Problem 84 - Chemistry: The Central Science in SI Units, Global Edition

Question

The distinctive odor of vinegar is due to aceticacid, \(\mathrm{CH}_{3} \mathrm{COOH}\), which reacts with sodium hydroxide according to: \(\mathrm{CH}_{3} \mathrm{COOH}(a q)+\mathrm{NaOH}(a q) \longrightarrow\) $$ \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{NaCH}_{3} \mathrm{COO}(a q) $$ If \(3.45 \mathrm{~mL}\) of vinegar needs \(42.5 \mathrm{~mL}\) of \(0.115 \mathrm{M} \mathrm{NaOH}\) to reach the equivalence point in a titration, how many grams of acetic acid are in a \(1.00-\) qt sample of this vinegar?

Step-by-Step Solution

Answer

The mass of acetic acid in a 1.00-quart sample of this vinegar is 80.67 grams.

Step 1: Find the moles of NaOH at the equivalence point

We are given that the volume of NaOH needed to reach the equivalence point is 42.5 mL, and the concentration of NaOH solution is 0.115 M. To find the moles of NaOH, we can use the formula: moles of NaOH = volume (in liters) × concentration First, we need to convert the volume of NaOH from mL to L: 42.5 mL = 42.5 / 1000 L = 0.0425 L Now we can find the moles of NaOH: moles of NaOH = 0.0425 L × 0.115 mol/L = 0.0048875 mol This is the moles of NaOH at the equivalence point.

Step 2: Use stoichiometry to find the moles of acetic acid

From the balanced chemical equation: CH3COOH(aq) + NaOH(aq) → H2O(l) + NaCH3COO(aq) At the equivalence point, the moles of acetic acid are equal to the moles of NaOH. Therefore, moles of acetic acid = 0.0048875 mol

Step 3: Calculate the concentration of acetic acid in the vinegar sample

We are given that the volume of vinegar sample used in the titration is 3.45 mL. First, we need to convert the volume of vinegar from mL to L: 3.45 mL = 3.45 / 1000 L = 0.00345 L Now, we can calculate the concentration of acetic acid in the vinegar sample using the formula: concentration of acetic acid = moles of acetic acid / volume (in liters) concentration of acetic acid = 0.0048875 mol / 0.00345 L = 1.4167 M

Step 4: Convert the volume of vinegar from milliliters to quarts

We need to find the amount of acetic acid in a 1.00-quart sample of this vinegar. First, we need to convert the volume of vinegar from quarts to liters: 1.00 qt = 1.00 × 0.946353 L/qt = 0.946353 L

Step 5: Calculate the mass of acetic acid in the 1.00-quart sample

To find the mass of acetic acid in the 1.00-quart sample, we can use the formula: mass of acetic acid = volume (in liters) × concentration × molar mass The molar mass of acetic acid is 60.05 g/mol. Therefore, mass of acetic acid = 0.946353 L × 1.4167 mol/L × 60.05 g/mol = 80.67 g So, there are 80.67 grams of acetic acid in a 1.00-quart sample of this vinegar.

Key Concepts

Understanding Acetic Acid in Vinegar

Acetic acid is the key ingredient in vinegar, giving it a distinct sour smell and taste. It is known chemically as \( \text{CH}_3\text{COOH} \), and plays an essential role in many chemical reactions, including titrations. In this titration problem, acetic acid reacts with sodium hydroxide, \( \text{NaOH} \), to form water and sodium acetate, \( \text{NaCH}_3\text{COO} \).

The titration process measures how much \( \text{NaOH} \) is needed to completely react with the acetic acid in vinegar. This helps determine the concentration of acetic acid in the sample. Understanding this reaction is important for applications in food science and chemistry.

Key Properties of Acetic Acid:

• Weak Acid: Only partially ionizes in water.
• Found naturally in vinegar.
• Used in household cleaning and food preservation.

Role of Sodium Hydroxide in Titration

Sodium hydroxide, \( \text{NaOH} \), is a strong base used commonly in titration experiments. It completely dissociates in water to form ions, making it very effective in neutralizing acids. In our exercise, the concentration of \( \text{NaOH} \) was crucial in calculating the moles to find the strength of the acetic acid.

Working with \( \text{NaOH} \) involves understanding its properties:

• Highly Alkaline: Strong base that reacts easily with acids.
• Safety Precautions: Can cause burns, so handle with care.
• Versatile: Used in many industries like paper, soap, and textiles.

The quantity of \( \text{NaOH} \) used at equivalence point tells us the amount of acetic acid present. By calculating moles and using the given concentration, precise titration measures help in deducing the molar concentration of acetic acid in vinegar.

Applying Stoichiometry in Titration Calculations

Stoichiometry is the quantitative relationship in chemistry that helps us understand the proportions in which reactants and products combine. In our titration problem, stoichiometry tells us that the moles of \( \text{CH}_3\text{COOH} \) and \( \text{NaOH} \) are equal at the equivalence point because of a 1:1 molar ratio in the balanced equation.

Using the balanced chemical equation:

\( \text{CH}_3\text{COOH} + \text{NaOH} \rightarrow \text{H}_2\text{O} + \text{NaCH}_3\text{COO} \)

This relationship allows us to calculate the unknown concentration of acetic acid when we know the moles of \( \text{NaOH} \) used. Here's how stoichiometry simplifies the process:

• Convert volumes to liters to work with concentrations.
• Use the molar ratio from the balanced equation.
• Determine moles from volume and concentration.

Once you have the moles, it's straightforward to find the concentration and mass of the acid in different volumes, such as converting mL to quarts, and finally calculating mass using its molar mass. These calculations are vital in laboratory settings to ensure precise measurements.