Chapter 7

We can draw an analogy between the attraction of an electron to a nucleus and seeing a lightbulb-in essence, the more nuclear charge the electron "sees," the greater the attraction. (a) Within this analogy, discuss how the shielding by core electrons is analogous to putting a frosted-glass lampshade between the lightbulb and your eyes, as shown in the illustration. (b) Explain how we could mimic moving to the right in a row of the periodic table by changing the wattage of the lightbulb. (c) How would you change the wattage of the bulb and/or the frosted glass to mimic the effect of moving down a column of the periodic table? [Section 7.2]

Make a simple sketch of the shape of the main part of the periodic table, as shown (a) Ignoring \(\mathrm{H}\) and \(\mathrm{He}\), write a single straight arrow from the element with the smallest bonding atomic radius to the element with the largest. (b) Ignoring \(\mathrm{H}\) and \(\mathrm{He}\), write a single straight arrow from the element with the smallest first ionization energy to the element with the largest. (c) What significant observation can you make from the arrows you drew in parts (a) and (b)? [Sections \(7.3\) and 7.4]

In the chemical process called electron transfer, an electron is transferred from one atom or molecule to another (We will talk about electron transfer extensively in Chapter 20.) A simple electron transfer reaction is $$ \mathrm{A}(g)+\mathrm{A}(g) \longrightarrow \mathrm{A}^{+}(g)+\mathrm{A}^{-}(g) $$ In terms of the ionization energy and electron affinity of atom A, what is the energy change for this reaction? For a representative nonmetal such as chlorine, is this process exothermic? For a representative metal such as sodium, is this process exothermic? [Sections \(7.4\) and \(7.51\)

An element \(X\) reacts with \(\mathrm{F}_{2}(g)\) to form the molecular product shown below. (a) Write a balanced equation for this reaction (do not worry about the phases for \(X\) and the product). (b) Do you think that \(X\) is a metal or nonmetal? Explain. [Section 7.6]

Why did Mendeleev leave blanks in his early version of the periodic table? How did he predict the properties of the elements that belonged in those blanks?

In Chapter 1 we learned that silicon is the second most abundant element in Earth's crust, accounting for more than one-fourth of the mass of the crust (Figure 1.6). Yet we see that silicon is not among the elements that have been known since ancient times (Figure \(7.2\) ), whereas iron, which accounts for less than \(5 \%\) of Earth's crust, has been known since prehistoric times. Given silicon's abundance how do you account for its relatively late discovery?

(a) During the period from about 1800 to about 1865 , the atomic weights of many elements were accurately measured. Why was this important to Mendeleev's formulation of the periodic table? (b) What property of the atom did Moseley associate with the wavelength of X-rays emitted from an element in his experiments? (c) Why are chemical and physical properties of the elements more closely related to atomic number than they are to atomic weight?

(a) What is meant by the term effective nuclear charge? (b) How does the effective nuclear charge experienced by the valence electrons of an atom vary going from left to right across a period of the periodic table?

(a) How is the concept of effective nuclear charge used to simplify the numerous electron-electron repulsions in ? many-electron atom? (b) Which experiences a greater effective nuclear charge in a Be atom, the 1 s electrons or the 2 s electrons? Explain.

Detailed calculations show that the value of \(Z_{\text {eff }}\) for \(\mathrm{Na}\) and \(K\) atoms is \(2.51+\) and \(3.49+\), respectively. (a) What value do you estimate for \(Z_{\text {eff }}\) experienced by the outermost electron in both Na and \(K\) by assuming core electrons contribute \(1.00\) and valence electrons contribute \(0.00\) to the screening constant? (b) What values do you estimate for \(Z_{\text {eff }}\) using Slater's rules? (c) Which approach gives a more accurate estimate of \(Z_{\text {eff }} ?\) (d) Does either method of approximation account for the gradual increase in \(Z_{\text {eff }}\) that occurs upon moving down a group?

Detailed calculations show that the value of \(Z_{\text {eff }}\) for \(\mathrm{Si}\) and \(\mathrm{Cl}\) atoms is \(4.29+\) and \(6.12+\), respectively. (a) What value do you estimate for \(Z_{\text {eff }}\) experienced by the outermost electron in both \(\mathrm{Si}\) and \(\mathrm{Cl}\) by assuming core electrons contribute \(1.00\) and valence electrons contribute \(0.00\) to the screening constant? (b) What values do you estimate for \(Z_{\text {eff }}\) using Slater's rules? (c) Which approach gives a more accurate estimate of \(Z_{\text {eff }} ?\) (d) Which method of approximation more accurately accounts for the steady increase in \(Z_{\text {eff }}\) that occurs upon moving left to right across a period?

Which will experience the greater effective nuclear charge, the electrons in the \(n=3\) shell in Ar or the \(n=3\) shell in Kr? Which will be closer to the nucleus? Explain.

Arrange the following atoms in order of increasing effective nuclear charge experienced by the electrons in the \(n=3\) electron shell: \(K, M g, P, R h\), and \(T\). Explain the basis for your order.

