Chapter 7

Consider the stable elements through lead \((Z=82) .\) In how many instances are the atomic weights of the elements out of order relative to the atomic numbers of the elements?

As we move across a period of the periodic table, why do the sizes of the transition elements change more gradually than those of the representative elements?

The following observations are made about two hypothetical elements \(A\) and \(B\) : The \(A-A\) and \(B-B\) bond lengths in the elemental forms of A and B are 236 and \(194 \mathrm{pm}\), respectively. A and B react to form the binary compound \(\mathrm{AB}_{2}\), which has a linear structure (that is \(\left.\angle \mathrm{B}-\mathrm{A}-\mathrm{B}=180^{\circ}\right)\). Based on these statements, predict the separation between the two B nuclei in a molecule of \(\mathrm{AB}_{2}\).

Elements in group 17 in the periodic table are called the halogens; elements in group 16 are called the chalcogens. (a) What is the most common oxidation state of the chalcogens compared to the halogens? (b) For each of the following periodic properties, state whether the halogens or the chalcogens have larger values: atomic radii, ionic radii of the most common oxidation state, first ionization energy, second ionization energy.

Note from the following table that there is a significant increase in atomic radius upon moving from \(\mathrm{Y}\) to La, whereas the radii of Zr to Hf are the same. Suggest an explanation for this effect. $$ \begin{aligned} &\text { Atomic Radii (pm) }\\\ &\begin{array}{cccc} \hline \text { Sc } & 170 & \text { Ti } & 160 \\ \text { Y } & 190 & \text { Zr } & 175 \\ \text { La } & 207 & \text { Hf } & 175 \\ \hline \end{array} \end{aligned} $$

(a) Use orbital diagrams to illustrate what happens when an Oxygen atom gains two electrons. (b) Why does \(\mathrm{O}^{3-}\) not exist?

Use electron configurations to explain the following observations: \((\mathbf{a})\) The first ionization energy of phosphorus is greater than that of sulfur. (b) The electron affinity of nitrogen is lower (less negative) than those of both carbon and oxygen. (c) The second ionization energy of oxygen is greater than the first ionization energy of fluorine. (d) The third ionization energy of manganese is greater than those of both chromium and iron.

Identify a +2 cation that has the following ground state electron configurations: (a) \([\mathrm{Ne}]\) (b) \([\mathrm{Ar}] 3 d^{9}\) (c) \([\mathrm{Xe}] 4 \mathrm{f}^{14} 5 d^{10} 6 s^{2}\).

Which of the following chemical equations is connected to the definitions of (a) the first ionization energy of oxygen, (b) the second ionization energy of ox ' ygen, and \((\mathbf{c})\) the electron affinity of oxygen? (i) \(\mathrm{O}(g)+\mathrm{e}^{-} \longrightarrow \mathrm{O}^{-}(g)\) (ii) \(\mathrm{O}(g) \longrightarrow \mathrm{O}^{+}(g)+\mathrm{e}^{-}\) (iii) \(\mathrm{O}(g)+2 \mathrm{e}^{-} \longrightarrow \mathrm{O}^{2-}(g)\) (iv) \(\mathrm{O}(g) \longrightarrow \mathrm{O}^{2+}(g)+2 \mathrm{e}^{-}\) \((\mathbf{v}) \mathrm{O}^{+}(g) \longrightarrow \mathrm{O}^{2+}(g)+\mathrm{e}^{-}\)

The electron affinities, in \(\mathrm{kJ} / \mathrm{mol}\), for the group 11 and group 12 metals are as follows: $$ \begin{array}{|c|l|} \hline \mathrm{Cu} & \mathrm{Zn} \\ -119 & >0 \\ \hline \mathrm{Ag} & \mathrm{Cd} \\ -126 & >0 \\ \hline \mathrm{Au} & \mathrm{Hg} \\ -223 & >0 \\ \hline \end{array} $$ (a) Why are the electron affinities of the group 12 elements greater than zero? (b) Why do the electron affinities of the group 11 elements become more negative as we move down the group?

