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 A and X? (b) In terms of \(d_{1}\) and \(d_{2}\), what would you predict for the \(X-X\) bond length of an \(X_{2}\) molecule? [Section \(\left.7.3\right]\)

Until the early 1960 s, the group 18 elements were called the inert gases. (a) Why was the term inert gases dropped? (b) What discovery triggered this change in name? (c) What name is applied to the group now?

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

(a) The five most abundant elements in the Earth's crust are \(\mathrm{O}, \mathrm{Si}, \mathrm{Al}, \mathrm{Fe},\) and Ca. Referring to Figure \(7.1,\) are any of these elements among those known before \(1700 ?\) If so which ones? (b) Seven of the nine elements known since ancient times are metals. Referring to Table \(4.5,\) are these metals mostly found at the bottom or top of the activity series?

Moseley's experiments on \(\mathrm{X}\) rays emitted from atoms led to the concept of atomic numbers. (a) If arranged in order of increasing atomic mass, which element would come after chlorine? (b) Describe two ways in which the properties of this element differ from the other elements in group \(8 \mathrm{~A}\).

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 (iii) Valence going left to right across a row of the periodic table. 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 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 \(\mathrm{Cl}\).

Which will experience the greater effect nuclear charge, the electrons in the \(n=2\) shell in \(\mathrm{F}\) or the \(n=2\) shell in \(\mathrm{B}\) ? Which will be closer to the nucleus?

Arrange the following atoms in order of increasing effective nuclear charge experienced by the electrons in the \(n=2\) shell: Be, Br, Na, P, Se.

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 274 pm. (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 W atoms.

Using only the periodic table, arrange each set of atoms in order from largest to smallest: \((\mathbf{a}) \mathrm{Ar},\) As, \(\mathrm{Kr} ;\) (b) \(\mathrm{Cd}, \mathrm{Rb}, \mathrm{Te} ;(\mathbf{c})\) \(\mathrm{C}, \mathrm{Cl}, \mathrm{Cu}\).

Using only the periodic table, arrange each set of atoms in (a) \(\mathrm{Cs}\), Se, Te; order of increasing radius: (b) \(\mathrm{S}, \mathrm{Si}, \mathrm{Sr} ;\) (c) P, Po, Pb.

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 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? \(\mathrm{H}^{-}, \mathrm{Ca}^{2+}, \mathrm{In}^{3+}, \mathrm{Ge}^{2+}\)

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 (d) \(\mathrm{Zn}^{2+}\) configuration. (a) \(\mathrm{Cl}^{-}\), (b) \(\mathrm{Sc}^{3+}\) (c) \(\mathrm{Fe}^{2+}\) (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, \(S .(\mathbf{d})\) 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 \(Z_{\text {eff }}\) for these two ions. (c) Repeat this calculation using Slater's rules to estimate the screening constant, \(S .(\mathbf{d})\) 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) \(\mathrm{Pb}, \mathrm{Pb}^{2+}, \mathrm{Pb}^{4+}\) (b) \(\mathrm{V}^{3+}, \mathrm{Co}^{2+}, \mathrm{Co}^{3+}\) (c) \(\mathrm{Se}^{2-}, \mathrm{S}^{2-}, \mathrm{Sn}^{2+}\) (d) \(\mathrm{K}^{+}, \mathrm{Rb}^{+}, \mathrm{Br}^{-}\)

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

Which element has the highest second ionization energy: Li, \(\mathrm{K},\) or Be?

Identify each statement as true or false: (a) lonization energies are always endothermic. (b) Potassium has a larger first ionization energy than lithium. (c) The second ionization energy of the sodium atom is larger than the second ionization energy of the magnesium atom. (d) The third ionization energy is three times the first ionization energy of an 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 17 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) \(\mathrm{Br}, \mathrm{Kr} ; \mathbf{( b )} \mathrm{C}, \mathrm{Ca} ;(\mathbf{c}) \mathrm{Li}, \mathrm{Rb} ;\); (d) \(\mathrm{Pb}, \mathrm{Si} ;\) (e) \(\mathrm{Al}, \mathrm{B}\).

