometric point has passed; at this point, equal volumes of titrant are continued to be added to titration cell 4 until the potential change of the potentiometer becomes gradual, at which point the addition of titrant is stopped.

[0210] The first and second derivatives of potential with respect to volume are calculated using an improved method; the volume of titrant at the stoichiometric point is calculated by interpolation; and the content of the analyte ion in the test sample is obtained based on the volume of titrant at the stoichiometric point, thus completing the detection of the analyte ion content.

[0211] Table 12 shows the potentiometric titration records for detecting calcium and magnesium content in tap water (modified method, unequal volume titration).

[0212]

[0213]

[0214] Improved method: First jump point -74.16 equivalent point V = 2.06 + (2.46 - 2.06) × (0 - (-239.46)) / (224.21 - (-239.46)) = 2.27 mL. Second jump point -43.50 equivalent point volume V = 3.04 + (3.60 - 3.04) × (0 - (-92.99)) / (66.57 - (-92.99)) = 3.37 mL.

[0215] Calcium or magnesium ion content in tap water (mg / L):

[0216]

[0217] Where ω is the calcium or magnesium ion content in tap water (mg / L), c is the concentration of the EDTA standard titration solution (mol / L), V is the volume of EDTA standard solution consumed by the sample (mL), and M is the calcium ion concentration (Ca). 2+ or magnesium ions (Mg 2+ The molar mass (g / mol) of the sample is given by v, where v is the volume (mL) of the sample.

[0218] Improved method: Calcium ion content in tap water: ω=0.02×2.27×40.078 / 50×1000=36.39mg / L, Magnesium ion content in tap water: ω=0.02×(3.37-2.27)×24.305 / 50×1000=10.69mg / L.

[0219] Therefore, the equivalence point volumes obtained by the ordinary unequal volume titration method (see Table 11) are 2.28 mL and 3.35 mL, with a calcium content of 36.55 mg / L and a magnesium content of 10.40 mg / L. The equivalence point volumes obtained by the improved unequal volume titration method (see Table 12) are 2.27 mL and 3.37 mL, with a calcium content of 36.36 mg / L and a magnesium content of 10.69 mg / L. Compared to the improved method, the ordinary method results in a 0.52% higher calcium content and a 2.71% lower magnesium content. In unequal volume titration, the improved method can clearly calculate the volume corresponding to the second derivative of the potential with respect to volume, f″(x2), as x2, while the ordinary method simply assumes that the volume corresponding to the second derivative of the potential with respect to volume, y″2, is x. 1.5 and x 2.5 The intermediate value is used, so the improved method is more accurate.

[0220] Example 6

[0221] Determination of total iron content in hematite using the ordinary method

[0222] The original potentiometric titration data were extracted from the paper "Determination of Total Iron Content in Hematite by Potentiometric Titration - Zhong Tong". Sample processing methods followed the group standard "Determination of Total Iron Content in Iron Ore - Titanium Trichloride Reduction Method" (GB / T 6730.5-2007). Table 2 of the paper "Recent Research Progress in Potentiometric Titration - Wu Chunqing" shows that potassium dichromate was used to titrate Fe... 2+ This is a redox titration. A platinum electrode is used as the indicator electrode, and a saturated calomel electrode is used as the reference electrode.

[0223] The specific steps are as follows: Weighing and processing the sample: Crush and grind the hematite to a particle size of less than 100 micrometers, dry it at 105℃ to constant weight, cool it to room temperature, accurately weigh 2g of the ground hematite sample, inject 10mL of sulfuric acid (1+1) (concentrated sulfuric acid (98wt%) and deionized water in a 1:1 volume ratio) to dissolve the sample, put the treated copper wire into an acid-resistant tube, fill the bottom with glass wool, pour the dissolved sample into the tube, and collect the solution in a clean beaker. At this time, Fe 3+ Converted to Fe 2+ Rinse the acid tube 2-3 times with 3 mL of sulfuric acid (1+1) each time, and combine the washings in a beaker. Transfer the solution in the beaker to a 250 mL volumetric flask, dilute with water to the mark, and shake well. This is the solution to be tested.

