Question

You are asked to prepare a \(\mathrm{pH}=3.00\) buffer solution starting from 1.25 \(\mathrm{L}\) of a 1.00 \(\mathrm{M}\) solution of hydrofluoric acid \((\mathrm{HF})\) and any amount you need of sodium fluoride \((\mathrm{NaF})\). (a) What is the \(\mathrm{pH}\) of the hydrofluoric acid solution prior to adding sodium fluoride? (b) How many grams of sodium fluoride should be added to prepare the buffer solution? Neglect the small volume change that occurs when the sodium fluoride is added.

Short answer

(a) The initial pH of the hydrofluoric acid solution is 0. (b) To find the grams of NaF required to prepare the buffer solution, first calculate the moles of F- needed using the Henderson-Hasselbalch equation: \(moles_{F^{-}} = 1.25 \, moles \times 10^{-0.17}\). Then, convert this value to grams using the molar mass of NaF: \(grams_{NaF} = 1.25 \, moles \times 10^{-0.17} \times 41.99 \, g/mol\). Calculate the value to get the required amount of NaF in grams.

Step-by-step solution

Calculate the initial pH of the hydrofluoric acid solution

The pH of the given hydrofluoric acid solution can be calculated using the formula: \[pH = -\log [H^+]\] Since it's a 1 M solution of hydrofluoric acid, the concentration of H+ ions will be equal to the concentration of the acid: \[[H^+] = 1.00 \, M\] Now, plug the concentration into the formula and calculate the pH: \[pH = -\log 1.00 = 0\] The initial pH of the hydrofluoric acid solution is 0.

Use the Henderson-Hasselbalch equation

Apply the Henderson-Hasselbalch equation to find the ratio of F- ions to HF in the buffer solution: \[pH = pK_a + \log \frac{[F^{-}]}{[HF]}\] In this case, we know that pH is 3.00 and pKa of hydrofluoric acid is 3.17. Now substitute these values in the equation. \[3.00 = 3.17 + \log \frac{[F^{-}]}{[HF]}\] Now, we need to solve for the ratio [F-]/[HF].

Calculate the moles of HF and F- ions needed

Solve the equation for the ratio [F-]/[HF]: \[\log \frac{[F^{-}]}{[HF]} = 3.00 - 3.17 = -0.17\] \[\frac{[F^{-}]}{[HF]} = 10^{-0.17}\] We know the initial concentration of HF is 1 M and the volume is 1.25 L, so the moles of HF are: \[moles_{HF} = 1.00 \, M \times 1.25 \, L = 1.25 \, moles\] Now, calculate the moles of F- needed: \[moles_{F^{-}} = moles_{HF} \times \frac{[F^{-}]}{[HF]} = 1.25 \, moles \times 10^{-0.17}\]

Find the amount of NaF required in grams

First, we need to find the molar mass of NaF. The molar mass of Na is 22.99 g/mol and the molar mass of F is 19.00 g/mol. Thus, the molar mass of NaF is: \[M_{NaF} = 22.99 \, g/mol + 19.00 \, g/mol = 41.99 \, g/mol\] Now, multiply the molar mass of NaF by the moles of F- needed to find the grams of NaF required: \[grams_{NaF} = moles_{F^{-}} \times M_{NaF} = 1.25 \, moles \times 10^{-0.17} \times 41.99 \, g/mol\] Calculate the grams of NaF required. So to recap: (a) The initial pH of the hydrofluoric acid solution is 0. (b) Calculate the grams of NaF required using the steps provided above.

Key concepts

pH calculation

Calculating pH is an essential skill in chemistry, especially when working with acids and bases. The pH value indicates the acidity or basicity of a solution. For our problem, the initial step is to calculate the pH of a 1.00 M hydrofluoric acid (HF) solution. To do this, you need to determine the concentration of hydrogen ions \[ H^+ \], which in the case of a strong acid, is equal to the concentration of the acid itself. Since the given HF concentration is 1.00 M, the concentration of \[ H^+ \] ions is also 1.00 M.
The pH is calculated using the formula:

• \[ pH = -\log [H^+] \]

Substituting the concentration into the formula, we get:

• \[ pH = -\log 1.00 = 0 \]

The initial pH of a solution, therefore, indicates it is at maximum acidity (for a strong, fully dissociated acid in solution).
Understanding this baseline helps prepare for modifying the pH with a buffer.

Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation is a critical tool in buffer chemistry used to relate the pH of a solution to the pKa of the acid and the ratio of the concentrations of the conjugate base and the acid. In our exercise, it's used to determine how much sodium fluoride (NaF) needs to be added to attain a specific pH of 3.00.
The equation is:

• \[ pH = pK_a + \log \frac{[F^-]}{[HF]} \]

Here, \( pK_a \) is the acid dissociation constant of HF, which is 3.17. For a desired \( pH \) of 3.00, the equation gets rearranged to solve for the ratio \[ \frac{[F^-]}{[HF]} \].
After substituting the values, we have:

• \[ 3.00 = 3.17 + \log \frac{[F^-]}{[HF]} \]

Solving this, we find:

• \[ \log \frac{[F^-]}{[HF]} = -0.17 \]
• \[ \frac{[F^-]}{[HF]} = 10^{-0.17} \]

This ratio guides us in balancing the buffer components, achieving the necessary buffer capacity and target pH.

acid-base chemistry

Acid-base chemistry principles are key when working with buffer solutions, which are systems designed to maintain a stable pH upon the addition of small amounts of acid or base. In this exercise, hydrofluoric acid (HF) paired with its conjugate base, sodium fluoride (NaF), forms a buffer solution. The buffer's efficacy is based on the equilibrium between the weak acid (HF) and its conjugate base (F⁻).
Buffers work because they utilize the reversible reactions that occur when hydrogen ions (H⁺) or hydroxide ions (OH⁻) are added. The equilibrium between the acid and base shifts to "absorb" this change, lessening the pH shift.
For HF:

• The weak acid dissociates partially: \( HF \rightleftharpoons H^+ + F^- \)

To establish a buffer, NaF is added to increase \( F^- \) ion concentration.

• This common ion effect reduces further dissociation of HF, stabilizing the pH.

The careful calculation of the components based on equilibrium principles and the Henderson-Hasselbalch equation ensures the pH remains stable, even when additional acids or bases are introduced.