Chapter 8

Draw the Lewis structures for each of the following molecules or ions. Which do not obey the octet rule? (a) \(\mathrm{NO},\) (b) \(\mathrm{BF}_{3}\), (c) \(\mathrm{ICl}_{2}^{-}\) (d) \(\mathrm{OPBr}_{3}\) (the \(\mathrm{P}\) is the central atom), (e) XeF 4 .

In the vapor phase, \(\mathrm{BeCl}_{2}\) exists as a discrete molecule. (a) Draw the Lewis structure of this molecule, using onlysingle bonds. Does this Lewis structure satisfy the octet rule? (b) What other resonance structures are possible that satisfy the octet rule? (c) On the basis of the formal charges, which Lewis structure is expected to be dominant for \(\mathrm{BeCl}_{2} ?\)

(a) Describe the molecule xenon trioxide, \(\mathrm{XeO}_{3}\), using four possible Lewis structures, one each with zero, one, two, or three Xe-O double bonds. (b) Do any of these resonance structures satisfy the octet rule for every atom in the molecule? (c) Do any of the four Lewis structures have multiple resonance structures? If so, how many resonance structures do you find? (d) Which of the Lewis structures in (a) yields the most favorable formal charges for the molecule?

Consider the following statement: "For some molecules and ions, a Lewis structure that satisfies the octet rule does not lead to the lowest formal charges, and a Lewis structure that leads to the lowest formal charges does not satisfy the octet rule." Illustrate this statement using the hydrogen sulfite ion, \(\mathrm{HSO}_{3}^{-}\), as an example (the \(\mathrm{H}\) atom is bonded to one of the \(\mathrm{O}\) atoms).

Some chemists believe that satisfaction of the octet rule should be the top criterion for choosing the dominant Lewis structure of a molecule or ion. Other chemists believe that achieving the best formal charges should be the top criterion. Consider the dihydrogen phosphate ion, \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-},\) in which the \(\mathrm{H}\) atoms are bonded to \(\mathrm{O}\) atoms. (a) What would be the predicted dominant Lewis structure if satisfying the octet rule is the top criterion? (b) What would it be if achieving the best formal charges is the top criterion? (c) Is there another Lewis structure you can draw that satisfies neither of these criteria?

Use Table 8.4 to estimate the enthalpy change for each of the following reactions: (a) \(\mathrm{H}_{2} \mathrm{C}=\mathrm{O}(g)+\mathrm{HCl}(g) \longrightarrow \mathrm{H}_{3} \mathrm{C}-\mathrm{O}-\mathrm{Cl}(g)\) (b) \(\mathrm{H}_{2} \mathrm{O}_{2}(g)+2 \mathrm{CO}(g) \longrightarrow \mathrm{H}_{2}(g)+2 \mathrm{CO}_{2}(g)\) (c) \(3 \mathrm{H}_{2} \mathrm{C}=\mathrm{CH}_{2}(g) \longrightarrow \mathrm{C}_{6} \mathrm{H}_{12}(g)\) (the six carbon atoms form a six-membered ring with two \(\mathrm{H}\) atoms on each \(\mathrm{C}\) atom \()\)

Given the following bond-dissociation energies, calculate the average bond enthalpy for the Ti-Cl bond. \begin{tabular}{ll} \hline & \(\Delta H(\mathbf{k J} /\) mol \()\) \\ \hline \(\mathrm{TiCl}_{4}(g) \longrightarrow \mathrm{TiCl}_{3}(g)+\mathrm{Cl}(g)\) & 335 \\ \(\mathrm{TiCl}_{3}(g) \longrightarrow \mathrm{TiCl}_{2}(g)+\mathrm{Cl}(g)\) & 423 \\ \(\mathrm{TiCl}_{2}(g) \longrightarrow \mathrm{TiCl}(g)+\mathrm{Cl}(g)\) & 444 \\\ \(\mathrm{TiCl}(g) \longrightarrow \mathrm{Ti}(g)+\mathrm{Cl}(g)\) & 519 \\ \hline \end{tabular}

(a) Using average bond enthalpies, predict which of the following reactions will be most exothermic: (i) \(\mathrm{C}(g)+2 \mathrm{~F}_{2}(g) \longrightarrow \mathrm{CF}_{4}(g)\) (ii) \(\mathrm{CO}(g)+3 \mathrm{~F}_{2} \longrightarrow \mathrm{CF}_{4}(g)+\mathrm{OF}_{2}(g)\) (iii) \(\mathrm{CO}_{2}(g)+4 \mathrm{~F}_{2} \longrightarrow \mathrm{CF}_{4}(g)+2 \mathrm{OF}_{2}(g)\) (b) Explain the trend, if any, that exists between reaction exothermicity and the extent to which the carbon atom is bonded to oxygen.