(a) Because an exact outer boundary cannot be measured or even calculated for an atom, how are atomic radii determined? (b) What is the difference between a bonding radius and a nonbonding radius? (c) For a given element, which one is larger?

(a) Why does the quantum mechanical description of many-electron atoms make it difficult to define a precise atomic radius? (b) When nonbonded atoms come up against one another, what determines how closely the nuclear centers can approach?

The distance between \(\mathrm{W}\) atoms in tungsten metal is \(2.74 \mathrm{~A}\). What is the atomic radius of a tungsten atom in this environment? (This radius is called the metallic radius)

The experimental \(\mathrm{Bi}-\mathrm{I}\) bond length in bismuth triiodide, \(\mathrm{BiI}_{3}\), is \(2.81 \AA\). Based on this value and data in Figure \(7.7\), predict the atomic radius of \(B\) i.

How do the sizes of atoms change as we move (a) from left to right across a row in the periodic table. (b) from top to bottom in a group in the periodic table? (c) Arrange the following atoms in order of increasing atomic radius \(\mathrm{F}, \mathrm{P}, \mathrm{S}\), As.

(a) Among the nonmetallic elements, the change in atomic radius in moving one place left or right in a row is smaller than the change in moving one row up or down. Explain these observations. (b) Arrange the following atoms in order of increasing atomic radius: \(S i\). \(\mathrm{A} 1\), Ge, Ga.

Using only the periodic table, arrange each set of atoms in order of increasing radius: (a) \(\mathrm{Ca}, \mathrm{Mg}\), Be; (b) \(\mathrm{Ga}, \mathrm{Br}\), \(\mathrm{Ge} ;\) (c) \(\mathrm{Al}, \mathrm{T}\), \(\mathrm{Si}\).

Using only the periodic table, arrange each set of atoms in order of increasing radius: (a) \(\mathrm{Ba}, \mathrm{Ca}, \mathrm{Na} ;\) (b) \(\mathrm{Sn}, \mathrm{Sb}\), As; (c) \(\mathrm{Al}, \mathrm{Be}, \mathrm{Si}\).

(a) Why are monatomic cations smaller than their corresponding neutral atoms? (b) Why are monatomic anions larger than their corresponding neutral atoms? (c) Why does the size of ions increase as one proceeds down a column in the periodic table?

Explain the following variations in atomic or ionic radii: (a) \(1^{-}>1>1^{+},(b) C a^{2+}>M g^{2+}>B e^{2+}\) (c) \(\mathrm{Fe}>\mathrm{Fe}^{2+}>\mathrm{Fe}^{3+}\).

(a) What is an isoelectronic series? (b) Which neutral atom is isoelectronic with each of the following ions: \(\mathrm{Al}^{3+}, \mathrm{Ti}^{4+}, \mathrm{Br}^{-}, \mathrm{Sn}^{2+}\)

Some ions do not have a corresponding neutral atom that has the same electron configuration. For each of the following ions identify the neutral atom that has the same number of electrons and determine if this atom has the same electron configuration. If such an atom does not exist explain why: (a) \(\mathrm{Cl}^{-}\) (b) \(\mathrm{Sc}^{3+}\) (c) \(\mathrm{Fe}^{2+}\), (d) \(\mathrm{Zn}^{2+}\), (e) \(\mathrm{Sn}^{4+}\).

Consider the isoelectronic ions \(\mathrm{F}^{-}\) and \(\mathrm{Na}^{+}\). (a) Which ion is smaller? (b) Using Equation \(7.1\) and assuming that core electrons contribute \(1.00\) and valence electrons contribute \(0.00\) to the screening constant, \(S\), calculate \(Z_{\text {efi }}\) for the \(2 \mathrm{p}\) electrons in both ions. (c) Repeat this calculation using Slater's rules to estimate the screening constant, \(S\). (d) For isoelectronic ions, how are effective nuclear charge and ionic radius related?

Consider \(\mathrm{S}, \mathrm{Cl}\), and \(\mathrm{K}\) and their most common ions. (a) List the atoms in order of increasing size (b) List the ions in order of increasing size. (c) Explain any differences in the orders of the atomic and ionic sizes.

For each of the following sets of atoms and ions, arrange the members in order of increasing size: (a) \(\mathrm{Se}^{2-}, \mathrm{Te}^{2-}, \mathrm{Se}\); (b) \(\mathrm{Co}^{3+}, \mathrm{Fe}^{2+}, \mathrm{Fe}^{3+}\), (c) \(\mathrm{Ca}, \mathrm{Ti}^{4+}, \mathrm{Sc}^{3+}\) (d) \(\mathrm{Be}^{2+}, \mathrm{Na}^{+}, \mathrm{Ne}\)

For each of the following statements, provide an explanation (a) \(\mathrm{O}^{2-}\) is larger than \(\mathrm{O} ;\) (b) \(\mathrm{S}^{2-}\) is larger than \(\mathrm{O}^{2-}\) : (c) \(S^{2-}\) is larger than \(K^{+}\); (d) \(\mathrm{K}^{+}\) is larger than \(\mathrm{Ca}^{2+}\).