Hydrogen is an unusual element because it behaves in some ways like the alkali metal elements and in other ways like nonmetals. Its properties can be explained in part by its electron configuration and by the values for its ionization energy and electron affinity. (a) Explain why the electron affinity of hydrogen is much closer to the values for the alkali elements than for the halogens. (b) Is the following statement true? "Hydrogen has the smallest bonding atomic radius of any element that forms chemical compounds." If not, correct it. If it is, explain in terms of electron configurations. (c) Explain why the ionization energy of hydrogen is closer to the values for the halogens than for the alkali metals. (d) The hydride ion is \(\mathrm{H}^{-}\). Write out the process corresponding to the first ionization energy of the hydride ion. (e) How does the process in part (d) compare to the process for the electron affinity of a neutral hydrogen atom?

The first ionization energy of the oxygen molecule is the energy required for the following process: $$ \mathrm{O}_{2}(g) \longrightarrow \mathrm{O}_{2}^{+}(g)+\mathrm{e}^{-} $$ The energy needed for this process is \(1175 \mathrm{~kJ} / \mathrm{mol}\), very similar to the first ionization energy of Xe. Would you expect \(\mathrm{O}_{2}\) to react with \(\mathrm{F}_{2} ?\) If so, suggest a product or products of this reaction.

Which of the following is the expected product of the reaction of \(\mathrm{Mg}(s)\) and \(\mathrm{N}_{2}(g)\) under heat? (i) \(\mathrm{Mg}_{3} \mathrm{~N}(s),(\mathbf{i i}) \mathrm{MgN}_{2}(s),\) (iii) \(\mathrm{Mg}_{3} \mathrm{~N}_{2}(s)\) (iv) \(\mathrm{Mg}(s)\) and \(\mathrm{N}_{2}(g)\) will not react with one another.

Elemental barium reacts more violently with water than does elemental calcium. Which of the following best explains this difference in reactivity? (i) Calcium has greater metallic character than does barium. (ii) The electron affinity of calcium is smaller than that of barium. (iii) The first and second ionization energies of barium are less than those of calcium. (iv) The atomic radius of barium is smaller than that of calcium. ( \(\mathbf{v}\) ) The ionic radius of the barium ion is larger than that of the calcium ion.

(a) One of the alkali metals reacts with oxygen to form a solid white substance. When this substance is dissolved in water, the solution gives a positive test for hydrogen peroxide, \(\mathrm{H}_{2} \mathrm{O}_{2}\). When the solution is tested in a burner flame, a lilac-purple flame is produced. What is the likely identity of the metal? (b) Write a balanced chemical equation for the reaction of the white substance with water.

In April 2010 , a research team reported that it had made Element 117 . This discovery was confirmed in 2012 by additional experiments. Write the ground- state electron configuration for Element 117 and estimate values for its first ionization energy, electron affinity, atomic size, and common oxidation state based on its position in the periodic table.

We will see in Chapter 12 that semiconductors are materials that conduct electricity better than nonmetals but not as well as metals. The only two elements in the periodic table that are technologically useful semiconductors are silicon and germanium. Integrated circuits in computer chips today are based on silicon. Compound semiconductors are also used in the electronics industry. Examples are gallium arsenide, GaAs; gallium phosphide, GaP; cadmium sulfide, CdS; and cadmium selenide, CdSe. (a) What is the relationship between the compound semiconductors' compositions and the positions of their elements on the periodic table relative to Si and Ge? (b) Workers in the semiconductor industry refer to "II-VI" and "III-V" materials, using Roman numerals. Can you identify which compound semiconductors are II-VI and which are III-V? (c) Suggest other compositions of compound semiconductors based on the positions of their elements in the periodic table.

Moseley established the concept of atomic number by studying \(X\) rays emitted by the elements. The \(X\) rays emitted by some of the elements have the following wavelengths: $$ \begin{array}{cc} \hline \text { Element } & \text { Wavelength (pm) } \\ \hline \text { Ne } & 1461 \\ \text { Ca } & 335.8 \\ \text { Zn } & 143.5 \\ \text { Zr } & 78.6 \\ \text { Sn } & 49.1 \\ \hline \end{array} $$ (a) Calculate the frequency, \(\nu,\) of the \(X\) rays emitted by each of the elements, in Hz. (b) Plot the square root of \(\nu\) versus the atomic number of the element. What do you observe about the plot? (c) Explain how the plot in part (b) allowed Moseley to predict the existence of undiscovered elements. (d) Use the result from part (b) to predict the X-ray wavelength emitted by iron. (e) A particular element emits X rays with a wavelength of \(98.0 \mathrm{pm}\). What element do you think it is?

