21.E: Exercises

21.1: Periodic Trends and Charge Density

Problems

1. List three physical properties that are important in describing the behavior of the main group elements.
2. Arrange K, Cs, Sr, Ca, Ba, and Li in order of

1. increasing ionization energy.
2. increasing atomic size.
3. increasing electronegativity.

3. Arrange Rb, H, Be, Na, Cs, and Ca in order of

1. decreasing atomic size.
2. decreasing magnitude of electron affinity.

4. Which periodic trends are affected by Z_eff? Based on the positions of the elements in the periodic table, which element would you expect to have the highest Z_eff? the lowest Z_eff?

5. Compare the properties of the metals and nonmetals with regard to their electronegativities and preferred oxidation states.

6. Of Ca, Br, Li, N, Zr, Ar, Sr, and S, which elements have a greater tendency to form positive ions than negative ions?

7. Arrange As, O, Ca, Sn, Be, and Sb in order of decreasing metallic character.

8. Give three reasons the chemistry of the second-period elements is generally not representative of their groups as a whole.

9. Compare the second-period elements and their heavier congeners with regard to
   1. magnitude of electron affinity.
   2. coordination number.
   3. the solubility of the halides in nonpolar solvents.

10. The heavier main group elements tend to form extended sigma-bonded structures rather than multiple bonds to other atoms. Give a reasonable explanation for this tendency.

11. What is the diagonal effect? How does it explain the similarity in chemistry between, for example, boron and silicon?

12. Although many of the properties of the second- and third-period elements in a group are quite different, one property is similar. Which one?

13. Two elements are effective additives to solid rocket propellant: beryllium and one other element that has similar chemistry. Based on the position of beryllium in the periodic table, identify the second element.

14. Give two reasons for the inert-pair effect. How would this phenomenon explain why Sn²⁺ is a better reducing agent than Pb²⁺?

15. Explain the following trend in electron affinities: Al (−41.8 kJ/mol), Si (−134.1 kJ/mol), P (−72.0 kJ/mol), and S (−200.4 kJ/mol).

16. Using orbital energy arguments, explain why electron configurations with more than four electron pairs around the central atom are not observed for second-period elements.

Answers

1. Cs > Rb > Ca > Na > Be > H
2. H > Na > Rb > Cs > Ca > Be

7. Ca > Be > Sn > Sb > As > O

13. aluminum

15. The magnitude of electron affinity increases from left to right in a period due to the increase in Z_eff; P has a lower electron affinity than expected due to its half-filled 3p shell, which requires the added electron to enter an already occupied 3p orbital.

Structure and Reactivity

1. The following table lists the valences, coordination numbers, and ionic radii for a series of cations. Which would you substitute for K⁺ in a crystalline lattice? Explain your answer.

Metal	Charge	Coordination Number	Ionic Radius (pm)
Li	+1	4	76
Na	+1	6	102
K	+1	6	138
Mg	+2	6	72
Ca	+2	6	100
Sr	+2	6	118

Answer

1. Sr²⁺; it is the ion with the radius closest to that of K⁺.

21.2: Group 1: The Alkali Metals

Problems

1. Which of the group 1 elements reacts least readily with oxygen? Which is most likely to form a hydrated, crystalline salt? Explain your answers.
2. The alkali metals have a significant electron affinity, corresponding to the addition of an electron to give the M⁻ anion. Why, then, do they commonly lose the ns¹electron to form the M⁺ cation rather than gaining an electron to form M⁻?
3. Lithium is a far stronger reductant than sodium; cesium is almost as strong as lithium, which does not agree with the expected periodic trend. What two opposing properties explain this apparent anomaly? Is the same anomaly found among the alkaline earth metals?
4. Explain why the ionic character of LiCl is less than that of NaCl. Based on periodic trends, would you expect the ionic character of BeCl₂ to be greater or less than that of LiCl? Why?
5. Alkali metals and carbon form intercalation compounds with extremely high electrical conductivity. Is this conductivity through the layers or along the layers? Explain your answer.
6. Electrolysis is often used to isolate the lighter alkali metals from their molten halides. Why are halides used rather than the oxides or carbonates, which are easier to isolate? With this in mind, what is the purpose of adding calcium chloride to the alkali metal halide?
7. The only alkali metal that reacts with oxygen to give a compound with the expected stoichiometry is lithium, which gives Li₂O. In contrast, sodium reacts with oxygen to give Na₂O₂, and the heavier alkali metals form superoxides. Explain the difference in the stoichiometries of these products.
8. Classify aqueous solutions of Li₂O, Na₂O, and CsO₂ as acidic, basic, or amphoteric.
9. Although methanol is relatively unreactive, it can be converted to a synthetically more useful form by reaction with LiH. Predict the products of reacting methanol with LiH. Describe the visual changes you would expect to see during this reaction.
10. Lithium reacts with atmospheric nitrogen to form lithium nitride (Li₃N). Why do the other alkali metals not form analogous nitrides? Explain why all the alkali metals react with arsenic to form the corresponding arsenides (M₃As).

