Question

For a solution of acetic acid (CH \(_{3} \mathrm{COOH}\) ) to be called "vinegar," it must contain \(5.00 \%\) acetic acid by mass. If a vinegar is made up only of acetic acid and water, what is the molarity of acetic acid in the vinegar? The density of vinegar is \(1.006 \mathrm{~g} / \mathrm{mL}\).

Short answer

Answer: The molarity of acetic acid in the vinegar solution is 0.838 M.

Step-by-step solution

Calculate the mass of acetic acid in 100 mL of vinegar

Since the concentration of acetic acid is given as 5.00% by mass, we can calculate the mass of acetic acid in 100 mL of the solution. First, let's find the mass of 100 mL of vinegar using the given density: mass of vinegar = volume × density = 100 mL × 1.006 g/mL = 100.6 g Next, let's find the mass of acetic acid in this 100 mL of vinegar: mass of acetic acid = 5.00% × mass of vinegar = 0.05 × 100.6 g = 5.03 g

Convert the mass of acetic acid to moles

To find the moles of acetic acid in the vinegar, we need to use the molar mass of acetic acid (C\(_{2}\)H\(_{4}\)O\(_{2}\)). The molar mass of acetic acid is: Molar mass = 2×12.01 g/mol (C) + 4×1.01 g/mol (H) + 2×16.00 g/mol (O)= 60.05 g/mol Now, we can convert the mass of acetic acid to moles: moles of acetic acid = mass of acetic acid / molar mass= 5.03 g / 60.05 g/mol = 0.0838 mol

Convert the volume of vinegar to liters

To calculate molarity, we need to express the volume of the solution in liters. As we calculated the moles of acetic acid in 100 mL of the solution, we will convert this volume to liters: volume of vinegar = 100 mL × (1 L / 1000 mL) = 0.100 L

Calculate the molarity of acetic acid

Now we can find the molarity of acetic acid by dividing the moles of acetic acid by the volume of the solution in liters: molarity of acetic acid = moles of acetic acid / volume of vinegar= 0.0838 mol / 0.100 L = 0.838 M The molarity of acetic acid in the vinegar is 0.838 M.

Key concepts

Solution Concentration

Understanding solution concentration is crucial when working with chemical solutions. Concentration refers to the amount of a substance, known as the solute, that is dissolved in a specific volume of solvent.

When we talk about molarity, which is a common unit of concentration, it's defined as the number of moles of solute per liter of solution. In the context of our acetic acid exercise, we are determining the molarity of the acetic acid in vinegar, which is a solution of acetic acid and water.

The formula for molarity is expressed as \( M = \frac{n}{V} \), where \( M \) is the molarity, \( n \) is the number of moles of the solute, and \( V \) is the volume of the solution in liters. By applying this formula to the given exercise, you can find out how concentrated the acetic acid is in the vinegar. This information is practical, not just for culinary purposes but also for scientific experiments where precise concentrations are necessary.

Molar Mass Calculation

The molar mass is a fundamental property in chemistry that represents the weight of one mole of a substance. It's measured in grams per mole (g/mol) and is calculated by summing the atomic masses of all atoms present in a molecule.

In our exercise, the molar mass of acetic acid (\( CH_3COOH \)) must be calculated to convert grams of acetic acid to moles. This step is essential for determining the molarity of a solution.

To illustrate with acetic acid, which has the molecular formula \( C_2H_4O_2 \), the molar mass is calculated as follows:\( Molar Mass = (2 \times 12.01 \, g/mol) + (4 \times 1.01 \, g/mol) + (2 \times 16.00 \, g/mol) = 60.05 \, g/mol \).

Understanding how to calculate molar mass is not only critical for determining solution concentration, but also for stoichiometry, where you need to know how molecules interact in chemical reactions.

Acid-Base Chemistry

Acid-base chemistry deals with the properties and reactions of acids and bases. Acids, like acetic acid in vinegar, are substances that can donate protons (\( H^+ \)) in a chemical reaction, while bases can accept them. The strength of an acid or base is measured on the pH scale. Strong acids completely dissociate in water, whereas weak acids like acetic acid only partially dissociate. This partial dissociation is crucial for preserving the flavor and preventing the over-acidity of vinegar.

Furthermore, the molarity of acids in a solution is important in titration—a technique used to determine the concentration of an unknown acid or base solution. It involves a reaction with a known volume and concentration of a base or acid. The completion of the reaction is usually indicated by a color change of an indicator or by measuring the pH of the solution.

Relevance in Vinegar Production

In vinegar production, knowing the molarity helps control the tartness and microbial activity, ensuring the product's safety and taste. With the correct molarity, vinegar can be used effectively as a preservative, in cooking, or even for cleaning, all of which rely on its acid-base properties.