Chapter 7

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.

Does the reactivity of a metal correlate with its first ionization energy? Explain.

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 atomic radii.

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

(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 reaction of the white substance with water.

Write a balanced equation for the reaction that occurs in each of the following cases: (a) Potassium metal burns in 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 is reacted with molten sulfur.

Write a balanced equation for the reaction that occurs in each of the following cases: (a) Cesium is added to water. (b) Strontium is added to water. (c) Sodium reacts with oxygen. (d) Calcium reacts with iodine.

(a) As described in Section \(7.7,\) the alkali metals react with hydrogen to form hydrides and react with halogens- for example, fluorine to form halides, Compare the roles of hydrogen and the halogen in these reactions. How are the forms of hydrogen and halogen in the products alike? (b) Write balanced equations for the reaction of fluorine with calcium and for the reaction of hydrogen with calcium. What are the similarities among the products of these reactions?

The interior of the planets Jupiter and Saturn are believed to contain metallic hydrogen: hydrogen that is put under such tremendous pressure that it no longer exists as \(\mathrm{H}_{2}\), molecules, but instead exists as an extended metallic solid. Predict what properties metallic hydrogen might have compared to "normal" hydrogen in terms of first ionization energy, atomic size, and reactivity.

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

Little is known about the properties of astatine, \(\mathrm{At}\), 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 \(\mathrm{Na}\) ?

Until the early 1960 s the group 8 A elements were called the inert gases; before that they were called the rare gases. The term rare gases was dropped after it was discovered that argon accounts for roughly \(1 \%\) of Earth's atmosphere. (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) Ozone decomposes to dioxygen. (b) Xenon reacts with fluorine. (Write three different equations.) (c) Sulfur reacts with hydrogen gas. (d) Fluorine reacts with water.

Write a balanced equation for the reaction that occurs in each of the following cases: (a) Chlorine reacts with water. (b) Barium metal is heated in an atmosphere of hydrogen gas. (c) Lithium reacts with sulfur. (d) Fluorine reacts with magnesium metal.

(a) If the core electrons were totally effective at screening the valence electrons and the valence electrons provided no screening for each other, what would be the effective nuclear charge acting on the \(3 s\) and \(3 p\) valence electrons in \(\mathrm{P}\) ? (b) Repeat these calculations using Slater's rules. (c) Detailed calculations indicate that the effective nuclear charge is \(5.6+\) for the \(3 s\) electrons and \(4.9+\) for the \(3 p\) electrons. Why are the values for the \(3 s\) and \(3 p\) electrons different? (d) If you remove a single electron from a \(\mathrm{P}\) atom, which orbital will it come from? Explain.

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?

Elements in group \(7 \mathrm{~A}\) in the periodic table are the halogens; elements in group \(6 \mathrm{~A}\) are called the chalcogens. (a) What is the most common oxidation state of the chalcogens compared to the halogens? Can you suggest an explanation for the difference? (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 the increase in atomic radius in moving from \(\mathrm{Zr}\) to \(\mathrm{Hf}\) is smaller than in moving from \(\mathrm{Y}\) to La. Suggest an explanation for this effect. \begin{tabular}{llll} \hline \multicolumn{3}{l} { Atomic Radii \((\AA)\)} \\ \hline Sc & 1.44 & \(\mathrm{Ti}\) & 1.36 \\ \(\mathrm{Y}\) & 1.62 & \(\mathrm{Zr}\) & 1.48 \\ \(\mathrm{La}\) & 1.69 & \(\mathrm{Hf}\) & 1.50 \end{tabular}

(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: (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.

The electron affinities, in \(\mathrm{kJ} / \mathrm{mol}\), for the group \(1 \mathrm{~B}\) and group \(2 \mathrm{~B}\) metals are $$ \begin{array}{|c|c|} \hline \mathrm{Cu} & \mathrm{Zn} \\ -119 & >0 \\\ \hline \mathrm{Ag} & \mathrm{Cd} \\ -126 & >0 \\ \hline \mathrm{Au} & \mathrm{Hg} \\ -223 & >0 \\ \hline \end{array} $$ (a) Why are the electron affinities of the group \(2 \mathrm{~B}\) elements greater than zero? (b) Why do the electron affinities of the group \(1 \mathrm{~B}\) elements become more negative as we move down the group? [Hint: Examine the trends in the electron affinity of other groups as we proceed down the periodic table. \(]\)

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 hydride. (e) How does the process you wrote in part (d) compare to the process for the electron affinity of elemental hydrogen?

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.

