7.E: Tendencias periódicas (ejercicios)

Conceptual Problems

1. The electrons of the 1 s shell have a stronger electrostatic attraction to the nucleus than electrons in the 2 s shell. Give two reasons for this.

2. Predict whether Na or Cl has the more stable 1 s ² shell and explain your rationale.

3. Arrange K, F, Ba, Pb, B, and I in order of decreasing atomic radius.

4. Arrange Ag, Pt, Mg, C, Cu, and Si in order of increasing atomic radius.

5. Using the periodic table, arrange Li, Ga, Ba, Cl, and Ni in order of increasing atomic radius.

6. Element M is a metal that forms compounds of the type MX ₂ , MX ₃ , and MX ₄ , where X is a halogen. What is the expected trend in the ionic radius of M in these compounds? Arrange these compounds in order of decreasing ionic radius of M.

7. The atomic radii of Na and Cl are 190 and 79 pm, respectively, but the distance between sodium and chlorine in NaCl is 282 pm. Explain this discrepancy.

8. Are shielding effects on the atomic radius more pronounced across a row or down a group? ¿Por qué?

9. What two factors influence the size of an ion relative to the size of its parent atom? Would you expect the ionic radius of S ²⁻ to be the same in both MgS and Na ₂ S? Why or why not?

10. Arrange Br ⁻ , Al ^{3 +} , Sr ^{2 +} , F ⁻ , O ²⁻ , and I ⁻ in order of increasing ionic radius.

11. Arrange P ³⁻ , N ³⁻ , Cl ⁻ , In ^{3 +} , and S ²⁻ in order of decreasing ionic radius.

12. How is an isoelectronic series different from a series of ions with the same charge? Do the cations in magnesium, strontium, and potassium sulfate form an isoelectronic series? Why or why not?

13. What isoelectronic series arises from fluorine, nitrogen, magnesium, and carbon? Arrange the ions in this series by

    1. increasing nuclear charge.
    2. increasing size.

14. What would be the charge and electron configuration of an ion formed from calcium that is isoelectronic with

    1. a chloride ion?
    2. Ar ⁺ ?

 

Conceptual Answers

1. The 1 s shell is closer to the nucleus and therefore experiences a greater electrostatic attraction. In addition, the electrons in the 2 s subshell are shielded by the filled 1 s ² shell, which further decreases the electrostatic attraction to the nucleus.

3. Ba > K > Pb > I > B > F

7. The sum of the calculated atomic radii of sodium and chlorine atoms is 253 pm. The sodium cation is significantly smaller than a neutral sodium atom (102 versus 154 pm), due to the loss of the single electron in the 3 s orbital. Conversely, the chloride ion is much larger than a neutral chlorine atom (181 versus 99 pm), because the added electron results in greatly increased electron–electron repulsions within the filled n = 3 principal shell. Thus, transferring an electron from sodium to chlorine decreases the radius of sodium by about 50%, but causes the radius of chlorine to almost double. The net effect is that the distance between a sodium ion and a chloride ion in NaCl is greater than the sum of the atomic radii of the neutral atoms.

 

Numerical Problems

1. Plot the ionic charge versus ionic radius using the following data for Mo: Mo ^{3 +} , 69 pm; Mo ^{4 +} , 65 pm; and Mo ^{5 +} , 61 pm. Then use this plot to predict the ionic radius of Mo ^{6 +} . Is the observed trend consistent with the general trends discussed in the chapter? Why or why not?

2. Internuclear distances for selected ionic compounds are given in the following table.

   1. If the ionic radius of Li ⁺ is 76 pm, what is the ionic radius of each of the anions?

      	LiF	LiCl	LiBr	LiI
      Distance (pm)	209	257	272	296

 

Conceptual Problems

1. Identify each statement as either true or false and explain your reasoning.

   1. Ionization energies increase with atomic radius.
   2. Ionization energies decrease down a group.
   3. Ionization energies increase with an increase in the magnitude of the electron affinity.
   4. Ionization energies decrease diagonally across the periodic table from He to Cs.
   5. Ionization energies depend on electron configuration.
   6. Ionization energies decrease across a row.

2. Based on electronic configurations, explain why the first ionization energies of the group 16 elements are lower than those of the group 15 elements, which is contrary to the general trend.

3. The first through third ionization energies do not vary greatly across the lanthanides. ¿Por qué? How does the effective nuclear charge experienced by the n s electron change when going from left to right (with increasing atomic number) in this series?

4. Most of the first row transition metals can form at least two stable cations, for example iron(II) and iron(III). In contrast, scandium and zinc each form only a single cation, the Sc ³⁺ and Zn ²⁺ ions, respectively. Use the electron configuration of these elements to provide an explanation.

5. Of the elements Nd, Al, and Ar, which will readily form(s) +3 ions? ¿Por qué?

6. Orbital energies can reverse when an element is ionized. Of the ions B ³⁺ , Ga ³⁺ , Pr ³⁺ , Cr ³⁺ , and As ³⁺ , in which would you expect this reversal to occur? Explain your reasoning.

