Calculate the ratio of NaF to HF required to create a buffer with pH = 3.90.

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Identify the relevant equation for buffer solutions, which is the Henderson-Hasselbalch equation: \( \text{pH} = \text{pK}_a + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \).

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 \( \text{pK}_a = -\log(K_a) \).

Substitute the given pH value (3.90) and the \( \text{pK}_a \) of HF into the Henderson-Hasselbalch equation.

Rearrange the equation to solve for the ratio \( \frac{[\text{NaF}]}{[\text{HF}]} \), which is \( 10^{(\text{pH} - \text{pK}_a)} \).

Calculate the ratio \( \frac{[\text{NaF}]}{[\text{HF}]} \) using the rearranged equation.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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, [HA] is the concentration of the weak acid, and pKa is the acid dissociation constant. This equation is essential for determining the ratio of NaF to HF needed to achieve the desired pH.

pKa and Acid-Base Strength

The pKa value is a measure of the strength of an acid in solution; it is the negative logarithm of the acid dissociation constant (Ka). A lower pKa indicates a stronger acid, while a higher pKa indicates a weaker acid. For HF, knowing its pKa allows for the calculation of the necessary concentrations of HF and NaF to achieve the target pH of 3.90 in the buffer solution.

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