How many elements in the periodic table are represented by a Lewis symbol with a single dot? Are all these elements in the same group? Explain.

(a) Explain the following trend in lattice energy: \(\mathrm{BeH}_{2}\), \(3205 \mathrm{~kJ} / \mathrm{mol} ; \mathrm{MgH}_{2}, 2791 \mathrm{~kJ} / \mathrm{mol} ; \mathrm{CaH}_{2}, 2410 \mathrm{~kJ} / \mathrm{mol} ; \mathrm{SrH}_{2}\) \(2250 \mathrm{~kJ} / \mathrm{mol} ; \mathrm{BaH}_{2}, 2121 \mathrm{~kJ} / \mathrm{mol}\) (b) The lattice energy of \(\mathrm{ZnH}_{2}\) is \(2870 \mathrm{~kJ} / \mathrm{mol}\). Based on the data given in part (a), the radius of the \(\mathrm{Zn}^{2+}\) ion is expected to be closest to that of which group \(2 \mathrm{~A}\) element?

Based on data in Table 8.2 , estimate (within \(30 \mathrm{~kJ} / \mathrm{mol}\) ) the lattice energy for (a) LiBr, (b) CsBr, (c) \(\mathrm{CaCl}_{2}\)

An ionic substance of formula MX has a lattice energy of \(6 \times 10^{3} \mathrm{k} \mathrm{J} / \mathrm{mol}\). Is the charge on the ion \(\mathrm{M}\) likely to be \(1+\), \(2+\) or \(3+?\) Explain your reasoning.

Construct a Born-Haber cycle for the formation of the hypothetical compound \(\mathrm{NaCl}_{2}\), where the sodium ion has a \(2+\) charge (the second ionization energy for sodium is given in Table 7.2). (a) How large would the lattice energy need to be for the formation of \(\mathrm{NaCl}_{2}\) to be exothermic? (b) If we were to estimate the lattice energy of \(\mathrm{NaCl}_{2}\) to be roughly equal to that of \(\mathrm{MgCl}_{2}\) ( \(2326 \mathrm{~kJ} / \mathrm{mol}\) from Table 8.2 ), what value would you obtain for the standard enthalpy of formation, \(\Delta H_{j}^{9}\), of \(\mathrm{NaCl}_{2}\) ?

(a) How does a polar molecule differ from a nonpolar one? (b) Atoms \(\mathrm{X}\) and \(\mathrm{Y}\) have different electronegativities. Will the diatomic molecule \(\mathrm{X}-\mathrm{Y}\) necessarily be polar? Explain. (c) What factors affect the size of the dipole moment of a diatomic molecule?

For the following collection of nonmetallic elements, \(\mathrm{O}, \mathrm{P},\) Te, \(I, B,(a)\) which two would form the most polar single bond? (b) Which two would form the longest single bond? (c) Which two would be likely to form a compound of formula \(\mathrm{XY}_{2} ?\) (d) Which combinations of elements would likely yield a compound of empirical formula \(\mathrm{X}_{2} \mathrm{Y}_{3} ?\) In each case explain your answer.

The substance chlorine monoxide, \(\mathrm{ClO}(g)\), is important in atmospheric processes that lead to depletion of the ozone layer. The ClO molecule has a dipole moment of \(1.24 \mathrm{D}\) and the (a) Determine the magnitude of \(\mathrm{Cl}-\mathrm{O}\) bond length is \(1.60 \mathrm{~A}\). the charges on the \(\mathrm{Cl}\) and \(\mathrm{O}\) atoms in units of the electronic charge, e. (b) Based on the electronegativities of the elements, which atom would you expect to have a negative charge in the ClO molecule? (c) By using formal charges as a guide, propose the dominant Lewis structure for the molecule. Are the formal charges consistent with your answers to parts (a) and (b)? Can you reconcile any differences you find?

