Chapter 7

Detailed calculations show that the value of \(Z_{\text {eff }}\) for the outermost electrons in 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 \(\mathrm{K}\).

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.

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 \(274 \mathrm{pm}\). (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 \(\mathrm{W}\) atoms.

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

Using only the periodic table, arrange each set of atoms in order of increasing radius: (a) Cs, Se, Te; (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 configuration. (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, \(S .(\mathbf{d})\) For isoelectronic ions, how are effective nuclear charge and ionic radius related?

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) \(\mathrm{Se}^{2-}, \mathrm{S}^{2-}, \mathrm{Sn}^{2+} ;(\mathbf{d}) \mathrm{K}^{+}, \mathrm{Rb}^{+}, \mathrm{Br}^{-}\)

Provide a brief explanation for each of the following: \((\mathbf{a}) \mathrm{Cl}^{-}\) is larger than Ar. (b) \(\mathrm{P}^{3-}\) is larger than \(\mathrm{S}^{2-}\). (c) \(\mathrm{K}^{+}\) is larger than \(\mathrm{Na}^{+} .(\mathbf{d}) \mathrm{F}^{-}\) is larger than \(\mathrm{F}\).

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?

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

Which element has the highest second ionization energy: Li, K, or Be?

Identify each statement as true or false: (a) Ionization 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) \(\mathrm{Br}, \mathrm{Kr} ;\) (b) C, Ca; (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) Cs, Cl; (b) Fe, Zn; (c) 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) \(\mathrm{Ti}^{2+}\), (b) \(\mathrm{Br}^{-}\), (c) \(\mathrm{Mg}^{2+}\), (d) \(\mathrm{Po}^{2-}\), (e) \(\mathrm{Pt}^{2+},(\mathbf{f}) \mathrm{V}^{3+} .\)

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.

Which of the following, I or \(\mathrm{I}^{-}\), will have a negative electron affinity?

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: $$ \mathrm{Al}^{3+}(g)+e^{-} \longrightarrow \mathrm{Al}^{2+}(g) $$ Which of the following statements are true? (i) The energy change for this process is the second electron affinity of \(\mathrm{Al}\) 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?

You read the following statement about two elements \(X\) and 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 \(X\) 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: \(\mathrm{ZnO}, \mathrm{K}_{2} \mathrm{O}, \mathrm{SO}_{2}, \mathrm{OF}_{2}, \mathrm{TiO}_{2}\)

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: \(\mathrm{K}_{2} \mathrm{O}, \mathrm{BaO}, \mathrm{ZnO}, \mathrm{H}_{2} \mathrm{O}, \mathrm{CO}_{2}, \mathrm{SO}_{2}\).

Write balanced equations for the following reactions: (a) boron trichloride with water, \((\mathbf{b})\) 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, \((\mathbf{d})\) 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.

Write a balanced equation for the reaction that occurs in each of the following cases: (a) Potassium metal is exposed to an atmosphere of chlorine gas. (b) Strontium oxide is added to water. (c) A fresh surface of lithium metal is exposed to oxygen gas. (d) Sodium metal reacts with molten sulfur.

Write a balanced equation for the reaction that occurs in each of the following cases: (a) Lithium is added to water. (b) Calcium is added to water. (c) Potassium reacts with chlorine gas. (d) Rubidium reacts with oxygen.

Compare the elements bromine and chlorine with respect to the following properties: (a) electron configuration, (b) most common ionic charge, \((\mathbf{c})\) first ionization energy, \((\mathbf{d})\) reactivity toward water, \((\mathbf{e})\) electron affinity, \((\mathbf{f})\) atomic radius. Account for the differences between the two elements.

Little is known about the properties of astatine, At, because of its rarity and high radioactivity. Nevertheless, it is possible for us to make many predictions about its properties. (a) Do you expect the element to be a gas, liquid, or solid at room temperature? Explain. (b) Would you expect At to be a metal, nonmetal, or metalloid? Explain. (c) What is the chemical formula of the compound it forms with Na?

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?

Write a balanced equation for the reaction that occurs in each of the following cases: (a) White phorphrous, \(\mathrm{P}_{4}(\mathrm{~s})\) reacts with chlorine gas. (b) Sodium metal reacts with water. (c) Hydrogen bromide gas reacts with chlorine gas. (d) Aluminum trichloride reacts with aqueous sodium hydroxide.

Write a balanced equation for the reaction that occurs in each of the following cases: (a) Calcium metal is heated in an atmosphere of oxygen gas. (b) Copper oxide is heated in an atmosphere of hydrogen gas. (c) Chlorine reacts with nitrogen gas. (d) Boron tribromide reacts with water.