[0224] Test: Take 25 mL of the test solution into titration cell 4 (e.g., 150 mL beaker), add 15 mL of deionized water and 10 mL of sulfuric acid + phosphoric acid mixture (1:1) (the volume ratio of concentrated H2SO4 (98 wt%) to concentrated H3PO4 (85 wt%) is 1:1), add 0.05 mol / L potassium dichromate standard solution to burette 1 for titration;

[0225] Add titrant to titration cell 4 through burette 1, record the initial reading of titrant volume in burette 1, and simultaneously turn on the magnetic stirrer and stir the solution in titration cell 4 with magnetic stirring rod 5.

[0226] The change in potential value during titration in titration cell 4 is measured using a potentiometer. Before and after the stoichiometric point, an equal volume of titrant is added to titration cell 4 each time, and the volume reading of the titrant in burette 1 and the corresponding potential value of the potentiometer are recorded. As the stoichiometric point approaches, the increase in potential of the potentiometer accelerates; therefore, the amount of titrant added to titration cell 4 each time from burette 1 is reduced, and more titrant is added to titration cell 4. When the potential of the potentiometer changes abruptly, the stoichiometric point has passed; at this point, an equal volume of titrant is continued to be added to titration cell 4 until the potential change of the potentiometer becomes gradual, at which point the addition of titrant is stopped.

[0227] The first and second derivatives of potential with respect to volume are calculated using the ordinary method; the volume of titrant at the stoichiometric point is calculated by interpolation; and the content of the analyte ion in the test sample is obtained based on the volume of titrant at the stoichiometric point, thus completing the detection of the analyte ion content.

[0228] Table 13 shows the potentiometric titration records for detecting total iron content in hematite (ordinary method, equal volume titration).

[0229]

[0230]

[0231] Ordinary method: Equivalence point V = 33.40 + (33.50 - 33.40) × (10000 - 0) / (10000 - (-7000)) - 0.00 = 33.46 mL. Percentage of total iron in hematite by mass:

[0232]

[0233] Where ω is the total iron content (%) in hematite, c is the concentration of potassium dichromate standard titration solution (mol / L), V is the volume of potassium dichromate standard solution consumed by the sample (mL), M is the molar mass of iron (g / mol), m is the mass of the sample (g), and 10 is the amount of 25 mL of the 250 mL solution to be prepared for testing.

[0234] Determination of total iron content in hematite using the ordinary method

[0235] The original potentiometric titration data were extracted from the paper "Determination of Total Iron Content in Hematite by Potentiometric Titration - Zhong Tong". To achieve unequal volume titration before and after the stoichiometric point, the data at the titration point of 33.40 g / L was deleted. The sample preparation method followed the group standard "Determination of Total Iron Content in Iron Ore - Titanium Trichloride Reduction Method" (GB / T 6730.5-2007). Table 2 of the paper "Recent Research Progress in Potentiometric Titration - Wu Chunqing" shows that potassium dichromate was used to titrate Fe... 2+ This is a redox titration. A platinum electrode is used as the indicator electrode, and a saturated calomel electrode is used as the reference electrode.

[0236] The specific steps are as follows: Weighing and processing the sample: Crush and grind the hematite to a particle size of less than 100 micrometers, dry it at 105℃ to constant weight, cool it to room temperature, accurately weigh 2g of the ground hematite sample, inject 10mL of sulfuric acid (1+1) (concentrated sulfuric acid (98wt%) and deionized water in a 1:1 volume ratio) to dissolve the sample, put the treated copper wire into an acid-resistant tube, fill the bottom with glass wool, pour the dissolved sample into the tube, and collect the solution in a clean beaker. At this time, Fe 3+ Converted to Fe 2+ Rinse the acid tube 2-3 times with 3 mL of sulfuric acid (1+1) each time, and combine the washings in a beaker. Transfer the solution in the beaker to a 250 mL volumetric flask, dilute with water to the mark, and shake well. This is the solution to be tested.

