Problem 44 - Chemistry: Principles and Reactions

Question

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"?

Step-by-Step Solution

Answer

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

Step 1: 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.

Step 2: 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

Step 3: 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

Step 4: 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

Step 5: 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.

Key Concepts

Vinegar

Vinegar is a well-known household ingredient and a staple in kitchens around the world. It is primarily composed of acetic acid and water. To be officially classified as vinegar, the product must contain a minimum of 5% acetic acid by mass. This concentration ensures the characteristic acidity and flavor vinegar is known for. Vinegar is often used as a condiment, preservative, and cleaning agent due to its acidity.

Understanding vinegar's composition helps us determine its label accuracy. In our exercise, we have a raspberry-flavored vinegar whose acetic acid content is questioned. Through titration, we can accurately assess whether this product fits the definition of vinegar by measuring its acetic acid percentage.

Acetic Acid

Acetic acid, scientifically known as \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\), is the main component responsible for vinegar's pungent smell and sour taste. It is a weak, monoprotic acid and an organic compound with a distinct smell commonly associated with vinegar.

In the industrial and culinary world, acetic acid's concentration in vinegar defines its strength. The exercise challenges us to calculate this concentration in a raspberry vinegar sample through a titration process to verify if it meets the minimum 5% requirement. Thus, knowing how much acetic acid is in a solution is essential for qualifying it as vinegar.

Stoichiometry

Stoichiometry is a core concept in chemistry that involves the calculation of reactants and products in chemical reactions. It enables chemists to predict the quantities involved in reactions accurately. In the context of our exercise, stoichiometry helps us determine the amount of acetic acid in the vinegar sample.

The balanced chemical equation \(2\mathrm{HC}_{2}\mathrm{H}_{3}\mathrm{O}_{2} + \mathrm{Ba}(\mathrm{OH})_{2} \rightarrow \mathrm{Ba}(\mathrm{C}_{2}\mathrm{H}_{3}\mathrm{O}_{2})_{2} + 2\mathrm{H}_{2}\mathrm{O}\) provides a stoichiometric relationship that shows two moles of acetic acid react with one mole of barium hydroxide. This means that for every mole of Ba(OH)\(_2\) used, two moles of \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) are consumed. This relationship is crucial for finding the moles of acetic acid once we know the moles of Ba(OH)\(_2\) used in the titration.

Titration Calculations

Titration is an analytical technique used to determine the concentration of a given component in a solution. Through this method, we can ascertain the exact amount of acetic acid in the raspberry vinegar sample.

In the exercise, using a 0.1250 M solution of barium hydroxide \(\mathrm{Ba}(\mathrm{OH})_{2}\), we can perform a titration that neutralizes the acetic acid present. By measuring the volume of \(\mathrm{Ba}(\mathrm{OH})_{2}\) solution used (37.50 mL), we calculate the number of moles of the base and use stoichiometry to find the corresponding moles of acetic acid.

• First, determine the moles of \(\mathrm{Ba}(\mathrm{OH})_{2}\) using its molarity and volume.
• From the balanced equation, find the moles of \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) using the stoichiometric ratio.
• Convert moles of acetic acid to mass using its molar mass.
• Compute the percentage of acetic acid to verify if it classifies as vinegar.

These calculations confirm that the sample has an adequate concentration of acetic acid to be called vinegar.