A particular sample of vinegar has a pH of 2.90. If acetic acid is the only acid that vinegar contains (Ka = 1.8 * 10^-5), calculate the concentration of acetic acid in the vinegar.

Name: Chemistry: The Central Science
Author: Brown
ISBN: 9780137542970

Verified step by step guidance

Step 1: Understand that pH is a measure of the hydrogen ion concentration \([H^+]\) in a solution. Use the formula \(pH = -\log[H^+]\) to find \([H^+]\).

Step 2: Rearrange the formula to solve for \([H^+]\): \([H^+] = 10^{-pH}\). Substitute the given pH value of 2.90 into this equation to calculate \([H^+]\).

Step 3: Recognize that acetic acid \((CH_3COOH)\) is a weak acid and partially dissociates in water according to the equation: \(CH_3COOH \rightleftharpoons CH_3COO^- + H^+\).

Step 4: Use the expression for the acid dissociation constant \(K_a\) for acetic acid: \(K_a = \frac{[CH_3COO^-][H^+]}{[CH_3COOH]}\). Assume \([CH_3COO^-] = [H^+]\) at equilibrium since each mole of acetic acid that dissociates produces one mole of \(H^+\) and one mole of \(CH_3COO^-\).

Step 5: Substitute \([H^+]\) from Step 2 and \(K_a = 1.8 \times 10^{-5}\) into the \(K_a\) expression to solve for the initial concentration of acetic acid \([CH_3COOH]\).

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

pH and pKa

pH is a measure of the acidity or basicity of a solution, defined as the negative logarithm of the hydrogen ion concentration. The pKa is the negative logarithm of the acid dissociation constant (Ka) and indicates the strength of an acid; lower pKa values correspond to stronger acids. Understanding the relationship between pH and pKa is essential for calculating the concentration of acids in solution.

Acid Dissociation Constant (Ka)

The acid dissociation constant (Ka) quantifies the strength of an acid in solution, representing the equilibrium constant for the dissociation of the acid into its ions. For acetic acid, the dissociation can be expressed as CH3COOH ⇌ H+ + CH3COO-. A higher Ka value indicates a stronger acid, while a lower value suggests a weaker acid. This concept is crucial for determining the concentration of acetic acid from the given pH.

Concentration Calculations

Concentration calculations involve determining the amount of solute present in a given volume of solution. In this context, the concentration of acetic acid can be derived from the pH and the Ka value using the formula that relates pH to the concentration of hydrogen ions and the dissociation of the acid. This process often requires rearranging equations and applying the principles of equilibrium to find the unknown concentration.

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