Problem 100 - Chemistry The Molecular Science

Question

Vinegar must contain at least \(4 \%\) acetic acid \((0.67 \mathrm{M}) .\) A 5.00-mL sample of commercial vinegar required \(33.5 \mathrm{~mL}\) of \(0.100-\mathrm{M} \mathrm{NaOH}\) to reach the equivalence point. Do calculations to determine whether the vinegar meets the legal requirement of at least \(4 \%\) acetic acid.

Step-by-Step Solution

Answer

Yes, the vinegar meets the legal requirement of at least 4% acetic acid.

Step 1: Calculate moles of NaOH

Since the concentration of the NaOH solution is given as 0.100 M and the volume required is 33.5 mL, we first convert this volume into liters. Thus, the volume in liters is \(33.5 \times 10^{-3} \text{ L}\). moles of NaOH = concentration \(\times\) volume = \(0.100 \text{ M} \times 33.5 \times 10^{-3} \text{ L} = 0.00335 \text{ mol NaOH}\).

Step 2: Relate moles of NaOH to moles of acetic acid

At the equivalence point, the moles of NaOH added are equal to the moles of acetic acid in the vinegar since the reaction between NaOH and acetic acid is a 1:1 stoichiometry. Therefore, moles of acetic acid = 0.00335 mol.

Step 3: Calculate mass of acetic acid

To find the mass of acetic acid, first calculate the molar mass of acetic acid \((\text{CH}_3\text{COOH})\), which is approximately 60.05 g/mol. Next, use the number of moles to find the mass: \(0.00335 \text{ mol} \times 60.05 \text{ g/mol} = 0.2011675 \text{ g}\). Round this value to 0.201 g for simplicity.

Step 4: Calculate mass percent of acetic acid in vinegar

The percentage mass of acetic acid is calculated by dividing the mass of acetic acid by the mass of the vinegar sample and multiplying by 100. Assuming the density of vinegar is approximately 1 g/mL, the mass of the 5.00 mL sample is roughly 5.00 g. Thus, \(\text{Percentage} = \left( \frac{0.201 \text{ g}}{5.00 \text{ g}} \right) \times 100\% = 4.02\%\).

Step 5: Determine if the legal requirement is met

Since the calculated percentage of acetic acid (4.02%) is greater than the required minimum (4%), the vinegar meets the legal requirement.

Key Concepts

Acetic Acid Concentration

Acetic acid (\(\text{CH}_3\text{COOH}\)) is the main component that determines vinegar's sharp flavor and quality. The concentration of acetic acid is critical as it ensures the vinegar's effectiveness in culinary and cleaning applications. In commercial vinegars, legally mandated levels often require a minimum concentration, expressed as a percentage. For instance, a requirement is typically set at a minimum of 4% by mass.

To measure this, one would determine the mass of acetic acid present in a sample and compare it to the total mass of the vinegar. In our problem, we calculated that the vinegar sample contains 4.02% acetic acid, which satisfies the minimum legal requirement. Understanding these values ensures both compliance and quality control in vinegar production.

Molarity Calculations

Molarity is a measure of concentration used to indicate the number of moles of solute per liter of solution, denoted as mol/L or simply M. This concept is pivotal in determining how concentrated a solution is, which is particularly useful in chemistry titrations.

In the given problem, the molarity of sodium hydroxide (\(\text{NaOH}\)) was used to calculate the moles of acetic acid in the vinegar sample. By using the formula for molarity: \[\text{Moles of Solute} = \text{Molarity} \times \text{Volume (L)}\]we determined the moles of NaOH. This calculation provided the information needed to deduce the moles of acetic acid in the sample since the two react in a 1:1 mole ratio.

Titration Process

Titration is a laboratory technique involving the gradual addition of a solution (titrant) of known concentration to another solution (analyte) to determine its concentration. The process proceeds until reaching the equivalence point, where the amount of titrant exactly reacts with the analyte.

During our vinegar test, the \(0.100\text{ M}\) NaOH was added incrementally to the vinegar until the equivalence point was reached, indicated by a noticeable change (often with a pH indicator). This end point marks the completion of the reaction, allowing for precise calculation of the acetic acid concentration. This method is dependable for ensuring that vinegar complies with acetic acid content standards.

Stoichiometry

Stoichiometry deals with the quantitative relationships between reactants and products in a chemical reaction. It is the backbone of chemical calculations, including titrations, as it reveals how substances interact in fixed proportions.

In our exercise, the stoichiometry of the reaction between acetic acid and NaOH is 1:1. This means one mole of acetic acid reacts with one mole of NaOH. Knowing this ratio allows us to equate the moles of NaOH used in the titration to those of acetic acid in the vinegar. Without this mole-to-mole relationship, it would be impossible to accurately determine the concentration of acetic acid required to meet legal standards.