Ch.17 - Acids and Bases

Problem 68

Chapter 17, Problem 68

Determine the [H3O+] and pH of a 0.100 M solution of formic acid.

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Identify the chemical formula for formic acid, which is HCOOH, and recognize that it is a weak acid.

Write the dissociation equation for formic acid in water: \( \text{HCOOH} + \text{H}_2\text{O} \rightleftharpoons \text{H}_3\text{O}^+ + \text{HCOO}^- \).

Use the acid dissociation constant \( K_a \) for formic acid to set up an expression: \( K_a = \frac{[\text{H}_3\text{O}^+][\text{HCOO}^-]}{[\text{HCOOH}]} \).

Assume that the initial concentration of \( \text{H}_3\text{O}^+ \) and \( \text{HCOO}^- \) is 0, and let \( x \) be the change in concentration at equilibrium, leading to \( [\text{H}_3\text{O}^+] = x \), \( [\text{HCOO}^-] = x \), and \( [\text{HCOOH}] = 0.100 - x \).

Substitute these expressions into the \( K_a \) expression and solve for \( x \), which represents \( [\text{H}_3\text{O}^+] \), then calculate the pH using \( \text{pH} = -\log[\text{H}_3\text{O}^+] \).

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Key Concepts

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

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 weak acids like formic acid, this equilibrium is established when the acid partially dissociates in water, producing hydronium ions (H3O+) and its conjugate base. Understanding this concept is crucial for calculating the concentration of H3O+ in the solution.

Dissociation Constant (Ka)

The dissociation constant (Ka) is a quantitative measure of the strength of an acid in solution. It represents the equilibrium constant for the dissociation of the acid into its ions. For formic acid, knowing its Ka value allows us to set up an equilibrium expression to calculate the concentration of H3O+ ions in a 0.100 M solution, which is essential for determining pH.

pH Scale

The pH scale is a logarithmic scale used to specify the acidity or basicity of a solution. It is defined as the negative logarithm of the hydronium ion concentration: pH = -log[H3O+]. A lower pH indicates a more acidic solution, while a higher pH indicates a more basic one. Understanding how to calculate pH from the concentration of H3O+ is vital for interpreting the acidity of the formic acid solution.

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