Calculate the pH of 0.250 L of a 0.36 M formic acid–0.30 M sodium formate buffer before and after the addition of (a) 0.0050 mol of NaOH. Assume that the volume remains constant. (b) 0.0050 mol of HCl. Assume that the volume remains constant.

Verified step by step guidance

1. Identify the components of the buffer system: formic acid (HCOOH) and sodium formate (HCOONa). Formic acid is the weak acid, and sodium formate is its conjugate base.
2. Use the Henderson-Hasselbalch equation to calculate the initial pH of the buffer: \( \text{pH} = \text{pK}_a + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \), where \( \text{pK}_a \) is the negative logarithm of the acid dissociation constant of formic acid.
3. For part (a), calculate the change in moles of formic acid and formate after adding 0.0050 mol of NaOH. NaOH will react with formic acid to form water and formate ions, changing their concentrations.
4. Recalculate the pH using the Henderson-Hasselbalch equation with the new concentrations of formic acid and formate after the addition of NaOH.
5. For part (b), calculate the change in moles of formic acid and formate after adding 0.0050 mol of HCl. HCl will react with formate ions to form formic acid, changing their concentrations. Recalculate the pH using the Henderson-Hasselbalch equation with the new concentrations.

Key Concepts

Buffer Solutions

Buffer solutions are mixtures that resist changes in pH when small amounts of acid or base are added. They typically consist of a weak acid and its conjugate base, or a weak base and its conjugate acid. In this case, formic acid (weak acid) and sodium formate (conjugate base) create a buffer system that helps maintain a stable pH despite the addition of NaOH or HCl.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a mathematical formula used to calculate the pH of a buffer solution. It is expressed as pH = pKa + log([A-]/[HA]), where pKa is the negative logarithm of the acid dissociation constant, [A-] is the concentration of the conjugate base, and [HA] is the concentration of the weak acid. This equation is essential for determining the pH before and after the addition of strong acids or bases.

Acid-Base Neutralization

Acid-base neutralization is a chemical reaction where an acid reacts with a base to produce water and a salt, often resulting in a change in pH. In this scenario, the addition of NaOH (a strong base) will react with formic acid, while the addition of HCl (a strong acid) will react with sodium formate. Understanding this concept is crucial for predicting how the buffer's pH will change upon the addition of these substances.