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## 17.6 End-of-Chapter Material

### 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:

$CaSO 4 ⋅ 2 H 2 O(s) ⇌ Ca 2 + (aq) + SO 4 2 − (aq) + 2 H 2 O(l)$
1. The Ksp 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 Ksp 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 Ksp 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? The Ksp of AuCl = 2.0 × 10−13; log Kf{[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 Ksp of 2.58 × 10−9. The pKa for $H2S⇌H++HS−$ is 6.97, and the pKa 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?