Structure and Reactivity

1. Write a balanced chemical equation to describe each reaction.

1. the electrolysis of fused (melted) sodium chloride
2. the thermal decomposition of KClO₃
3. the preparation of hydrogen fluoride from calcium fluoride and sulfuric acid
4. the oxidation of sodium metal by oxygen

2. What products are formed at the anode and the cathode during electrolysis of

1. molten lithium hydride?
2. molten lithium chloride?
3. aqueous sodium fluoride?

Write the corresponding half-reactions for each reaction.

3. Sodium metal is prepared by electrolysis of molten NaCl. If 25.0 g of chlorine gas are produced in the electrolysis of the molten salt using 9.6 A (C/s) of current, how many hours were required for the reaction? What mass of sodium was produced?

4. Sodium peroxide can remove CO₂ from the air and replace it with oxygen according to the following unbalanced chemical equation:

Na₂O₂(s) + CO₂(g) → Na₂CO₃(s) + O₂(g)

1. Balance the chemical equation.
2. Identify each oxidation and reduction half-reaction.
3. Assuming complete reaction, what will be the pressure inside a sealed 1.50 L container after reacting excess sodium peroxide with carbon dioxide that was initially at 0.133 atm and 37°C?

5. Predict the products of each chemical reaction and then balance each chemical equation.

1. K(s) + CH₃CH₂OH(l) →
2. Na(s) + CH₃CO₂H(l) →
3. NH₄Cl(s) + Li(s) →
4. (CH₃)₂NH(l) + K(s) →

6. Predict the products of each reaction.

1. an alkyl chloride with lithium metal
2. rubidium with oxygen

7. A 655 mg sample of graphite was allowed to react with potassium metal, and 744 mg of product was isolated. What is the stoichiometry of the product?

8. Perchloric acid, which is used as a reagent in a number of chemical reactions, is typically neutralized before disposal. When a novice chemist accidentally used K₂CO₃ to neutralize perchloric acid, a large mass of KClO₄ (K_sp = 1.05 × 10⁻²) precipitated from solution. What mass of potassium ion is present in 1.00 L of a saturated solution of KClO₄?

9. A key step in the isolation of the alkali metals from their ores is selective precipitation. For example, lithium is separated from sodium and potassium by precipitation of Li₂CO₃ (K_sp = 8.15 × 10⁻⁴). If 500.0 mL of a 0.275 M solution of Na₂CO₃ are added to 500.0 mL of a 0.536 M lithium hydroxide solution, what mass of Li₂CO₃ will precipitate (assuming no further reactions occur)? What mass of lithium will remain in solution?