A major challenge in implementing the "hydrogen economy" is finding a safe, lightweight, and compact way of storing hydrogen for use as a fuel. The hydrides of light metals are attractive for hydrogen storage because they can store a high weight percentage of hydrogen in a small volume. For example, \(\mathrm{NaAlH}_{4}\) can release \(5.6 \%\) of its mass as \(\mathrm{H}_{2}\) upon decomposing to \(\mathrm{NaH}(s), \mathrm{Al}(s),\) and \(\mathrm{H}_{2}(\mathrm{~g}),\) NaAlH \(_{4}\) possesses both covalent bonds, which hold polyatomic anions together, and ionic bonds. (a) Write a balanced equation for the decomposition of \(\mathrm{NaAlH}_{4}\) (b) Which element in \(\mathrm{NaAlH}_{4}\) is the most electronegative? Which one is the least electronegative? (c) Based on electronegativity differences, what do you think is the identity of the polyatomic anion? Draw a Lewis structure for this ion.

Although \(\mathrm{I}_{3}^{-}\) is known, \(\mathrm{F}_{3}^{-}\) is not. Using Lewis structures, explain why \(\mathrm{F}_{3}^{-}\) does not form.

Calculate the formal charge on the indicated atom in each of the following molecules or ions: (a) the central oxygen atom in \(\mathrm{O}_{3},\) (b) phosphorus in \(\mathrm{PF}_{6}^{-},(\mathrm{c})\) nitrogen in \(\mathrm{NO}_{2},(\mathrm{~d})\) iodine in \(\mathrm{ICl}_{3}\) (e) chlorine in \(\mathrm{HClO}_{4}\) (hydrogen is bonded to \(\mathrm{O}\) ).

(a) Determine the formal charge on the chlorine atom in the hypochlorite ion, \(\mathrm{ClO}^{-},\) and the perchlorate ion, \(\mathrm{ClO}_{4}^{-},\) using resonance structures where the \(\mathrm{Cl}\) atom has an octet. (b) What are the oxidation numbers of chlorine in \(\mathrm{ClO}^{-}\) and in \(\mathrm{ClO}_{4}^{-} ?\) (c) Is it uncommon for the formal charge and the oxidation state to be different? Explain. (d) Perchlorate is a much stronger oxidizing agent than hypochlorite. Would you expect there to be any relationship between the oxidizing power of the oxyanion and either the oxidation state or the formal charge of chlorine?

The following three Lewis structures can be drawn for \(\mathrm{N}_{2} \mathrm{O}:\) \(\mathrm{N} \equiv \mathrm{N}-\ddot{\mathrm{O}}: \longleftrightarrow: \mathrm{N}^{*}-\mathrm{N} \equiv \mathrm{O}: \longleftrightarrow: \ddot{\mathrm{N}}=\mathrm{N}=\ddot{\mathrm{O}}:\) (a) Using formal charges, which of these three resonance forms is likely to be the most important? (b) The \(\mathrm{N}-\mathrm{N}\) bond length in \(\mathrm{N}_{2} \mathrm{O}\) is \(1.12 \mathrm{~A}\), slightly longer than a typical \(\mathrm{N} \equiv \mathrm{N}\) bond; and the \(\mathrm{N}-\mathrm{O}\) bond length is \(1.19 \AA\), slightly shorter than a typical \(\mathrm{N}=\mathrm{O}\) bond. (See Table \(8.5 .\) ) Rationalize these observations in terms of the resonance structures shown previously and your conclusion for part (a).

(a) Triazine, \(\mathrm{C}_{3} \mathrm{H}_{3} \mathrm{~N}_{3}\), is like benzene except that in triazine every other \(\mathrm{C}-\mathrm{H}\) group is replaced by a nitrogen atom. Draw the Lewis structure(s) for the triazine molecule. (b) Estimate the carbon-nitrogen bond distances in the ring.

Consider the hypothetical molecule \(\mathrm{B}-\mathrm{A}=\mathrm{B}\). Are the following statements true or false? (a) This molecule cannot exist. (b) If resonance was important, the molecule would have identical A-B bond lengths.

