Problem 23 - Chemistry: The Central Science in SI Units, Global Edition

Question

The substances \(\mathrm{NaF}\) and \(\mathrm{CaO}\) are isoelectronic (have the same number of valence electrons). (a) What are the charges on each of the cations in each compound? (b) What are the charges of each of the anions in each compound? (c) Without looking up lattice energies, which compound is predicted to have the larger lattice energy? (d) Using the lattice energies in Table 8.1 , predict the lattice energy of ScN.

Step-by-Step Solution

Answer

The charges on the cations in NaF and CaO are \(+1\) and \(+2\), respectively. The charges on the anions in NaF and CaO are \(-1\) and \(-2\), respectively. CaO is predicted to have a larger lattice energy than NaF due to the stronger Coulombic attraction between its ions. To predict the lattice energy of ScN, look for trends in Table 8.1 and find compounds with similar ionic charges and compositions.

Step 1: Determine the charges on the cations

In both compounds, NaF and CaO, the cations are the positively charged ions. In NaF, the cation is Na (sodium), while in CaO, the cation is Ca (calcium). To determine the charges on the cations, we must know the number of electrons each ion loses. Sodium usually loses one electron, forming a \(+1\) charged ion. So the charge on a Na cation is \(+1\). Calcium usually loses two electrons, forming a \(+2\) charged ion. So, the charge on a Ca cation is \(+2\).

Step 2: Determine the charges on the anions

In both compounds, the anions are the negatively charged ions. In NaF, the anion is F (fluorine), while in CaO, the anion is O (oxygen). To determine the charges on the anions, we need to know the number of electrons each ion gains. Fluorine usually gains one electron, forming a \(-1\) charged ion. So the charge on an F anion is \(-1\). Oxygen usually gains two electrons, forming a \(-2\) charged ion. So, the charge on an O anion is \(-2\).

Step 3: Compare the lattice energies

Lattice energy is the energy required to separate one mole of an ionic crystal into its gaseous ions. A higher lattice energy indicates a stronger ionic bond, as more energy is needed to separate the ions. Based on the Coulombic attraction, the lattice energy increases with the charge of the ions and decreases with increasing ionic distance. Since both anions F\(^-\) and O\(^{2-}\) have negative charges and cations Na\(^+\) and Ca\(^{2+}\) have positive charges, their lattice energy can be compared using the following formula: \(Lattice\, Energy = k * \frac{(q_1 * q_2)}{r}\) where: - \(k\) is a proportionality constant - \(q_1\) and \(q_2\) are charges of the ions - \(r\) is the distance between the ions Comparing the lattice energies of NaF and CaO, we have: - For NaF: \(q_1 = +1\) (Na\(^+\)), \(q_2 = -1\) (F\(^-\)) - For CaO: \(q_1 = +2\) (Ca\(^{2+}\)), \(q_2 = -2\) (O\(^{2-}\)) Considering the charges, we can predict that CaO would have a larger lattice energy due to the stronger Coulombic attraction between its ions, as the charges on the ions in CaO are higher than those in NaF.

Step 4: Predict the lattice energy of ScN using Table 8.1

Table 8.1 is assumed to contain lattice energies of various ionic compounds. To make a prediction for the lattice energy of ScN (Scandium Nitride), we can look for trends in the table. We should look for compounds with similar ionic charges and compositions, as their lattice energies will be closer to that of ScN. ScN has Sc\(^{3+}\) as the cation and N\(^{3-}\) as the anion. When we find compound(s) in Table 8.1 with similar charges, we can estimate the lattice energy of ScN based on the given values in the table. (Note: Since Table 8.1 is not provided, an actual numerical prediction for the lattice energy of ScN cannot be given in this step. However, this is the general approach one would take when using the table to make a prediction.)

Key Concepts

Ionic Compounds

Ionic compounds are formed when atoms transfer electrons between each other, creating charged particles called ions. These compounds are characterized by a strong electrical attraction between positively charged ions (cations) and negatively charged ions (anions). When an ionic bond forms, it generally results in the formation of a crystalline structure which maximizes the number of attractive interactions between the oppositely charged ions.
For instance:

• In the compound \(\text{NaF}\), sodium \(\text{(Na)}\) loses one electron to become a cation, while fluorine \(\text{(F)}\) gains that electron to become an anion.
• In \(\text{CaO}\), calcium \(\text{(Ca)}\) loses two electrons to form Ca\(^{2+}\), whereas oxygen \(\text{(O)}\) gains those two electrons to become O\(^{2-}\).

Understanding these electron transfers is crucial in predicting the properties of ionic compounds, such as their high melting and boiling points, owing to the lattice structure of the ions.

Cation Charges

Cations are ions with a positive electric charge, formed when an atom loses one or more electrons. The charge on a cation depends on the number of electrons an atom loses, which is often related to its position in the periodic table.
Here's how the cation charges are determined for NaF and CaO:

• For \(\text{NaF}\), the \(\text{Na}\) atom loses one electron to obtain a stable electronic configuration, resulting in a charge of \(+1\).
• For \(\text{CaO}\), the \(\text{Ca}\) atom loses two electrons, resulting in a \(+2\) charge.

Thus, cation charges are critical in determining how these ions will interact with anions to form stable compounds with unique properties.

Anion Charges

Anions are negatively charged ions, formed when an atom gains extra electrons, achieving stability by filling its outer electron shell. The charge on anions often correlates with the group number in the periodic table, reflecting how many electrons are typically gained.
Let's examine the anions in NaF and CaO:

• In \(\text{NaF}\), the \(\text{F}\) atom gains one electron, yielding a \(-1\) charge.
• In \(\text{CaO}\), the \(\text{O}\) atom gains two electrons, resulting in a charge of \(-2\).

This transfer of electrons to form anions results in significant changes in electron configuration, influencing the compound's overall stability and characteristics.

Coulombic Attraction

Coulombic attraction refers to the force of attraction between oppositely charged ions in an ionic compound. This concept is essential for understanding the strength of ionic bonds, which affects the stability and structure of ionic compounds.
The strength of Coulombic attraction depends on two main factors:

Magnitude of Charge**: Stronger attractions occur when ions have higher charges. For example, the high lattice energy of CaO compared to NaF is primarily due to the higher charges (\(\text{Ca}^{2+}, \text{O}^{2-}\) vs. \(\text{Na}^+, \text{F}^-\)).Distance Between Ions**: Attractions are stronger when ions are closer to each other. As such, ionic compounds with smaller ions may have higher lattice energies.

By understanding these principles, predictions about the relative lattice energies and, consequently, the stability of different ionic compounds can be made, as demonstrated when comparing NaF and CaO or predicting the lattice energy of ScN based on similar compounds.