Answer

9. 5.54 g Li₂CO₃; 0.82 g Li⁺

21.3: Group 2: The Alkaline Earth Metals

Problems

1. The electronegativities of Li and Sr are nearly identical (0.98 versus 0.95, respectively). Given their positions in the periodic table, how do you account for this?
2. Arrange Na, Ba, Cs, and Li in order of increasing Z_eff.
3. Do you expect the melting point of NaCl to be greater than, equal to, or less than that of MgCl₂? Why?
4. Which of the group 2 elements would you expect to form primarily ionic rather than covalent organometallic compounds? Explain your reasoning.
5. Explain why beryllium forms compounds that are best regarded as covalent in nature, whereas the other elements in group 2 generally form ionic compounds.
6. Why is the trend in the reactions of the alkaline earth metals with nitrogen the reverse of the trend seen for the alkali metals?
7. Is the bonding in the alkaline earth hydrides primarily ionic or covalent in nature? Explain your answer. Given the type of bonding, do you expect the lighter or heavier alkaline earth metals to be better reducing agents?
8. Using arguments based on ionic size, charge, and chemical reactivity, explain why beryllium oxide is amphoteric. What element do you expect to be most similar to beryllium in its reactivity? Why?
9. Explain why the solubility of the carbonates and sulfates of the alkaline earth metals decreases with increasing cation size.
10. Beryllium oxide is amphoteric, magnesium oxide is weakly basic, and calcium oxide is very basic. Explain how this trend is related to the ionic character of the oxides.
11. Do you expect the \(\Delta H^\circ_\textrm f\) of CaH₂ to be greater than, the same as, or less than that of BaH₂? Why or why not?
12. Which of the s-block elements would you select to carry out a chemical reduction on a small scale? Consider cost, reactivity, and stability in making your choice. How would your choice differ if the reduction were carried out on an industrial scale?

Structure and Reactivity

1. Beryllium iodide reacts vigorously with water to produce HI. Write a balanced chemical equation for this reaction and explain why it is violent.
2. Predict the products of each reaction and then balance each chemical equation.

1. Mg(OH)₂(aq) + (NH₄)₃PO₄(aq) →
2. calcium carbonate and sulfuric acid →
3. CaCl₂(aq) + Na₃PO₄(aq) →
4. the thermal decomposition of SrCO₃

3. Predict the products of each reaction and then balance each chemical equation.
   1. Sr(s) + O₂(g) →
   2. the thermal decomposition of CaCO₃(s)
   3. CaC₂(s) + H₂O(l) →
   4. RbHCO₃(s) + H₂SO₄(aq) →

4. Indicate whether each pair of substances will react and, if so, write a balanced chemical equation for the reaction.
   1. an alkyl chloride and magnesium metal
   2. strontium metal and nitrogen
   3. magnesium metal and cold water
   4. beryllium and nitrogen

5. Using a thermodynamic cycle and information presented in Chapter 7 and Chapter 8, calculate the lattice energy of magnesium nitride (Mg₃N₂). (\(\Delta H^\circ_\textrm f\) for Mg₃N₂ is −463 kJ/mol, and ΔH° for N(g) + 3e⁻ → N³⁻ is +1736 kJ.) How does the lattice energy of Mg₃N₂ compare with that of MgCl₂ and MgO? (See Chapter 25 for the enthalpy of formation values.)

6. The solubility products of the carbonate salts of magnesium, calcium, and strontium are 6.82 × 10⁻⁶, 3.36 × 10⁻⁹, and 5.60 × 10⁻¹⁰, respectively. How many milligrams of each compound would be present in 200.0 mL of a saturated solution of each? How would the solubility depend on the pH of the solution? Why?

7. The solubility products of BaSO₄ and CaSO₄ are 1.08 × 10⁻¹⁰ and 4.93 × 10⁻⁵, respectively. What accounts for this difference? When 500.0 mL of a solution that contains 1.00 M Ba(NO₃)₂ and 3.00 M Ca(NO₃)₂ is mixed with a 2.00 M solution of Na₂SO₄, a precipitate forms. What is the identity of the precipitate? How much of it will form before the second salt precipitates?

8. Electrolytic reduction is used to produce magnesium metal from MgCl₂. The goal is to produce 200.0 kg of Mg by this method.
   1. How many kilograms of MgCl₂ are required?
   2. How many liters of chlorine gas will be released at standard temperature and pressure?
   3. How many hours will it take to process the magnesium metal if a total current of 1.00 × 10⁴ A is used?

9. A sample consisting of 20.35 g of finely divided calcium metal is allowed to react completely with nitrogen. What is the mass of the product?

10. What mass of magnesium hydride will react with water to produce 1.51 L of hydrogen gas at standard temperature and pressure?

