Two Experiments Illustrating the Importance of Sampling in a Quantitative Chemical Analysis

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With many instructors of quantitative analysis courses emphasizing the analysis of "real-world" samples, there is a need for more experiments illustrating the importance of sampling as a source of uncertainty. Unfortunately, the few available experiments are either very lengthy or use instrumentation that is not widely available. This paper describes modifications to two previously published experiments illustrating the importance of sampling. The gross sample, a mixture of the acid-base indicator erythrosin B coated on crystalline NaCl, is analyzed spectrophotometrically after diluting individual samples with distilled water. The first experiment uses a four-level nested design to determine the contribution to the total variance of sampling, sample preparation, the spectrometer, and the sample cell's positioning in the spectrometer. The second experiment investigates the relationship between sampling variance and sample size. Each experiment can be completed in less than three hours. At first glance, the sample appears to be homogeneous and students are often surprised to discover that sampling is the greatest source of variance. This discrepancy between the expectation that sampling uncertainty is insignificant and experimental evidence to the contrary helps emphasize the importance of sampling.