What is the mass of sodium formate required to be dissolved in 250.0 cm³ of a 1.4 M formic acid solution to prepare a buffer solution with a pH of 3.36?

Verified step by step guidance

1. Identify the components of the buffer solution: formic acid (HCOOH) and sodium formate (HCOONa).
2. Use the Henderson-Hasselbalch equation for buffer solutions: \( \text{pH} = \text{pK}_a + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \), where \([\text{A}^-]\) is the concentration of the conjugate base (sodium formate) and \([\text{HA}]\) is the concentration of the acid (formic acid).
3. Look up or calculate the \(\text{pK}_a\) of formic acid. It is typically around 3.75.
4. Rearrange the Henderson-Hasselbalch equation to solve for \([\text{A}^-]\): \([\text{A}^-] = [\text{HA}] \times 10^{(\text{pH} - \text{pK}_a)}\).
5. Calculate the moles of sodium formate needed using the concentration \([\text{A}^-]\) and the volume of the solution (250.0 cm³ or 0.250 L), then convert moles to mass using the molar mass of sodium formate.

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 (a weak acid) and sodium formate (its conjugate base) are used to create a buffer solution with a specific pH.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation relates the pH of a buffer solution to the concentration of its acid and conjugate base. It is expressed as pH = pKa + log([A-]/[HA]), where pKa is the acid dissociation constant. This equation is essential for calculating the required concentrations of sodium formate and formic acid to achieve the desired pH.

Molarity and Dilution

Molarity (M) is a measure of concentration defined as moles of solute per liter of solution. In this problem, the molarity of the formic acid solution is given, and understanding how to calculate the number of moles from this concentration is crucial. Additionally, the concept of dilution is important when preparing solutions to ensure the correct final concentrations are achieved.