For each of the following pairs, indicate which element has the smaller first ionization energy: (a) \(\mathrm{Cs}, \mathrm{Cl} ;(\mathbf{b}) \mathrm{Fe}, \mathrm{Zn} ;\) (c) \(\mathrm{I}, \mathrm{Cl} ;(\mathbf{d}) \mathrm{Se}, \mathrm{Sn}\)

Write the electron configurations for the following ions, and determine which have noble-gas configurations: (a) \(\mathrm{Cu}^{2+}\) (b) \(\mathrm{Ca}^{2+},(\mathbf{c}) \mathrm{N}^{3-}\) (d) \(\mathrm{Ru}^{2+}\), (e) \(\mathrm{H}^{-}\).

Write the electron configurations for the following ions, and determine which have noble-gas configurations: (a) \(\mathrm{Ti}^{2+},(\mathbf{b})\) (d) \(\mathrm{PO}^{2-}\), (f) \(\mathrm{V}^{3+}\) \(\mathrm{Br}^{-}\) (c) \(\mathrm{Mg}^{2+}\) (e) \(\mathrm{Pt}^{2+}\)

Give three examples of +2 ions that have an electron configuration of \(n d^{10}(n=3,4,5 \ldots)\)

Give examples of transition metal ions with +3 charge that have an electron configuration of \(n d^{5}(n=3,4,5 \ldots)\).

Write an equation for the first electron affinity of helium. Would you predict a positive or a negative energy value for this process? Is it possible to directly measure the first electron affinity of helium?

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.

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, \(\mathrm{F}\) ?

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: $$ \mathrm{Al}^{3+}(g)+e^{-} \longrightarrow \mathrm{Al}^{2+}(g) $$ Which of the following statements are true? (i) The energy change for this process is the second electron affinity of Al atom since \(\mathrm{Al}^{2+}(g)\) is formed. (ii) The energy change for this process is the negative of the third ionization energy of the Al atom. (iii) The energy change for this process is the electron affinity of the \(\mathrm{Al}^{2+}\) ion.

(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?

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?

Predict whether each of the following oxides is ionic or molecular: \(\mathrm{ZnO}, \mathrm{K}_{2} \mathrm{O}, \mathrm{SO}_{2}, \mathrm{OF}_{2}, \mathrm{TiO}_{2}\)

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 balinced chemical equation to support vour answer.

Would you expect zirconium(II) oxide, \(\mathrm{ZrO},\) to react more readily with \(\mathrm{HCl}(a q)\) or \(\mathrm{NaOH}(a q) ?\)

Arrange the following oxides in order of increasing acidity: \(\mathrm{K}_{2} \mathrm{O}, \mathrm{BaO}, \mathrm{ZnO}, \mathrm{H}_{2} \mathrm{O}, \mathrm{CO}_{2}, \mathrm{SO}_{2}\)

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) Would you expect \(\mathrm{Cl}_{2} \mathrm{O}_{7}\) to be more reactive toward \(\mathrm{H}^{+}(a q)\) or \(\mathrm{OH}^{-}(a q) ?(\mathbf{d})\) 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 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 \(1000^{\circ} \mathrm{C}\) ). 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) boron trichloride with water, (b) cobalt (II) oxide with nitric acid, (c) phosphorus pentoxide with water, (d) carbon dioxide with aqueous barium hydroxide.

Write balanced equations for the following reactions: (a) sulfur dioxide with water, (b) lithium oxide in water, \((\mathbf{c})\) zinc oxide with dilute hydrochloric acid, (d) arsenic trioxide with aqueous potassium hydroxide.

(a) Why is calcium generally more reactive than beryllium? (b) Why is calcium generally less reactive than rubidium?

Copper and calcium both form +2 ions, but copper is far less reactive. Suggest an explanation, taking into account the ground-state electron configurations of these elements and their atomic radii.