Given a 0.300 M solution of HF, what concentration of NaF is required to achieve [H3O+] = 2.3 × 10^{-4} M? (Assume Ka for HF = 7.2 × 10^{-4} and that NaF fully dissociates.)

• A. 0.20 M
• B. 0.30 M
• C. 0.40 M
• D. 0.10 M

Answer: (D)

Verified step by step guidance

1. Recognize that this problem involves a buffer solution made from a weak acid (HF) and its conjugate base (F⁻) from NaF. The goal is to find the concentration of NaF needed to achieve a specific hydronium ion concentration, [H₃O⁺].
2. Write the expression for the acid dissociation constant, \(K_a\), of HF: \[K_a = \frac{[H_3O^+][F^-]}{[HF]}\] Here, \([H_3O^+]\) is given, \([HF]\) is the initial concentration (0.300 M), and \([F^-]\) comes from the dissociation of NaF, which we need to find.
3. Rearrange the \(K_a\) expression to solve for \([F^-]\): \[[F^-] = \frac{K_a \times [HF]}{[H_3O^+]}\] This equation assumes that the concentrations of HF and F⁻ do not change significantly due to dissociation or association, which is valid for buffer calculations.
4. Substitute the known values into the rearranged equation: - \(K_a = 7.2 \times 10^{-4}\) - \([HF] = 0.300\) M - \([H_3O^+] = 2.3 \times 10^{-4}\) M Calculate \([F^-]\) to find the concentration of NaF required, since NaF fully dissociates to give \([F^-]\).
5. Interpret the result: the calculated \([F^-]\) concentration corresponds to the NaF concentration needed to maintain the desired \([H_3O^+]\) in the buffer solution.