Answers

3

1. 2Sr(s) + O₂(g) → 2SrO(s)
2. \(\mathrm{CaCO_3(s)}\xrightarrow\Delta\mathrm{CaO(s)}+\mathrm{CO_2(g)}\)
3. CaC₂(s) + 2H₂O(l) → C₂H₂(g) + Ca(OH)₂(aq)
4. 2RbHCO₃(s) + H₂SO₄(aq) → Rb₂SO₄(aq) + 2CO₂(g) + 2H₂O(l)

7. The Ba²⁺ ion is larger and has a lower hydration energy than the Ca²⁺ ion. The precipitate is BaSO₄; 117 g of BaSO₄.

9. 25.09 g of Ca₃N₂

21.4: Group 13: The Boron Family

Conceptual Problems

1. None of the group 13 elements was isolated until the early 19th century, even though one of these elements is the most abundant metal on Earth. Explain why the discovery of these elements came so late and describe how they were finally isolated.
2. Boron and aluminum exhibit very different chemistry. Which element forms complexes with the most ionic character? Which element is a metal? a semimetal? What single property best explains the difference in their reactivity?
3. The usual oxidation state of boron and aluminum is +3, whereas the heavier elements in group 13 have an increasing tendency to form compounds in the +1 oxidation state. Given that all group 13 elements have an ns²np¹ electron configuration, how do you explain this difference between the lighter and heavier group 13 elements?
4. Do you expect the group 13 elements to be highly reactive in air? Why or why not?
5. Which of the group 13 elements has the least metallic character? Explain why.
6. Boron forms multicenter bonds rather than metallic lattices with delocalized valence electrons. Why does it prefer this type of bonding? Does this explain why boron behaves like a semiconductor rather than a metal? Explain your answer.
7. Because the B–N unit is isoelectronic with the C–C unit, compounds that contain these units tend to have similar chemistry, although they exhibit some important differences. Describe the differences in physical properties, conductivity, and reactivity of these two types of compounds.
8. Boron has a strong tendency to form clusters. Does aluminum have this same tendency? Why or why not?
9. Explain why a B–O bond is much stronger than a B–C bond.
10. The electron affinities of boron and aluminum are −27 and −42 kJ/mol, respectively. Contrary to the usual periodic trends, the electron affinities of the remaining elements in group 13 are between those of B and Al. How do you explain this apparent anomaly?
11. The reduction potentials of B and Al in the +3 oxidation state are −0.87 V and −1.66 V, respectively. Do you expect the reduction potentials of the remaining elements of group 13 to be greater than or less than these values? How do you explain the differences between the expected values and those given in Table \(\PageIndex{1}\) "Selected Properties of the Group 13 Elements"?
12. The compound Al₂Br₆ is a halide-bridged dimer in the vapor phase, similar to diborane (B₂H₆). Draw the structure of Al₂Br₆ and then compare the bonding in this compound with that found in diborane. Explain the differences.
13. The compound AlH₃ is an insoluble, polymeric solid that reacts with strong Lewis bases, such as Me₃N, to form adducts with 10 valence electrons around aluminum. What hybrid orbital set is formed to allow this to occur?

Answers

1. The high stability of compounds of the group 13 elements with oxygen required powerful reductants such as metallic potassium to be isolated. Al and B were initially prepared by reducing molten AlCl₃ and B₂O₃, respectively, with potassium.

5. Due to its low electronegativity and small size, boron is an unreactive semimetal rather than a metal.

7. The B–N bond is significantly more polar than the C–C bond, which makes B–N compounds more reactive and generally less stable than the corresponding carbon compounds. Increased polarity results in less delocalization and makes the planar form of BN less conductive than graphite.

9. Partial pi bonding between O and B increases the B–O bond strength.

11. Periodic trends predict that the cations of the heavier elements should be easier to reduce, so the elements should have less negative reduction potentials. In fact, the reverse is observed because the heavier elements have anomalously high Z_eff values due to poor shielding by filled (n − 1)d and (n − 2)f subshells.

