A 0.185 M solution of a weak acid (HA) has a pH of 2.95. Calculate the acid ionization constant (K_a) for the acid.

Verified step by step guidance

1. Step 1: Understand the problem. We are given the concentration of a weak acid (HA) and its pH. We need to find the acid ionization constant (K_a).
2. Step 2: Calculate the concentration of hydrogen ions [H^+]. Use the pH formula: \( \text{pH} = -\log[H^+] \). Rearrange to find \([H^+] = 10^{-\text{pH}}\).
3. Step 3: Write the equilibrium expression for the dissociation of the weak acid: \( \text{HA} \rightleftharpoons \text{H}^+ + \text{A}^- \).
4. Step 4: Set up the expression for the acid ionization constant \( K_a \): \( K_a = \frac{[H^+][A^-]}{[HA]} \). Assume \([H^+] = [A^-]\) at equilibrium and \([HA] = [HA]_0 - [H^+]\).
5. Step 5: Substitute the values into the \( K_a \) expression. Use the initial concentration of HA and the calculated [H^+] to find \( K_a \).

Key Concepts

pH and pOH

pH is a measure of the hydrogen ion concentration in a solution, defined as the negative logarithm of the hydrogen ion concentration (pH = -log[H+]). A lower pH indicates a higher concentration of hydrogen ions, which is typical for acidic solutions. Understanding pH is crucial for calculating the concentration of ions in weak acid solutions.

Weak Acids and Ionization

Weak acids do not completely dissociate in solution, establishing an equilibrium between the undissociated acid (HA) and its ions (H+ and A-). The degree of ionization is essential for calculating the acid ionization constant (Ka), which quantifies the strength of the acid. The equilibrium expression for a weak acid is given by Ka = [H+][A-]/[HA].

Acid Ionization Constant (Ka)

The acid ionization constant (Ka) is a quantitative measure of the strength of an acid in solution. It reflects the extent to which an acid donates protons to water, with larger Ka values indicating stronger acids. Calculating Ka involves using the concentrations of the ions at equilibrium, which can be derived from the initial concentration and the pH of the solution.