Chapter 7

(a) Evaluate the expressions \(2 \times 1,2 \times(1+3)\) \(2 \times(1+3+5),\) and \(2 \times(1+3+5+7)\) . (b) How do the atomic numbers of the noble gases relate to the numbers from part (a)? (c) What topic discussed in Chapter 6 is the source of the number \(" 2 "\) in the expressions in part (a)?

Moseley's experiments on \(X\) 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 8A.

Among elements 1-18, which element or elements have the smallest effective nuclear charge if we use Equation 7.1 to calculate \(Z_{\text { eff}}\)? Which element or elements have the largest effective nuclear charge?

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

Detailed calculations show that the value of \(Z_{\text { eff }}\) for the outermost electrons in Si and Cl atoms is \(4.29+\) and \(6.12+\) , respectively.(a) What value do you estimate for \(Z\) 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 \(Z_{\text { eff? }} ?(\mathbf{d})\) 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 Si and Cl.

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

Which quantity must be determined experimentally in order to determine the bonding atomic radius of an atom? (a) The distance from the nucleus where the probability of finding an electron goes to zero. (b) The distance between the nuclei of two atoms that are bonded together. (c) The effective nuclear charge of an atom.

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 A. (a) What is the atomic radius of atungsten atom in this environment? (This radius is called the metallic radius.) 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: \((\mathbf{a}) \mathrm{K},\) Li, \(\mathrm{Cs} ;(\mathbf{b}) \mathrm{Pb}, \mathrm{Sn}, \mathrm{Si} ;(\mathbf{c}) \mathrm{F},\) \(\mathrm{O}, \mathrm{N} .\)

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

Identify each statement as true or false: (a) Cations are larger than their corresponding neutral atoms. (b) 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? \(\mathrm{Ga} ^{3+}, \mathrm{Zr}^{4+}, \mathrm{Mn}^{7+}, \mathrm{I}^{-}, \mathrm{Pb}^{2+}.\)

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

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 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, \(S.\) (d) For isoelectronic ions, how are effective nuclear charge and ionic radius related?

Consider \(S, C 1,\) and \(K\) 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: \((\mathbf{a}) \mathrm{Se}^{2-}, \mathrm{Te}^{2-}, \mathrm{Se} ;(\mathbf{b}) \mathrm{Co}^{3+}, \mathrm{Fe}^{2+}, \mathrm{Fe}^{3+};\) \((\mathbf{c}) \mathrm{Ca}, \mathrm{Ti}^{4+}, \mathrm{Sc}^{3+} ;(\mathbf{d}) \mathrm{Be}^{2+}, \mathrm{Na}^{+}, \mathrm{Ne}.\)

Provide a brief explanation for each of the following: \((\mathbf{c}) \mathrm{O}^{2-}\) is larger than O.\((\mathbf{b}) S^{2-}\) is larger than \(\mathrm{O}^{2-} .(\mathbf{c}) \mathrm{S}^{2-}\) is larger than \(\mathrm{K}^{+} .(\mathbf{d}) \mathrm{K}^{+}\) 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.

Which element has the highest second ionization energy: Li, K, or 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 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 fourthperiod 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\(:(\mathbf{a}) \mathrm{Cl}, \mathrm{Ar} ;(\mathbf{b}) \mathrm{Be}, \mathrm{Ca} ;(\mathbf{c}) \mathrm{K}, \mathrm{Co} ;(\mathbf{d}) \mathrm{S}, \mathrm{Ge} ;(\mathbf{e}) \mathrm{Sn}, \mathrm{Te}.\)

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

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

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

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

Give three examples of ions that have an electron configuration of \(n d^{6}(n=3,4,5, \ldots).\)

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

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.

Would a neutral \(\mathrm{K}\) atom or a \(\mathrm{K}^{+}\) ion have a more negative value of electron affinity?

What is the relationship between the ionization energy of an anion with a \(1-\) charge such as \(F^{-}\) 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: $$\mathrm{Ca}^{+}(g)+\mathrm{e}^{-} \longrightarrow \mathrm{Ca}(g)$$ Which of the following statements are true? (i) The energy change for this process is the electron affinity of the Ca' ion. (ii) The energy change for this process is the negative of the first ionization energy of the Ca atom. (ii) The energy change for this process is the negative of the electron affinity of the 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?

You read the following statement about two elements \(\mathrm{X}\) and \(\mathrm{Y} :\) One of the elements is a good conductor of electricity, and the other is a semiconductor. Experiments show that the first ionization energy of \(\mathrm{X}\) is twice as great as that of Y. Which element has the greater metallic character?

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

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.

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

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 Cl? What is the electron configuration of Cl in this oxidation state?

An element \(\mathrm{X}\) reacts with oxygen to form \(\mathrm{XO}_{2}\) and with chlorine to form \(\mathrm{XCl}_{4} . \mathrm{XO}_{2}\) 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 \(\mathrm{X}\).

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.

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?