[0237] Test: Take 25 mL of the test solution into titration cell 4 (e.g., 150 mL beaker), add 15 mL of deionized water and 10 mL of sulfuric acid + phosphoric acid mixture (1:1) (the volume ratio of concentrated H2SO4 (98 wt%) to concentrated H3PO4 (85 wt%) is 1:1), add 0.05 mol / L potassium dichromate standard solution to burette 1 for titration;

[0238] Add titrant to titration cell 4 through burette 1, record the initial reading of titrant volume in burette 1, and simultaneously turn on the magnetic stirrer and stir the solution in titration cell 4 with magnetic stirring rod 5.

[0239] The change in potential value during titration in titration cell 4 is measured using a potentiometer. Before and after the stoichiometric point, it is not necessary to add an equal volume of titrant to titration cell 4 each time. The volume reading of the titrant in burette 1 and the corresponding potential value of the potentiometer are recorded. As the stoichiometric point approaches, the increase in potential of the potentiometer accelerates. The amount of titrant added to titration cell 4 each time from burette 1 is reduced, and more titrant is added to titration cell 4. When the potential of the potentiometer changes abruptly, the stoichiometric point has passed. At this point, an equal volume of titrant is added to titration cell 4 until the potential change of the potentiometer becomes gradual, at which point the addition of titrant is stopped.

[0240] The first and second derivatives of potential with respect to volume are calculated using the ordinary method; the volume of titrant at the stoichiometric point is calculated by interpolation; and the content of the analyte ion in the test sample is obtained based on the volume of titrant at the stoichiometric point, thus completing the detection of the analyte ion content.

[0241] Table 14 shows the potentiometric titration records for detecting total iron content in hematite (ordinary method unequal volume titration).

[0242]

[0243] Ordinary method: Equivalence point V = 4.33 + (4.48 - 4.33) × (4333.33 - 0) / (4333.33 - (-1333.33)) - 0.00 = 33.44 mL. Percentage of total iron in hematite by mass:

[0244]

[0245] Where ω is the total iron content (%) in hematite, c is the concentration of potassium dichromate standard titration solution (mol / L), V is the volume of potassium dichromate standard solution consumed by the sample (mL), M is the molar mass of iron (g / mol), m is the mass of the sample (g), and 10 is the amount of 25 mL of the 250 mL solution to be prepared for testing.

[0246] Determination of total iron content in hematite using an improved method

[0247] The original potentiometric titration data were extracted from the paper "Determination of Total Iron Content in Hematite by Potentiometric Titration - Zhong Tong". To achieve unequal volume titration before and after the stoichiometric point, the data at the titration point of 33.40 g / L was deleted. The sample preparation method followed the group standard "Determination of Total Iron Content in Iron Ore - Titanium Trichloride Reduction Method" (GB / T 6730.5-2007). Table 2 of the paper "Recent Research Progress in Potentiometric Titration - Wu Chunqing" shows that potassium dichromate was used to titrate Fe... 2+ This is a redox titration. A platinum electrode is used as the indicator electrode, and a saturated calomel electrode is used as the reference electrode.

[0248] The specific steps are as follows: Weighing and processing the sample: Crush and grind the hematite to a particle size of less than 100 micrometers, dry it at 105℃ to constant weight, cool it to room temperature, accurately weigh 2g of the ground hematite sample, inject 10mL of sulfuric acid (1+1) (concentrated sulfuric acid (98wt%) and deionized water in a 1:1 volume ratio) to dissolve the sample, put the treated copper wire into an acid-resistant tube, fill the bottom with glass wool, pour the dissolved sample into the tube, and collect the solution in a clean beaker. At this time, Fe 3+ Converted to Fe 2+ Rinse the acid tube 2-3 times with 3 mL of sulfuric acid (1+1) each time, and combine the washings in a beaker. Transfer the solution in the beaker to a 250 mL volumetric flask, dilute with water to the mark, and shake well. This is the solution to be tested.

