I need some help with these uncertanity problems. ( Can you please show the work
ID: 477372 • Letter: I
Question
I need some help with these uncertanity problems. ( Can you please show the work for them) Thank You
(a) A solution is prepared by dissolving 0.2222 (±0.0002) g of KIO3 [FW 214.0010 (±0.0009)] in 50.00 (±0.05) mL. Find the molarity and its uncertainty with an appropriate number of significant figures.
(b) Here are two methods that you might use to prepare a dilute silver nitrate solution:
Method 1: Weigh out 0.0463 g AgNO3 and dissolve it in a 100mL volumetric flask.
Method 2: Weigh out 0.4630 g AgNO3 and dissolve it in a 100mL volumetric flask. THen pipet 10mL of this solution into a fresh 100mL flask and dilute to the mark.
The uncertainty in the balance is ±3 in the last decimal plac. Which method is more accuate?
Explanation / Answer
a) First we need to divide weight / molecular weight to get mol of KIO3 so we need to find the relative
error
(A±B) / (C±D) = (A/C) ± [(B/A)2 + (D/C)2]1/2
error = [(B/A)2 + (D/C)2]1/2
mol of KIO3 = (0.2222 ±0.0002) gm / (214.0010 ±0.0009) gm/mol = (0.2222 / 214.0010) ± error
error = [ (0.0002 / 0.2222)2 + (0.0009 / 214.0010)2 ]1/2 = 9.0009*10-4
mol of KIO3 = (0.2222 / 214.0010) ± error = 1.0383*10-3 ± 9.0009*10-4
molarity = mol of KIO3 / volume = (1.0383*10-3 ± 9.0009*10-4) / (50 ± 0.05)
[ (1.0383*10-3 / 50) ] ± error = molarity
repeat the same calculation to get the molarity.
b) Method 2 is more accurate.