Analytical Chem istry - DePauw University

Chapter 4 Evaluating Analytical Data135In a typical analysis the following data are obtained (with estimateduncertainties in parentheses)g = 0.118 g (± 0.002 g)R = 0.082056 L atm mol –1 K –1 (± 0.000001 L atm mol –1 K –1 )T = 298.2 K (± 0.1 K)P = 0.724 atm (± 0.005 atm)V = 0.250 L (± 0.005 L)(a) What is the compound’s formula weight and its estimated uncertainty?(b) To which variable(s) should you direct your attention if youwish to improve the uncertainty in the compound’s molecular weight?6. To prepare a standard solution of Mn 2+ a 0.250 g sample of Mn is dissolvedin 10 mL of concentrated HNO 3 (measured with a graduatedcylinder). The resulting solution is quantitatively transferred to a 100-mL volumetric flask and diluted to volume with distilled water. A 10mL aliquot of the solution is pipeted into a 500-mL volumetric flaskand diluted to volume. (a) Express the concentration of Mn in mg/L,and estimate its uncertainty using a propagation of uncertainty. (b)Can you improve the concentration’s uncertainty by using a pipet tomeasure the HNO 3 , instead of a graduated cylinder?7. The mass of a hygroscopic compound is measured using the techniqueof weighing by difference. In this technique the compound is placed ina sealed container and weighed. A portion of the compound is removed,and the container and the remaining material are reweighed. The differencebetween the two masses gives the sample’s mass. A solution ofa hygroscopic compound with a gram formula weight of 121.34 g/mol(±0.01 g/mol) was prepared in the following manner. A sample of thecompound and its container has a mass of 23.5811 grams. A portionof the compound was transferred to a 100-mL volumetric flask anddiluted to volume. The mass of the compound and container after thetransfer is 22.1559 grams. Calculate the compound’s molarity and estimateits uncertainty by a propagation of uncertainty.Many of the problems that follow require accessto statistical tables. For your convenience,here are hyperlinks to the appendices containingthese tables.Appendix 3: Single-Sided Normal DistributionAppendix 4: Critical Values for the t-TestAppendix 5: Critical Values for the F-TestAppendix 6: Critical Values for Dixon’s Q-TestAppendix 7: Critical Values for Grubb’s Test8. Show using a propagation of uncertainty that the standard error of themean for n determinations is s n .9. Beginning with equation 4.17 and equation 4.18, use a propagation ofuncertainty to derive equation 4.19.10. What is the smallest mass that we can measure on an analytical balancethat has a tolerance of ±0.1 mg, if the relative error must be less than0.1%?