(b) Calculate the percent ionization of 0.0075 M butanoic acid in a solution containing 0.085 M sodium butanoate.

Verified step by step guidance

1. Identify the chemical equilibrium involved: Butanoic acid (C₃H₇COOH) partially ionizes in water to form butanoate ions (C₃H₇COO⁻) and hydrogen ions (H⁺).
2. Recognize that this is a buffer solution problem, as it contains a weak acid (butanoic acid) and its conjugate base (sodium butanoate).
3. Use the Henderson-Hasselbalch equation to find the pH of the solution: \( \text{pH} = \text{pK}_a + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \), where \([\text{A}^-]\) is the concentration of the conjugate base and \([\text{HA}]\) is the concentration of the acid.
4. Calculate the percent ionization using the formula: \( \text{Percent Ionization} = \left( \frac{[\text{H}^+]}{[\text{HA}]} \right) \times 100 \% \), where \([\text{H}^+]\) is the concentration of hydrogen ions at equilibrium.
5. Substitute the values obtained from the Henderson-Hasselbalch equation and the initial concentration of butanoic acid into the percent ionization formula to find the percent ionization.

Key Concepts

Ionization of Weak Acids

Weak acids, like butanoic acid, do not completely dissociate in solution. Instead, they establish an equilibrium between the undissociated acid and its ions. The degree to which a weak acid ionizes can be quantified, and this is crucial for calculating percent ionization, which indicates how much of the acid has converted to ions.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation relates the pH of a buffer solution to the concentration of the acid and its conjugate base. In this case, butanoic acid and sodium butanoate form a buffer system. This equation is essential for determining the pH, which is necessary for calculating the percent ionization of the weak acid in the presence of its salt.

Percent Ionization Calculation

Percent ionization is calculated by taking the concentration of ionized acid at equilibrium, dividing it by the initial concentration of the acid, and multiplying by 100. This metric provides insight into the strength of the acid and its behavior in solution, especially when influenced by the presence of a conjugate base, as seen with sodium butanoate.