Mercury in the environment can exist in oxidation states 0 , + 1 , and +2 . One major question in environmental chemistry research is how to best measure the oxidation state of mercury in natural systems; this is made more complicated by the fact that mercury can be reduced or oxidized on surfaces differently than it would be if it were free in solution. XPS, X-ray photoelectron spectroscopy, is a technique related to PES (see Exercise 7.111 ), but instead of using ultraviolet light to eject valence electrons, X rays are used to eject core electrons. The energies of the core electrons are different for different oxidation states of the element. In one set of experiments, researchers examined mercury contamination of minerals in water. They measured the XPS signals that corresponded to electrons ejected from mercury's \(4 f\) orbitals at \(105 \mathrm{eV},\) from an \(\mathrm{X}\) -ray source that provided \(1253.6 \mathrm{eV}\) of energy \(\left(1 \mathrm{ev}=1.602 \times 10^{-19} \mathrm{~J}\right)\) The oxygen on the mineral surface gave emitted electron energies at \(531 \mathrm{eV}\), corresponding to the \(1 s\) orbital of oxygen. Overall the researchers concluded that oxidation states were +2 for \(\mathrm{Hg}\) and -2 for O. (a) Calculate the wavelength of the \(X\) rays used in this experiment. (b) Compare the energies of the \(4 f\) electrons in mercury and the \(1 s\) electrons in oxygen from these data to the first ionization energies of mercury and oxygen from the data in this chapter. (c) Write out the ground-state electron configurations for \(\mathrm{Hg}^{2+}\) and \(\mathrm{O}^{2-}\); which electrons are the valence electrons in each case?

When magnesium metal is burned in air (Figure 3.6), two products are produced. One is magnesium oxide, \(\mathrm{MgO}\). The other is the product of the reaction of \(\mathrm{Mg}\) with molecular nitrogen, magnesium nitride. When water is added to magnesium nitride, it reacts to form magnesium oxide and ammonia gas. (a) Based on the charge of the nitride ion (Table 2.5), predict the formula of magnesium nitride. (b) Write a balanced equation for the reaction of magnesium nitride with water. What is the driving force for this reaction? (c) In an experiment, a piece of magnesium ribbon is burned in air in a crucible. The mass of the mixture of \(\mathrm{MgO}\) and magnesium nitride after burning is \(0.470 \mathrm{~g}\). Water is added to the crucible, further reaction occurs, and the crucible is heated to dryness until the final product is \(0.486 \mathrm{~g}\) of \(\mathrm{MgO}\). What was the mass percentage of magnesium nitride in the mixture obtained after the initial burning? (d) Magnesium nitride can also be formed by reaction of the metal with ammonia at high temperature. Write a balanced equation for this reaction. If a 6.3-g Mg ribbon reacts with \(2.57 \mathrm{~g} \mathrm{NH}_{3}(g)\) and the reaction goes to completion, which component is the limiting reactant? What mass of \(\mathrm{H}_{2}(g)\) is formed in the reaction? (e) The standard enthalpy of formation of solid magnesium nitride is \(-461.08 \mathrm{~kJ} / \mathrm{mol}\). Calculate the standard enthalpy change for the reaction between magnesium metal and ammonia gas.

Potassium superoxide, \(\mathrm{KO}_{2},\) is often used in oxygen masks (such as those used by firefighters) because \(\mathrm{KO}_{2}\) reacts with \(\mathrm{CO}_{2}\) to release molecular oxygen. Experiments indicate that 2 mol of \(\mathrm{KO}_{2}(s)\) react with each mole of \(\mathrm{CO}_{2}(g) .(\mathbf{a})\) The products of the reaction are \(\mathrm{K}_{2} \mathrm{CO}_{3}(s)\) and \(\mathrm{O}_{2}(g) .\) Write a balanced equation for the reaction between \(\mathrm{KO}_{2}(s)\) and \(\mathrm{CO}_{2}(g) .(\mathbf{b})\) Indicate the oxidation number for each atom involved in the reaction in part (a). What elements are being oxidized and reduced? (c) What mass of \(\mathrm{KO}_{2}(s)\) is needed to consume \(18.0 \mathrm{~g} \mathrm{CO}_{2}(g)\) ? What mass of \(\mathrm{O}_{2}(g)\) is produced during this reaction?