Analytical Chem istry - DePauw University

344 Analytical Chemistry 2.0Nominal Mass (g) Actual Mass (g) % w/w KH 2 PO 42.50 2.496 0.7662.504 0.7692.496 0.6822.496 0.6092.557 0.5892.509 0.617(a) Prepare a graph of % w/w KH 2 PO 4 versus the actual sample massand discuss how this graph is consistent with your understanding of thefactors affecting sampling variance. (b) For each nominal mass, calculatethe percent relative standard deviation for the analysis. The value ofK s for this analysis has been estimated as 350. For each nominal mass,use this K s to determine the percent relative standard deviation dueto sampling. Considering these calculations, what is your conclusionabout the importance of indeterminate sampling errors for this analysis?(c) For each nominal mass, convert the percent relative standarddeviation to an absolute standard deviation. Plot points on your graphcorresponding to ±1 absolute standard deviations about the overallaverage % w/w KH 2 PO 4 . Draw smooth curves through these two setsof points. Considering these curves, does the sample appear to be homogeneouson the scale at which it is sampled?12. In this problem you will collect and analyze data in a simulation of thesampling process. Obtain a pack of M&M’s (or other similar candy).Collect a sample of five candies and count the number that are red (orany other color of your choice). Report the result of your analysis as% red. Return the candies to the bag, mix thoroughly, and repeat theanalysis for a total of 20 determinations. Calculate the mean and thestandard deviation for your data. Remove all candies from the bag anddetermine the true % red for the population. Sampling in this exerciseshould follow binomial statistics. Calculate the expected mean valueand the expected standard deviation, and compare to your experimentalresults.13. Determine the error (a = 0.05) for the following situations. In each caseassume that the variance for a single determination is 0.0025 and thatthe variance for collecting a single sample is 0.050. (a) Nine samples arecollected, each analyzed once. (b) One sample is collected and analyzednine times. (c) Three samples are collected, each analyzed three times.14. Which of the sampling schemes in problem 13 is best if you wish tolimit the overall error to less than ±0.25, and the cost of collecting asingle sample is 1 (arbitrary units), and the cost of analyzing a single