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Chapter 17: Problem 73

A solution contains \(1.0 \times 10^{-4} \mathrm{Ca}^{2+}(a q)\) and $1.0 \times 10^{-4}\( \)\mathrm{La}^{3+}(a q) .\( If \)\mathrm{NaF}$ is added, will \(\mathrm{CaF}_{2}\left(K_{s p}=3.9 \times 10^{-11}\right)\) or \(\mathrm{LaF}_{3}\left(K_{s p}=2 \times 10^{-19}\right)\) precipitate first? Specify the concentration of \(\mathrm{F}^{-}(a q)\) needed to begin precipitation.

Short Answer

Expert verified
When adding \(\mathrm{NaF}\), \(\mathrm{LaF}_3\) will precipitate first. The concentration of \(\mathrm{F}^-\) needed to start the precipitation is \(1.26 \times 10^{-5} \mathrm{M}\).

Step by step solution

01

Write Solubility Product Expressions

Write the solubility product expressions for the two salts. For \(\mathrm{CaF}_2\), it is: \[K_{sp} = [\mathrm{Ca}^{2+}][\mathrm{F}^-]^2\] For \(\mathrm{LaF}_3\), it is: \[K_{sp} = [\mathrm{La}^{3+}][\mathrm{F}^-]^3\]
02

Calculate the concentration of \(\mathrm{F}^-\) at which each salt will precipitate

Using the solubility product expressions, find the concentration of \(\mathrm{F}^-\) needed for precipitation to start for each salt. For \(\mathrm{CaF}_2\): \[3.9 \times 10^{-11} = (1.0 \times 10^{-4})[\mathrm{F}^-]^2\] Solve for \([\mathrm{F}^-]\): \[[\mathrm{F}^-]_1 = \sqrt{\frac{3.9 \times 10^{-11}}{1.0 \times 10^{-4}}} = 6.24 \times 10^{-4} \mathrm{M}\] For \(\mathrm{LaF}_3\): \[2 \times 10^{-19} = (1.0 \times 10^{-4})[\mathrm{F}^-]^3\] Solve for \([\mathrm{F}^-]\): \[[\mathrm{F}^-]_2 = \sqrt[3]{\frac{2 \times 10^{-19}}{1.0 \times 10^{-4}}} = 1.26 \times 10^{-5} \mathrm{M}\]
03

Compare the concentration values and determine which salt will precipitate first

Comparing the \(\mathrm{F}^-\) concentration values, we find that the concentration needed to start precipitation for \(\mathrm{CaF}_2\) is \(6.24 \times 10^{-4} \mathrm{M}\) and for \(\mathrm{LaF}_3\) is \(1.26 \times 10^{-5} \mathrm{M}\). Since the concentration required for \(\mathrm{LaF}_3\) to precipitate is lower, it will precipitate first. The concentration of \(\mathrm{F}^-\) needed to start the precipitation is \(1.26 \times 10^{-5} \mathrm{M}\).

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Most popular questions from this chapter

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}\( of base had been added in the titration, the \)\mathrm{pH}$ was found to be \(6.50 .\) What is the \(K_{a}\) for the unknown acid?

(a) Will \(\mathrm{Co}(\mathrm{OH})_{2}\) precipitate from solution if the \(\mathrm{pH}\) of a \(0.020 \mathrm{M}\) solution of \(\mathrm{Co}\left(\mathrm{NO}_{3}\right)_{2}\) is adjusted to $8.5 ?(\mathbf{b})\( Will \)\mathrm{AgIO}_{3}\( precipitate when \)20 \mathrm{~mL}$ of \(0.010 \mathrm{M} \mathrm{AgIO}_{3}\) is mixed with \(10 \mathrm{~mL}\) of $0.015 \mathrm{M} \mathrm{NaIO}_{3} ?\left(K_{s p}\right.\( of \)\mathrm{AgIO}_{3}$ is \(3.1 \times 10^{-8} .\) )

A solution of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) is added dropwise to a solution that is \(0.010 \mathrm{M}\) in \(\mathrm{Ba}^{2+}(a q)\) and $0.010 \mathrm{M}\( in \)\mathrm{Sr}^{2+}(a q) .(\mathbf{a}) \mathrm{What}$ concentration of \(\mathrm{SO}_{4}^{2-}\) is necessary to begin precipitation? (Neglect volume changes. $\mathrm{BaSO}_{4}: K_{s p}=1.1 \times 10^{-10} ; \mathrm{SrSO}_{4}:\( \)K_{s p}=3.2 \times 10^{-7} .$ ) (b) Which cation precipitates first? (c) What is the concentration of $\mathrm{SO}_{4}^{2-}(a q)$ when the second cation begins to precipitate?

You are asked to prepare a pH \(=2.50\) buffer solution starting from $1.50 \mathrm{~L}\( of a \)0.75 \mathrm{M}$ solution of hydrofluoric acid (HF) and any amount you need of sodium fluoride (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.

(a) Calculate the percent ionization of \(0.0085 \mathrm{Mbutanoic}\) acid \(\left(K_{a}=1.5 \times 10^{-5}\right) .(\mathbf{b})\) Calculate the percent ionization of \(0.0085 \mathrm{M}\) butanoic acid in a solution containing \(0.075 M\) sodium butanoate.
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