Analytical Chem istry - DePauw University

Chapter 4 Evaluating Analytical Data83Example 4.9Which of the following methods for preparing a 0.0010 M solution froma 1.0 M stock solution provides the smallest overall uncertainty?(a) A one-step dilution using a 1-mL pipet and a 1000-mL volumetricflask.(b) A two-step dilution using a 20-mL pipet and a 1000-mL volumetricflask for the first dilution, and a 25-mL pipet and a 500-mL volumetricflask for the second dilution.So l u t i o nThe dilution calculations for case (a) and case (b) are1.000 mLcase (a): 1.0 M× = 0.0010 M1000.0 mL20.00 mL 25.00 mLcase(b): 1.0 M× × = 0.0010 M1000.0 mL 500.0 mLUsing tolerance values from Table 4.2, the relative uncertainty for case (a)isuRR=2⎛ 0.006⎞⎝⎜⎠⎟ +⎛ 03 . ⎞1.000 ⎝⎜1000.0⎠⎟ =20.006and for case (b) the relative uncertainty isuRR=22 2⎛ 003 . ⎞⎝⎜⎠⎟ +⎛ 03 . ⎞20.00 ⎝⎜1000. 0⎠⎟ +⎛ 003 . ⎞⎝⎜⎠⎟ +⎛ 02 . ⎞25.00 ⎜⎝500.0⎠⎟ =20.002Since the relative uncertainty for case (b) is less than that for case (a), thetwo-step dilution provides the smallest overall uncertainty.4DThe Distribution of Measurements and ResultsEarlier we reported results for a determination of the mass of a circulatingUnited States penny, obtaining a mean of 3.117 g and a standard deviationof 0.051 g. Table 4.11 shows results for a second, independent determinationof a penny’s mass, as well as the data from the first experiment.Although the means and standard deviations for the two experiments aresimilar, they are not identical. The difference between the experimentsraises some interesting questions. Are the results for one experiment betterthan those for the other experiment? Do the two experiments provideequivalent estimates for the mean and the standard deviation? What is ourbest estimate of a penny’s expected mass? To answers these questions weneed to understand how to predict the properties of all pennies by analyz-