Chapter 7

We can draw an analogy between the attraction of an electron to a nucleus and seeing a lightbulb -in essence, the more \(n u=\) clear charge the electron "sees," the greater the attraction. (a) Within this analogy, discuss how the screening 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]

Consider the \(\mathrm{A}_{2} \mathrm{X}_{4}\) molecule depicted here, where \(\mathrm{A}\) and \(\mathrm{X}\) are elements. The \(\mathrm{A}-\mathrm{A}\) bond length in this molecule is \(d_{1},\) and the four \(\mathrm{A}-\mathrm{X}\) bond lengths are each \(d_{2}\). (a) In terms of \(d_{1}\) and \(d_{2}\), how could you define the bonding atomic radii of atoms \(A\) and \(X ?(b)\) In terms of \(d_{1}\) and \(d_{2}\), what would you predict for the \(\mathrm{X}-\mathrm{X}\) bond length of an \(\mathrm{X}_{2}\) molecule? \([\) Section 7.3\(]\)

Make a simple sketch of the shape of the main part of the periodic table, as shown. (a) Ignoring \(\mathrm{H}\) and He, write a single straight arrow from the element with the smallest bonding atomic radius to the element with the largest. Ignoring \(\mathrm{H}\) and 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 7.5\(]\)

Explain the structure of the periodic table- two columns on the left, a block of ten for the transition metals, a block of six on the right, and a pair of 14 -member rows below, with reference to the orbitals we discussed in Chapter \(\underline{6}\).

(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 a manyelectron 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 the outermost electrons in \(\mathrm{Si}\) 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 Si and 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? (e) Predict \(Z_{\text {eff }}\) for a valence electron in P, phosphorus, based on the calculations for \(\mathrm{Si}\) and \(\mathrm{Cl}\).

(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? (d) If a free atom reacts to become part of a molecule, would you say that the atom gets smaller or larger?

(a) Why does the quantum mechanical description of manyelectron 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?

Tungsten has the highest melting point of any metal in the periodic table: \(3422{ }^{\circ} \mathrm{C}\). The distance between \(\mathrm{W}\) atoms in tungsten metal is \(2.74 \AA\). (a) What is the atomic radius of a tungsten atom in this environment? (This radius is called the metallic radius.) (b) If you put tungsten metal under high pressure, predict what would happen to the distance between \(\mathrm{W}\) atoms.

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: \(\mathrm{O}, \mathrm{Si}, \mathrm{I}, \mathrm{Ge} .\)

(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: \(\mathrm{Si}, \mathrm{Al}, \mathrm{Ge}, \mathrm{Ga}\).

Using only the periodic table, arrange each set of atoms in order from largest to smallest: (a) \(\mathrm{K}, \mathrm{Li}, \mathrm{Cs} ;\) (b) \(\mathrm{Pb}, \mathrm{Sn}, \mathrm{Si} ;\) (c) \(\mathrm{F}, \mathrm{O}, \mathrm{N}\)

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

Explain the following variations in atomic or ionic radii: (a) \(\Gamma>\mathrm{I}>\mathrm{I}^{+},(\mathrm{b}) \mathrm{Ca}^{2+}>\mathrm{Mg}^{2+}>\mathrm{Be}^{2+}\) (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: \(\mathrm{Ga}^{3+}, \mathrm{Zr}^{4+}\) \(\mathrm{Mn}^{7+}, \Gamma, \mathrm{Pb}^{2+} ?\)

Identify at least two ions that have the following ground-state electron configurations: (a) \([\mathrm{Ar}] ;\) (b) \([\mathrm{Ar}] 3 d^{5}\); (c) \([\mathrm{Kr}] 5 s^{2} 4 d^{10}\)

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. (b) \(\mathrm{Sc}^{3+}\) (d) \(\mathrm{Zn}^{2+},(\mathrm{e}) \mathrm{Sn}^{4+}\) (a) \(\mathrm{Cl}\) (c) \(\mathrm{Fe}^{2+}\)

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 \(Z_{\text {eff }}\) for the \(2 p\) 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 the isoelectronic ions \(\mathrm{Cl}^{-}\) and \(\mathrm{K}\). (a) Which ion is smaller? (b) Using Equation 7.1 and assuming that core electrons contribute 1.00 and valence electrons contribute nothing to the screening constant, \(S,\) calculate \(Z_{\mathrm{eff}}\) for these two 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) \(\mathrm{Co}^{3+}, \mathrm{Fe}^{2+}, \mathrm{Fe}^{3+}\) (d) \(\mathrm{Be}^{2+}, \mathrm{Na}^{+}, \mathrm{Ne}\). (c) \(\mathrm{Ca}, \mathrm{Ti}^{4+}, \mathrm{Sc}^{3+}\)

Write equations that show the processes that describe the first, second, and third ionization energies of an aluminum atom. Which process would require the least amount of energy?

Identify each statement as true or false. If it is false, rewrite it so that it is true: (a) Ionization energies are always negative quantitites. (b) Oxygen has a larger first ionization energy than fluorine. (c) The second ionization energy of an atom is 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 smaller first ionization energy: (a) \(\mathrm{Cl}, \mathrm{Ar} ;\) (b) \(\mathrm{Be}, \mathrm{Ca}\) (c) \(\mathrm{K}\), Co; (d) \(\mathrm{S}, \mathrm{Ge} ;\) (e) Sn. Te.

