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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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