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based upon the comparison of two chromatograms obtained successively without changing the control settings of the chromatograph (Figure 1.12). The first chromatogram is acquired from a standard solution (reference solution) with a known concentration C_ref of the analyte in a solvent. A volume V of this solution is injected. On the resulting chromatogram, the area A_ref of the corresponding peak is measured. The second chromatogram results from the injection of the same volume V of the sample in solution, containing an unknown concentration of the compound to be measured (conc. C_unk). The area of the corresponding peak is A_unk. Since an identical volume of both samples has been injected, the ratio of the areas is proportional to the ratio of concentrations, which depend upon the masses injected (m_i = C_i · V). Applied to the two chromatograms, Eq. (1.42) leads to Eq. (1.43), which characterizes this method:

(1.43)

Figure 1.12 Analysis by the external standard method. The precision of this basic method is improved when several solutions of varying concentrations are used in order to create a calibration curve. For trace analyses by liquid chromatography, it is sometimes advisable to replace the areas of the peaks by their heights, as the latter are less sensitive to variations in the mobile phase flow rate.

      The single‐point calibration method, as depicted in Figure 1.12, assumes that the calibration line goes through the origin. Precision will be improved if the concentrations of the reference solution and of the sample solution are similar. That means the device settings do not need to be changed between injections.

      This technique, employing the absolute response factors, yields very reliable results with current high‐performance chromatographs equipped with an autosampler: a combination of a carousel sample holder and an automatic injector. This gives numerous measurements without human intervention. A single reference solution compensates for a potential drift of the instrument with scheduled control re‐injections.

      Precision of the assay can obviously be improved if several injections of the sample and the reference solutions are made, always using equal volumes. The average peak area is then calculated; however, unless several measurements are made, it is preferable to conduct a multilevel calibration, in which case equal volumes of a series of standard solutions are injected. The analytical results are obtained directly from the calibration curve, A = f (C).

      This method, the only one adapted to gas samples but also applicable in LC, has the added advantage of its ease of execution and its rapidity. However, it requires perfect reproducibility of injected volumes, which automatic injectors can do nowadays.

1.16 INTERNAL STANDARD METHOD

      This second method relies on the relative response factor of each compound to be measured against a marker added as a reference. This compensates for any imprecision in the injected volumes, which is the main drawback of the previous method.

As above, this more reliable method requires two chromatograms, one to calculate the relative response factors of the compounds of interest, and the other to analyse the sample.

      The areas of the peaks to be quantified are compared with that of an internal standard (designated by IS), added at a known concentration to the sample solution.

      1.16.1 Calculation of the Relative Response Factors

Let us suppose that a sample contains two compounds 1 and 2 to be measured and that compound IS represents an additional compound for use as an internal standard (Figure 1.13).

      In the first stage, a solution containing compound 1 at known concentration C₁, compound 2 at known concentration C₂, and the internal standard IS at known concentration C_IS is prepared and then injected onto the chromatograph. A₁, A₂, and A_IS are the areas of the elution peaks in the chromatogram due to the three compounds. If m₁, m₂, and m_IS represent the real quantities of these three substances introduced onto the column, then three equations of the type of Eq. (1.42) can be derived:

      These ratios enable the calculation of the relative response factors of 1 and 2, with respect to IS. They are designated by K_1/IS and K_2/IS:

Figure 1.13 Method of analysis by internal standard.

Since the injected masses m_i are proportional to the corresponding mass concentrations C_i (m_i = C_i V), the above equations can be rewritten as:

      1.16.2 Chromatogram of the Sample – Calculation of the Concentrations

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