With reference to the "Chemistry Put to Work" box on explosives, (a) use bond enthalpies to estimate the enthalpy change for the explosion of \(1.00 \mathrm{~g}\) of nitroglycerin. (b) Write a balanced equation for the decomposition of TNT. Assume that, upon explosion, TNT decomposes into \(\mathrm{N}_{2}(g), \mathrm{CO}_{2}(g)\), \(\mathrm{H}_{2} \mathrm{O}(g),\) and \(\mathrm{C}(s)\)

The \(\mathrm{Ti}^{2+}\) ion is isoelectronic with the Ca atom. (a) Are there any differences in the electron configurations of \(\mathrm{Ti}^{2+}\) and Ca? (b) With reference to Figure 6.24 , comment on the changes in the ordering of the \(4 s\) and \(3 d\) subshells in Ca and \(\mathrm{Ti}^{2+}\), (c) Will Ca and \(\mathrm{Ti}^{2+}\) have the same number of unpaired electrons? Explain.

(a) Write the chemical equations that are used in calculating the lattice energy of \(\mathrm{SrCl}_{2}(s)\) via a Born-Haber cycle. (b) The second ionization energy of \(\operatorname{Sr}(g)\) is \(1064 \mathrm{~kJ} / \mathrm{mol}\). Use this fact along with data in Appendix \(\mathrm{C}\), Figure 7.9 , Figure \(7.11,\) and Table 8.2 to calculate \(\Delta H_{f}^{\circ}\) for \(\operatorname{Sr} \mathrm{Cl}_{2}(s)\)

The electron affinity of oxygen is \(-141 \mathrm{~kJ} / \mathrm{mol}\), corresponding to the reaction $$ \mathrm{O}(g)+\mathrm{e}^{-} \longrightarrow \mathrm{O}^{-}(g) $$ The lattice energy of \(\mathrm{K}_{2} \mathrm{O}(s)\) is \(2238 \mathrm{~kJ} / \mathrm{mol}\). Use these data along with data in Appendix \(\mathrm{C}\) and Figure 7.9 to calculate the "second electron affinity" of oxygen, corresponding to the reaction $$ \mathrm{O}^{-}(g)+\mathrm{e}^{-} \longrightarrow \mathrm{O}^{2-}(g) $$

You and a partner are asked to complete a lab entitled "Oxides of Ruthenium" that is scheduled to extend over two lab periods. The first lab, which is to be completed by your partner, is devoted to carrying out compositional analysis. In the second lab, you are to determine melting points. Upon going to lab you find two unlabeled vials, one containing a soft yellow substance and the other a black powder. You also find the following notes in your partner's notebook-Compound 1: \(76.0 \%\) \(\mathrm{Ru}\) and \(24.0 \% \mathrm{O}\) (by mass), Compound 2: \(61.2 \% \mathrm{Ru}\) and \(38.8 \%\) O (by mass). (a) What is the empirical formula for Compound \(1 ?\) (b) What is the empirical formula for Compound \(2 ?\) (c) Upon determining the melting points of these two compounds, you find that the yellow compound melts at \(25^{\circ} \mathrm{C},\) while the black powder does not melt up to the maximum temperature of your apparatus, \(1200^{\circ} \mathrm{C}\). What is the identity of the yellow compound? What is the identity of the black compound? Be sure to use the appropriate naming convention depending on whether the compound is better described as a molecular or ionic compound.

One scale for electronegativity is based on the concept that the electronegativity of any atom is proportional to the ionization energy of the atom minus its electron affinity: electronegativity \(=k(I E-E A),\) where \(k\) is a proportionality constant. (a) How does this definition explain why the electronegativity of \(\mathrm{F}\) is greater than that of \(\mathrm{Cl}\) even though Cl has the greater electron affinity? (b) Why are both ionization energy and electron affinity relevant to the notion of electronegativity? (c) By using data in Chapter \(7,\) determine the value of \(k\) that would lead to an electronegativity of 4.0 for \(\mathrm{F}\) under this definition. (d) Use your result from part (c) to determine the electronegativities of \(\mathrm{Cl}\) and \(\mathrm{O}\) using this scale. Do these values follow the trend shown in Figure \(8.7 ?\)

The compound chloral hydrate, known in detective stories as knockout drops, is composed of \(14.52 \% \mathrm{C}, 1.83 \% \mathrm{H},\) \(64.30 \% \mathrm{Cl}\), and \(19.35 \% \mathrm{O}\) by mass and has a molar mass of \(165.4 \mathrm{~g} / \mathrm{mol}\) (a) What is the empirical formula of this substance? (b) What is the molecular formula of this substance? (c) Draw the Lewis structure of the molecule, assuming that the \(\mathrm{Cl}\) atoms bond to a single \(\mathrm{C}\) atom and that there are a \(\mathrm{C}-\mathrm{C}\) bond and two \(\mathrm{C}-\mathrm{O}\) bonds in the compound.