Zinc in its \(2+\) oxidation state is an essential metal ion for life. \(\mathrm{Zn}^{2+}\) is found bound to many proteins that are involved in biological processes, but unfortunately \(\mathrm{Zn}^{2+}\) is hard to detect by common chemical methods. Therefore, scientists who are interested in studying \(\mathrm{Zn}^{2+}\) -containing proteins will frequently substitute \(\mathrm{Cd}^{2+}\) for \(\mathrm{Zn}^{2+}\), since \(\mathrm{Cd}^{2+}\) is easier to detect. (a) On the basis of the properties of the elements and ions discussed in this chapter and their positions in the periodic table, describe the pros and cons of using \(\mathrm{Cd}^{2+}\) as a \(\mathrm{Zn}^{2+}\) substitute. (b) Proteins that speed up (catalyze) chemical reactions are called enzymes. Many enzymes are required for proper metabolic reactions in the body. One problem with using \(\mathrm{Cd}^{2+}\) to replace \(\mathrm{Zn}^{2+}\) in enzymes is that \(\mathrm{Cd}^{2+}\) substitution can decrease or even eliminate enzymatic activity. Can you suggest a different metal ion that might replace \(\mathrm{Zn}^{2+}\) in enzymes instead of \(\mathrm{Cd}^{2+} ?\) Justify your answer.

A historian discovers a nineteenth-century notebook in which some observations, dated \(1822,\) were recorded on a substance thought to be a new element. Here are some of the data recorded in the notebook: "Ductile, silver- white, metallic looking. Softer than lead. Unaffected by water. Stable in air. Melting point: \(153^{\circ} \mathrm{C}\). Density: \(7.3 \mathrm{~g} / \mathrm{cm}^{3} .\) Electrical conductivity: \(20 \%\) that of copper. Hardness: About \(1 \%\) as hard as iron. When \(4.20 \mathrm{~g}\) of the unknown is heated in an excess of oxygen, \(5.08 \mathrm{~g}\) of a white solid is formed. The solid could be sublimed by heating to over \(800{ }^{\circ} \mathrm{C}\). (a) Using information in the text and the CRC Handbook of Chemistry and Physics, and making allowances for possible variations in numbers from current values, identify the element reported. (b) Write a balanced chemical equation for the reaction with oxygen. (c) Judging from Figure \(7.1,\) might this nineteenth-century investigator have been the first to discover a new element?

In April \(2010,\) a research team reported that they had made Element 117 . The report has yet to be confirmed. Write out Element 117's ground-state electron configuration, 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; cadium selenide, CdSe. (a) What is the relationship between the compound semiconductors' compositions and the positions of their elements on the periodic table relative to \(\mathrm{Si}\) and Ge? (b) Workers in the semiconductor industry refer to \({ }^{4} \mathrm{II}-\mathrm{VI}^{m}\) and \({ }^{4} \mathrm{III}-\mathrm{V}^{n} \mathrm{ma}-\) terials, using Roman numerals; can you identify which compound semiconductors are II-VI and which are III-V? 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: $$ \begin{array}{ll} \hline \text { Element } & \text { Wavelength }(\AA) \\\ \hline \mathrm{Ne} & 14.610 \\ \mathrm{Ca} & 3.358 \\ \mathrm{Zn} & 1.435 \\\ \mathrm{Zr} & 0.786 \\ \mathrm{Sn} & 0.491 \\ \hline \end{array} $$

(a) Write the electron configuration for \(\mathrm{Li}\), and estimate the effective nuclear charge experienced by the valence electron. (b) The energy of an electron in a one-electron atom or ion equals \(\left(-2.18 \times 10^{-18} \mathrm{~J}\right)\left(\frac{Z^{2}}{n^{2}}\right)\) where \(Z\) is the nuclear charge and \(n\) is the principal quantum number of the electron. Estimate the first ionization energy of Li. (c) Compare the result of your calculation with the value reported in Table 7.4 and explain the difference. (d) What value of the effective nuclear charge gives the proper value for the ionization energy? Does this agree with your explanation in \((\mathrm{c}) ?\)

One way to measure ionization energies is ultraviolet photoelectron spectroscopy (UPS, or just PES), a technique based on the photoelectric effect. coo (Section 6.2 ) In PES, monochromatic light is directed onto a sample, causing electrons to be emitted. The kinetic energy of the emitted electrons is measured. The difference between the energy of the photons and the kinetic energy of the electrons corresponds to the energy needed to remove the electrons (that is, the ionization energy). Suppose that a PES experiment is performed in which mercury vapor is irradiated with ultraviolet light of wavelength \(58.4 \mathrm{nm}\). (a) What is the energy of a photon of this light in eV? (b) Write an equation that shows the process corresponding to the first ionization energy of \(\mathrm{Hg}\). (c) The kinetic energy of the emitted electrons is measured to be \(10.75 \mathrm{eV}\). What is the first ionization energy of Hg in kJ/mol? (d) Using Figure 7.9 , determine which of the halogen elements has a first ionization energy closest to that of mercury.

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 7.107 ), 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 forbitals at \(105 \mathrm{eV},\) from an X-ray source that provided \(1253.6 \mathrm{eV}\) of energy. 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 \(\mathrm{O} .\) (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? (d) Use Slater's rules to estimate \(Z_{\text {eff }}\) for the \(4 f\) and valence electrons of \(\mathrm{Hg}^{2+}\) and \(\mathrm{O}^{2-}\); assume for this purpose that all the inner electrons with \((n-3)\) or less screen a full + \(1 .\)

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 \(2 \mathrm{~mol}\) of \(\mathrm{KO}_{2}(s)\) react with each mole of \(\mathrm{CO}_{2}(g) .\) (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 \(\mathrm{CO}_{2}(g) .\) (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?