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Chapter 8: Problem 21

(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?

Short Answer

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(a) Lattice energy is usually exothermic as it represents the energy released when gaseous ions combine to form an ionic solid. (b) The chemical equation representing the process of lattice energy for NaCl is: \[ \mathrm{Na^+(g) + Cl^-(g) \rightarrow NaCl(s)} \] (c) Salts with doubly charged ions, such as CaO, would generally have larger lattice energies compared to salts with singly charged ions like NaCl, due to the higher charges on the ions involved, as predicted by Coulomb's Law.

Step by step solution

01

(a) Understanding Lattice Energy

Lattice energy is the energy required to break one mole of a solid ionic compound into its gaseous ions, or conversely, it is the energy released when gaseous ions combine to form an ionic solid. Considering that the process of forming an ionic solid releases energy, lattice energy is usually exothermic.
02

(b) Chemical Equation for NaCl Lattice Energy

In the case of NaCl, lattice energy refers to the energy released when gaseous sodium cations (Na+) and chloride anions (Cl-) combine to form one mole of solid sodium chloride (NaCl). Therefore, the chemical equation representing this process is: \[ \mathrm{Na^+(g) + Cl^-(g) \rightarrow NaCl(s)} \]
03

(c) Comparing Lattice Energies of Singly and Doubly Charged Salts

In order to compare the lattice energies of salts with singly charged ions (e.g., NaCl) and those with doubly charged ions (e.g., CaO), we need to consider Coulomb's Law, which states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. According to Coulomb's Law, the lattice energy is higher when the charges of the two ions are higher. In salts like NaCl, which has singly charged ions (Na+ and Cl-), the lattice energy would be smaller compared to salts like CaO, where the ions are doubly charged (Ca虏鈦� and O虏鈦�). In conclusion, the lattice energies of salts with doubly charged ions would typically be larger than those with singly charged ions.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Ionic Compounds
Ionic compounds are interesting entities formed from the attraction between oppositely charged ions. Imagine it like a strong magnetic pull that is hard to separate! These compounds are typically formed when a metal transfers its electrons to a non-metal, resulting in a positive ion (cation) and a negative ion (anion). Take sodium chloride (NaCl), for example. Here, sodium (Na) gives away an electron to chlorine (Cl), creating Na鈦� and Cl鈦� ions.

The uniqueness of ionic compounds is in their structure. They arrange themselves in a crystalline lattice, which is a repeating pattern of ions. This structure is responsible for many of the compound's properties, like high melting and boiling points. Ionic compounds are usually solid at room temperature and can conduct electricity when melted or dissolved in water. This is because their ions are free to move and carry an electric current.
  • Ionic bonding is strong, requiring significant energy to break.
  • Compounds form a crystalline lattice structure.
  • They conduct electricity when liquid or dissolved in water.
Coulomb's Law
Coulomb's Law is key to understanding the interactions in ionic compounds. It tells us how strong the force is between two charged objects (like ions). In simple terms, the law states that the force of attraction or repulsion between two charged particles is directly proportional to the product of their charges. That means more charge equals more force!

Furthermore, the force is inversely proportional to the square of the distance between them. The closer the two charges are, the stronger the force. This is like the gravity we feel on Earth鈥攃loser means a stronger pull. In the context of ionic compounds, Coulomb's Law helps explain why doubly charged ions like in calcium oxide (CaO) have stronger attractions and thus, larger lattice energies compared to singly charged ions like in sodium chloride (NaCl).
  • Force is stronger with higher charges.
  • Force decreases with increasing distance.
  • Important for calculating lattice energy in ionic compounds.
Chemical Equations
Chemical equations are like recipes; they tell us how compounds react to form new substances. They are important in discussing lattice energies, as they capture the process at the molecular level. For instance, the chemical equation for the lattice energy of NaCl is: \[ \mathrm{Na^+(g) + Cl^-(g) \rightarrow NaCl(s)} \]This equation highlights the transformation of gaseous Na鈦� and Cl鈦� ions into solid NaCl.

What's nice about chemical equations is how they show a balanced view of chemical reactions. You'll see that the number of each type of atom is the same on both sides of the equation. This conservation of mass is fundamental in chemistry and tells us that matter is neither created nor destroyed in reactions.
  • Show reactants and products of reactions.
  • Must balance for the conservation of mass.
  • Essential for illustrating processes like the formation of ionic solids.

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Most popular questions from this chapter

Consider the element silicon, Si. (a) Write its electron configuration. (b) How many valence electrons does a silicon atom have? (c) Which subshells hold the valence electrons?

Which of these elements are unlikely to form ionic bonds? \(\mathrm{Mg}, \mathrm{Al}, \mathrm{Si}, \mathrm{Br}, \mathrm{I}\).

State whether each of these statements is true or false. (a) An oxygen-oxygen double bond is shorter than an oxygenoxygen single bond. (b) There are three lone pair electrons in the \(\mathrm{NH}_{3}\) molecule. (c) The \(\mathrm{C}-\mathrm{C}\) bond in ethene is longer than the \(\mathrm{C}-\mathrm{C}\) bond in polyethene. (d) The \(\mathrm{C}-\mathrm{Cl}\) bond is shorter than the \(\mathrm{C}-\mathrm{Br}\) bond. \((\mathbf{e})\) The greater the difference in the electronegativity of atoms in a bond, the stronger the bond.

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, \(\mathrm{NH}_{3}\).

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 \(184.3 \mathrm{~g} / \mathrm{mol}\). 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 \(205 \mathrm{pm} .\) ) \((\mathbf{d})\) 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 \(222.8 \mathrm{~kJ} / \mathrm{mol}\). Estimate the average bond enthalpy in the compound.
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