QUESTION 1 9 MARKS A 1.309 ± 0.002 g of solid sample containing 2-Hydroxybenzoic

Question

QUESTION 1                9 MARKS
A 1.309 ± 0.002 g of solid sample containing 2-Hydroxybenzoic acid, (OH)C6H5COOH
(MW = 138.12 g/mol) was analysed using acid-base titration method. The end point of
titration (EP) was reached at 43.85 ± 0.05 mL with an initial reading = 0.25 ± 0.05 mL
when 0.1056 ± 0.0008 M NaOH titrant solution was used.
Calculate weight % of 2-Hydroxybenzoic acid in the solid sample and report the value
with statistically valid uncertainty.

This question was given to us in statistical chemistry and quite frankly i have no idea how to do this and ive never had stats before

Explanation / Answer

First let us write down the balanced equation for the reaction:

(OH)C6H4COOH (aq) + NaOH (aq) -------> (OH)C6H4COO-Na+ + H2O (l)

There is a 1:1 molar ratio between the acid and the base.

Weight of sample taken = 1.309 ± 0.002 g;

Titer value of NaOH = (43.85 – 0.25) mL = 43.6 mL; offcourse, the reading will be 43.6 mL ± 0.05 mL.

Concentration of NaOH = 0.1056 M ± 0.0008 M.

Therefore, moles of NaOH required for the titration = (43.6 mL)*(1 L/1000 mL)*(0.1056 mole/L) = 4.60416*10-3 mole.

Since NaOH and the acid has a 1:1 molar ratio, the moles of acid titrated = 4.6014*10-3 mole.

Molar mass of acid = 138.12 gm/mol.

Therefore, weight of acid = (4.6014*10-3 mole)*(138.12 gm/mol) = 0.636 gm.

Weight percentage of acid = (0.6359/1.309)*100 = 63.59 (ans)

Now we must use propagation of error.

Uncertainty in weighing percentage = [weight percent (acid)/weight percent (acid)]2 = [concentration (base)/concentration (base)]2 + [volume (base)/volume (base)]2 + [weight percent (sample)/weight percent (sample)]2 = (0.0008 M/0.1056 M)2 + (0.05 mL/43.6 mL)2 + (0.002 gm/1.309 gm)2 = 5.739*10-5 + 1.315*10-6 + 2.33*10-6 = 6.1035*10-5

===> [weight percent (acid)/weight percent (acid)] = 7.812*10-3

===> weight percent (acid) = 7.812*10-3*weight percent (acid) = 7.812*10-3*63.59 = 0.496 0.5

Ans: The weight percent of the acid = (63.59±0.5)%

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