Chapter 7

Consider the \(\mathrm{A}_{2} \mathrm{X}_{4}\) molecule depicted here, where \(\mathrm{A}\) and \(\mathrm{X}\) are elements. The A-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 \(\mathrm{A}\) and \(\mathrm{X}\) ? (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]

(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?

Which of the following statements about effective nuclear charge for the outermost valence electron of an atom is incorrect? (i) The effective nuclear charge can be thought of as the true nuclear charge minus a screening constant due to the other electrons in the atom. (ii) Effective nuclear charge increases going left to right across a row of the periodic table. (iii) Valence electrons screen the nuclear charge more effectively than do core electrons. (iv) The effective nuclear charge shows a sudden decrease when we go from the end of one row to the beginning of the next row of the periodic table. (v) The change in effective nuclear charge going down a column of the periodic table is generally less than that going across a row of the periodic table.

Detailed calculations show that the value of \(Z_{\text {eff }}\) for the outermost electrons in \(\mathrm{Na}\) and \(\mathrm{K}\) 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 \(\mathrm{Na}\) and \(\mathrm{K}\) 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? (e) Predict \(Z_{\text {eff }}\) for the outermost electrons in the \(\mathrm{Rb}\) atom based on the calculations for \(\mathrm{Na}\) and \(\mathrm{K}\).

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

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

Arrange the following atoms in order of increasing effective nuclear charge experienced by the electrons in the \(n=3\) electron shell: K, Mg, P, Rh, Ti.

(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.

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

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

Identify each statement as true or false: (a) Cations are larger than their corresponding neutral atoms. (b) \(\mathrm{Li}^{+}\)is smaller than Li. (c) \(\mathrm{Cl}^{-}\)is bigger than \(\mathrm{I}^{-}\).

Explain the following variations in atomic or ionic radii: (a) \(\mathrm{I}^{-}>\mathrm{I}>\mathrm{I}^{+}\) (b) \(\mathrm{Ca}^{2+}>\mathrm{Mg}^{2+}>\mathrm{Be}^{2+}\) (c) \(\mathrm{Fe}>\mathrm{Fe}^{2+}>\mathrm{Fe}^{3+}\)

Which neutral atom is isoelectronic with each of the following ions? \(\mathrm{Ga}^{3+}, \mathrm{Zr}^{4+}, \mathrm{Mn}^{7+}, \Gamma, \mathrm{Pb}^{2+}\).

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 \(Z_{\text {eff }}\) 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 \(\mathrm{S}, \mathrm{Cl}\), 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.

Arrange each of the following sets of atoms and ions, 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) \(\mathrm{Ca}^{2 \mathrm{Ti}^{4+}}, \mathrm{Sc}^{3+}\); (d) \(\mathrm{Be}^{2+}, \mathrm{Na}^{+}, \mathrm{Ne}\).

Provide a brief explanation for each of the following: (a) \(\mathrm{O}^{2-}\) is larger than O. (b) \(\mathrm{S}^{2-}\) is larger than \(\mathrm{O}^{2-}\). (c) \(\mathrm{S}^{2-}\) is larger than \(\mathrm{K}^{+}\). (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 an aluminum atom. Which process would require the least amount of energy?

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

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

Identify each statement as true or false: (a) Ionization energies are always negative quantities. (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. (d) The third ionization energy is the energy needed to ionize three electrons from a neutral atom.

(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 7A 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) Be, Ca; (c) K, Co; (d) S, Ge; (e) Sn, Te.

For each of the following pairs, indicate which element has the smaller first ionization energy: (a) Ti, Ba; (b) \(\mathrm{Ag}, \mathrm{Cu}\); (c) \(\mathrm{Ge}, \mathrm{Cl}\); (d) \(\mathrm{Pb}, \mathrm{Sb}\).

Write the electron configurations for the following ions, and determine which have noble-gas configurations: (a) \(\mathrm{Co}^{2+}\), (b) \(\mathrm{Sn}^{2+}\), (c) \(\mathrm{Zr}^{4+}\), (d) \(\mathrm{Ag}^{+}\), (e) \(\mathrm{S}^{2-}\).

Write the electron configurations for the following ions, and determine which have noble-gas configurations: (a) \(\mathrm{Ru}^{3+}\), (b) \(\mathrm{As}^{3-}\), (c) \(\mathrm{Y}^{3+}\), (d) \(\mathrm{Pd}^{2+}\), (e) \(\mathrm{Pb}^{2+}\), (f) \(\mathrm{Au}^{3+}\).

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

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 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 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?

Consider the following equation: $$ \mathrm{Ca}^{+}(g)+\mathrm{e}^{-} \longrightarrow \mathrm{Ca}(g) $$ Which of the following statements are true? (i) The energy change for this process is the electron affinity of the \(\mathrm{Ca}^{+}\)ion. (ii) The energy change for this process is the negative of the first ionization energy of the Ca atom. (iii) The energy change for this process is the negative of the electron affinity of the \(\mathrm{Ca}\) atom.

(a) Does metallic character increase, decrease, or remain unchanged as one goes from left to right across a row of the periodic table? (b) Does metallic character increase, decrease, or remain unchanged as one goes down a column of the periodic table? (c) Are the periodic trends in (a) and (b) the same as or different from those for first ionization energy?

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: \(\mathrm{SnO}_{2}, \mathrm{Al}_{2} \mathrm{O}_{3}, \mathrm{CO}_{2}, \mathrm{Li}_{2} \mathrm{O}, \mathrm{Fe}_{2} \mathrm{O}_{3}, \mathrm{H}_{2} \mathrm{O}\).

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: $$ \mathrm{CO}_{2}, \mathrm{CaO}, \mathrm{Al}_{2} \mathrm{O}_{3}, \mathrm{SO}_{3}, \mathrm{SiO}_{2}, \mathrm{P}_{2} \mathrm{O}_{5} \text {. } $$

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 \(\mathrm{OH}^{-}(a q)\) ? (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 \(\mathrm{Cl}\) ? What is the electron configuration of \(\mathrm{Cl}\) in this oxidation state?

An element \(\mathrm{X}\) reacts with oxygen to form \(\mathrm{XO}_{2}\) and with chlorine to form \(\mathrm{XCl}_{4} \cdot \mathrm{XO}_{2}\) is a white solid that melts at high temperatures (above \(1000^{\circ} \mathrm{C}\) ). 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? (c) By using a sourcebook such as the CRC Handbook of Chemistry and Physics, try to determine the identity of element 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.

Write balanced equations for the following reactions: (a) potassium oxide with water, (b) diphosphorus trioxide with water, (c) chromium(III) oxide with dilute hydrochloric acid, (d) selenium dioxide with aqueous potassium hydroxide.

(a) Why is calcium generally more reactive than magnesium? (b) Why is calcium generally less reactive than potassium?

Silver and rubidium both form \(+1\) ions, but silver is far less reactive. Suggest an explanation, taking into account the ground-state electron configurations of these elements and their atomic radii.