13. dsp³

Structure and Reactivity

1. Is B(OH)₃ a strong or a weak acid? Using bonding arguments, explain why.
2. Using bonding arguments, explain why organoaluminum compounds are expected to be potent Lewis acids that react rapidly with weak Lewis bases.
3. Imagine that you are studying chemistry prior to the discovery of gallium, element 31. Considering its position in the periodic table, predict the following properties of gallium:

1. chemical formulas of its most common oxide, most common chloride, and most common hydride
2. solubility of its oxide in water and the acidity or basicity of the resulting solution
3. the principal ion formed in aqueous solution

4. The halides of Al, Ga, In, and Tl dissolve in water to form acidic solutions containing the hydrated metal ions, but only the halides of aluminum and gallium dissolve in aqueous base to form soluble metal-hydroxide complexes. Show the formulas of the soluble metal–hydroxide complexes and of the hydrated metal ions. Explain the difference in their reactivities.
5. Complete and balance each chemical equation.

1. BCl₃(g) + H₂(g) \(\xrightarrow{\Delta}\)
2. 6C₂H₄(g) + B₂H₆(g) →
3. B₂H₆(g) + 3Cl₂(g) →
4. B₂H₆(g) + 2(C₂H₅)₂S(g) →

6. Complete and balance each chemical equation.
   1. BBr₃(g) + H₂(g) \(\xrightarrow{\Delta}\)
   2. BF₃(g) + F⁻(g) →
   3. LiH(s) + B₂H₆(g) →
   4. B(OH)₃(s) + NaOH(aq) →

7. Write a balanced chemical equation for each reaction.
   1. the dissolution of Al₂O₃ in dilute acid
   2. the dissolution of Ga₂O₃ in concentrated aqueous base
   3. the dissolution of Tl₂O in concentrated aqueous acid
   4. Ga(l) + S₈(s)
   5. Tl(s) + H₂S(g)

8. Write a balanced chemical equation for the reaction that occurs between Al and each species.
   1. Cl₂
   2. O₂
   3. S
   4. N₂
   5. H₂O
   6. H⁺(aq)

9. Write a balanced chemical equation that shows how you would prepare each compound from its respective elements or other common compounds.
   1. In₂I₆
   2. B(OH)₃
   3. Ga₂O₃
   4. [Tl(H₂O)₆]³⁺
   5. Al(OH)₄⁻
   6. In₄C₃

10. Write a balanced chemical equation that shows how you would prepare each compound from its respective elements or other common compounds.
    1. BCl₃
    2. InCl₃
    3. Tl₂S
    4. Al(OH)₃
    5. In₂O₃
    6. AlN

11. Diborane is a spontaneously flammable, toxic gas that is prepared by reacting NaBH₄ with BF₃. Write a balanced chemical equation for this reaction.

12. Draw the Lewis electron structure of each reactant and product in each chemical equation. Then describe the type of bonding found in each reactant and product.
    1. 2B(s) + 3X₂(g) \(\xrightarrow{\Delta}\) 2BX₃(g)
    2. 4B(s) + 3O₂(g) \(\xrightarrow{\Delta}\) 2B₂O₃(s)
    3. 2B(s) + N₂(g) \(\xrightarrow{\Delta}\) 2BN(s)

13. Draw the Lewis electron structure of each reactant and product in each chemical equation. Then describe the type of bonding found in each reactant and product.
    1. B₂H₆(g) + 3O₂(g) → B₂O₃(s) + 3H₂O(l)
    2. B₂H₆(g) + 6CH₃CH=CH₂(g) → 2[B(CH₂CH₂CH₃)₃](l)

Answers

1. 12BCl₃(g) + 18H₂(g) \(\xrightarrow{\Delta}\) B₁₂(s) + 36HCl(g)
2. 6C₂H₄(g) + B₂H₆(g) → 2B(C₂H₅)₃(l)
3. 6B₂H₆(g) + 18Cl₂(g) → B₁₂(s) + 36HCl(g)
4. B₂H₆(g) + 2(C₂H₅)₂S(g) → 2H₃B·S(C₂H₅)₂(l)

1. Al₂O₃(s) + 6H₃O⁺(aq) + 3H₂O(l) → 2Al(H₂O)₆³⁺(aq)
2. Ga₂O₃(s) + 2OH⁻(aq) + 3H₂O(l) → 2Ga(OH)₄⁻(aq)
3. Tl₂O(s) + 2H⁺(aq) + 9H₂O(l) → 2Tl(H₂O)₆⁺(aq)
4. 16Ga(l) + 3S₈(s) → 8Ga₂S₃(s)
5. 2Tl(s) + H₂S(g) → Tl₂S(s) + H₂(g)

