Question

An empty flask is found to have a mass of 97.34 grams. A sample of vinegar is added to the flask and the total
mass is measured at 119.22 grams. A 5.023-gram sample of tartaric acid is dissolved in water and diluted to
250.0 mL in a volumetric flask. A 34.2 ml portion of this tartaric
acid solution reacts completely with 28.3 ml of a sodium hydroxide solution. The vinegar sample requires 40.1 ml of this same sodium hydroxide solution for complete reaction. Calculate the percent (w/w) of acetic acid in the vinegar.

Answer 1

The acetic acid in the 21.88 g mass of vinegar that reacts with 40.1 mL of

sodium hydroxide, has a percentage (w/w) of approximately 35%.

How can the percentage by weight be calculated?

Known and derived parameters;

Mass of vinegar added to the flask = 119.22 g - 97.34 g = 21.88 g

Mass of the of the tartaric acid in 250.0 mL of water = 5.023 grams

The reaction between tartaric acid and sodium hydroxide is presented as follows;

C₄H₆O₄ (aq) + 2NaOH(aq) $\longrightarrow$ C₄H₄O₄Na₂ + 2H₂O

Therefore;

1 mole of tartaric acid reacts with 2 moles of sodium hydroxide.

Molar mass of tartaric acid = 150.087 g/mol

$Number \ of \ moles \ of \ tartaric \ acid = \dfrac{5.023}{150.087} \times \dfrac{34.2}{250.0} \approx \mathbf{4.578 \times 10^{-3}}$

Which gives;

Number of moles in 40.1 ml of the sodium hydroxide solution is therefore;

$Moles \ of \ NaOH \approx \dfrac{40.1}{28.3} \times 2 \times 4.578 \times 10^{-3 } \approx \mathbf{0.13}$

The reaction between acetic acid and NaOH is presented as follows;

CH₃COOH + NaOH $\longrightarrow$ CH₃COONa + H₂O

Number of moles of acetic acid = Number of moles of NaOH

Which gives;

Number of moles of acetic acid in the vinegar = 0.13 moles

Molar mass of acetic acid = 60.052 g/mol

Mass of acetic acid = 60.052 g/mol × 0.13 moles = 7.80676 g

$Percentage \ by \ weight = \dfrac{7.80676}{21.88} \times 100 \approx \mathbf{35.68\%}$

• The percentage (w/w) of acetic acid in the vinegar = 35.68%

Learn more about finding the percentage by weight of a substance here:

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