Calculate the ratio of NaF to HF required to create a buffer with pH = 4.00.

Verified step by step guidance

1. Identify the relevant equation for buffer solutions, which is the Henderson-Hasselbalch equation: \( \text{pH} = \text{pK}_a + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \).
2. Determine the \( \text{pK}_a \) of HF. The \( \text{pK}_a \) is the negative logarithm of the acid dissociation constant \( K_a \) for HF. Look up or calculate \( \text{pK}_a \) using \( \text{pK}_a = -\log(K_a) \).
3. Substitute the given pH value and the \( \text{pK}_a \) of HF into the Henderson-Hasselbalch equation: \( 4.00 = \text{pK}_a + \log \left( \frac{[\text{NaF}]}{[\text{HF}]} \right) \).
4. Rearrange the equation to solve for the ratio \( \frac{[\text{NaF}]}{[\text{HF}]} \): \( \log \left( \frac{[\text{NaF}]}{[\text{HF}]} \right) = 4.00 - \text{pK}_a \).
5. Calculate the antilogarithm to find the ratio: \( \frac{[\text{NaF}]}{[\text{HF}]} = 10^{(4.00 - \text{pK}_a)} \).

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, the buffer is formed from hydrofluoric acid (HF) and sodium fluoride (NaF), which helps maintain a stable pH in the solution.

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 [A-] is the concentration of the conjugate base and [HA] is the concentration of the weak acid. This equation is essential for determining the ratio of NaF to HF needed to achieve a specific pH.

pKa and Acid-Base Strength

The pKa is the negative logarithm of the acid dissociation constant (Ka) and indicates the strength of an acid; lower pKa values correspond to stronger acids. For HF, knowing its pKa allows us to calculate the necessary concentrations of HF and NaF to achieve the desired pH. Understanding the relationship between pKa and pH is crucial for effective buffer preparation.