[0249] Test: Take 25 mL of the test solution into titration cell 4 (e.g., 150 mL beaker), add 15 mL of deionized water and 10 mL of sulfuric acid + phosphoric acid mixture (1:1) (the volume ratio of concentrated H2SO4 (98 wt%) to concentrated H3PO4 (85 wt%) is 1:1), add 0.05 mol / L potassium dichromate standard solution to burette 1 for titration;

[0250] Add titrant to titration cell 4 through burette 1, record the initial reading of titrant volume in burette 1, and simultaneously turn on the magnetic stirrer and stir the solution in titration cell 4 with magnetic stirring rod 5.

[0251] The change in potential value during titration in titration cell 4 is measured using a potentiometer. Before and after the stoichiometric point, it is not necessary to add an equal volume of titrant to titration cell 4 each time. The volume reading of the titrant in burette 1 and the corresponding potential value of the potentiometer are recorded. As the stoichiometric point approaches, the increase in potential of the potentiometer accelerates. The amount of titrant added to titration cell 4 each time from burette 1 is reduced, and more titrant is added to titration cell 4. When the potential of the potentiometer changes abruptly, the stoichiometric point has passed. At this point, an equal volume of titrant is added to titration cell 4 until the potential change of the potentiometer becomes gradual, at which point the addition of titrant is stopped.

[0252] The first and second derivatives of potential with respect to volume are calculated using the ordinary method; the volume of titrant at the stoichiometric point is calculated by interpolation; and the content of the analyte ion in the test sample is obtained based on the volume of titrant at the stoichiometric point, thus completing the detection of the analyte ion content.

[0253] Table 15 shows the potentiometric titration records for detecting total iron content in hematite (modified method unequal volume titration).

[0254]

[0255]

[0256] Improved method: Equivalence point V = 33.30 + (33.50 - 33.30) × (4333.33 - 0) / (4333.33 - (-1333.33)) - 0.00 = 33.45 mL. Percentage of total iron in hematite by mass:

[0257]

[0258] Where ω is the total iron content (%) in hematite, c is the concentration of potassium dichromate standard titration solution (mol / L), V is the volume of potassium dichromate standard solution consumed by the sample (mL), M is the molar mass of iron (g / mol), m is the mass of the sample (g), and 10 is the amount of 25 mL of the 250 mL solution to be prepared for testing.

[0259] Therefore, the equivalence point volume obtained by the ordinary equal-volume titration method (see Table 13) is 33.46 mL, the equivalence point volume obtained by the ordinary unequal-volume titration method (see Table 14) is 13.44 mL, and the equivalence point volume obtained by the improved unequal-volume titration method (see Table 15) is 13.45 mL. The ordinary equal-volume titration method has an additional titration point of 33.40 mL, takes longer, but is the most accurate; the ordinary unequal-volume titration method does not have a titration point of 33.40 mL, takes less time, but the test result is lower; the ordinary equal-volume titration method does not have a titration point of 33.40 mL, takes less time, and the test result is relatively accurate.

[0260] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them; although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications can still be made to the specific implementation of the invention or equivalent substitutions can be made to some technical features without departing from the spirit of the technical solutions of the present invention, and all such modifications and substitutions should be covered within the scope of the technical solutions claimed in the present invention.

