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Chapter 8: Problem 74

We can define average bond enthalpies and bond lengths for ionic bonds, just like we have for covalent bonds. Which ionic bond is predicted to have the smaller bond enthalpy, \(\mathrm{Li}-\mathrm{F}\) or \(\mathrm{Cs}-\mathrm{F}\) ?

Short Answer

Expert verified
The \(\mathrm{Cs}-\mathrm{F}\) bond is predicted to have a smaller bond enthalpy than the \(\mathrm{Li}-\mathrm{F}\) bond, as the bond length of \(\mathrm{Cs}-\mathrm{F}\) is larger due to the increase in ionic radius of \(\mathrm{Cs}^+\) compared to \(\mathrm{Li}^+\), and bond enthalpy decreases with increasing bond length.

Step by step solution

01

Understand the relationship between bond length and bond enthalpy

In general, as the bond length increases, the bond enthalpy decreases. This is because the atoms are farther apart, and the interaction between the ions is weaker, leading to a lower amount of energy needed to break the bond. Keeping this relationship in mind, we can compare the bond lengths of \(\mathrm{Li}-\mathrm{F}\) and \(\mathrm{Cs}-\mathrm{F}\) to determine which bond has a lower bond enthalpy.
02

Examine the factors that determine bond lengths in ionic compounds

The bond length in ionic compounds is determined by the sum of the ionic radii of the two ions involved in the bond. The ionic radii of cations and anions decrease across a period and increase down a group in the periodic table. Since lithium (Li) and cesium (Cs) are both in Group 1, and fluorine (F) is in Group 17, we can use these trends to predict which bond will have a smaller bond enthalpy.
03

Compare the ionic radii of \(\mathrm{Li}^+\) and \(\mathrm{Cs}^+\)

Li and Cs are both Group 1 elements, with Cs being below Li in the periodic table. As we move down a group, the ionic radii increase due to the addition of electron shells. Therefore, the ionic radius of \(\mathrm{Cs}^+\) is larger than the ionic radius of \(\mathrm{Li}^+\).
04

Compare the bond lengths of \(\mathrm{Li}-\mathrm{F}\) and \(\mathrm{Cs}-\mathrm{F}\)

Since the ionic radius of \(\mathrm{Cs}^+\) is larger than the ionic radius of \(\mathrm{Li}^+\), and both compounds have a \(\mathrm{F}^-\) anion with the same ionic radius, the bond length of \(\mathrm{Cs}-\mathrm{F}\) will be larger than the bond length of \(\mathrm{Li}-\mathrm{F}\).
05

Determine which bond has a smaller bond enthalpy

Recall that as the bond length increases, the bond enthalpy decreases. Since the bond length of \(\mathrm{Cs}-\mathrm{F}\) is greater than the bond length of \(\mathrm{Li}-\mathrm{F}\), the bond enthalpy of \(\mathrm{Cs}-\mathrm{F}\) is predicted to be smaller than that of \(\mathrm{Li}-\mathrm{F}\).
06

Conclusion

Based on the relationship between bond lengths and bond enthalpies, as well as the trends in ionic radii in the periodic table, the ionic bond with a smaller bond enthalpy is the \(\mathrm{Cs}-\mathrm{F}\) bond.

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Most popular questions from this chapter

A common form of elemental phosphorus is the white phosphorus, where four \(\mathrm{P}\) atoms are arranged in a tetrahedron. All four phosphorus atoms are equivalent. White phosphorus reacts spontaneously with the oxygen in air to form \(\mathrm{P}_{4} \mathrm{O}_{6} .\) (a) How many valance electron pairs are in the \(\mathrm{P}_{4} \mathrm{O}_{6}\) molecule? (b) When $\mathrm{P}_{4} \mathrm{O}_{6}\( is dissolved in water, it produces a \)\mathrm{H}_{3} \mathrm{PO}_{3}\(, molecule. \)\mathrm{H}_{3} \mathrm{PO}_{3}$ has two forms, \(\mathrm{P}\) forms 3 covalent bonds in the first form and \(\mathrm{P}\) forms 5 covalent bonds in the second form. Draw two possible Lewis structures of \(\mathrm{H}_{3} \mathrm{PO}_{3}\). (c) Which structure obeys the octet rule?

(a) Using Lewis symbols, make a sketch of the reaction between potassium and bromine atoms to give the ionic substance KBr. (b) How many electrons are transferred? (c) Which atom loses electrons in the reaction?

Acetylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\) and nitrogen \(\left(\mathrm{N}_{2}\right)\) both contain a triple bond, but they differ greatly in their chemical properties. (a) Write the Lewis structures for the two substances. (b) By referring to Appendix C, look up the enthalpies of formation of acetylene and nitrogen. Which compound is more stable? (c) Write balanced chemical equations for the complete oxidation of \(\mathrm{N}_{2}\) to form \(\mathrm{N}_{2} \mathrm{O}_{5}(g)\) and of acetylene to form \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O (g) .\) (d) Calculate the enthalpy of oxidation per mole for \(\mathrm{N}_{2}\) and for $\mathrm{C}_{2} \mathrm{H}_{2}\( (the enthalpy of formation of \)\mathrm{N}_{2} \mathrm{O}_{5}(g)\( is \)11.30 \mathrm{~kJ} / \mathrm{mol}\( ). \)(\mathbf{e})$ Both \(\mathrm{N}_{2}\) and \(\mathrm{C}_{2} \mathrm{H}_{2}\) possess triple bonds with quite high bond enthalpies (Table 8.3). Calculate the enthalpy of hydrogenation per mole for both compounds: acetylene plus \(\mathrm{H}_{2}\) to make methane, \(\mathrm{CH}_{4}\); nitrogen plus \(\mathrm{H}_{2}\) to make ammonia, \(\mathrm{NH}_{3}\).

(a) Is lattice energy usually endothermic or exothermic? (b) Write the chemical equation that represents the process of lattice energy for the case of NaCl. (c) Would you expect salts like \(\mathrm{NaCl}\), which have singly charged ions, to have larger or smaller lattice energies compared to salts like CaO which are composed of doubly-charged ions?

Using Lewis symbols and Lewis structures, diagram the formation of \(\mathrm{BF}_{3}\) from \(\mathrm{B}\) and \(\mathrm{F}\) atoms, showing valence- shell electrons. (a) How many valence electrons does B have initially? (b) How many bonds F has to make in order to achieve an octet? (c) How many valence electrons surround the \(\mathrm{B}\) in the \(\mathrm{BF}_{3}\) molecule? (d) How many valence electrons surround each \(\mathrm{F}\) in the \(\mathrm{BF}_{3}\) molecule? (e) Does \(\mathrm{BF}_{3}\) obey the octet rule?
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