17.6: End-of-Chapter Material

A general chemistry Libretexts Textmap organized around the textbook
Chemistry: Principles, Patterns, and Applications
by Bruce A. Averill

I    II    III    IV   V    VI    VII    VIII    IX    X    XI    XII  XIII    XIV    XV    XVI    XVII    XVIII    XIX     XX    XXI    XXII   XXIII   XXIV   ● Homework

Template:HideTOC

These are homework exercises to accompany the Textmap created for "Chemistry: Principles, Patterns, and Applications" by Bruce A. Averill and Patricia Eldredge. Complementary General Chemistry question banks can be found for other Textmaps and can be accessed here. In addition to these publicly available questions, access to private problems bank for use in exams and homework is available to faculty only on an individual basis; please contact Delmar Larsen for an account with access permission.

Application Problems

Problems marked with a ♦ involve multiple concepts.

1. ♦ Gypsum (CaSO₄·2H₂O) is added to soil to enhance plant growth. It dissolves according to the following equation:

CaSO₄⋅2H₂O(s) ⇌ Ca²⁺(aq) + SO₄²⁻(aq) + 2H₂O(l)

1. The K_sp of gypsum is 3.14 × 10⁻⁵. How much gypsum should you add to your 5.0 L watering can to produce a saturated solution?
2. Gibbsite [Al(OH)₃] is a component of clay, found in places such as Molokai, Hawaii. It dissolves according to the following equation: Al(OH)₃(s) ⇌ Al³⁺(aq) + 3OH⁻(aq), with a K_sp of 1.3 × 10⁻³³. You are interested in using gypsum to counteract harmful growth effects of Al³⁺ on plants from dissolved gibbsite, and you have found the pH of your soil to be 8.7. What is the apparent concentration of OH⁻ in your soil?

2. Egyptian blue, which is difficult to prepare, is a synthetic pigment developed about 4500 yr ago. It was the only blue pigment identified in a study of stocks of dry pigments found in color merchants’ shops in Pompeii. The pigment contains 12.9% calcium carbonate (calcite). A major source of CaCO₃ is limestone, which also contains MgCO₃. Assuming that the masses of CaCO₃ and MgCO₃ are equal, and that a sample of limestone is dissolved in acidified water to give [Ca²⁺] = [Mg²⁺] = 0.010 M in 5.0 L of solution, would selective precipitation be a viable method for purifying enough CaCO₃ from limestone to produce 1.0 g of pigment? Why? The K_sp values are 3.36 × 10⁻⁹ for CaCO₃ and 6.8 × 10⁻⁶ for MgCO₃.

3. One method of mining gold is to extract it through the process of cyanidation. Mined ores are milled and treated with aqueous cyanide solution to produce a gold complex ion {[Au(CN)₂]⁻} that is very stable. Given a sample of AuCl, what is the solubility of AuCl in each situation? TheK_sp of AuCl = 2.0 × 10⁻¹³; log K_f{[Au(CN)₂]⁻} = 38.3.

1. pure water
2. a 1.68 M solution of NaCN

4. ♦ Almost all barium carbonate is produced synthetically. The compound is used in manufacturing clay tiles and ceramic products as well as in cathode ray tubes and special optical glasses. BaCO₃ is synthesized by allowing barium sulfate to react with coal at 1000°C–1200°C in a rotary kiln, followed by treatment of a solution of the product with either CO₂ (reaction 1) or Na₂CO₃ (reaction 2). The reactions are as follows:

BaSO₄(s) + 4C(s) → 4BaS(s) + 4CO(g)

reaction 1. BaS(s) + CO₂(g) + H₂O(l) → BaCO₃(aq) + H₂S(g)

reaction 2. BaS(s) + Na₂CO₃(aq) ⇌ BaCO₃(aq) + Na₂S(aq)

Barium carbonate has a K_sp of 2.58 × 10⁻⁹. The pK_a for H₂S ⇌ H⁺ + HS⁻ is 6.97, and the pK_a for HS⁻⇌ H⁺ + S²⁻ is 12.90. Given this information, answer the following questions:

1. If reaction 1 occurs, what is the pH of the solution if 80.0 g of BaS react with CO₂ in 1.00 L of water?
2. If reaction 2 occurs, how many grams of BaCO₃ are produced by the reaction of 80.0 g of BaS with excess Na₂CO₃?

5. A person complaining of chronic indigestion continually consumed antacid tablets containing Ca(OH)₂ over a two-week period. A blood test at the end of this period showed that the person had become anemic. Explain the reactions that caused this test result.