Barium azide is \(62.04 \% \mathrm{Ba}\) and \(37.96 \% \mathrm{~N}\). Each azide ion has a net charge of \(1-\) (a) Determine the chemical formula of the azide ion. (b) Write three resonance structures for the azide ion. (c) Which structure is most important? (d) Predict the bond lengths in the ion.

Under special conditions, sulfur reacts with anhydrous liquid ammonia to form a binary compound of sulfur and nitrogen. The compound is found to consist of \(69.6 \% \mathrm{~S}\) and \(30.4 \% \mathrm{~N}\). Measurements of its molecular mass yield a value of \(184.3 \mathrm{~g} \mathrm{~mol}^{-1}\). The compound occasionally detonates on being struck or when heated rapidly. The sulfur and nitrogen atoms of the molecule are joined in a ring. All the bonds in the ring are of the same length. (a) Calculate the empirical and molecular formulas for the substance. (b) Write Lewis structures for the molecule, based on the information you are given. (Hint: You should find a relatively small number of dominant Lewis structures.) (c) Predict the bond distances between the atoms in the ring. (Note: The \(\mathrm{S}-\mathrm{S}\) distance in the \(\mathrm{S}_{8}\) ring is \(2.05 \AA\). \()\) (d) The enthalpy of formation of the compound is estimated to be \(480 \mathrm{~kJ} \mathrm{~mol}^{-1} . \Delta H_{f}^{\circ}\) of \(\mathrm{S}(g)\) is \(222.8 \mathrm{~kJ} \mathrm{~mol}^{-1}\). Estimate the average bond enthalpy in the compound.

A common form of elemental phosphorus is the tetrahedral \(\mathrm{P}_{4}\) molecule, where all four phosphorus atoms are equivalent: At room temperature phosphorus is a solid. (a) Do you think there are any unshared pairs of electrons in the \(\mathrm{P}_{4}\) molecule? (b) How many \(\mathrm{P}-\mathrm{P}\) bonds are there in the molecule? (c) Can you draw a Lewis structure for a linear \(\mathrm{P}_{4}\) molecule that satisfies the octet rule? (d) Using formal charges, what can you say about the stability of the linear molecule versus that of the tetrahedral molecule?

Consider benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) in the gas phase. (a) Write the reaction for breaking all the bonds in \(\mathrm{C}_{6} \mathrm{H}_{6}(g)\), and use data in Appendix \(\mathrm{C}\) to determine the enthalpy change for this reaction. (b) Write a reaction that corresponds to breaking all the carbon-carbon bonds in \(\mathrm{C}_{6} \mathrm{H}_{6}(g) .\) (c) By combining your answers to parts (a) and (b) and using the average bond enthalpy for \(\mathrm{C}-\mathrm{H}\) from Table \(8.4,\) calculate the average bond enthalpy for the carbon-carbon bonds in \(\mathrm{C}_{6} \mathrm{H}_{6}(g)\). (d) Comment on your answer from part (c) as compared to the values for \(\mathrm{C}-\mathrm{C}\) single bonds and \(\mathrm{C}=\mathrm{C}\) double bonds in Table 8.4

Average bond enthalpies are generally defined for gas-phase molecules. Many substances are liquids in their standard state. coo (Section 5.7) By using appropriate thermochemical data from Appendix C, calculate average bond enthalpies in the liquid state for the following bonds, and compare these values to the gas-phase values given in Table 8.4: (a) \(\mathrm{Br}-\mathrm{Br}\), from \(\mathrm{Br}_{2}(l) ;\) (b) \(\mathrm{C}-\mathrm{Cl},\) from \(\mathrm{CCl}_{4}(l) ;\) (c) \(\mathrm{O}-\mathrm{O},\) from \(\mathrm{H}_{2} \mathrm{O}_{2}(I)\) (assume that the \(\mathrm{O}-\mathrm{H}\) bond enthalpy is the same as in the gas phase). (d) What can you conclude about the process of breaking bonds in the liquid as compared to the gas phase? Explain the difference in the \(\Delta H\) values between the two phases.