An unknown solid acid is either citric acid or tartaric acid. To determine which acid you have, you titrate a sample of the solid with NaOH. The appropriate reactions are as follows:Citric acid:H3C6H5O79(aq) + 3NaOH (aq) >>>>>>> 3H2O (l) + Na2C6H5O7 (aq)Tataric Acid:H2C4H4O6 (aq) + 2NaOH (aq) >>>>>>>> 2H2O (l) + Na2C4H4O6 (aq)A 0.956 g sample requires 29.1 ml of 0.513 M NaOH for titration to the equivalence point. What is the unknown acid?

The unknown acid is citric acid.

Explanation:

Based on the reactions:

Citric acid: H3C6H5O7(aq) + 3NaOH (aq) → 3H2O (l) + Na2C6H5O7 (aq)

Tartaric acid: H2C4H4O6 (aq) + 2NaOH (aq) → 2H2O (l) + Na2C4H4O6 (aq)

0.956g of sample if tartaric acid requires:

0.956g × (1mol / 150,087 g) = 0.006370 moles of tartaric acid. As 1 mole reacts with 2 moles of NaOH:

0.006370 moles of tartaric acid × (2 mol NaOH / 1 moles tartaric acid) = 0.0127 moles of NaOH. As the concentration of the NaOH is 0.513M:

0.0127 moles of NaOH × (1L / 0.513mol) = 0.0248L ≡ 24.8mL

Now, 0.956g of citric acid requires:

0.956g × (1mol / 192,124g) = 0.004976 moles of citric acid. As 1 mole reacts with 3 moles of NaOH:

0.004976 moles of citric acid × (3 mol NaOH / 1 moles tartaric acid) = 0.0149 moles of NaOH. As the concentration of the NaOH is 0.513M:

0.0149 moles of NaOH × (1L / 0.513mol) = 0.0291L ≡ 29.1mL

As the titration requires 29.1mL of the base, the unknown acid is citric acid.

Explanation:

Equation of the reaction:

Citric acid: H3C6H5O7(aq) + 3NaOH (aq) ---> 3H2O (l) + Na2C6H5O7 (aq)

Tataric Acid: H2C4H4O6 (aq) + 2NaOH (aq) ---> 2H2O (l) + Na2C4H4O6 (aq)

Given:

Mass of solid acid = 0.956 g

Volume of base, vb = 29.1 ml

Concentration of base, cb = 0.513 M

Number of moles of NaOH = concentration × volume

= 0.513 × 29.1 × 10^-3

= 0.0149 moles

From equation 1,

By stoichiometry, 1 mole of citric acid will react with 3 moles of NaOH. Therefore, number of moles of citric acid = 0.0149/3

= 0.00498 moles

Molar mass of citric acid, H3C6H5O79 = (8 × 1) + (6 × 12) + (79 × 16)

= 192 g/mol

Mass = number of moles × molar mass

= 192 × 0.00498

= 0.956 g

Therefore the solid acid is citric acid.

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