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Chapter 16: Problem 27

Calculate the solubility (g/100 mL) of iron(II) hydroxide in buffered solutions with the following pH's. (a) 4 (b) 7 (c) 10

Short Answer

Expert verified
The solubility of iron(II) hydroxide in buffered solutions with pH levels 4, 7, and 10 is 0.219 g/100 mL, 0.438 g/100 mL, and 4.38 × 10⁻⁷ g/100 mL, respectively.

Step by step solution

01

Write the balanced chemical equation for the dissolution of Fe(OH)₂

The balanced chemical equation for the dissolution of iron(II) hydroxide is: Fe(OH)₂(s) ⇌ Fe²⁺(aq) + 2OH⁻(aq)
02

Find the solubility product constant (Ksp) of Fe(OH)₂

The Ksp of Fe(OH)₂ is 4.87 × 10⁻¹⁷ (found in a chemistry reference table). This constant represents the equilibrium between the dissolved ions and the solid compound.
03

Write the equation for the relationship between pH and the concentration of hydroxide ions

The relationship between pH and the concentration of hydroxide ions is given by the following formula: \[pH + pOH = 14\] Since pOH = -log[OH⁻], we can rewrite the equation as: \[pH + -\log[OH⁻] = 14\]
04

Determine the concentration of hydroxide ions for each pH level

Use the relationship derived in step 3 to calculate the concentration of OH⁻ ions for each pH level: (a) For pH 4: \[4 + -\log[OH⁻] = 14\] \[10^{-10} = [OH⁻]\] (b) For pH 7: \[7 + -\log[OH⁻] = 14\] \[10^{-7} = [OH⁻]\] (c) For pH 10: \[10 + -\log[OH⁻] = 14\] \[10^{-4} = [OH⁻]\]
05

Calculate the concentration of Fe²⁺ ions using the Ksp expression

Using the Ksp expression, we can calculate the concentration of Fe²⁺ ions for each pH level: Ksp = [Fe²⁺][OH⁻]² For each pH level: (a) For pH 4: \[4.87 × 10^{-17} = [Fe²⁺](10^{-10})^2\] \[2.44 × 10^{-3} = [Fe²⁺]\] (b) For pH 7: \[4.87 × 10^{-17} = [Fe²⁺](10^{-7})^2\] \[4.87 × 10^{-3} = [Fe²⁺]\] (c) For pH 10: \[4.87 × 10^{-17} = [Fe²⁺](10^{-4})^2\] \[4.87 × 10^{-9} = [Fe²⁺]\]
06

Convert the concentration of Fe²⁺ ions to grams per 100 mL

In order to find the solubility in grams per 100 mL, we will multiply the molar concentration of Fe²⁺ by the molar mass of Fe(OH)₂ and then multiply by 100 mL: Solubility = [Fe²⁺] × (molar mass of Fe(OH)₂) × 100 mL For each pH level: (a) For pH 4: Solubility = (2.44 × 10⁻³ mol/L) × (89.86 g/mol) × 0.1 L = 0.219 g (b) For pH 7: Solubility = (4.87 × 10⁻³ mol/L) × (89.86 g/mol) × 0.1 L = 0.438 g (c) For pH 10: Solubility = (4.87 × 10⁻⁹ mol/L) × (89.86 g/mol) × 0.1 L = 4.38 × 10⁻⁷ g The solubility of iron(II) hydroxide in buffered solutions with pH levels 4, 7, and 10 is 0.219 g/100 mL, 0.438 g/100 mL, and 4.38 × 10⁻⁷ g/100 mL, respectively.

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Most popular questions from this chapter

Lead azide, \(\mathrm{Pb}\left(\mathrm{N}_{3}\right)_{2}\), is used as a detonator in car airbags. The impact of a collision causes \(\mathrm{Pb}\left(\mathrm{N}_{3}\right)_{2}\) to be converted into an enormous amount of gas that fills the airbag. At \(25^{\circ} \mathrm{C}\), a saturated solution of lead azide is prepared by dissolving \(25 \mathrm{mg}\) in water to make \(100.0 \mathrm{~mL}\) of solution. What is \(K_{\mathrm{sp}}\) for lead azide?

What is the \(\mathrm{I}^{-}\) concentration just as \(\mathrm{AgCl}\) begins to precipitate when \(1.0 \mathrm{M} \mathrm{AgNO}_{3}\) is slowly added to a solution containing \(0.020 \mathrm{M} \mathrm{Cl}^{-}\) and \(0.020 M \mathrm{I}^{-}\)

Given \(K_{s p}\) and the equilibrium concentration of one ion, calculate the equilibrium concentration of the other ion. (a) cadmium(II) hydroxide: \(K_{\text {sp }}=2.5 \times 10^{-14} ;\left[\mathrm{Cd}^{2+}\right]=1.5 \times 10^{-6} M\) (b) copper(II) arsenate \(\left(\mathrm{Cu}_{3}\left(\mathrm{AsO}_{4}\right)_{2}\right): K_{\mathrm{sp}}=7.6 \times 10^{-36} ;\left[\mathrm{AsO}_{4}^{3-}\right]=\) \(2.4 \times 10^{-4} M\) (c) zinc oxalate: \(K_{s p}=2.7 \times 10^{-8} ;\left[\mathrm{C}_{2} \mathrm{O}_{4}{ }^{2-}\right]=8.8 \times 10^{-3} M\)

Which of the following statements are true? (a) For an insoluble metallic salt, \(K_{\text {sp }}\) is always less than 1 . (b) More \(\mathrm{PbCl}_{2}\) can be dissolved at \(100^{\circ} \mathrm{C}\) than at \(25^{\circ} \mathrm{C}\). One can conclude that dissolving \(\mathrm{PbCl}_{2}\) is an exothermic process. (c) When strips of copper metal are added to a saturated solution of \(\mathrm{Cu}(\mathrm{OH})_{2}\), a precipitate of \(\mathrm{Cu}(\mathrm{OH})_{2}\) can be expected to form because of the common ion effect.

Write the equilibrium equations on which the following \(K_{s p}\) expressions are based. (a) \(\left[\mathrm{Hg}_{2}{ }^{2+}\right]\left[\mathrm{Cl}^{-}\right]^{2}\) (b) \(\left[\mathrm{Pb}^{2+}\right]\left[\mathrm{CrO}_{4}^{2-}\right]\) (c) \(\left[\mathrm{Mn}^{4+}\right]\left[\mathrm{O}^{2-}\right]^{2}\) (d) \(\left[\mathrm{Al}^{3+}\right]^{2}\left[\mathrm{~S}^{2-}\right]^{3}\)
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