1. 2In(s) + 3I₂(s) \(\xrightarrow{\Delta}\) In₂I₆(s)
2. B₁₂(s) + 18Cl₂(g) → 12BCl₃(l)

BCl₃(l) + 3H₂O(l) → B(OH)₃(aq) + 3HCl(aq)

3. 4Ga(l) + 3O₂(g) \(\xrightarrow{\Delta}\) 2Ga₂O₃(s)
4. 2Tl(s) + 3Cl₂(g) → 2TlCl₃(s); TlCl₃(s) + 6H₂O(l) → Tl(H₂O₆)³⁺(aq) + 3Cl⁻(aq)
5. 2Na(s) + 2H₂O(l) → 2NaOH(aq) + H₂(g); 2Al(s) + 2NaOH(aq) + 6H₂O(l) → 2Al(OH)₄⁻ + 3H₂(g) + 2Na⁺(aq)
6. 4In(s) + 3C(s) \(\xrightarrow{\Delta}\) In₄C₃(s)

21.5: Group 14: The Carbon Family

Conceptual Problems

1. Why is the preferred oxidation state of lead +2 rather than +4? What do you expect the preferred oxidation state of silicon to be based on its position in the periodic table?
2. Carbon uses pπ–pπ overlap to form compounds with multiple bonds, but silicon does not. Why? How does this same phenomenon explain why the heavier elements in group 14 do not form catenated compounds?
3. Diamond is both an electrical insulator and an excellent thermal conductor. Explain this property in terms of its bonding.
4. The lighter chalcogens (group 16) form π bonds with carbon. Does the strength of these π bonds increase or decrease with increasing atomic number of the chalcogen? Why?
5. The heavier group 14 elements can form complexes that contain expanded coordination spheres. How does this affect their reactivity compared with the reactivity of carbon? Is this a thermodynamic effect or a kinetic effect? Explain your answer.
6. Refer to Table \(\PageIndex{1}\) for the values of the electron affinities of the group 14 elements. Explain any discrepancies between these actual values and the expected values based on usual periodic trends.
7. Except for carbon, the elements of group 14 can form five or six electron-pair bonds. What hybrid orbitals are used to allow this expanded coordination? Why does carbon not form more than four electron-pair bonds?
8. Which of the group 14 elements is least stable in the +4 oxidation state? Why?

Structure and Reactivity

1. Predict the products of each reaction and balance each chemical equation.
   1. CaC₂(s) + HCl(g) →
   2. Pb(s) + Br₂(l) \(\xrightarrow{\Delta}\)
   3. (CH₃)₃N(l) + H₂O₂(aq) →
   4. Pb(N₃)₂(s) \(\xrightarrow{\Delta}\)

2. Write a balanced chemical equation to indicate how you would prepare each compound.
   1. SiF₆²⁻ from its elements and other common compounds
   2. SiO₂ from SiCl₄
   3. GeS₂ from its elements
   4. Si(CH₃)₄ from Si

3. Write a balanced chemical equation to indicate how you would prepare each compound.
   1. CO₂ from CuO
   2. methane from Be₂C
   3. Si(OH)₄ from Si
   4. Si₃N₄ from Si

Answers

1. CaC₂(s) + 2HCl(g) → CaCl₂(s) + C₂H₂(g)
2. Pb(s) + Br₂(l) \(\xrightarrow{\Delta}\) PbBr₂(s)
3. (CH₃)₃N(l) + H₂O₂(aq) → (CH₃)₃N–O(l) + H₂O(l)
4. Pb(N₃)₂(s) \(\xrightarrow{\Delta}\) Pb(s) + 3N₂(g)

1. CuO(s) + CO(s) \(\xrightarrow{\Delta}\) Cu(s) + CO₂(g)
2. Be₂C(s) + 4HCl(aq) → 2BeCl₂(aq) + CH₄(g)
3. Si(s) + 2Cl₂(g) → SiCl₄(l); SiCl₄(l) + 4H₂O(l) → Si(OH)₄(s) + 4HCl(aq)
4. 3Si(s) + 2N₂(g) \(\xrightarrow{\Delta}\) Si₃N₄(s)