6. Although the commercial production of radium has virtually ceased since artificial radionuclides were discovered to have similar properties and lower costs, commercial radium is still isolated using essentially the same procedure developed by Marie Curie, as outlined here. Explain what is happening chemically at each step of the purification process. What is precipitate A? What metal ions are present in solution A? What is precipitate B? What metal ions are present in solution B?

7. In a qualitative analysis laboratory, a student initially treated his sample of metal ions with 6 M HNO₃ instead of 6 M HCl, recognizing his mistake only after the acid-insoluble sulfides had been precipitated. He decided to simply add 6 M HCl to the filtrate from which the sulfides had been removed, but he obtained no precipitate. The student therefore concluded that there were no Ag⁺, Hg₂²⁺, or Pb²⁺ cations in his original sample. Is this conclusion valid?

8. Using qualitative analysis, a student decided to treat her sample with (NH₄)₂S solution directly, skipping the HCl and acidic H₂S treatments because she was running out of time. In a sample that contained Ag⁺, Hg₂²⁺, Cd²⁺, Sb³⁺, and Zn²⁺, which metal ions was she most likely to obtain in the resulting precipitate?

Answers

1.

Video Solution

1. 4.3 g
2. 5 × 10⁻⁶ M

1. 4.4 × 10⁻⁷ M
2. 0.84 M

7. No; these cations would precipitate as sulfides.

17.3: The Formation of Complex Ions

Conceptual Problems

1. What is the difference between K_eq and K_f?
2. Which would you expect to have the greater tendency to form a complex ion: Mg²⁺ or Ba²⁺? Why?
3. How can a ligand be used to affect the concentration of hydrated metal ions in solution? How is K_sp affected? Explain your answer.
4. Co(II) forms a complex ion with pyridine (C₅H₅N). Which is the Lewis acid, and which is the Lewis base? Use Lewis electron structures to justify your answer.

Numerical Problems

1. Fe(II) forms the complex ion [Fe(OH)₄]²⁻ through equilibrium reactions in which hydroxide replaces water in a stepwise manner. If log K₁ = 5.56, log K₂ = 4.21, log K₃ = −0.10, and log K₄ = −1.09, what is K_f? Write the equilibrium equation that corresponds to each stepwise equilibrium constant. Do you expect the [Fe(OH)₄]²⁻ complex to be stable? Explain your reasoning.
2. Zn(II) forms the complex ion [Zn(NH₃)₄]²⁺ through equilibrium reactions in which ammonia replaces coordinated water molecules in a stepwise manner. If log K₁ = 2.37, log K₂ = 2.44, log K₃ = 2.50, and log K₄ = 2.15, what is the overall K_f? Write the equilibrium equation that corresponds to each stepwise equilibrium constant. Do you expect the [Zn(NH₃)₄]²⁺ complex to be stable? Explain your reasoning.
3. Although thallium has limited commercial applications because it is toxic to humans (10 mg/kg body weight is fatal to children), it is used as a substitute for mercury in industrial switches. The complex ion [TlBr₆]³⁻ is highly stable, with log K_f = 31.6. What is the concentration of Tl(III)(aq) in equilibrium with a 1.12 M solution of Na₃[TlBr₆]?

Answer

[Fe(H₂O)₆]²⁺(aq) + OH⁻(aq) ⇌ [Fe(H₂O(aq))₅(OH)] + (aq) + H₂O log K₁ = 5.56

[Fe(H₂O)₅(OH)] + (aq) + OH⁻(aq) ⇌ [Fe(H₂O)₄(OH)₂](aq) + H₂O(aq) log K₂ = 9.77

[Fe(H₂O)₄(OH)₂](aq) + OH⁻(aq) ⇌ [Fe(H₂O)₃(OH)₃]⁻(aq) + H₂O(aq) log K₃ = 9.67

[Fe(H₂O)₃(OH)₃]⁻(aq) + OH⁻(aq) ⇌ [Fe(OH)₄]²⁻(aq) + 3H₂O(l) log K₄ = 8.58

[Fe(H₂O)₆]²⁺(aq) + 4OH⁻(aq) ⇌ [Fe(OH)₄]²⁻(aq) + 6H₂O(l)

log K_f = log K₁ + log K₂ + log K₂ + log K₄

= 33.58

Thus, K_f = 3.8 × 10³³. Because [Fe(OH)₄]²⁻ has a very large value of K_f, it should be stable in the presence of excess OH⁻.