Self-test 9.2 B

The HPLC analysis of benzoic acid (BA), a food preservative, in mayonnaise is carried out as follows. A sample of mayonnaise with mass between 1 and 5 g (m_sample) is taken for analysis. The exact amount depends on BA content of the mayonnaise. Sample preparation procedure (consisting of a dissolution, centrifugation, extraction, etc steps) is carried out and as a result a sample solution is obtained in a 50 ml volumetric flask (V_sample). Calibration solutions are prepared in the concentration range of 1 ... 10 mg/l and linear calibration graph with slope b₁ [mAU·s·l/mg] and intercept b₀ [mAU·s] is constructed. Peak area of the BA peak on the chromatogram of sample solution is A_BA,sample [mAU·s]. The uncertainty of the peak area takes into account a number of uncertainty sources, e.g. uncertainty of integration, possible overlap with a possible co-eluter, repeatability of injection, etc. The HPLC injection volume (V_inj) is 5 μl both in the case of calibration solutions and sample solution. The method recovery R takes into account possible analyte losses (e.g. due to incomplete extraction) and has been determined separately and is 0.93 (unitless).

Which of the following equations is the correct model equation for finding the analysis result C_BA,sample [mg/g]?