7. The periodic trends in electron affinities are not as regular as periodic trends in ionization energies, even though the processes are essentially the converse of one another. Why are there so many more exceptions to the trends in electron affinities compared to ionization energies?

8. Elements lying on a lower right to upper left diagonal line cannot be arranged in order of increasing electronegativity according to where they occur in the periodic table. ¿Por qué?

9. Why do ionic compounds form, if energy is required to form gaseous cations?

10. Why is Pauling’s definition of electronegativity considered to be somewhat limited?

11. Based on their positions in the periodic table, arrange Sb, O, P, Mo, K, and H in order of increasing electronegativity.

12. Based on their positions in the periodic table, arrange V, F, B, In, Na, and S in order of decreasing electronegativity.

 

Conceptual Answers

Numerical Problems

1. The following table gives values of the first and third ionization energies for selected elements:

   Number of Electrons	Element	I 1 (E → E + + e − , kJ/mol)	Element	I 3 (E 2+ → E 3+ + e − , kJ/mol)
   11	Na	495.9	Al	2744.8
   12	Mg	737.8	Si	3231.6
   13	Al	577.6	P	2914.1
   14	Si	786.6	S	3357
   15	P	1011.9	Cl	3822
   16	S	999.6	Ar	3931
   17	Cl	1251.2	K	4419.6
   18	Ar	1520.6	Ca	4912.4

   Plot the ionization energies versus number of electrons. Explain why the slopes of the I ₁ and I ₃ plots are different, even though the species in each row of the table have the same electron configurations.

2. Would you expect the third ionization energy of iron, corresponding to the removal of an electron from a gaseous Fe ²⁺ ion, to be larger or smaller than the fourth ionization energy, corresponding to removal of an electron from a gaseous Fe ³⁺ ion? ¿Por qué? How would these ionization energies compare to the first ionization energy of Ca?

3. Which would you expect to have the highest first ionization energy: Mg, Al, or Si? Which would you expect to have the highest third ionization energy. ¿Por qué?

4. Use the values of the first ionization energies given in Figure 7.11 to construct plots of first ionization energy versus atomic number for (a) boron through oxygen in the second period; and (b) oxygen through tellurium in group 16. Which plot shows more variation? Explain the reason for the variation in first ionization energies for this group of elements.

5. Arrange Ga, In, and Zn in order of increasing first ionization energies. Would the order be the same for second and third ionization energies? Explain your reasoning.

6. Arrange each set of elements in order of increasing magnitude of electron affinity.

   1. Pb, Bi, and Te
   2. Na, K, and Rb
   3. P, C, and Ge

7. Arrange each set of elements in order of decreasing magnitude of electron affinity.

   1. As, Bi, and N
   2. O, F, and Ar
   3. Cs, Ba, and Rb

8. Of the species F, O ⁻ , Al ³⁺ , and Li ⁺ , which has the highest electron affinity? Explain your reasoning.

9. Of the species O ⁻ , N ²⁻ , Hg ²⁺ , and H ⁺ , which has the highest electron affinity? Which has the lowest electron affinity? Justify your answers.

10. The Mulliken electronegativity of element A is 542 kJ/mol. If the electron affinity of A is −72 kJ/mol, what is the first ionization energy of element A? Use the data in the following table as a guideline to decide if A is a metal, a nonmetal, or a semimetal. If 1 g of A contains 4.85 × 10 ²¹ molecules, what is the identity of element A?

    	Na	Al	Si	S	Cl
    EA (kJ/mol)	−59.6	−41.8	−134.1	−200.4	−348.6
    I (kJ/mol)	495.8	577.5	786.5	999.6	1251.2

11. Based on their valence electron configurations, classify the following elements as either electrical insulators, electrical conductors, or substances with intermediate conductivity: S, Ba, Fe, Al, Te, Be, O, C, P, Sc, W, Na, B, and Rb.

12. Using the data in Problem 10, what conclusions can you draw with regard to the relationship between electronegativity and electrical properties? Estimate the approximate electronegativity of a pure element that is very dense, lustrous, and malleable.

13. Of the elements Al, Mg, O ₂ , Ti, I ₂ , and H ₂ , which, if any, would you expect to be a good reductant? Explain your reasoning.

14. Of the elements Zn, B, Li, Se, Co, and Br ₂ , which if any, would you expect to be a good oxidant? Explain your reasoning.

15. Determine whether each species is a good oxidant, a good reductant, or neither.

    1. Ba
    2. Mo
    3. Al
    4. Ni
    5. O ₂
    6. Xe

16. Determine whether each species is a good oxidant, a good reductant, or neither.

    1. Ir
    2. Cs
    3. Be
    4. B
    5. N
    6. Po
    7. Ne

17. Of the species I ₂ , O ⁻ , Zn, Sn ²⁺ , and K ⁺ , choose which you would expect to be a good oxidant. Then justify your answer.

18. Based on the valence electron configuration of the noble gases, would you expect them to have positive or negative electron affinities? What does this imply about their most likely oxidation states? their reactivity?