Claims

1. A method for detecting ion content based on potentiometric titration, characterized in that, The method specifically includes the following steps: S1, weigh the sample to be tested and dissolve it into a solution to be tested and place it in the titration cell (4). Place a magnetic stirring rod (5) in the titration cell (4) and place the titration cell (4) on a magnetic stirrer. S2, add titrant to titration cell (4) through burette (1), record the initial reading of titrant volume in burette (1), and turn on magnetic stirrer at the same time, and stir solution in titration cell (4) with magnetic stirring rod (5). S3, measure the change in potential value during the titration process in the titration cell (4) using a potential measuring instrument; record the volume reading of the titrant in the burette (1) and the corresponding potential value of the potential measuring instrument each time a titrant is added; When approaching the stoichiometric point, the potential of the potentiometer increases rapidly. At this time, reduce the amount of titrant added to the titration cell (4) by the burette (1) each time. When the potential of the potentiometer changes abruptly, the stoichiometric point has passed. At this time, continue to add titrant to the titration cell (4) until the potential change of the potentiometer tends to be gradual, and stop adding titrant. The specific steps for titrating the titration in the titration cell (4) using the burette (1) in S3 are as follows: S31, when titrant is added to the titration cell (4) in equal volumes before and after the stoichiometric point, the first and second derivatives of the potential with respect to volume are calculated by the ordinary method; The specific formulas for calculating the first and second derivatives of potential with respect to volume using the ordinary method are as follows: ， ， ， in, This represents the first derivative of the potential with respect to volume. This is the first derivative of the potential with respect to volume obtained by the ordinary method. For the first The potential value at each titration point For the first Volume reading of burette (1) at each titration point This represents the second derivative of the potential with respect to volume. This is the second derivative of the potential with respect to volume obtained by the ordinary method. Indicates the first Group volume and potential data, Indicates total Group volume and potential data; S32, when titrant is added to the titration cell (4) in unequal volumes before and after the stoichiometric point, the first derivative of the potential with respect to volume is first calculated by the ordinary method. When the maximum value of the first derivative of the potential with respect to volume is not unique, the first and second derivatives of the potential with respect to volume are calculated by the improved method. When the maximum value of the first derivative of the potential with respect to volume is unique, the second derivative of the potential with respect to volume is calculated by the ordinary method. The specific formulas for calculating the first and second derivatives of the potential with respect to volume using the improved method are as follows: ， ， ， in, This represents the first derivative of the potential with respect to volume. To obtain the first derivative of the potential with respect to volume using the improved method, For the first The potential value at each titration point For the first Volume reading of burette (1) at each titration point This represents the second derivative of the potential with respect to volume. To obtain the second derivative of the potential with respect to volume using the improved method, Indicates the first Group volume and potential data; Indicates total Group volume and potential data; S4. Calculate the first and second derivatives of the potential with respect to volume based on the recorded volume reading of the titrant in the burette (1) and the corresponding potential value of the potential measuring instrument. Obtain the maximum value of the first derivative and two second derivatives near the maximum value of the first derivative. These two second derivatives are adjacent and one is positive and the other is negative. Obtain the two volumes corresponding to these two second derivatives. S5. Calculate the volume of titrant at the stoichiometric point using interpolation. Based on the obtained volume of titrant at the stoichiometric point, obtain the content of the analyte ion in the test sample, and complete the detection of the analyte ion content. In S5, the volume of titrant at the stoichiometric point is the volume of titrant consumed when the second derivative of potential with respect to volume is 0, as specified in the formula: ， in, This represents the volume of titrant consumed when the second derivative is 0. This refers to the volume of titrant before the stoichiometric point. The second derivative of the potential before the stoichiometric point with respect to volume. This refers to the volume of titrant after the stoichiometric point. This represents the second derivative of the potential with respect to volume after the stoichiometric point. This is the initial reading of the titrant volume in the burette (1).

2. The method for detecting ion content based on potentiometric titration according to claim 1, characterized in that, The potential measuring instrument includes a potentiometer, a reference electrode (2) and an indicator electrode (3). The potentiometer is connected to the reference electrode (2) and the indicator electrode (3) respectively. The potentiometer is used to display the potential change in the titration cell (4).

3. The method for detecting ion content based on potentiometric titration according to claim 1, characterized in that, The specific steps for calculating the first and second derivatives of the potential with respect to volume using the improved method are as follows: S41, expressing the potential in volume using Taylor's formula. The relationship between potential and volume in the vicinity. ， in, Potential, For volume; S42, will See as , See as According to Taylor's formula in S41 and taking the first three terms of Taylor's formula, we get: ， （1）， in, ; Will See as , See as According to Taylor's formula in S41 and taking the first three terms of Taylor's formula, we get: ， （2）， According to (1) and (2): ， S44, in formula S43 Change to , Change to , Change to , Change to , Change to , Change to Formulas for obtaining the first and second derivatives: ， in, : No. Group volume and potential data, :common Group volume and potential data.

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