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Quantitation using Linear Calibration Curves

The general procedure quantitation using the calibration curve method is to obtain measurements on several (3 or more) calibration standards and then to fit a regression function to the data. Linear calibration curves are desirable because they result in the best accuracy and precision. A plot of the calibration data and the fitted line should always be examined to check for outliers and to verify linear behavior.

In all of these examples, the residuals are used to calculate standard errors of the point estimates. The assumptions for such a calculation (eg, homogeneous noise, correct regression model) should be kept in mind.

Example 1

The following data was obtained in the analysis of copper using flame atomic absorption spectroscopy.

conc, ppm % transmittance
5.1 78.1
17.0 43.2
25.5 31.4
34.0 18.8
42.5 14.5
51.0 8.7

Following calibration, a sample of unknown copper concentration was analyzed. The measured transmittance was 35.6%. Report the concentration of analyte in the form of a confidence interval.

Answer: 21.8 +/- 3.9 ppm (95% CI)

Example 2

The determination of lead in an industrial waste stream is carried out using atonic stripping voltammetry. A calibration curve is prepared with arsenic standard solutions as given below. From the calibration curve, and the sample current of 0.175 uA, calculate a confidence interval for the concentration of arsenic in the waste stream in ppb.

As, ppb Limiting Current, uA
blank 0.003
6.1 0.134
11.2 0.259
19.4 0.398

Answer: 8.0 +/- 3.8 ppb (95% CI)

When a blank measurement is obtained during calibration, as in the previous example, there are two possibilities: either include the blank measurement in the regression, or subtract the blank value from all the calibration and sample measurements. Either way gives the same results.