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Chapter 17: Problem 70

(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 \(3.1 \times 10^{-8} .\) )

Short Answer

Expert verified
In part (a), Co(OH)₂ will precipitate from the solution when the pH is adjusted to 8.5 since the ion product (2.00 × 10^(-11)) is greater than the Ksp of Co(OH)₂ (1.6 × 10^(-15)). In part (b), AgIO₃ will precipitate after mixing the solutions, as the ion product (3.34 × 10^(-5)) is greater than the given Ksp value (3.1 × 10^(-8)).

Step by step solution

01

1. Calculate the concentration of hydroxide ions

To find the concentration of OH- ions in the solution, we will use the relationship between pH and pOH, and the relationship between pOH and the concentration of OH-: pH + pOH = 14 From the given pH value, we can calculate pOH: pOH = 14 - 8.5 = 5.5 Then, using the formula: pOH = -log[OH-] we can calculate the concentration of hydroxide ions: [OH-] = 10^(-5.5) = 3.16 × 10^(-6) M #a) Check if Co(OH)2 will precipitate#
02

2. Calculate the solubility product constant for Co(OH)2

The solubility product constant, Ksp, for Co(OH)2 can be expressed as: Ksp = [Co²⁺] × [OH⁻]² We are given the concentration of Co²⁺ ions as 0.020 M. Using the calculated OH- concentration, we can determine if precipitation occurs according to the Ksp value. If the ion product ([Co²⁺] × [OH⁻]²) is greater than Ksp, then Co(OH)2 will precipitate. Ion product = (0.020) × (3.16 × 10^(-6))^2 = 2.00 × 10^(-11) The Ksp of Co(OH)2 is 1.6 × 10^(-15). Since the ion product is greater than Ksp (2.00 × 10^(-11) > 1.6 × 10^(-15)), Co(OH)2 will precipitate from the solution. #b) Check if AgIO3 will precipitate after mixing the solutions#
03

3. Calculate the new concentrations of Ag+ and IO3- ions after mixing

After mixing the AgIO3 and NaIO3 solutions, the concentration of each ion should be calculated by applying the dilution formula C1V1=C2V2: [Ag⁺] = (0.010 M × 20 mL) / (20 mL + 10 mL) = 6.67 × 10^(-3) M [IO3⁻] = (0.015 M × 10 mL) / (20 mL + 10 mL) = 5.00 × 10^(-3) M #b) Compare the ion product to the given Ksp value#
04

4. Determine if AgIO3 will precipitate

Now, with the new concentrations of Ag⁺ and IO3⁻ ions, we can determine if AgIO3 will precipitate by comparing the ion product to the given Ksp value: Ion product = [Ag⁺] × [IO3⁻] = (6.67 × 10^(-3)) × (5.00 × 10^(-3)) = 3.34 × 10^(-5) The given Ksp value for AgIO3 is 3.1 × 10^(-8). Since the ion product is greater than the Ksp value (3.34 × 10^(-5) > 3.1 × 10^(-8)), AgIO3 will precipitate after mixing the solutions.

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Most popular questions from this chapter

In the course of various qualitative analysis procedures, the following mixtures are encountered: (a) \(\mathrm{Zn}^{2+}\) and \(\mathrm{Cd}^{2+}\) (b) \(\mathrm{Cr}(\mathrm{OH})_{3}\) and \(\mathrm{Fe}(\mathrm{OH})_{3}\), (c) \(\mathrm{Mg}^{2+}\) and \(\mathrm{K}^{+}\), (d) \(\mathrm{Ag}^{+}\) and \(\mathrm{Mn}^{2+} .\) Suggest how each mixture might be separated.

For each of the following slightly soluble salts, write the net ionic equation, if any, for reaction with a strong acid: (a) MnS, (b) \(\mathrm{PbF}_{2}\), (c) \(\mathrm{AuCl}_{3}\) (d) \(\mathrm{Hg}_{2} \mathrm{C}_{2} \mathrm{O}_{4},\) (e) CuBr.

A 20.0-mL sample of \(0.150 \mathrm{MKOH}\) is titrated with \(0.125 \mathrm{M}\) \(\mathrm{HClO}_{4}\) solution. Calculate the pH after the following volumes of acid have been added: $(\mathbf{a}) 20.0 \mathrm{~mL},(\mathbf{b}) 23.0 \mathrm{~mL},\( (c) \)24.0 \mathrm{~mL}\( (d) \)25.0 \mathrm{~mL},\( (e) \)30.0 \mathrm{~mL}$.

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.

A solution containing several metal ions is treated with dilute HCl; no precipitate forms. The pH is adjusted to about 1, and $\mathrm{H}_{2} \mathrm{~S}$ is bubbled through. Again, no precipitate forms. The \(\mathrm{pH}\) of the solution is then adjusted to about 8 . Again, \(\mathrm{H}_{2} \mathrm{~S}\) is bubbled through. This time a precipitate forms. The filtrate from this solution is treated with \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{HPO}_{4}\). No precipitate forms. Which of these metal cations are either possibly present or definitely absent: \(\mathrm{Al}^{3+}, \mathrm{Na}^{+}, \mathrm{Ag}^{+}, \mathrm{Mg}^{2+}\) ?
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