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Chapter 4: Problem 44

For a product to be called "vinegar," it must contain at least \(5.0 \%\) acetic acid, \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\), by mass. A \(10.00-\mathrm{g}\) sample of a "raspberry vinegar" is titrated with \(0.1250 \mathrm{M} \mathrm{Ba}(\mathrm{OH})_{2}\) and required \(37.50 \mathrm{~mL}\) for complete neutralization. Can the product be called a "vinegar"?

Short Answer

Expert verified
Answer: Yes, the raspberry vinegar contains approximately 5.63% acetic acid by mass, which is above the 5.0% requirement.

Step by step solution

01

Write the balanced chemical equation for the reaction

For the reaction between acetic acid (HC2H3O2) and barium hydroxide [Ba(OH)2], the balanced chemical equation is: 2HC2H3O2 + Ba(OH)2 → Ba(C2H3O2)2 + 2H2O This equation tells us that 2 moles of acetic acid reacts with 1 mole of barium hydroxide.
02

Calculate the moles of barium hydroxide used in the reaction

We are given the volume (37.50 mL) and the molarity (0.1250 M) of Ba(OH)2 solution. Using this information, we can calculate the moles of Ba(OH)2 used in the reaction: Moles of Ba(OH)2 = Molarity × Volume = 0.1250 mol/L × 37.50 × 10^{-3} L = 0.0046875 mol
03

Use stoichiometry to find the moles of acetic acid

From the balanced chemical equation: 2 moles of HC2H3O2 react with 1 mole of Ba(OH)2. So, Moles of HC2H3O2 = 2 × Moles of Ba(OH)2 = 2 × 0.0046875 mol = 0.009375 mol
04

Calculate the mass of acetic acid in the sample

Now, we need to find the mass of acetic acid in the 10.00-g sample. The molar mass of HC2H3O2 is approximately 60.05 g/mol. Mass of acetic acid = Moles of HC2H3O2 × Molar mass = 0.009375 mol × 60.05 g/mol = 0.563 g
05

Determine the percentage of acetic acid

Finally, we can find the percentage of acetic acid in the raspberry product: Percentage of acetic acid = (Mass of acetic acid / Total mass of sample) × 100% = (0.563 g / 10.00 g) × 100% ≈ 5.63% Since the percentage of acetic acid in the raspberry product is approximately 5.63%, it can be called a "vinegar" because it contains at least 5.0% acetic acid by mass.

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