For each of the following pairs, indicate which element has the smaller first ionization energy: (a) \(\mathrm{Ti}, \mathrm{Ba} ;(\mathrm{b}) \mathrm{Ag}, \mathrm{Cu} ;(\mathrm{c}) \mathrm{Ge}\) \(\mathrm{Cl} ;\) (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) \(\mathrm{Fe}^{2+},(\mathbf{b}) \mathrm{Hg}^{2+},(\mathbf{c}) \mathrm{Mn}^{2+},(\mathrm{d}) \mathrm{Pt}^{2+},(\mathrm{e}) \mathrm{P}^{3-}\).

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

Find three examples of ions in the periodic table that have an electron configuration of \(n d^{8}(n=3,4,5 \ldots) .\)

Find three atoms in the periodic table whose ions have an electron configuration of \(n d^{6}(n=3,4,5 \ldots) .\)

The first ionization energy and electron affinity of Ar are both positive values. (a) What is the significance of the positive value in each case? (b) What are the units of electron affinity?

If the electron affinity for an element is a negative number, does it mean that the anion of the element is more stable than the neutral atom? Explain.

Although the electron affinity of bromine is a negative quantity, it is positive for \(\mathrm{Kr}\). 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?

It is possible to define metallic character as we do in this book and base it on the reactivity of the element and the ease with which it loses electrons. Alternatively, one could measure how well electricity is conducted by each of the elements to determine how "metallic" the elements are. On the basis of conductivity, there is not much of a trend in the periodic table: Silver is the most conductive metal, and manganese the least. Look up the first ionization energies of silver and manganese; which of these two elements would you call more metallic based on the way we define it in this book?

Discussing this chapter, a classmate says, "An element that commonly forms a cation is a metal." Do you agree or disagree? Explain your answer.

Discussing this chapter, a classmate says, "Since elements that form cations are metals and elements that form anions are nonmetals, elements that do not form ions are metalloids." Do you agree or disagree? Explain your answer.

Predict whether each of the following oxides is ionic or molecular: \(\mathrm{SnO}_{2}, \mathrm{Al}_{2} \mathrm{O}_{3}, \mathrm{CO}_{2}, \mathrm{Li}_{2} \mathrm{O}, \mathrm{Fe}_{2} \mathrm{O}_{3}, \mathrm{H}_{2} \mathrm{O} .\) 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.

(a) What is meant by the terms acidic oxide and basic oxide? (b) How can we predict whether an oxide will be acidic or basic based on its composition?

Arrange the following oxides in order of increasing acidity: \(\mathrm{CO}_{2}, \mathrm{CaO}, \mathrm{Al}_{2} \mathrm{O}_{3}, \mathrm{SO}_{3}, \mathrm{SiO}_{2},\) and \(\mathrm{P}_{2} \mathrm{O}_{5}\)

Chlorine reacts with oxygen to form \(\mathrm{Cl}_{2} \mathrm{O}_{7} .\) (a) What is the name of this product (see Table 2.6 )? (b) Write a balanced equation for the formation of \(\mathrm{Cl}_{2} \mathrm{O}_{7}(l)\) from the elements. (c) Under usual conditions, \(\mathrm{Cl}_{2} \mathrm{O}_{7}\) is a colorless liquid with a boiling point of \(81^{\circ} \mathrm{C}\). Is this boiling point expected or surprising? (d) Would you expect \(\mathrm{Cl}_{2} \mathrm{O}_{7}\) to be more reactive toward \(\mathrm{H}^{+}(a q)\) or \(\mathrm{OH}^{-}(a q) ?\) Explain. (e) If the oxygen in \(\mathrm{Cl}_{2} \mathrm{O}_{7}\) is considered to have the -2 oxidation state, what is the oxidation state of the Cl? What is the electron configuration of \(\mathrm{Cl}\) in this oxidation state?

An element \(X\) reacts with oxygen to form \(\mathrm{XO}_{2}\) and with chlorine to form \(\mathrm{XCl}_{4} . \mathrm{XO}_{2}\) is a white solid that melts at high temperatures (above \(\left.1000^{\circ} \mathrm{C}\right)\). Under usual conditions, \(\mathrm{XCl}_{4}\) is a colorless liquid with a boiling point of \(58^{\circ} \mathrm{C}\). (a) \(\mathrm{XCl}_{4}\) reacts with water to form \(\mathrm{XO}_{2}\) and another product. What is the likely identity of the other product? (b) Do you think that element \(\mathrm{X}\) is a metal, nonmetal, or metalloid? Explain. (c) \(\mathrm{By}\) using a sourcebook such as the CRC Handbook of Chemistry and Physics, try to determine the identity of element \(\mathrm{X}\).

Write balanced equations for the following reactions: (a) barium oxide with water, (b) iron(II) oxide with perchloric acid, (c) sulfur trioxide with water, (d) carbon dioxide with aqueous sodium hydroxide.