Write equations that show the processes that describe the first, second, and third ionization energies of a boron atom.

Write equations that show the process for (a) the first two ionization energies of tin and (b) the fourth ionization energy of titanium.

(a) Why are ionization energies always positive quantities? (b) Why does \(\mathrm{F}\) have a larger first ionization energy than \(\mathrm{O}\) ? (c) Why is the second ionization energy of an atom always greater than its first ionization energy?

(a) Why does Li have a larger first ionization energy than Na? (b) The difference between the third and fourth ionization energies of scandium is much larger than the difference between the third and fourth ionization energies of titanium. Why? (c) Why does Li have a much larger second ionization energy than Be?

(a) What is the general relationship between the size of an atom and its first ionization energy? (b) Which element in the periodic table has the largest ionization energy? Which has the smallest?

(a) What is the trend in first ionization energies as one proceeds down the group 7 A elements? Explain how this trend relates to the variation in atomic radii. (b) What is the trend in first ionization energies as one moves across the fourth period from \(\mathrm{K}\) to \(\mathrm{Kr}\) ? How does this trend compare with the trend in atomic radii?

Based on their positions in the periodic table, predict which atom of the following pairs will have the larger first ionization energy: (a) \(\mathrm{Cl}\), \(\mathrm{Ar} ;\) (b) Be, \(\mathrm{Ca} ;\) (c) \(\mathrm{K}, \mathrm{Co}\); (d) S, Ge; (e) \(\mathrm{Sn}\), Te.

For each of the following pairs, indicate which element has the larger first ionization energy: (a) \(\mathrm{Ti}\), \(\mathrm{Ba} ;\) (b) \(\mathrm{Ag}\), \(\mathrm{Cu} ;\) (c) Ge, \(\mathrm{Cl} ;\) (d) \(\mathrm{Pb}\), Sb. (In each case use electron configuration and effective nuclear charge to explain your answer.)

Write the electron configurations for the following ions: (a) \(\ln ^{3+}\) (b) \(\mathrm{Sb}^{3+}\) (c) \(\mathrm{Te}^{2-}\), (d) \(\mathrm{Te}^{6+}\) (e) \(\mathrm{Hg}^{2+}\) (f) \(\mathrm{Rh}^{3+}\),

Write electron configurations for the following ions, and determine which have noble-gas configurations: (a) \(\mathrm{Cr}^{3+}\), (b) \(\mathrm{N}^{3-}\) (c) \(\mathrm{Sc}^{3+}\), (d) \(\mathrm{Cu}^{2+}\), (e) \(\mathrm{Tl}^{+}\), (f) \(\mathrm{Au}^{+}\).

Write the electron configuration for (a) the \(\mathrm{Ni}^{2+}\) ion and (b) the \(\mathrm{Sn}^{2+}\) ion. How many unpaired electrons does each contain?

Identify the element whose ions have the following electron configurations: (a) a \(2+\) ion with \([\operatorname{Ar}] 3 d^{9}\), (b) a \(1+\) ion with \([\mathrm{Xe}] 4 f^{14} 5 d^{10} 6 \mathrm{~s}^{2}\). How many unpaired electrons does each ion contain?

The first ionization energy of Ar and the electron affinity of \(\mathrm{Ar}\) are both positive values. What is the significance of the positive value in each case?

The electron affinity of lithium is a negative value, whereas the electron affinity of beryllium is a positive value. Use electron configurations to account for this observation.

While the electron affinity of bromine is a negative quantity, it is positive for Kr. Use the electron configurations of the two elements to explain the difference.

What is the relationship between the ionization energy of an anion with a \(1-\) charge such as \(\mathrm{F}\) and the electron affinity of the neutral atom, F?

Consider the first ionization energy of neon and the electron affinity of fluorine. (a) Write equations, including electron configurations, for each process. (b) These two quantities will have opposite signs. Which will be positive, and which will be negative? (c) Would you expect the magnitudes of these two quantities to be equal? If not, which one would you expect to be larger? Explain your answer.

How are metallic character and first ionization energy related?

For each of the following pairs, which element will have the greater metallic character: (a) Li or Be, (b) Li or Na, (c) Sn or \(\mathrm{P}_{\text {, }}\) (d) \(\mathrm{Al}\) or \(\mathrm{B}\) ?

Predict whether each of the following oxides is ionic or molecular. \(\mathrm{SO}_{2}, \mathrm{MgO}, \mathrm{Li}_{2} \mathrm{O}, \mathrm{P}_{2} \mathrm{O}_{5}, \mathrm{Y}_{2} \mathrm{O}_{3}, \mathrm{~N}_{2} \mathrm{O}\), and \(\mathrm{XeO}_{3}\) Explain the reasons for your choices.

Some metal oxides, such as \(\mathrm{Sc}_{2} \mathrm{O}_{3}\), do not react with pure water, but they do react when the solution becomes either acidic or basic. Do you expect \(\mathrm{Sc}_{2} \mathrm{O}_{3}\) to react when the solution becomes acidic or when it becomes basic? Write a balanced chemical equation to support your answer.