Analytical Chem istry - DePauw University

Chapter 4 Evaluating Analytical Data794C.4 Uncertainty for Mixed OperationsMany chemical calculations involve a combination of adding and subtracting,and multiply and dividing. As shown in the following example, we cancalculate uncertainty by treating each operation separately using equation4.6 and equation 4.7 as needed.Example 4.7For a concentration technique the relationship between the signal and thean analyte’s concentration isS = k C + Stotal A A mbWhat is the analyte’s concentration, C A , and its uncertainty if S total is24.37 ± 0.02, S mb is 0.96 ± 0.02, and k A is 0.186 ± 0.003 ppm –1 .So l u t i o nRearranging the equation and solving for C ACAS=total−SkAmb24. 37 −096.== 125. 9 ppm−10.186 ppmgives the analyte’s concentration as 126 ppm. To estimate the uncertaintyin C A , we first determine the uncertainty for the numerator using equation4.6.2 2u R= ( 002 . ) + ( 0. 02) = 0.028The numerator, therefore, is 23.41 ± 0.028. To complete the calculationwe estimate the relative uncertainty in C A using equation 4.7.uRR=2⎛ 0.028⎞⎝⎜⎠⎟ +⎛ 0.003⎞23.41 ⎜⎝0.186⎠⎟ =20.0162The absolute uncertainty in the analyte’s concentration isu R= ( 125. 9 ppm) × ( 0. 0162) = 20 . ppmThus, we report the analyte’s concentration as 126 ppm ± 2 ppm.Practice Exercise 4.2To prepare a standard solution of Cu 2+ you obtain a piece of copper from a spool of wire. The spool’s initialweight is 74.2991 g and its final weight is 73.3216 g. You place the sample of wire in a 500 mL volumetricflask, dissolve it in 10 mL of HNO 3 , and dilute to volume. Next, you pipet a 1 mL portion to a 250-mLvolumetric flask and dilute to volume. What is the final concentration of Cu 2+ in mg/L, and its uncertainty?Assume that the uncertainty in the balance is ±0.1 mg and that you are using Class A glassware.Click here when to review your answer to this exercise.