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Chapter 17: Problem 25

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

Expert verified
(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

01

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.
02

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].
03

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: \[moles_{F^{-}} = moles_{HF} \times \frac{[F^{-}]}{[HF]} = 1.25 \, moles \times 10^{-0.17}\]
04

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.

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Most popular questions from this chapter

Using the value of \(K_{s p}\) for \(\mathrm{Ag}_{2} \mathrm{S}, K_{a 1}\) and \(K_{a 2}\) for \(\mathrm{H}_{2} \mathrm{S},\) and \(K_{f}=1.1 \times 10^{5}\) for \(\mathrm{AgCl}_{2}^{-}\) , calculate the equilibrium constant for the following reaction: \(\mathrm{Ag}_{2} \mathrm{S}(s)+4 \mathrm{Cl}^{-}(a q)+2 \mathrm{H}^{+}(a q) \rightleftharpoons 2 \mathrm{AgCl}_{2}^{-}(a q)+\mathrm{H}_{2} \mathrm{S}(a q)\)

Consider a beaker containing a saturated solution of \(\mathrm{CaF}_{2}\) in equilibrium with undissolved \(\mathrm{CaF}_{2}(s)\). Solid \(\mathrm{CaCl}_{2}\) is then added to the solution. (a) Will the amount of solid \(\mathrm{CaF}_{2}\) at the bottom of the beaker increase, decrease, or remain the same? (b) Will the concentration of \(\mathrm{Ca}^{2+}\) ions in solution increase or decrease? (c) Will the concentration of \(\mathbf{F}^{-}\) ions in solution increase or decrease?

(a) Will \(\mathrm{Ca}(\mathrm{OH})_{2}\) precipitate from solution if the \(\mathrm{p} \mathrm{H}\) of a 0.050 M solution of \(\mathrm{CaCl}_{2}\) is adjusted to 8.0? (b) Will \(\mathrm{Ag}_{2} \mathrm{SO}_{4}\) precipitate when 100 mL of 0.050 M \(\mathrm{AgNO}_{3}\) is mixed with 10 mL of \(5.0 \times 10^{-2} \mathrm{MNa}_{2} \mathrm{SO}_{4}\) solution?

Consider the equilibrium $$\mathrm{B}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{HB}^{+}(a q)+\mathrm{OH}^{-}(a q)$$ Suppose that a salt of \(\mathrm{HB}^{+}(a q)\) is added to a solution of \(\mathrm{B}(a q)\) at equilibrium. (a) Will the equilibrium constant for the reaction increase, decrease, or stay the same? (b) Will the concentration of \(\mathrm{B}(a q)\) increase, decrease, or stay the same? (c) Will the \(\mathrm{pH}\) of the solution increase, decrease, or stay the same?

A sample of 0.2140 \(\mathrm{g}\) of an unknown monoprotic acid was dissolved in 25.0 \(\mathrm{mL}\) of water and titrated with 0.0950 \(\mathrm{M}$$ \mathrm{NaOH}\). The acid required 30.0 \(\mathrm{mL}\) of base to reach the equivalence point. (a) What is the molar mass of the acid? (b) After 15.0 \(\mathrm{mL}\) of base had been added in the titration, the pH was found to be \(6.50 .\) What is the \(K_{a}\) for the unknown acid?
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