Acetic acid 1CH3COOH; Ka = 1.8 * 10-52 has a concentration in vinegar of 3.50% by mass. What is the pH of vinegar? (The density of vinegar is 1.02 g/mL.)

Verified step by step guidance

1. Calculate the mass of vinegar used, assuming a sample volume of 1 mL. Use the density of vinegar (1.02 g/mL) to find the mass in grams.
2. Determine the mass of acetic acid in the sample by using the percentage concentration (3.50% by mass). Multiply the total mass of the vinegar by 3.50% to find the mass of acetic acid.
3. Convert the mass of acetic acid to moles using its molar mass (60.05 g/mol for CH3COOH). Divide the mass of acetic acid by its molar mass.
4. Calculate the molarity of acetic acid in the solution. Since the volume of the solution is 1 mL, convert this volume to liters and use it to find the molarity (moles of solute per liter of solution).
5. Use the acid dissociation constant (Ka) for acetic acid and the molarity calculated in the previous step to set up the expression for Ka. Solve for the concentration of H+ ions and use the pH formula pH = -log[H+] to find the pH of the vinegar.

Key Concepts

Acid-Base Equilibrium

Acid-base equilibrium refers to the balance between the concentrations of acids and their conjugate bases in a solution. In the case of acetic acid, it partially dissociates in water to form acetate ions and hydrogen ions. The equilibrium constant, Ka, quantifies this dissociation, indicating the strength of the acid. Understanding this concept is crucial for calculating pH, as it directly relates to the concentration of hydrogen ions in the solution.

Concentration and Density

Concentration is a measure of how much solute is present in a given volume of solution, often expressed in terms of mass percent or molarity. In this question, the concentration of acetic acid is given as 3.50% by mass, which means 3.50 grams of acetic acid per 100 grams of solution. Density, defined as mass per unit volume, is used to convert mass percent into molarity, allowing for the calculation of the number of moles of acetic acid in a specific volume of vinegar.

pH Calculation

pH is a logarithmic scale used to specify the acidity or basicity of a solution, calculated as the negative logarithm of the hydrogen ion concentration (pH = -log[H+]). To find the pH of vinegar, one must first determine the concentration of hydrogen ions produced from the dissociation of acetic acid. This involves using the Ka value and the initial concentration of acetic acid to find the equilibrium concentrations, which can then be used to calculate the pH.