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    • In analytical chemistry textbooks, it is simply explained, 

      "Make a standard sample, analyze it, make a calibration curve, and quantitate the concentration". 

      Indeed, the principle is simple. However, when practicing environmental analytical chemistry, the most difficult part is quantifying this concentration. Exercise (1-1) is an easy example. Exercise (2) and beyond are more difficult.


    • Plotting the results of a standard sample analysis, the problem of finding the concentration of an unknown sample from the regression equation of the calibration curve


      　Inorganic ion components in rainwater were measured by ion chromatography. Find the concentration of nitrate ion (NO3-) using the intensity method.


      Background on analyzing rainwater：Cloud water, which is formed by condensation of water vapor, is similar to fresh water. However, in order for cloud particles to form, they must have water-soluble particles at their core. Cloud particles contain a little bit of water-soluble components. To find out what forms the core of a cloud, we can examine the constituents of rainwater. The atmosphere contains acid gases, ammonia gases, and organic gases that are absorbed by cloud particles and raindrops. If they are pollutants, rainwater analysis is also needed to determine the pollution status.


      The procedures for rainwater analysis ① through ④ are shown below.

      ①　Collecting raindrops falling from the sky with a funnel open to the atmosphere

      ②　Store collected rainwater in bottles

      ③　Sample water (rainwater) is filtered and then imported into ion chromatography

      ④　Detects the signal intensity of water-soluble ionic components in sample water by ion chromatography

      Fig. 1


      Principle of signal strength detection－Measurement of ionic components by ion chromatography－

      　A rainwater sample is passed through a column packed with ion exchange resin. Since the time required for each ionic component to pass through the column differs, measuring the electrical conductivity of the sample water as it passes through the column over time allows each component to be separated and the signal intensity to be obtained (see figure below). The higher the concentration of NO3- in the sample water, the greater the conductivity value. The amount of NO3- in the sample water can be determined from the difference in the magnitude of the conductivity.

    • Example (1-1) question statement
      　First, we prepare a standard sample based on pure water and measure it by ion chromatography; the peak height of conductivity (signal intensity) when NO3- comes out is obtained as follows. Download the data file and find a) and b).

       

      　　Standard sample   　    　Adjusted concentration　                  　Measurement results　

      ①　blank　　　　　 （NO3- concentration = 0）                          →　peak height =    1030

      ②　Standard sample（NO3- concentration = 0.002 mg L-1）      →　peak height =    3500

      ③　Standard sample（NO3- concentration = 0.02 mg L-1）        →　peak height =   36150

      ④　Standard sample（NO3- concentration = 0.10 mg L-1）        →　peak height =  163223

      ⑤　Standard sample（NO3- concentration = 0.20 mg L-1）        →　peak height =  330409

      ⑥　Standard sample（NO3- concentration = 0.50 mg L-1）        →　peak height =  814093

    • Folder ikon
      Example (1-1) data file Download Folder

      　We have also included a brief description of how to plot the calibration curve (regression curve) on the figure.

      　Please follow the instructions in A) and B) below in this excel file.

    • A）Plot the relationship between NO3- concentration in the standard sample and signal intensity (peak height) in the downloaded data file (Excel).

      　The signal intensity should be on the horizontal axis (X) and the concentration on the vertical axis (Y).

      ※　Generally, a calibration curve is plotted with signal intensity on the vertical axis and concentration on the horizontal axis. In this course, however, we have reversed the process and substituted signal intensity for (x) in the regression equation y=ax+b to calculate concentration (y).

      B）Calculate the concentration of the unknown sample from the signal intensity of unknown samples 1-4).

      　Right-click on the plot drawn in A) and select "Add Approximate Curve". Display the regression equation for that approximate curve to obtain the formula. Substitute the signal intensity of the unknown sample for X in the formula to calculate the concentration.

      　（How to create approximate curves, etc., is described in a separate sheet in the same Excel file.）

      ★ When the regression equation for the approximate curve is displayed in the Excel plot, the number of significant digits may be too small by default. You need to increase the number of significant digits by adjusting how many decimal places are displayed.


    • Explanation of Example (1-1)

      Did the example (1-1) look like the figure below?

      （The figure below was drawn in a different software than Excel）

      Fig. 2

      　Please also display the regression equation (calibration curve equation). By default, Excel displays only two digits for the regression equation. Since this can lead to a large error, we recommend that you display more digits, about 10.

    • 　The signal intensity of the unknown sample (measurement result) 5.1 × 105 is plotted on the figure, and then the concentration is calculated by substituting it into the regression equation of the calibration curve.

      Fig. 3

      　By noting the signal intensity of the unknown sample on the horizontal axis and reading the value (concentration) on the vertical axis indicated by the calibration curve, we find that the value is approximately 0.3 mg/L. To obtain an accurate value, we substitute the signal intensity of the unknown sample into the regression equation.

      Unknown sample: Signal intensity (peak height) of 5.1・105

      (Concentration of unknown sample) = 0.0016079+5.9215×10-7×（5.1・105）=  0.30 (mg L-1)

      The graph of the calibration curve matched the value read visually.


      So far, this is an example problem where the concentration can be obtained by calculation without any problems.

      Analytical chemistry textbooks also explain up to this point.

      In the next course, you will learn what processing is required when the signal intensity of an unknown sample is small or large.


  • Exercise (1-1)